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UBC Theses and Dissertations

Stresses and vibrations in bandsaw blades Eschler, Andreas 1982

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c, I STRESSES AND VIBRATIONS IN BANDSAW BLADES by ANDREAS ESCHLER M.A.SC , The U n i v e r s i t y of B r i t i s h Columbia, 1982 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE (Department of Mechanical E n g i n e e r i n g ) We accept t h i s t h e s i s as conforming to the r e q u i r e d standard THE UNIVERSITY OF BRITISH COLUMBIA October 1982 (cp Andreas E s c h l e r , 1982 I I I n p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f t h e r e q u i r e m e n t s f o r a n a d v a n c e d d e g r e e a t t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a , I a g r e e t h a t t h e L i b r a r y s h a l l m a k e i t f r e e l y a v a i l a b l e f o r r e f e r e n c e a n d s t u d y . I f u r t h e r a g r e e t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s m a y b e g r a n t e d b y t h e h e a d o f m y d e p a r t m e n t o r b y h i s o r h e r r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l n o t b e a l l o w e d w i t h o u t m y w r i t t e n p e r m i s s i o n . D e p a r t m e n t o f /TecticrspScaf £r<f?<?//7-e<? T h e U n i v e r s i t y o f B r i t i s h C o l u m b i a 1956 M a i n M a l l V a n c o u v e r , C a n a d a V6T 1Y3 D a t e ZZ. fp D E - 6 ( 3 / 8 1 ) ABSTRACT Due to r i s i n g lumber c o s t s i t has become more and more important to optimize the c u t t i n g performance of bandsaws as they are used i n the f o r e s t products i n d u s t r y . One important aim i s t o reduce the l a t e r a l and t o r s i o n a l d e f l e c t i o n s of the blade to minimize the t h i c k n e s s of the c u t . T h i s study t r i e s to assess the i n f l u e n c e of v a r i o u s t y p i c a l bandsaw parameters on the s t r e s s d i s t r i b u t i o n i n the bandsaw blade and on the v i b r a t i o n a l behaviour of the s t a t i o n a r y and the running sawblade. Experiments were performed with a f u l l s i z e i n d u s t r i a l p r o d u c t i o n bandsaw. The experimental r e s u l t s f o r the s t r e s s - s t r a i n measurements of the s t a t i o n a r y sawblade are compared with r e s u l t s from t h e o r e t i c a l s o l u t i o n s . V i b r a t i o n measurements of the s t a t i o n a r y and of the running blade are compared to valu e s d e r i v e d from MOTE'S [9] f l e x i b l e band s o l u t i o n and KANAUCHI'S s o l u t i o n [21] f o r l a t e r a l d e f l e c t i o n and with ALSPAUGH'S [2] s o l u t i o n f o r t o r s i o n a l v i b r a t i o n s . The r e s u l t s presented show that the s t a t i c s t r e s s measurements agree very w e l l with the a n a l y t i c a l l y p r e d i c t e d r e s u l t s . Major f a c t o r s i n f l u e n c i n g the s t r e s s d i s t r i b u t i o n i n the b l a d e : the a x i a l p r e s t r e s s , s t r e s s e s due to bending of the blade over the bandsaw wheels, and s t r e s s e s due to t i l t i n g of the top bandsaw wheel were examined. A comparison of the experimental and a n a l y t i c a l r e s u l t s of the v i b r a t i o n measurements f o r the s t a t i o n a r y sawblade showed very good agreement f o r the l a t e r a l n a t u r a l f r e q u e n c i e s , while the t o r s i o n a l n a t u r a l f r e q u e n c i e s were c o n s i d e r a b l y higher than the a n a l y t i c a l l y p r e d i c t e d v a l u e s . S i m i l a r r e s u l t s c o u l d be observed f o r the n a t u r a l f r e q u e n c i e s of the running blade. The mode shapes of the s t a t i o n a r y sawblade at the n a t u r a l f r e q u e n c i e s were measured. I t was found that the modeshapes c o n s i s t e d of coupled modes f o r most t i l t s t r e s s d i f f e r e n c e s . V TABLE OF CONTENTS Chapter Page A b s t r a c t I l l L i s t of Tables VIII L i s t of F i g u r e s IX Nomenclature XV Acknowledgements XVII 1. I n t r o d u c t i o n 1 1 . 1 Background 1 1.2 Experimental aims 2 1.3 Previous r e s e a r c h 3 2. Expermental set up 5 2.1 Bandsaw f a c i l i t i e s 5 2.2 Instrumentation and data a c q u i s i t i o n system 5 3. T h e o r e t i c a l s t r e s s e v a l u a t i o n f o r a bandsaw blade 20 3.1 Fundamental theory of s t r e s s c a l c u l a t i o n of a bandsaw blade 20 3.2 S t a t i c s t r e s s e s f o r the s t a t i o n a r y blade 21 3.2.1 A x i a l p r e s t r e s s due to the a x i a l p r e s t r e s s i n g f o r c e 21 V I 3.2.2 Bending s t r e s s due to the r a d i u s of the bandsaw wheels 21 3.2.3 S t r e s s due to the crown up of the bandsaw wheels 22 3.2.4 S t r e s s as a f u n c t i o n of the t i l t 22 3.2.5 S t r e s s due to the notch f a c t o r of the blade t e e t h 23 3.2.6 S t r e s s due to p r e t e n s i o n i n g of the blade 23 3.3 A d d i t i o n a l s t r e s s e s d u r i n g i d l i n g 24 3.3.1 S t r e s s due to c e n t r i f u g a l f o r c e s 24 3.4 A d d i t i o n a l s t r e s s e s d u r i n g c u t t i n g 24 3.4.1 S t r e s s due to the c u t t i n g f o r c e s .....24 3.4.2 S t r e s s due to temperature changes 25 4. S t a t i c s t r e s s - s t r a i n measurements 27 4.1 Experiments 27 4.2 S t r e s s - s t r a i n measurements f o r d i f f e r e n t t i l t a n g l e s 31 4.3 S t r e s s - s t r a i n measurements around the bandsaw 40 5. Dynamic v i b r a t i o n measurements with a s t a t i o n a r y blade 48 5.1 Experimental set up and t h e o r e t i c a l bandsaw blade models 48 5.2 L a t e r a l and t o r s i o n a l n a t u r a l V I I f r e q u e n c i e s of the blade between the guides 63 5.3 T r a n s m i s s i b i l i t y of the blade 78 5.4 Dynamic v i b r a t i o n measurements with a moving blade 94 6. C o n c l u s i o n s 102 REFERENCES 105 APPENDIX I S t r e s s as a f u n c t i o n of the t i l t a n g l e 105 APPENDIX II Wheel support s t i f f n e s s Ks 111 APPENDIX III E r r o r c a l c u l a t i o n formulae 112 APPENDIX IV Computer programs 113 V I I I LIST OF TABLES Table Page I Parameter l i s t of the saw and the sawblade used i n the experiments 10 l a L i s t of i n s t r u m e n t a t i o n and equipment 19 II Average s t r a i n data at the o u t s i d e and i n s i d e of the blade at pos.E 39 III Values f o r t h e o r e t i c a l and experimental n a t u r a l f r e q u e n c i e s and r e l a t e d a b s o l u t e and r e l a t i v e e r r o r s 69 IV Change of the n a t u r a l f r e q u e n c i e s fL,T as a f u n c t i o n of the t i l t s t r e s s d i f f e r e n c e TSD 72 V T r a n s m i s s i b i l i t y of the s t a t i o n a r y sawblade at the two lowest l a t e r a l and t o r s i o n a l n a t u r a l f r e q u e n c i e s f o r d i f f e r e n t i l t s t r e s s d i f f e r e n c e s and a x i a l p r e s t r e s s e s 88 VI Values f o r t h e o r e t i c a l and experimental n a t u r a l f r e q u e n c i e s and and r e l a t e d e r r o r s f o r the running blade 101 IX LIST OF FIGURES FIGURES Page 1 Bandsaw set up 6 2 S t r a i n i n g system and t i l t a n g l e motor 7 3 Dimensions of the bandsaw 8 4 Straingage l o c a t i o n on the blade and blade dimensions 9 5 C a l i b r a t i o n f o r l o a d c e l l LC of the wheel support system under a pr e s s (mechanical E n g i n e e r i n g UBC) 12 6 C a l i b r a t i o n of l o a d c e l l f o r the e x c i t a t i o n f o r c e 'of the e l e c t r o magnet with weights 13 7 C a l i b r a t i o n of a #300 Bentley Nevada eddy-current displacement transducer with a f e e l e r g a g e 16 8 C a l i b r a t i o n of a #300 Bentley Nevada eddy-current displacement transducer with a f e e l e r g a g e 17 9 Measurement chain 18 10 Straingage p o s i t i o n s around the saw 28 11 Average t e n s i l e s t r a i n v a r i a t i o n i n x-' d i r e c t i o n around the saw f o r a t i l t a n g l e TA=0.06° 32 X 12 Average compresed s t r a i n v a r i a t i o n i n y - d i r e c t i o n around the saw f o r a t i l t a n g l e TA=0.06° 33 13 Average s t r e s s d i s t r i b u t i o n i n x-d i r e c t i o n around the saw f o r a t i l t a n g l e TA=1.33° 34 14 Average s t r a i n v a r i a t i o n between p o s i t i o n C and D 36 15 Average s t r e s s v a r i a t i o n between p o s i t i o n C and D 37 16 S t r e s s i n x - d i r e c t i o n a c r o s s the blade at d i f f e r e n t p o s i t i o n s around the saw, TA = 0.06°, p o s i t i o n C 41 17 S t r e s s i n x - d i r e c t i o n across the blade at d i f f e r e n t p o s i t i o n s around the saw, TA = 0.60°, p o s i t i o n C 42 18 S t r e s s i n x - d i r e c t i o n across the blade at d i f f e r e n t p o s i t i o n s around the saw, TA = 1.33°, p o s i t i o n C 43 19 S t r e s s i n x - d i r e c t i o n across the blade at d i f f e r e n t p o s i t i o n s around the saw, TA = 0.06°, p o s i t i o n G 44 20 S t r e s s i n x - d i r e c t i o n a c r o s s the blade at p o s i t i o n A and E f o r d i f f e r e n t a x i a l p r e s t r e s s e s SIG0(x), t i l t a n g l e TA = 0.00° 45 XI 21a P o s i t i o n of i n s t r u m e n t a t i o n f o r v i b r a t i o n measurements 49 21b D e f i n i t i o n of the t i l t s t r e s s -d i f f e r e n c e and r e l a t e d s t r e s s e s 49 22 RMS s p e c t r a f o r e x c i t a t i o n and response of the s t a t i o n a r y sawblade 51 23 T r a n s f e r f u n c t i o n of the s t a t i o n a r y sawblade (magnetic e x c i t a t i o n ) 52 24 Real and imaginary p a r t of the t r a n s f e r f u n c t i o n 53 25 Coherence of the s t a t i o n a r y sawblade 54 26 S h i f t of n a t u r a l f r e q u e n c i e s f o r d i f f e r e n t a x i a l p r e s t r e s s e s RO* 55 27 T r a n s m i s s i b i l i t y of the sawblade a t n a t u r a l f r e q u e n c i e s 56 27 T i l t s t r e s s d i f f e r e n c e of the s t a t i o n a r y sawblade as a f u n c t i o n of the t i l t a n g l e 60 29 Lowest l a t e r a l and t o r s i o n a l n a t u r a l f r e q u e n c i e s f o r d i f f e r e n t a x i a l p r e s t r e s s e s RO* and v a r i o u s t i l t s t r e s s d i f f e r e n c e s TSD 64 30 Lowest l a t e r a l n a t u r a l f r e q u e n c i e s fL1 f o r d i f f e r e n t a x i a l p r e s t r e s s e s RO* and v a r i o u s TSD 65 31 2nd lowest n a t u r a l frequency fL2 f o r . X I I d i f f e r e n t a x i a l p r e s t r e s s e s RO* and v a r i o u s TSD 66 32 Lowest t o r s i o n a l n a t u r a l frequency fT1 f o r d i f f e r e n t a x i a l p r e s t r e s s e s RO* and v a r i o u s TSD 67 33 2nd lowest t o r s i o n a l n a t u r a l frequency fT2 f o r d i f f e r e n t a x i a l p r e s t r e s s e s RO* and v a r i o u s TSD 68 34 1st and 2nd lowest t o r s i o n a l and l a t e r a l n a t u r a l f r e q u e n c i e s f o r d i f f e r e n t TSD and RO* 72 35 Lowest l a t e r a l n a t u r a l frequency•fL1 as a f u n c t i o n of .the TSD f o r a x i a l p r e s t r e s s RO* 73 36 • 2nd lowest l a t e r a l n a t u r a l frequency fL2- as a f u n c t i o n of the TSD f o r a x i a l p r e s t r e s s RO* 74 37 Lowest t o r s i o n a l n a t u r a l frequency fT1 as a f u n c t i o n of the TSD f o r a x i a l p r e s t r e s s RO* 75 38 2nd lowest t o r s i o n a l n a t u r a l frequency fT2 as a f u n c t i o n of the TSD f o r a x i a l p r e s t r e s s RO* 76 39 t r a n s m i s s i b i l i t y of the s t a t i o n a r y sawblade (measurement at the t o o t h s i d e f o r fL1) as a f u n c t i o n of RO* f o r X I I I d i f f e r e n t TSD 80 40 t r a n s m i s s i b i l i t y of the s t a t i o n a r y sawblade (measurement at the backside f o r f L l ) as a f u n c t i o n of RO* f o r d i f f e r e n t TSD 81 41 t r a n s m i s s i b i l i t y of the s t a t i o n a r y sawblade (measurement at the t o o t h s i d e f o r fL2) as a f u n c t i o n of RO* f o r d i f f e r e n t TSD 82 42 t r a n s m i s s i b i l i t y of the s t a t i o n a r y sawblade (measurement at the backside f o r fL2) as a f u n c t i o n of RO* f o r d i f f e r e n t TSD 83 43 t r a n s m i s s i b i l i t y of the s t a t i o n a r y sawblade (measurement at the t o o t h s i d e f o r fT1) as a f u n c t i o n of RO* f o r d i f f e r e n t TSD 84 44 t r a n s m i s s i b i l i t y of the s t a t i o n a r y sawblade (measurement at the backside f o r fT1) as a f u n c t i o n of RO* f o r d i f f e r e n t TSD 85 45 t r a n s m i s s i b i l i t y of the s t a t i o n a r y sawblade (measurement at the t o o t h s i d e f o r fT2) as a f u n c t i o n of RO* f o r d i f f e r e n t TSD . .86 46 t r a n s m i s s i b i l i t y of the s t a t i o n a r y X I V sawblade (measurement at the backside f o r fT2) as a f u n c t i o n of RO* f o r d i f f e r e n t TSD 87 47 Mode shapes of the s t a t i o n a r y sawblade 90 48 N a t u r a l f r e q u e n c i e s of the running blade f o r d i f f e r e n t a x i a l p r e s t r e s s e s RO*, c = 40.7 m/s 95 49 N a t u r a l f r e q u e n c i e s fL1 of the running blade f o r d i f f e r e n t a x i a l p r e s t r e s s e s RO*, c = 40.7 m/s 96 50 N a t u r a l f r e q u e n c i e s fL2 of the running blade f o r d i f f e r e n t a x i a l p r e s t r e s s e s RO*, c = 40.7 m/s 97 51 N a t u r a l f r e q u e n c i e s fT1 of the running blade f o r d i f f e r e n t a x i a l p r e s t r e s s e s R0*, c = 40.7 m/s 98 52 N a t u r a l f r e q u e n c i e s fT2 of the running blade f o r d i f f e r e n t a x i a l p r e s t r e s s e s R0*, c = 40.7 m/s 99 53a Non uniform s t r e s s d i s t r i b u t i o n a c r o s s the blade as a f u n c t i o n of the t i l t a n g l e TA 110 53b Change of s t r a i n as a f u n c t i o n of the t i l t a n g l e TA 110 NOMENCLATURE A = c r o s s s e c t i o n of the blade BO = width of the blade from t o o t h g u l l e t to backside B = t o t a l width of blade Bw = width of bandsaw wheel Bs = d i s t a n c e between s t r a i n g a g e l o c a t i o n SG1 and SG7 Bt = d i s t a n c e center of top wheel to p o i n t of t i l t a n g l e r o t a t i o n cO = wave v e l o c i t y c = sawblade v e l o c i t y D = band f l e x u r a l r i g i d i t y = ( E H 3 / 1 2 ( 1 - v 2 ) ) fL1 = 1. l a t e r a l n a t u r a l frequency fL2 = 2. l a t e r a l n a t u r a l frequency f T l = 1. t o r s i o n a l n a t u r a l frequency fT2 = 2. t o r s i o n a l n a t u r a l frequency E = Young's modulus of e l a s t i c i t y F v e r t = v e r t i c a l c u t t i n g f o r c e ( i n x - d i r e c t i o n ) F l a t = l a t e r a l c u t t i n g f o r c e ( i n z - d i r e c t i o n ) Fhor = h o r i z o n t a l c u t t i n g f o r c e ( i n y - d i r e c t i o n ) fc = height of crown G = shear modulus of e l a s t i c i t y g = g r a v i t a t i o n a l a c c e l e r a t i o n H' = band t h i c k n e s s Ks = wheel support system s t i f f n e s s L = band le n g t h between guides Lw = d i s t a n c e between center of r o t a t i o n of saw wheels n = number of data samples 2 R 0 = t o t a l a x i a l p r e s t r e s s i n g f o r c e RO* = a x i a l p r e s t r e s s r = r a d i u s of saw wheels rc = crown r a d i u s s = standard d e v i a t i o n SIGO(x) = a x i a l p r e s t r e s s SIGb(x) = bending s t r e s s due to r SIGc(y) = bending s t r e s s due to crown SIGf(x) = s t r e s s due to c e n t r i f u g a l f o r c e s SIGn(x) = s t r e s s due to the notch f a c t o r at the blade SIGr(x) = s t r e s s due to p r e t e n s i o n i n g SIGta(x) = s t r e s s due to the t i l t a n g l e SIG(x) = s t r e s s i n x - d i r e c t i o n SIGtemp(x) = s t r e s s due to temperature changes t e e t h X V I I SIGw(x) = s t r e s s due to c u t t i n g f o r c e s T = t r a n s m i s s i b i l i t y t = temperature TA = t i l t a n g l e u = feedspeed u = mean va lue of n data v a l u e s x Z = t o o t h s p a c i n g a = temperature g r a d i e n t v = P o i s o n ' s r a t i o K = wheel support s t i f f n e s s f a c t o r p = d e n s i t y n = support s t i f f n e s s c o n s t a n t (H = 1 - K ) 1 1 INTRODUCTION 1.1 Background Due to the r i s i n g c o s t of lumber i n the f o r e s t products i n d u s t r y the need of a thorough understanding of the i n f l u e n c e of the governing parameters on the c u t t i n g performance of the bandsaw has become a n e c e s s i t y . To achieve t h i s o b j e c t i v e , i n 1981 a woodcutting l a b o r a t o r y was set up a t the Department of Mechanical E n g i n e e r i n g at the U n i v e r s i t y of B r i t i s h Columbia, c o n s i s t i n g of a v e r t i c a l 5 foot p r o d u c t i o n bandsaw together with a s p e c i a l l y designed l o g c a r r i a g e system and a s o p h i s t i c a t e d i n s t r u m e n t a t i o n and data a c q u i s i t i o n system. The parameters governing the performance of a bandsaw can be separated i n t o three d i f f e r e n t groups: a) human i n f l u e n c e f a c t o r s ( i . e . The bandsaw operator chooses c e r t a i n bandsaw parameters by experience) b) design parameters e s t a b l i s h e d by the bandsaw designer c) s t o c h a s t i c i n f l u e n c e f a c t o r s (e.g. inhomogenities i n the lumber, temperature changes, e t c . ) The o b j e c t i v e of t h i s study i s to examine the i n f l u e n c e of parameters c h a r a c t e r i z e d under 1.a) and 1.b) on the s t r e s s d i s t r i b u t i o n i n the sawblade and on the v i b r a t i o n a l behaviour of the saw. 1.2 Experimental aims To a chieve t h i s o b j e c t i v e the experiments were d i v i d e d i n t o three major p a r t s : The f i r s t p a r t c o n s i s t s of s t r a i n measurements of the s t a t i o n a r y sawblade. The parameters which were changed were the a x i a l p r e s t r e s s SIGO(x) , the t i l t a n g l e TA and the p o s i t i o n of the blade around the saw. The t i l t a n g l e TA d e s c r i b e s the r o t a t i o n of the top wheel around the z - a x i s ( F i g u r e 3 ) . The second part c o n s i s t e d of v i b r a t i o n measurements of the s t a t i o n a r y sawblade, e x c i t e d with an e l e c t r o magnet. The two lowest l a t e r a l and t o r s i o n a l n a t u r a l f r e q u e n c i e s were measured for v a r i o u s a x i a l p r e s t r e s s e s RO* and d i f f e r e n t t i l t s t r e s s d i f f e r e n c e s TSD. In t h i s p art a d i f f e r e n t r e p r e s e n t a t i o n f o r the a x i a l p r e s t r e s s and f o r the t i l t a n g l e were chosen to allow normalized q u a n t i t i e s . The t r a n s m i s s i b i l i t y of the blade was measured at the p r e v i o u s l y i d e n t i f i e d n a t u r a l f r e q u e n c i e s f o r d i f f e r e n t a x i a l p r e s t r e s s e s RO* and t i l t s t r e s s d i f f e r e n c e s TSD. The t h i r d p a r t of the r e s e a r c h program c o n s i s t e d of v i b r a t i o n measurements of a f r e e running sawblade at d i f f e r e n t a x i a l p r e s t r e s s e s RO*. The wheel support s t i f f n e s s Ks (MOTE [9]) was measured. 1.3 Previous r e s e a r c h Over the years v a r i o u s r e s e a r c h e r s have covered some of the experiments done i n t h i s study. In 1970 THUNELL [22,23] summarized i n a p u b l i c a t i o n . v a r i o u s mathematical formulae to c a l c u l a t e s t r e s s e s i n a sawblade due to the geometry of the saw, to i d l i n g and to c u t t i n g . In 1971 PORTER [ 1 9 ] d i d s t r e s s experiments with a s t a t i o n a r y sawblade and compared h i s r e s u l t s with a n a l y t i c a l s o l u t i o n s . In 1972 PAHLITSCH [13,14] analysed the d i f f e r e n t s t r e s s e s i n bandsaw blades and compared them to experimental r e s u l t s . In 1977 KIRBACH and BONACH [7] measured the e f f e c t of wheel t i l t i n g and saw t e n s i o n i n g on the n a t u r a l f r e q u e n c i e s of a s t a t i o n a r y sawblade. In 1981 TANAKA [21] d i d an e x t e n s i v e experimental study on s t r e s s e s in bandsaw blades comparing the behaviour^ of f i v e d i f f e r e n t blades with each other. He a l s o examined the v i b r a t i o n a l behaviour of these blades f o r s t a t i o n a r y and running c o n d i t i o n s and compared them to a n a l y t i c a l s o l u t i o n s . In the l a s t 20 years a number of r e s e a r c h e r s presented a n a l y t i c a l s o l u t i o n s to t r y to p r e d i c t the n a t u r a l f r e q u e n c i e s of a running bandsaw blade. To compare the experimental data of t h i s study with a n a l y t i c a l s o l u t i o n s , MOTE'S f l e x i b l e band s o l u t i o n [9] and KANAUCHI'S model f o r l a t e r a l v i b r a t i o n s [21] and ALSPAUGH'S a n a l y t i c a l s o l u t i o n [2] f o r t o r s i o n a l v i b r a t i o n s were used. 2 EXPERIMENTAL SET UP 2.1 Band saw f a c i l i t i e s For the experiments presented i n t h i s study a v e r t i c a l 5 foot p r o d u c t i o n bandmill was used (see F i g u r e 1). The saw i s equipped with a h y d r a u l i c s t r a i n i n g system (Figure 2) which can p r o v i d e an a x i a l p r e s t r e s s i n g f o r c e 2R0 = 45000 N to 90000 N. The top wheel can be t i l t e d by an e l e c t r o motor ( F i g u r e 2) and the whole saw can be p o s i t i o n e d towards a c a r r i e r which passes a l o g by the saw. Above and below the c u t t i n g r e g i o n , the bandsaw blade i s guided by two pressure guides. During i d l i n g and c u t t i n g the blade i s c o o l e d by w a t e r j e t s . The saw was equipped with a p r e t e n s i o n e d bandsaw blade with an unknown i n t e r n a l s t r e s s d i s t r i b u t i o n . The dimensions and the chosen c o o r d i n a t e system f o r the saw and the blade are shown in F i g u r e s 3 and 4 and are a l s o l i s t e d i n Table I. 2.2 Instrumentation and data a c q u i s i t i o n system To measure the a x i a l p r e s t r e s s i n g f o r c e 2R0, a l i n k i n the h y d r a u l i c s t r a i n i n g system was equipped with a 4-arm temperature compensated s t r a i n g a g e b r i d g e . T h i s transducer w i l l be r e f e r r e d to as " l o a d c e l l " or "LC". top guide instrumen-tation frame electro-magne t bottom guide FIGURE 1 BANDSAW SET-UP 7 tilting system t ii tang!e counter I oadcel I hydraulic straining system FIGURE 2 STRAINING SYSTEM AND TILTANGLE MOTOR 8 FIGURE 3 DIMENSIONS OF THE BANDSAW Bo J~ - B H = 1.651 mm Z =44.375 mm Ba = 242. mm B = 260. mm FIGURE 4 STRAINGAGE LOCATION ON THE BLADE 10 AO = 398.7 mm BO = 241.5 mm B = 260 mm Bw = 228.6 mm Bs = 222 mm Bt = 222.3 mm c =40.7 m/s D = 86347 Nmm E = 2.1*l0 5N/mm 2 f c = 0.102 mm G = 80000 N/mm2 H = 1.651 mm Ks = 825 N/mm L = 762 mm Lw = 2464 mm r = 762.5 mm rc = 64 m t = 19 mm Z = 44.23 mm c r o s s - s e c t i o n area of the blade width of the blade from backside to gullet. t o t a l width of blade width of wheel d i s t a n c e between SG1 and SG7 d i s t a n c e between LC and center of wheel blade v e l o c i t y f l e x u r a l r e g i d i t y Young's modulus height of crown modulus of e l a s t i c i t y t h i c k n e s s of blade support s t i f f n e s s blade l e n g t h between guides d i s t a n c e between saw wheel axes ra d i u s of bandsaw wheels ra d i u s of bandsaw crown overhang of pressure guides tooth spacing Table I Parameter l i s t f o r the saw used i n the experiments The c a l i b r a t i o n curve f o r the l o a d c e l l LC i n c l u d i n g the standard d e v i a t i o n s and the e r r o r bounds f o r a con f i d e n c e value of 95% are shown i n F i g u r e 5. The t i l t a n g l e of the top wheel c o u l d be measured with a c a l i b r a t e d d i g i t a l counter (see F i g u r e 2 ) . The c a l i b r a t i o n f a c t o r of the t i l t a n g l e counter i s 675 d i g i t s /degree t i l t , with a standard d e v i a t i o n of 59 d i g i t s / d e g r e e f o r n=lO. The measurement ch a i n s d e s c r i b e d below are shown i n F i g u r e 9 and the equipment and in s t r u m e n t a t i o n used i n the experiments are l i s t e d i n Table l a . To measure s t a t i c as w e l l as dynamic q u a n t i t i e s , two d i f f e r e n t measurement systems were used. For s t a t i c and dynamic s t r a i n measurements, 9 s t r a i n g a g e s were cemented on the o u t s i d e of the blade (see F i g u r e 4). For some experiments 3 s t r a i n g a g e s were mounted at p o s i t i o n 1,4 and 7 on the i n s i d e of the blade. The data a c q u i s i t i o n system f o r these s t r a i n g a g e s c o n s i s t e d of a NEFF 620/300 s i g n a l c o n d i t i o n e r which pr o v i d e d constant v o l t a g e supply and bri d g e completion r e s i s t o r s as w e l l as i n d i v i d u a l bridge b a l a n c i n g f o r up to 64 channels s i m u l t a n e o u s l y . The c o n d i t i o n e d s i g n a l s were then fed i n t o a NEFF 620/100 A/D c o n v e r t e r and a m p l i f i e r which p r o v i d e d f i x e d and programmable a m p l i f i c a t i o n and analog d i g i t a l c o n v e r s i o n f o r each channel. The d i g i t a l i z e d data values were then m u l t i p l e x e d and sent from the. 0 5 10 15 20 25 30 35 40 45 50 55 60 LOAD C 33 N> F I G U R E 5 C A L I B R A T I O N FOR L O A D C E L L L C OF THE WHEEL S U P P O R T S Y S T E M UNDER A P R E S S C M E C H A N I C A L E N G I N E E R I N G U B O 0 10 20 30 40 50 60 70 LOAD CN> F I G U R E 6 C A L I B R A T I O N OF L O A D C E L L FOR THE E X C I T A T I O N F O R C E OF THE E L E C T R O M A G N E T WITH W E I G H T S l a b o r a t o r y through a NEFF 620/500 c o n t r o l p r o c e s s i n g u n i t to a PDP 11-34 computer f o r data p r o c e s s i n g . The data h a n d l i n g and p r o c e s s i n g c o u l d be c o n t r o l l e d through an i n t e l l i g e n t T e k t r o n i x 4051 t e r m i n a l i n the l a b o r a t o r y which was i n t e r f a c e d to the PDP 11-34. Software graphing f a c i l i t i e s allowed one to view the experimental r e s u l t s on the T e k t r o n i x screen and to make hardcopies on a connected d i g i t a l p l o t t e r . To run t h i s system, v a r i o u s FORTRAN programs were developed; these are documented i n APPENDIX IV. The program NEFF2 scans n channels with a chosen scanning frequency and sampling r a t e and s t o r e s the data i n u s e r - s p e c i f i e d data f i l e s . The program STRAIN c a l c u l a t e s the s t a t i c two-dimensional s t r e s s d i s t r i b u t i o n i n the blade from s t r a i n g a g e readings at d i f f e r e n t p o s i t i o n s around the saw. I t compiles the data from the s t r a i n g a g e s on the blade and the l o a d c e l l , u s i n g p r e v i o u s l y e s t a b l i s h e d c a l i b r a t i o n f a c t o r s . The program DYN c a l c u l a t e s the s t r e s s d i s t r i b u t i o n i n the blade from s t r a i n g a g e readings d u r i n g a chosen time d u r a t i o n . For v i b r a t i o n measurements a d i f f e r e n t data a c q u i s i t i o n system was used. The blade was e x c i t e d with an e l e c t r o magnet. The e x c i t a t i o n c u r r e n t was generated by a B r u e l and Kjaer frequency generator, a m p l i f i e d by a power a m p l i f i e r and fed i n t o the e l e c t r o magnet. The magnet was mounted i n a frame which allowed a t h r e e -dimensional p o s i t i o n i n g of the magnet behind the blade between the guides. The e x c i t a t i o n f o r c e of the magnet was measured with a p i e z o - e l e c t r i c l o a d c e l l and a m p l i f i e d by a charge a m p l i f i e r . The c a l i b r a t i o n curve of the l o a d c e l l with i t s standard d e v i a t i o n and the e r r o r bounds f o r a 95% confidence value i s shown i n F i g u r e 6. V i b r a t i o n s of the sawblade were measured wi t h 2 non c o n t a c t i n g eddy-current t r a n s d u c e r s . T h e i r c a l i b r a t i o n curves are shown i n F i g u r e 7 and 8. Both the e x c i t a t i o n and the blade response s i g n a l s were fed i n t o a 660A N i c o l e t t Dual Channel Frequency A n a l y z e r . The a n a l y s e r c o u l d be programmed to accept the necessary c a l i b r a t i o n f a c t o r s and then c a l c u l a t e the t r a n s f e r f u n c t i o n , t r a n s m i s s i b i l i t y , RMS spectrum and the coherence f u n c t i o n between the two channels. R e s u l t s c o u l d be shown on a screen and be p l o t t e d out onto a hard copy. A second method of documentation was to enter the data from the frequency a n a l y s e r i n t o the PDP11-34 and p l o t them out with the T e k t r o n i x t e r m i n a l and the d i g i t a l p l o t t e r . ,1 / S E N S I T I V I T Y - 0 . 3 4 4 mm/V I N T H E R A N G E FROM 1mm TO 2 . 7 5 m m P R O B E #1 I = D A T A R A N G E FOR A C O N F I D E N C E R A N G E O F 95%, n = 3 1 2 I ~ ~ ~ ~ ! " ~ — " I 3 4 5 6 GAP CMM? C A L I B R A T I O N OF # 3 9 9 B E N T L E Y NEVADA E D D Y - - C U R R E N T D I S P L A C E -M ENT P R O B E WITH A F E E L E R G A G E 10 P R 0 X I M I T 0 R 0 U T P U T 8 J 6 J 4 J 2 J 0 F I G U R E 8 0 SENSITIVITY = - 0 . 3 6 mm/V IN THE RANGE FROM 1mm TO 2 . 7 5 TO 2.75mm PROBE #2 I « DATA RANGE FOR A CONFIDENCE RANGE OF 95%, n «= 3 T T 6 1 2 3 4 5 GAP CmnO C A L I B R A T I O N OF # 3 0 0 B E N T L E Y NEVADA EDDY-CURRENT D I S P L A C E -MENT PROBE WITH A FEELERGAGE Signal Conditioner Sample and Hold amplifier A/0 Converter / / / © 7— ® Main frame Computer Data I/O System FIGURE 9 MEASUREMENT CHAINS I—' oo •• 1 four arm s t r a i n g a g e l o a d c e l l , EA-06-125AD-120, K=2.065, 120Ohms 2 p i e z o - e l e c t r i c l o a d c e l l , B r u e l + Kjaer 3 9 s t r a i n g a g e s , Kiowa KFC-5-c1.11, K=2.10 4 2 non-contacting eddy c u r r e n t probes, Bentley Nevada 5 2 p r o x i m i t o r s , Bentley Nevada 6 e l e c t r o magnet 7 NEFF 620/300 s i g n a l c o n d i t i o n e r 8 NEFF 620/100 a m p l i f i e r and A/D c o n v e r t e r 9 NEFF 620/500 demutiplexor and data storage 10 PDP 11/34 mainframe computer 11 TEKTRONIX Terminal 4051 12 TEKTRONIX d i g i t a l p l o t t e r 4662 13 sine-random generator, B r u e l + Kjaer 14 660A dual channel a n a l y s e r , N i c h o l e t 15 charge a m p l i f i e r 504D, K i s t l e r Table Ia LIST OF INSTRUMENTATION AND EQUIPMENT 3 THEORETICAL STRESS EVALUATION FOR A BANDSAW BLADE 3.1 Fundamental theory of s t r e s s c a l c u l a t i o n f o r a  bandsaw blade The bandsaw blade i s su b j e c t to a v a r i e t y of d i f f e r e n t s t r e s s e s while i t i s s t a t i o n a r y , d u r i n g i d l i n g and d u r i n g c u t t i n g . To keep the blade p o s i t i o n e d on the wheels and to i n c r e a s e the blade s t i f f n e s s an a x i a l p r e s t r e s s SIGO i s imposed on the blade by f o r c i n g the top wheel upwards with a f o r c e 2R0. T h i s f o r c e r e s u l t s i n a constant s t r e s s d i s t r i b u t i o n a c r o s s the blade. A d d i t i o n a l to t h i s constant s t r e s s d i s t r i b u t i o n a c r o s s the blade, non constant s t r e s s e s e x i s t due to the crown of the wheels, the t i l t a n g l e of the wheels, the amount of p r e - t e n s i o n i n g ( r o l l i n g ) done to the blade and s t r e s s c o n c e n t r a t i o n at the g u l l e t of the t e e t h . During i d l i n g and c u t t i n g the blade furthermore i s subject to c e n t r i f u g a l f o r c e s , temperature s t r e s s e s and s t r e s s e s r e s u l t i n g from the c u t t i n g f o r c e s . The s t r e s s e s a c t i n g i n a bandsaw blade can be c l a s s i f i e d i n the f o l l o w i n g way: s t a t i c s t r e s s e s - a x i a l s t r e s s SIGO(x) due to a x i a l p r e s t r e s s i n g f o r c e 2R0 -bending s t r e s s SIGb(x) due to bending of the blade over the wheels - s t r e s s SIGc(y) due to crown of the wheels - s t r e s s SIGta(x) due to the t i l t a n g l e of the top wheel 21 - s t r e s s SIGn(x) due to the notch f a c t o r of the blade t e e t h - s t r e s s SIGr(x) due to p r e - t e n s i o n i n g of the blade a d d i t i o n a l s t r e s s e s d u r i n g i d l i n g - s t r e s s SIGf(x) due to c e n t r i f u g a l f o r c e s a d d i t i o n a l s t r e s s e s d u r i n g c u t t i n g - s t r e s s SIGw(x) due to the c u t t n g f o r c e s - s t r e s s SIGtemp(x) due to temperature changes 3.2 S t a t i c s t r e s s " f o r the s t a t i o n a r y blade  3.2.1 A x i a l p r e s t r e s s SIGO(x) due to the a x i a l  p r e s t r e s s i n g f o r c e 2R0 The a x i a l p r e s t r e s s SIGO(x) i s caused by the fo r c e 2R0. Using the c r o s s s e c t i o n area A0=B0*H of the blade, where BO i s the width of the blade from the backside to the g u l l e t and H i s the t h i c k n e s s of the blade, the a x i a l p r e s t r e s s SIGO(x) can be c a l c u l a t e d from: 2R0 1 SIGO(x) = * 2 B0*H 3.2.2 Bending s t r e s s SIGb(x) due to the r a d i u s r of the bandsaw wheels The s t r e s s SIGb(x), r e s u l t i n g from bending of the blade over the c y l i n d r i c a l wheels r e s u l t s i n a s t r e s s which can be c a l c u l a t e d from: E H SIGb(x) = * 1-v 2 2r With E=Young's modulus, v =Poison's r a t i o and r - r a d i u s of the bandsaw wheels. For the saw used i n these experiments t h i s s t r e s s component amounts t o : SIGb(x) = 250N/mm2 3.2.3 S t r e s s SIGc(y) due to crown of the wheels Under the assumption that the cu r v a t u r e of the crown f o l l o w s a c i r c u l a r arc of r a d i u s r c , the s t r e s s SIGc(y) can be c a l c u l a t e d from: E H 1 v SiGc(y) = * - (-—+ — ) 1 - v 2 2 rc r with rc=radius of crown, Again f o r our saw t h i s r e s u l t s i n a 'maximum stress: '1*2. 1*1u5N/mm2 1.675mm2: . SIGc(y) = 1-0.3 2 2 _1 1 0.3 64*103mm 762.5mm ) = 79 N/mm2 3.2.4 S t r e s s SIGta(x) as a f u n c t i o n of the t i l t Using the geometric r e l a t i o n s h i p of the top wheel support and the t i l t system (see APPENDIX I) the s t r e s s SIGta(x) due to the t i l t a n g l e f o r each s t r a i n g a g e p o s i t i o n can be c a c u l a t e d from: IT ( s t r a i n g a g e p o s i t i o n ) SIGta(x) = *TA*E* 180 Lw where' T A = t i l t a n g l e of the topwheel (degrees) and Lw=distance between wheel axes. 3.2.5 S t r e s s SIGn(x) due to the notch f a c t o r of the  blade t e e t h P h o t o e l a s t i c s t u d i e s of e l l i p t i c a l shaped g u l l e t s (PORTER [19]) show that the s t r e s s c o n c e n t r a t i o n f a c t o r can reach a magnitude of 2.0 to 2.5. S t u d i e s by other authors show s i m i l a r r e s u l t s : .SUGIHARA [22] r e p o r t s a s t r e s s c o n c e n t r a t i o n f a c t o r of 1.3 to 2.5 while KRILOV [8] c i t e s a value of 1.35 f o r bending and 2.0 f o r t e n s i o n . 3.2.6 S t r e s s SIGr(x) due to p r e t e n s i o n i n g of the blade The d i r e c t measurement of the inplane s t r e s s e s induced i n t o a blade d u r i n g the p r e t e n s i o n i n g process i s very d i f f i c u l t . T h e r e f o r e i n many sawmills the shape of the d e f l e c t e d blade i n x and y - d i r e c t i o n i s measured ( l i g h t - g a p method) to o b t a i n a measure of the i n f l u e n c e of the p r e t e n s i o n i n g . N e v e r t h e l e s s measurements have been taken by some r e s e a r c h e r s . KRILOV [8] r e p o r t s that the s t r e s s SIGr(x) reaches a t e n s i l e l e v e l of 30 to 70N/mm2 while BAJKOWSKJ measures a t e n s i l e s t r e s s SIGr=65N/mm2 with i n t e r m i t t e n d compressive s t r e s s zones O f up to 550N/mm2 (PAHLITSCH [ 1 3 ] ) . 3.3 A d d i t i o n a l s t r e s s e s d u r i n g i d l i n g 3.3.1 S t r e s s SIGf(x) due to c e n t r i f u g a l f o r c e s The c e n t r i f u g a l f o r c e s which act on the blade d u r i n g running r e s u l t i n a s t r e s s : SIGf(x) = P * c 2 with p =mass d e n s i t y of the blade During the experiments the bandsaw ran with a v e l o c i t y of c = 40.7m/s, which r e s u l t s i n a s t r e s s SIGf(x) = 15.8N/mm2. 3.4 A d d i t i o n a l s t r e s s e s d u r i n g c u t t i n g 3.4.1 S t r e s s SIGw(x) due to the c u t t i n g f o r c e s Up to date very l i t t l e experimental r e s e a r c h has been done concerning the c u t t i n g f o r c e s . FEOKTISKOV [13] re p o r t s that under extreme c o n d i t i o n s (c=45m/s, u=1m/s and depth of cut i s 300mm) a c u t t i n g f o r c e Flat=900N can be reached. He c a l c u l a t e d that even under such unfavorable c o n d i t i o n s the r e s u l t i n g s t r e s s e s are n e g l i b l e compared to the s t r e s s e s r e s u l t i n g from the a x i a l p r e t e n s i o n i n g f o r c e 2R0 and from bending of the blade over the wheels. . The same can be s a i d f o r s t r e s s e s r e s u l t i n g from the c u t t i n g f o r c e s F l a t and Fhor (PAHLITSCH [ 1 3 ] ) . KRILOV [8] determines that the s t r e s s SIG(x) r e s u l t i n g from the c u t t i n g f o r c e s can reach l e v e l s of up to 7N/mm2 3.4.2 S t r e s s SIGtemp(x) due to temperature changes A study by SAITO and MOVI (1953 [22]) shows an average temperature change i n the blade of 45° C du r i n g c u t t i n g moist wood with a feed speed of u=0.47m/s. Such a temperature d i f f e r e n c e (assuming r i g i d wheelsupports) would r e s u l t i n a temperature s t r e s s o f : SIGtemp = E * a t * ( t 2 - t 1 ) 1 1 * 1 0 - 6 = 2. 1*1u5N/mm2* *45deg = l04N/mm2 deg with a t = l i n e a r c o e f f i c i e n t of expansion, (t2-t1)=temperature change in the blade This shows that a temperature change i n the blade has a s i g n i f i c a n t i n f l u e n c e on the sum of the a x i a l s t r e s s e s acting in a bandsaw blade. 4 STATIC STRESS-STRAIN MEASUREMENTS WITH A STATIONARY SAWBLADE 4.1 Experimental procedure Using the i n s t r u m e n t a t i o n set-up d e s c r i b e d i n chapter 2, s t r a i n measurements i n x and y - d i r e c t i o n s were taken, while changing the f o l l o w i n g saw parameters: i ) a x i a l p r e s t r e s s SIGO i i ) t i l t a n g l e of the top wheel i i i ) p o s i t i o n of the s t r a i n g a g e s on the blade r e l a t i v e to the bandsaw The change of the p o s i t i o n of the st r a i n g a g e l o c a t i o n around the saw was achieved by r o t a t i n g the blade by hand around the bandsaw. The chosen s t r a i n g a g e p o s i t i o n s are shown i n F i g u r e 10 and are l a b e l l e d from A to N. To c a l c u l a t e the s t r e s s e s from the s t r a i n measurements Hooke's law was used (TIMOSHENKO, "Theory of P l a t e s " [24]) a ( ex + v e y } / FIGURE 10 STRAINGAGE POSITIONS AROUND THE SAW A l l measurements represented here only r e f l e c t s t r a i n s and s t r e s s e s which were imposed onto the blade a f t e r the st r a i n g a g e s were a p p l i e d . I t i s not p o s s i b l e from these measurements to determine the i n i t i a l i n - p l a n e s t r e s s c o n f i g u r a t i o n of the blade (due to r o l l i n g , welding, s t r a i n i n g e t c . of the blade) which were present before the experiments were done. To measure s t r a i n s on the blade a c c u r a t e l y , the s t r a i n g a g e s had to be balanced before each experiment. T h i s was done to minimize the common mode v o l t a g e of the st r a i n g a g e s i g n a l so that the whole range of the a n a l o g / d i g i t a l converter i n the NEFF 100 system c o u l d be used f o r the change of the str a i n g a g e s i g n a l d u r i n g an experiment. The s t r a i n g a g e s were balanced at p o s i t i o n E (between the g u i d e s ) . To be able to perform repeatable experiments, the i n i t a l c o n d i t i o n s of the blade had to be i d e n t i c a l f o r each experiment. I t was observed that without any a x i a l p r e l o a d 2R0 the blade at p o s i t o n E would d e f l e c t i n y-d i r e c t i o n and the d e f l e c t e d shape would vary from experiment to experiment. T h i s d e f l e c t i o n induces bending s t r a i n s i n the s t r a i n g a g e s during the b a l a n c i n g of the s t r a i n g a g e s and r e s u l t s i n an e r r o r of the str a i n g a g e readings, once the blade i s s t r a i n e d . To assure that i d e n t i c a l c o n d i t i o n s from experiment to experiment e x i s t , the blade was p r e s t r a i n e d with an a x i a l p r e l o a d of 2R0=2700N/mm2 before b a l a n c i n g . T h i s procedure r e s u l t s i n i d e n t i c a l i n i t i a l c o n d i t i o n s d u r i n g the b a l a n c i n g of the s t r a i n g a g e s f o r each experiment. While the average s t r a i n l e v e l of the blade between experiments i s not e f f e c t e d by t h i s p r e s t r a i n i n g f o r c e , i t does reduce the slope of the measured s t r a i n d i s t r i b u t i o n a c r o s s the blade due to a t i l t a n g l e change. During the experiments i t was found that the average s t r a i n measured on the o u t s i d e of the blade was a f a c t o r of 1.3 higher than the c o r r e s p o n d i n g p r e s t r a i n l e v e l c a l c u l a t e d from the l o a d c e l l readings from LC. The experiments were repeated with s t r a i n g a g e s mounted on the i n s i d e of the blade and i t was found that the measured average s t r a i n on the i n s i d e of the blade was smaller by a f a c t o r of 1.1 than the corresponding p r e s t r a i n l e v e l from LC. Experiments with s t r a i n g a g e s mounted on the i n s i d e of the blade c o u l d only be performed at p o s i t i o n E (between the guides) and at p o s i t i o n L (at the back of the saw). These r e s u l t s show that even with a p r e l o a d of 2700 N d u r i n g b a l a n c i n g of the s t r a i n g a g e s , there are s t i l l bending e f f e c t s i n the blade although to an observer the blade appears to be s t r a i g h t . 31 4.2 S t r e s s - s t r a i n measurements with a s t a t i o n a r y  sawblade In F i g u r e 11 and 12 the s t r a i n l e v e l s on the o u t s i d e of the blade i n x and y - d i r e c t i o n f o r d i f f e r e n t p o s i t i o n s around the saw, averaged over the corresponding s t r a i n g a g e s have been p l o t t e d out. For p o s i t i o n E and L the average s t r a i n l e v e l s on the i n s i d e of the blade have been added. The s t r a i n d i f f e r e n c e between the average s t r a i n s at p o s i t i o n E and L ( s t r a i g h t blade) and the p o s i t i o n s , where the blade i s in bending over the wheels amounts to 1534 -409 =1125 m i c r o s t r a i n . The t h e o r e t i c a l s t r a i n value f o r bending of the blade over the wheels from chapter 3.2.2 r e s u l t s i n a value of 1191 m i c r o s t r a i n or a d i f f e r e n c e of 5.5%. These measurements have been repeated f o r t i l t a n g l e s of 0.60° and 1.33°. The s t r a i n d i f f e r e n c e s f o r bending over the wheels are 1168 m i c r o s t r a i n s and 1187 m i c r o s t r a i n r e s p e c t i v e l y and the d i f f e r e n c e s between t h e o r e t i c a l and experimental r e s u l t s are 1.9% and 0.3%. The average s t r e s s - d i s t r i b u t i o n i n x - d i r e c t i o n on the o u t s i d e of the blade i n F i g u r e 13 i s c a l c u l a t e d from the s t r a i n data in F i g u r e 11 and 12 and shows the change of a x i a l s t r e s s the blade undergoes, while t r a v e l l i n g over the saw wheels. As d e s c r i b e d i n chapter 3 the 2000 T E N S I L E M I C R 0 S T R A I N 1750 J 1500 J 1250 1000 J 750 J 500 J 250 J 0 *—* BLADE OUTSIDE Q BLADE INSIDE PRESTRESS SIG0Cx>»e57.dN/mm2 RESTRAIN MEPSCx>«322 H£ H ll A + / C •E •0 A B —r-c D T 1 -E F 1 — 6 H K T -L T 0 2000 — j — 4000 j — 6000 MEPSCX} POS. T M N 8000 FIGURE 1 1 , - i STRAINGAGE POSITION AROUND THE SAW Cmm> AVERAGE TENSILE STRAIN VARIATION IN X-DIRECTION AROUND FOR A TILTANGLE TA«0.06° 00 2 0 8 0 C 0 M P R E S S I V E M I C R 0 S T R A I N 1750 _ 1500 _ 1250 _ 1000 _ 7 5 0 „ 5 0 0 2 5 0 0 J F I G U R E 12 A A B L A D E O U T S I D E P R E S T R E S S S IG0Cx>=67.6N/mm2 P R E S T R A I N MEPSCx ) = 3 2 2 ^ £ P O S . A B D E F H L M N T 0 2000 4000 6 0 0 0 8 0 0 0 S T R A I N G A G E P O S I T I O N AROUND T H E SAW CmiO A V E R A G E C O M P R E S S I V E S T R A I N V A R I A T I O N I N Y - D I R E C T I O N AROUND T H E SAW FOR A T I L T A N G L E T A = 0 . 0 6 ° U) (jO 5 0 0 4 0 0 S 3 0 0 T R E S S 2 0 0 CN/mm^V 100 0 F I G U R E 13 A — A B L A D E O U T S I D E P R E S T R E S S S I G 0 < x » = 6 7 . 6 N / m m 2 Q B L A D E I N S I D E A B C D E F G H I J K L M N < i i 1 — i — i 1 i i i i i « • n ; r 1 1 ; 1 1 0 2 0 0 0 4 0 0 0 6 0 0 0 8 0 0 0 S T R A I N G A G E P O S I T I O N AROUND T H E SAW CmnO A V E R A G E S T R E S S D I S T R I B U T I O N I N X - D I R E C T I O N AROUND T H E SAW FOR A T I L T A N G L E O F T A = 0 . 0 6 ° s t r e s s i n the blade while p a s s i n g over the wheels c o n s i s t s mainly of the sum of the s t r e s s e s SIGO(x) and SIGb(x). The s t r e s s changes between p o s i t i o n E and A amounts to 255N/mm2 which agrees w e l l with the s t r e s s v alues f o r bending over the wheels from chapter 3.2.2 of 250N/mm2 F i g u r e 14 shows the experimental r e s u l t s of s t r a i n changes on the o u t s i d e of the blade while i t t r a v e l s away from the wheel-blade c o n t a c t i n g zone f o r a t i l t a n g l e TA=0.60°. Measurements of s t r a i n s on the i n s i d e of the blade c o u l d not be performed without damaging the s t r a i n g a g e s . The geometric l o c a t i o n of p o s i t i o n C1 to C5 and X1 to X7 are shown i n F i g u r e 6. C3 repre s e n t s the exact c o n t a c t p o i n t between the blade and the bandsaw wheel. I t can be observed that at p o s i t i o n C5, which i s 35mm away from C3, the s t r a i n i n x-d i r e c t i o n has almost reached a constant value which then r a i s e s s l i g h t l y up to p o s i t i o n D - the upper guide. Going from p o s i t i o n C1 to p o s i t i o n C3 the s t r a i n i n x-d i r e c t i o n decreases at a ra t e of 19 microstrain/mm. At the same time the s t r a i n i n y - d i r e c t i o n i n c r e a s e s with a rat e of 0.61 microstrain/mm. The s t r e s s v a l u e s i n Fi g u r e 15 are c a l c u l a t e d from the s t r a i n data i n Fi g u r e 14. While the s t r e s s i n x - d i r e c t i o n drops at a rate of 5N/mm2/mm while the blade t r a v e l s from p o s i t i o n C1 to C3, i t reaches a minimum of 85N/mm2 at p o s i t i o n X4 2 0 0 0 M I C R 0 s T R A I N . ~ * T E N S I L E S T R A I N I N X - D I R E C T I O N , B L A D E O U T S I D E 1 7 5 0 J B BCOMPRESSIVE S T R A I N I N Y - D I R E C T I O N , B L A D E O U T S I D E 1 5 0 0 1 2 5 0 J 1 0 0 0 7 5 0 J 5 0 0 2 5 0 J 0 A X I A L P R E S T R E S S S I G 0 C x ! > = 7 0 N / W C5 XI X2 X3 X4 X5 XS X7 A A —-a*> A A •0" -B- -B- -B- -B- -B-T T T 0 D -B F I G U R E 14 1 0 0 2 0 0 3 0 0 4 0 0 5 0 0 6 0 3 7 0 0 8 0 0 S T R A I N G A G E P O S I T I O N S B E T W E E N P O S . C AND D (mm) S T R A I N V A R I A T I O N BETWEEN P O S I T I O N C AND D C B E T W E E N CONTACT ZONE AND G U I D E } , T I L T A N G L E T A = 0 . 6 0 ° U) 5 8 0 4 0 0 J S T R E S S 3 0 0 J 2 0 0 J CN/mm 2 > 1 0 0 0 J A — * S T R E S S I N X - D I R E C T I O N , B L A D E O U T S I D E C 1 B B S T R E S S I N Y - D I R E C T I O N , B L A D E O U T S I D E A X . P R E S T R E S S S I G 0 < x > = 7 0 . 0 N / m m 2 C 5 XI X 2 X 3 X 4 X 5 X 6 X 7 A A A - -h —h A — D -A S I G O C x ) • -. B 0 1 0 0 2 0 0 3 0 0 4 0 0 5 0 0 6 0 0 7 0 0 8 0 0 S T R A I N G A G E P O S I T I O N B E T W E E N P O S . C AND D (mm) F I G U R E 15 A V E R A G E S T R E S S V A R I A T I O N BETWEEN P O S I T I O N C AND D CBETWEEN CONTACT ZONE AND G U I D E ; , T I L T A N G L E TA = 0 . 6 0 ° compared to an a x i a l p r e s t r e s s of 70N/mm2. The s t r e s s i n y - d i r e c t i o n approaches zero a f t e r the blade leaves the contact zone as one would expect to happen from a t h i n p l a t e supported on two s i d e s i n x-d i r e c t i o n and having f r e e edges i n the y - d i r e c t i o n . At p o s i t i o n E and L the experiments have been repeated 3 times f o r 4 d i f f e r e n t t i l t a n g l e s at the f r o n t of the blade and at the back of the blade. The data from these experiments with t h e i r standard d e v i a t i o n s and e r r o r bounds are shown in Table I I . 39 1 2 3 4 5 t i l t a n g l e a v e r a g e s t r a i n f r o m a v e r a g e f r o m TA LC s t r a i n g a g e s on b l a d e 3 a n d 4 ( d e g r e e s ) o u t s i d e i n s i d e '(ye) (ye) (ye) (ye) 0 . 0 0 332 4 0 2 278 340 0 . 3 3 320 4 0 8 291 349 0 . 6 0 319 404 280 342 1 . 3 0 319 398 276 337 a v e r a g e s t r a i n 320 4 0 3 281 342 (ye) r > ? . s t a n d a r d d e v i a t i o n s (ye) 6 . 7 1 4 . 0 1 3 . 5 1 1 . 6 e r r o r b o u n d s (ye) - + 4 . 3 + 8 . 9 + 8 . 6 + 7 . 4 The s t a n d a r d d e v i a t i o n s a r e c a l c u l a t e d f o r n=12 ( t h r e e e x p e r i m e n t s f o r e a c h t i l t a n g l e ) . H e r e a r e o n l y t h e a v e r a g e s t r a i n s f o r n=3 f o r e a c h t i l t a n g l e s h o w n . The e r r o r b o u n d s a r e c a l c u l a t e d f o r a c o n f i d e n c e v a l u e o f 9 5 % . T a b l e I I A v e r a g e s t r a i n d a t a a t t h e o u t s i d e a n d t h e i n s i d e o f t h e b l a d e a t p o s i t i o n E 4.3 S t r a i n measurements acr o s s the blade at d i f f e r e n t  l o c a t i o n s around the saw f o r d i f f e r e n t a x i a l p r e s t r e s s e s  and t i l t a n g l e s F i g u r e 16, 17 and 18 show the s t r e s s - d i s t r i b u t i o n a c r o s s the blade f o r d i f f e r e n t t i l t a n g l e s between p o s i t i o n E (between the guides) and p o s i t i o n C (contact zone between blade and saw wheel). P o s i t i o n C1 and C5 are 70 mm apart.The r e s u l t s show that i n these 70 mm the blade undergoes the t o t a l average s t r e s s change of 250N.mm2 - due to bending over the wheel. For a blade v e l o c i t y of c=40m/s (as used l a t e r i n the dynamic experiments) t h i s means that t h i s s t r e s s change happens i n 1.7ms. The change of the slope of the s t r e s s -d i s t r i b u t i o n across the blade due to a t i l t a n g l e change can not be measured a c c u r a t e l y , because by a p p l y i n g an a x i a l p r e l o a d of 2700N/mm2 before b a l a n c i n g of the s t r a i n g a g e s , l o c a l s t r e s s e s r e s u l t i n g from a t i l t a n g l e are reduced. For a t i l t a n g l e of TA=0.06° the above measurements were repeated at p o s i t i o n G (Figure 19). The slope of the s t r e s s - d i s t r i b u t i o n a c r o s s the blade at p o s i t i o n G5 i s 50% l e s s than the slope at p o s i t i o n C5 f o r the same c o n d i t i o n s which shows that the i n f l u e n c e of the t i l t a n g l e on the s t r e s s - d i s t r i b u t i o n i s g r e a t e r at the top wheel than at the bottom wheel. T h i s i s due to the 5 0 0 4 0 0 J S T R E S S 3 0 0 J 2 0 0 J CN/mm2> 100 0 0 F I G U R E 16 A ApQS. E B — a pos. CI « — » P O S . C2 * P O S . C3 o — ® P O S , C4 v POS . C5 A X I A L P R E S T R E S S S I S 0 C x ^ ~ 6 7 . 6 N / m m 2 B L A D E O U T S I D E S I G 0 C x > 5 0 1 1 1 1 1 100 150 2 0 0 2 5 0 S T R A I N G A G E P O S I T I O N A C R O S S T H E B L A D E (mm) S T R E S S I N X - D I R E C T I O N A C R O S S T H E B L A D E A T P O S I T I O N C CCONTACT Z O N E ) , T I L T A N G L E T A « . 0 6 ° 5 0 0 4 0 0 J S T R E S S C N / 3 0 0 J 2 0 0 J mm 100 J 0 0 A — P O S . E B —epos. Ci *~"*POS. C2 *--*POS. C3 Q GPOS. C4 V— VPOS. C5 A V E R A G E P R E S T R E S S S I G 0 C x ) = 7 0 N / m m ' BLADE OUTSIDE J¥ y S I G 0 C X ) ~ r 1 r 1 r ™ 50 100 150 200 250 S T R A I N G A G E P O S I T I O N A C R O S S T H E B L A D E (mm) F I G U R E 17 S T R E S S I N X - D I R E C T I O N A C R O S S T H E B L A D E AT P O S I T O N C CCONTACT Z O N E ) , T I L T A N G L E T A = 0 . 6 ° it* 5 0 0 4 0 0 J * — A P O S . E 0 — B P O S . C l - ^ P O S . C 2 * P C S . C 3 °—°POS. C 4 * P O S . C 5 A V E R A G E P R E S T R E S S S I G < x ) = 6 6 N / m m 2 BLADE OUTSIDE S T R E S S C N / m m 2 ) 3 0 0 2 0 0 J 1 0 0 J 0 0 S I G 0 C x > 1 0 0 1 5 0 2 0 0 2 5 0 S T R A I N G A G E P O S I T I O N A C R O S S T H E B L A D E CmirO F I G U R E 18 S T R E S S I N X - D I R E C T I O N A C R O S S T H E B L A D E AT P O S I T I O N C CCONTApT Z O N E D , T I L T A N G L E T A = 1 . 3 3 ° U) 5 0 0 4 0 0 J S T R E S s 3 0 0 J 2 0 0 CN/mm^} 1 0 0 J 0 F I G U R E 1 9 A — A P O S . <s> & pos . * P O S . G O p Q S . v — v pos E G1 G2 G3 G4 G5 A X I A L P R E S T R E S S S I G 0 C x ) = 6 7 . 6 N / m m 2 B L A D E O U T S I D E ¥  S I G 0 C x > I 1 1 1 1 — r ~ ~ — 0 • 5 0 1 0 0 1 5 0 2 0 0 2 5 0 S T R A I N G A G E P O S I T I O N A C R O S S T H E B L A D E CmmD S T R E S S I N X - D I R E C T I O N A C R O S S T H E B L A D E AT P O S I T I O N S <CONTACT Z O N E D , T I L T A N G L E TA=0.06<> 4^ 5 0 0 4 0 0 J S T R E S S 3 0 0 2 0 0 J C N / m m 2 ) 1 0 0 0 0 B L A D E O U T S I D E P O S . A A *SIGCX!>= 50 N / m m 2 B — B S I G C X > = 6 0 N / m m 2 ^ - ^ S I G C X ) = 70 N / m m 2 + SIGCX^= 76 N / m m 2 © e S I G C X ) - 86 N / m m 2 5 0 1 0 0 1 5 0 2 0 0 2 5 0 S T R A I N G A G E P O S I T I O N A C R O S S T H E B L A D E (mm) F I G U R E 20 S T R E S S I N X - D I R E C T I O N A C R O S S THE B L A D E AT P O S . A AND E FOR I N C R E A S I N G A X . P R E S T R E S S E S S I G O C x ) , T I L T A N G L E T A = 0 . 0 ° i t * f a c t that only the top wheel r o t a t e s around the z - a x i s d u r i n g a t i l t a n g l e change, while the bottom wheel remains s t a t i o n a r y . A d i f f e r e n t s e r i e s of experiments are shown i n F i g u r e 20. The a x i a l p r e s t r e s s was r a i s e d i n f i v e s t e p s . The l e v e l s of the a x i a l p r e s t r e s s e s were measured with the l o a d c e l l LC i n c o r p o r a t e d i n t o the s t r a i n i n g system while the s t r e s s changes i n x - d i r e c t i o n i n the blade were measured with the s t r a i n g a g e set-up on the o u t s i d e of the blade. The experiments were performed at two d i f f e r e n t l o c a t i o n s , at p o s i t i o n E (between the guides) and at p o s i t i o n A (on top of the top wheel) . The o b j e c t i v e of t h i s experimental s e r i e s i s to examine the i n f l u e n c e of p r e s t r e s s i n c r e a s e s on the s t r e s s d i s t r i b u t i o n at p o s i t i o n E and A. The r e s u l t s show t h a t the s t r e s s i n c r e a s e at p o s i t i o n E i s equal to the s t r e s s i n c r e a s e at p o s i t i o n A. While the s t r e s s - d i s t r i b u t i o n a c r o s s the blade at p o s i t i o n E i s n e a r l y l i n e a r , the s t r e s s - d i s t r i b u t i o n at p o s i t i o n A f o l l o w s a p a r a b o l i c curve with a maximum at s t r a i n g a g e p o s i t i o n 5 (one t h i r d a c r o s s the blade away from the t o o t h g u l l e t ) . A s i m i l a r p a r a b o l i c s t r e s s - d i s t r i b u t i o n has been measured by PAHLITSCH [13] and i s due to the f a c t that the blade i s simultaneously bent over the wheels in two d i r e c t i o n s , -i n x - d i r e c t i o n due to the c u r v a t u r e of the bandsaw wheel diameter and i n y - d i r e c t i o n due to the crown of the wheel. The s t r e s s maximum a c r o s s the wheel c o i n c i d e s with the geometric l o c a t i o n of the hig h e s t peak of the crown of the wheel. T h i s p a r a b o l i c s t r e s s - d i s t r i b u t i o n a t p o s i t i o n A r e s u l t s i n maximum s t r e s s v a l u e s which are c o n s i d e r a b l y higher than the average s t r e s s a c r o s s the blade. For the t i l t a n g l e of TA=0.00° at p o s i t i o n A the maximum s t r e s s at SG5 averaged over the f i v e experiments i s 65.6N/mm2 or 18.5% higher than the a x i a l s t r e s s averaged over a l l SG a c r o s s the blade.. The t h e o r e t i c a l s t r e s s c a l c u l a t i o n s i n chapter 3 do not account f o r the f a c t that the s t r e s s d i s t r i b u t i o n a c r o s s the blade, while subject to an a x i a l p r e s t r e s s and to bending f o l l o w s a p a r a b o l i c curve arid has t h e r e f o r e a maximum va l u e . If f a t i g u e l i m i t c a l c u l a t i o n s f o r sawblades are performed t h i s f a c t has to be taken i n t o c o n s i d e r a t i o n . 5 DYNAMIC VIBRATION MEASUREMENTS WITH A STATIONARY BLADE 5.1 Experimental set up and t h e o r e t i c a l bandsaw models To measure the n a t u r a l f r e q u e n c i e s of the s t a t i o n a r y blade in the c u t t i n g region (between the guides) an e l e c t r o magnet was mounted on the i n s i d e of the sawblade at a p o s i t i o n between the guides, two t h i r d s of the span l e n g t h L down from the top guide and away from the center of the blade over to the t o o t h s i d e to simulate the f o r c e i n f l u e n c e of the c u t t i n g p r o c e s s . On the o u t s i d e of the blade two non c o n t a c t i n g displacement probes were s i t u a t e d at the same height as the e l e c t r o magnet, one on the t o o t h s i d e , the other on the backside of the blade (see F i g u r e 21a). The e l e c t r o magnet was connected to a frequency generator which s u p p l i e d a broad e x c i t a t i o n to the sawblade, ranging from 0-200 Hz. The e x c i t a t i o n f o r c e c o u l d be measured with a l o a d c e l l . The e x c i t a t i o n f o r c e as w e l l as the response s i g n a l s ( d e f l e c t i o n s ) of the blade were fed i n t o a FFT dual channel frequency a n a l y s e r which c a l c u l a t e d and d i s p l a y e d the t r a n s f e r f u n c t i o n between input ( e x c i t a t i o n ) i n t o the blade and output (displacement) of the blade. Besides many other f u n c t i o n s the RMS values of the input and output s i g n a l , the coherence (a measure 49 back -side of the blade top guide electro-magnet bottom guide d isplacemenf tr ansdu cers POSITIONING OF INSTRUMENTATION FOR VIBRATION MEASUREMENTS TSD = SIG/-SIG1 = 2SIGt FIGURE 21 b DEFINITION OF THE TILTSTRESS -DIFFERENCE AND RELATED STRESSES of the l i n e a r r e l a t i o n s h i p between input and output d a t a ) , and the t r a n s m i s s i b i l i t y ( r a t i o pf RMS v a l u e s between input and output data, i n our case t h i s i s the i n v e r s e of the s t i f f n e s s of the blade) were of s p e c i a l i n t e r e s t and c o u l d be c a l c u l a t e d and d i s p l a y e d . These f u n c t i o n s w i l l be e x p l a i n e d l a t e r i n more d e t a i l by means of an example. In F i g u r e 22 the RMS v a l u e s of the e x c i t a t i o n f o r c e from the e l e c t r o magnet and the blade response are recorded. The numerical v a l u e s i n s i d e the graph frame (.234, .137, ...) represent the RMS values ( l o g . Scale) f o r channel A and B over 10 Hz i n t e r v a l s around the n a t u r a l f r e q u e n c i e s . The r a t i o of the RMS values of channel B d i v i d e d by channel A give the t r a n s m i s s i b i l i t y of the blade (see F i g u r e 27). F i g u r e 23 shows a t y p i c a l t r a n s f e r f u n c t i o n from the frequency a n a l y s e r d i s p l a y . A phase s h i f t of 90 degrees and a maximum (peak) i n the magnitude of the t r a n s f e r f u n c t i o n i n d i c a t e s a n a t u r a l frequency. The phase and the magnitude are n u m e r i c a l l y d i s p l a y e d f o r a chosen frequency (61 Hz). The same in f o r m a t i o n can be obtained i f the r e a l and imaginary p a r t s of the t r a n s f e r f u n c t i o n are p l o t t e d . A s i g n change in the r e a l part and a peak in the imaginary p a r t i n d i c a t e a n a t u r a l frequency ( F i g u r e 24). F i g u r e 25 shows the coherence f u n c t i o n , an i n d i c a t i o n of the l i n e a r c a u s e / e f f e c t RMS SPECTRUM CH. A CEXClt) CN) 5 6 . 5 0 0 0 0 HZ 2 3 4 . 6 6 . 5 0 0 0 0 HZ 1 3 7 . R0*= 28L;.0 , TSD= +15.7 N/mm2 - 0 3 RMS - 0 3 RMS L G RS RMS SPECTRUM CH.B CBLADE-RESPONSE) Cmm) F I G U R E 22 • :FREQUENCY CHz) 2 0 0 RMS SPECTRA FOR EXCITATION AND RESPONSE OF THE STATIONARY SAWBLADE R0*= ; 28.6 TSD= -1.5 .,7N/mm2 6 1 . 0 0 0 0 0 H Z 1 4 5 . 8 D G 1 . 5 4 + 0 0 E L G TRANSFER FUNCTION C D E G R E E S T F + CMH/N> + LAJ + J i .54 1 + 1 ^ F I G U R E 2 3 : FREQUENCY CHO 2 0 0 TRANSFER FUNCTION OF THE STATIONARY SAWBLADE CMASNETIC EXCITATION} Ln R 0 * « « 2 8 . 0 TSD= + 15 .7 N/mm2 6 1 . 0 0 0 0 0 HZ 1 . 2 7 + 0 0 E 8 6 6 . - 0 3 E L N REAL PART R Cmm/N) IMAG. ^ PART Cmm/N) F I G U R E 2 4 FREQUENCY CHz) 2 0 0 REAL AND IMAGINARY PART OF THE TRANSFER FUNCTION 1 5 8 . 0 0 0 0 HZ 6 1 . 0 0 0 0 0 HZ R 0 * = 2 8 . 0 , T S D = 1 5 . 7 N / M M 2 COHERENCE COH + 0 T H h 5 2 1 . - 8 3 H r r t f L 2 r-rri ^ H 1 h L N H h 1 FT2 »1 ft H h F I G U R E 2 5 FREQUENCY (Hz) COHERENCE OF THE STATIONARY SAWBLADE 2 0 0 TILTANSLE =1.2° 3 . 1 6 + 0 0 E L G TSD= +15.7N/MM2 FREQUENCY F I G U R E 2 6 SHIFT OF NATURAL FREQUENCIES FOR DIFFERENT AXIAL PRESTRESSES RO* R0*= 2 8 . 8 TSD=Ht5.7N/mm2 6 1 . 0 0 0 0 0 HZ 2 . 1 3 + 0 0 E L G TRANS-MISSIBILITY Cmm/N> 4-TM + F I G U R E 2 7 ^ ' FREQUENCY CHz) TRANSMISSIBILITY OF THE SAWBLADE AT NATURAL FREQUENCIES 2 0 0 r e l a t i o n s h i p between channel A and channel B. L i n e a r t r a n s m i s s i o n systems e x c i t e d only by channel A y i e l d a coherence f a c t o r of 1. Non l i n e a r i t i e s or inputs i n a d d i t i o n to channel A produce coherent f a c t o r s between. 0 and 1. In F i g u r e 26 the s h i f t of the v a r i o u s l a t e r a l and t o r s i o n a l n a t u r a l f r e q u e n c i e s as we l l as the change of the t r a n s f e r f u n c t i o n magnitude due to an i n c r e a s e of the a x i a l p r e s t r e s s i n g f o r c e 2R0 (RO* = f (2R0)) can be seen. To o b t a i n general v a l u e s independent of geometric f a c t o r s t y p i c a l f o r our bandsaw, the a x i a l p r e s t r e s s 2R0 and the t i l t a n g l e TA were normalized.' To d e s c r i b e the i n f l u e n c e of the a x i a l p r e s t r e s s the n o r m a l i z a t i o n : / 2R0 L 2 ' R 0 * = ( * ) I 2 B*D was used (TIMOSHENKO 1959, "Theory of P l a t e s and S h e l l s " [ 2 4 ] ) . In case of the i n f l u e n c e of the t i l t a n g l e a v a r i e t y of p o s s i b i l i t i e s were c o n s i d e r e d . D i f f e r e n t authors on bandsaw v i b r a t i o n s have suggested v a r i o u s formulae to take the e f f e c t of changes of the t i l t a n g l e TA i n t o c o n s i d e r a t i o n . ULSOY [25] d e f i n e d the t i l t s t r e s s r a t i o TSR: TSR = (SIG7 / SIG1) - 1 SIG7 i s s t r e s s at l o c a t i o n of s t r a i n g a g e 7 (t o o t h s i d e ) SIG1 i s s t r e s s a t l o c a t i o n of s t r a i n g a g e 1 (backside) T h i s y i e l d s a value of TSR = 0 i f SIG7 = SIG1. KIRBACH [7] d e f i n e s the t i l t s t r e s s r a t i o as ranging from 1.0 (no t i l t ) to 0, no t e n s i o n s t r e s s at SG1. TANAKA [21] def i n e s : TSR = SIG7 / SIG1 In c o n t r a s t to Ulsoy.' s d e f i n i t i o n t h i s y i e l d s the value of TSR = 1 i f SIG7 = SIG1. A problem inherent to a l l these d e f i n i t i o n s i s the f a c t t h a t these t i l t s t r e s s r a t i o s are not only a f u n c t i o n of the t i l t a n g l e and the geometric s i t u a t i o n of the t i l t i n g system but a l s o a f u n c t i o n of the a x i a l p r e s t r e s s . To f i n d a d e f i n i t i o n which i s only a f u n c t i o n of the t i l t a n g l e and the i n d i v i d u a l c h a r a c t e r i s t i c of the t i l t i n g system the f o l l o w i n g formulae d e s c r i b i n g a t i l t a n g l e d i f f e r e n c e TSD was used: TSD = SIG1 - SIG7 TSD = MSIGO + SIGt - (MSIGO - SIGt) = 2SIGt 59 For a d e f i n i t i o n of the d i f f e r e n t s t r e s s e s see F i g u r e 21b. Because the TSD i s a d i f f e r e n c e of two s t r e s s values as compared to TSR, i t i s not dimension f r e e . The experimental r e l a t i o n s h i p between TSD and TA f o r the tensioned blade used i n these experiments i s shown in F i g u r e 28 with the corresponding e r r o r bounds for a confidence value of 95%. The mathematical s o l u t i o n that p r e d i c t the l a t e r a l n a t u r a l f r e q u e n c i e s i n a s t a t i o n a r y and i n a moving bandsaw blade have been d e r i v e d (as a f u n c t i o n of such parameters as bandsaw v e l o c i t y c, span l e n g t h L, a x i a l p r e s t r e s s i n g f o r c e 2R0, d e n s i t y and c r o s s s e c t i o n area A of the saw blade) by v a r i o u s r e s e a r c h e r s . The s o l u t i o n s d e r i v e d by MOTE [9] and KANAUCHI [21] are used to compare the experimental data obtained with the t h e o r e t i c a l data. Mote's and Kanauchi's s o l u t i o n s are d e r i v e d f o r a band in t r a n s v e r s e v i b r a t i o n s with small amplitudes and simply supported boundary c o n d i t i o n s at x =+L. The s o l u t i o n s a r e : Mote's f l e x i b l e band s o l u t i o n pA*c 2 ( 1 - K ) b [RO1 RO fL= 2LjpA pAc 2 (1 + O - e ) ) RO 20 C N / m m 2 ) - 0 . 2 0 0 . 2 0 . 4 0 . 6 0 . 8 1 1.2 1.4 T I L T A N G L E C D E G R E E S ) F I G U R E 2 8 T I L T S T R E S S D I F F E R E N C E OF THE S A W B L A D E A S A F U N C T I O N OF THE T I L T A N G L E o w i t h the d e f i n i t i o n of the wave v e l o c i t y cO RO1 cO = — • pA we can w r i t e : 1 - K c0 : fL =—*c0 2L 1 + ( 1-K ) c 0 : The v e l o c i t y dependent p a r t of Motes f l e x i b l e band s o l u t i o n w i l l be examined in c h a p t e r 6 w h i l e here on ly the s o l u t i o n for c = 0 i s of i n t e r e s t . Kanauchi deve loped the f o l l o w i n g s o l u t i o n : b JRO-1 p A c 2 b c 2 fL = *(1 ) = — * ( 1 ) *c0 2 L , p A RO 2L c O 2 In comparison to K a n a u c h i ' s s o l u t i o n , Mote d e f i n e s and uses the va lue K (see Appendix II ) - a measure of the wheel support s t i f f n e s s (0<K<1). K = 0 when the wheel support i s r i g i d and K = 1 when the support i s f l e x i b l e (the wheel support s t i f f n e s s of a l l p r o d u c t i o n b a n d m i l l s equipped wi th a i r or h y d r a u l i c s t r a i n systems i s c l o s e or e q u a l to 1) . For a s t a t i o n a r y sawblade Cc = 0) K a n a u c h i ' s and M o t e ' s s o l u t i o n s are i d e n t i c a l : b [RO1 b f L ( c = 0) = = — * c 0 2L IpA 2L The experimental data f o r the t o r s i o n a l n a t u r a l f r e q u e n c i e s were compared with the r e s u l t s from the a n a l y t i c a l s o l u t i o n developed by Alspaugh [ 2 ] : b c 2 fT = *( 1 ) *c0 2L cO 2 H 2 G SIGO(x) with cO 2 =4*—* + B 2 p P He d e r i v e d t h i s formula f o r a t h i n r e c t a n g u l a r s t r i p moving at a constant speed i n the x - d i r e c t i o n . The s t r i p i s assumed to be simply supported t o r s i o n a l ] ^ at two l i n e s at x=±L as f o r example, a band running between f i x e d r o l l e r s supports. For the s t a t i o n a r y sawblade the a n a l y t i c a l s o l u t i o n f o r t o r s i o n a l n a t u r a l f r e q u e n c i e s i s : b H 2 G SIG(x) b f T ( c = 0) =—*4 * —+ = *c0 2L B 2 p p 2L Experiments showed that i n ge n e r a l coupled modes were observed. However to the purpose of t h i s work a mode shape i n which the t o o t h s i d e and backside of the blade d e f l e c t e d i n t o the same d i r e c t i o n s along the z- a x i s were c a l l e d l a t e r a l n a t u r a l f r e q u e n c i e s and a mode shape i n which the t o o t h s i d e and the backside of the blade d e f l e c t e d i n t o o p p o s i t e d i r e c t i o n s along the z - a x i s were c a l l e d t o r s i o n a l n a t u r a l f r e q u e n c i e s . 63 5.2 L a t e r a l and t o r s i o n a l n a t u r a l f r e q u e n c i e s of the blade between the guides The two lowest l a t e r a l and t o r s i o n a l n a t u r a l f r e q u e n c i e s of the sawblade as a f u n c t i o n of the a x i a l p r e s t r e s s RO* f o r d i f f e r e n t t i l t s t r e s s d i f f e r e n c e s are shown i n F i g u r e 29. These four f r e q u e n c i e s have been p l o t t e d each by . i t s e l f with expanded frequency s c a l e s f o r a b e t t e r r e s o l u t i o n i n F i g u r e 30 through 33. With i n c r e a s i n g a x i a l p r e s t r e s s RO* a l l measured n a t u r a l f r e q u e n c i e s e s s e n t i a l l y i n c r e a s e l i n e a r l y but with d i f f e r e n t s l o p e s . The t h e o r e t i c a l r e s u l t s from Mote's Kanauchi's and Alspaugh's s o l u t i o n s are added to the experimental data i n F i g u r e s 30 t o 33. The a b s o l u t e and r e l a t i v e e r r o r s between the a n a l y t i c a l and experimental r e s u l t s f o r the four d i f f e r e n t n a t u r a l f r e q u e n c i e s are c a l c u l a t e d from the formulae in APPENDIX I l i a and are summarized i n Table III f o r two a x i a l p r e s t r e s s e s RO* spanning the t o t a l range of the experimental a x i a l p r e s t r e s s v a l u e s and a t i l t s t r e s s d i f f e r e n c e TSD=-40.7N/mm2. T h i s t i l t s t r e s s d i f f e r e n c e corresponds to the t i l t a n g l e f o r the running sawblade. Examining the r e s u l t s i n Table III i t becomes evident that the l a t e r a l n a t u r a l f r e q u e n c i e s agree very w e l l with the value s p r e d i c t e d by theory f o r the whole measurement range of RO*. From the F i g u r e s 30 2 0 0 175 _ N 2 2 24 26 28 3 0 A X I A L P R E S T R E S S R 0 * F I G U R E 2 9 LOWEST L A T E R A L AND T O R S I O N A L N A T U R A L F R E Q U E N C I E S FOR D I F F . A X I A L P R E S T R E S S E S R0* AND T I L T S T R E S S - D I F F E R E N C E S T S D 4^ 9 0 N A 8 0 _ T U R A 2 2 2 4 2 6 2 8 3 0 A X I A L P R E S T R E S S R 0 * F I G U R E 3 0 LOWEST L A T E R A L N A T U R A L F R E Q U E N C Y f u FOR D I F F E R E N T A X I A L P R E S T R E S S E S R 0 * AND T I L T S T R E S S - D I F F E R E N C E S T S D Ln 1 4 8 2 2 2 4 2 6 2 8 3 0 A X I A L P R E S T R E S S R 0 * F I G U R E 31 2 n d LOWEST L A T E R A L N A T U R E L F R E Q U E N C Y f L 2 FOR D I F F E R E N T A X I A L P R E S T R E S S E S R 0 * AND T I L T S T R E S S - D I F F E R E N C E S T S D 9 0 N A T U R A L r R E Q U E N C I E S 8 0 J 7 0 J 6 0 J 5 0 J f T 1 C H z ? 4 0 2 2 ~T~ 2 4 A — * T S D = - 9 5 . 6 B B y s r j » = - 4 7 . 9 « ^ T S D = - 4 0 . 7 * " ~ * T S D = » - 1 2 . 9 0 © J S D = 2 2 . 0 C N / M M 2 ) C N / M M 2 } C N / M M ^ CN/MM^} C N / M M 2 } _ T j p 2 6 2 8 3 0 A X I A L P R E S T R E S S R 0 * F I G U R E 32 LOWEST T O R S I O N A L N A T U R A L F R E Q U E N C Y f T 1 F O R D I F F E R E N T A X I A L P R E S T R E S S E S R 0 * AND T I L T S T R E S S - D I F F E R E N C E S T S D 2 2 2 4 2 6 2 8 3 0 A X I A L P R E S T R E S S R 0 * F I G U R E 33 2 n d LOWEST T O R S I O N A L N A T U R A L F R E Q U E N C Y f J 2 FOR D I F F E R E N T A X I A L P R E S T R E S S E S R 0 * AND T I L T S T R E S S - D I F F E R E N C E S T S D CO RO* f L l a b s o l u t e r e l . t h e o r . e x p . e r r o r e r r o r ( H z ) ( H z ) ( H z ) (*) 2 3 5 1 . 4 5 1 . 5 0 . 3 0 . 6 3 1 6 9 . 0 6 8 . 0 - 1 . 0 - 1 . 4 RO* t h e o r . ( H z ) . 2 e x p . ( H Z ) a b s o l u t e e r r o r ( H z ) r e l . e r r o r (%) 23 3 1 102.3 1 3 7 . 9 1 0 1 . 6 1 3 5 . 4 - 0 . 7 -2 . 5 - 0 . 7 - 1 . 8 RO* r t h e o r . ( H z ) r i e x p . ( H z ) a b s o l u t e e r r o r ( H z ) r e l . e r r o r (%) 23 3 1 5 7 . 0 7 2 . 4 7 4 . 4 85.2 1 7 . 4 1 2 . 8 3 0 . 5 1 7 . 7 RO* f " t h e o r . ( H z ) r2 e x p . ( H z ) a b s o l u t e e r r o r ( H z ) r e l . e r r o r (%) 23 3 1 1 1 4 . 1 1 4 4 . 8 147.2 173.2 33 . 1 2 8 . 4 2 9 . 0 1 9 . 6 I T a b l e I I I V a l u e s f o r t h e o r e t i c a l a n d e x p e r i m e n t a l n a t u r a l f r e q u e n c i e s , a n d r e l a t e d a b s o l u t e a n d r e l a t i v e e r r o r s to 33 i t can be seen that the c a l c u l a t e d d i f f e r e n c e between t h e o r e t i c a l and experimental values reaches a minimum f o r the t i l t s t r e s s d i f f e r e n c e TSD=-40.7N/mm2. For d i f f e r e n t t i l t s t r e s s d i f f e r e n c e s the d e v i a t i o n between t h e o r e t i c a l and experimental values i n c r e a s e s . L a t e r i n t h i s chapter i t w i l l be seen that f o r a t i l t s t r e s s d i f f e r e n c e of about -40.7N/mm2 the l a t e r a l and t o r s i o n a l modeshapes are uncoupled, while f o r higher or lower t i l t s t r e s s d i f f e r e n c e s the modes are coupled. The t o r s i o n a l n a t u r a l f r e q u e n c i e s of the blade are on the average 29.7% higher than the t h e o r e t i c a l p r e d i c t e d values f o r lower a x i a l p r e s t r e s s e s (R0*=23). T h i s e r r o r decreases f o r higher a x i a l p r e s t r e s s e s (R0*=31) on the average to 18.7%. S i m i l a r experiments by TANAKA [21] show that the t o r s i o n a l n a t u r a l f r e q u e n c i e s of a pre t e n s i o n e d blade are 9 to 17% higher than the comparable t h e o r e t i c a l v a l u e s , while the t o r s i o n a l n a t u r a l f r e q u e n c i e s f o r an untensioned blade show a good agreement with t h e o r e t i c a l p r e d i c t e d frequency l e v e l s . A t h e o r e t i c a l study by ULSOY [25] shows that the t o r s i o n a l n a t u r a l f r e q u e n c i e s r i s e l i n e a r l y with the l e v e l of p r e t e n s i o n i n the blade (assuming a p a r a b o l i c s t r e s s d i s t r i b u t i o n i n the b l a d e ) . He c a l c u l a t e s that f o r a p a r a b o l i c s t r e s s d i s t r i b u t i o n with a maximum s t r e s s value at the t o o t h s i d e and the backside of the blade of SIG(x)* and a minimum s t r e s s value at the center of the blade of SIG(x)*/2, the lowest t o r s i o n a l frequency of the blade i s 17Hz higher than f o r an untensioned blade with a uniform s t r e s s d i s t r i b u t i o n a c r o s s the blade. Because Alspaugh's theory does not c o n s i d e r d i f f e r e n t s t r e s s d i s t r i b u t i o n a c r o s s the blade, but assumes a uniform s t r e s s d i s t r i b u t i o n the t h e o r e t i c a l values f o r the t o r s i o n a l f r e q u e n c i e s are lower than the experimental values f o r the p r e t e n s i o n e d blade used i n these experiments. A f i r s t order polynominal using the l e a s t square f i t t i n g method was f i t to the experimental data and the n a t u r a l f r e q u e n c i e s were p l o t t e d as a f u n c t i o n of the t i l t s t r e s s d i f f e r e n c e TSD f o r v a r i o u s a x i a l p r e s t r e s s e s RO*. These r e s u l t s are shown i n the F i g u r e s 34 through 38. Both l a t e r a l n a t u r a l f r e q u e n c i e s f o l l o w a p a r a b o l i c curve with a maximum at the t i l t s t r e s s d i f f e r e n c e TSD =-26.7 N/mm2 while the t o r s i o n a l n a t u r a l frequency fT1 has a minimum f o r the same t i l t s t r e s s d i f f e r e n c e . Table IV shows that the i n f l u e n c e of d i f f e r e n t t i l t s t r e s s d i f f e r e n c e s on the l a t e r a l n a t u r a l f r e q u e n c i e s i s of g r e a t e r magnitude and of o pposite s i g n as i t s e f f e c t on the t o r s i o n a l n a t u r a l f r e q u e n c i e s . The absolute and r e l a t i v e changes of the n a t u r a l f r e q u e n c i e s are c a l c u l a t e d a c c o r d i n g to the formulae i n Appendix I l l b . 2 0 0 N A T U R A L F R E Q U E N C I E S 1 7 5 J 1 5 0 J 1 2 5 J 1 0 0 J 7 5 5 0 J 2 5 J 0 9 ^ m i m ^ -•h-B 7 — — 0 * • -—4$ • -B A G •e— — v — 0 •e- •B--<=> •B • -A * R 0 * = 2 3 0 — B R 0 * = 2 S . 0 * R 0 * = 2 6 . 5 * — * R 0 * = 2 7 . 9 Q £ > R 0 * = 2 9 . 3 ^ R 0 * = 3 0 . 6 - 1 0 0 - 8 0 ^ [ j 1 I - 6 0 - 4 0 - 2 0 0 2 0 T I L T S T R E S S - D I F F E R E N C E TSD C N / m m 2 ) F I G U R E 3 4 1 s t AND 2 n d LOWEST L A T E R A L AND T O R S I O N A L N A T U R A L F R E Q U E N C I E S FOR D I F F E R E N T T I L T S T R E S S - D I F F , TSD AND A X . P R E S T R E S S E S R 0 * 8 0 N A T U R A L F R E Q U E N C Y f L 1 C H z > 7 0 J 6 0 J 5 0 J 4 0 J 3 0 A — * R 0 * = 2 3 . 4 0 — S R 0 * « 2 5 . 0 4 * R 0 * « 2 6 . 5 * — * R 0 » « 2 7 . 9 o — © R 0 * = 2 9 . 3 V—V R0**»30 . 6 - 1 0 0 - 8 0 T T •60 - 4 0 - 2 0 0 2 0 T I L T S T R E S S - D I F F E R E N C E T S D C N / m m 2 } F I G U R E 3 5 LOWEST L A T E R A L N A T U R A L F R E Q U E N C Y f u A S A F U N C T I O N OF T H E T I L T S T R E S S - D I F F E R E N C E T S D FOR A X I A L P R E S T R E S S E S R 0 * 3 0 R 9 * = 2 9 . 3 - 1 0 0 - 8 0 - 6 0 - 4 0 - 2 0 0 2 9 T I L T S T R E S S - D I F F E R E N C E T S D C N / m m 2 } F I G U R E 3 6 2 n d LOWEST L A T E R A L N A T U R A L F R E Q U E N C Y f L 2 A S A F U N C T I O N O F THE T I L T S T R E S S - D I F F E R E N C E TSD FOR A X I A L P R E S T R E S S E S R 0 * 1 0 0 N A T U R A L F R E Q U E N C Y T1 9 0 8 0 J 7 0 J 6 0 J 5 0 0 <•> B-— V 9 -€> 0 A A R 0 * = 2 3 . 4 B - ~ - 0 R 0 * = 2 5 . 0 3 ©• R 0 * = 2 6 . 5 *-—A R 0 * = 2 7 . 9 9 © R 0 * = 2 9 . 3 R 0 * « 3 0 . 6 T T T - 1 0 0 - 8 0 - 6 0 - 4 0 - 2 0 0 2 0 T I L T S T R E S S - D I F F E R E N C E T S D C N / M M 2 } F I G U R E 3 7 LOWEST T O R S I O N A L N A T U R A L F R E Q U E N C Y f T , A S A F U N C T I O N OF THE T I L T S T R E S S - D I F F E R E N C E T S D FOR A X I A L P R E S T R E S S E S R 0 * 1 8 0 N A T U R A L F R E Q U E N C Y 1 7 0 J 1 6 0 150 1 4 0 J f T ; , C H z } 3 0 -1 2 0 A A R 0 * = 2 3 . 4 0 — B R 0 * = 2 5 . 0 4 » R 0 * = 2 6 . 5 * R 0 * = 2 7 . 9 0 €> R 0 * = 2 9 . 3 7 - - - V R0*=*30 . 6 - 5 0 0 - 8 0 - 6 0 - 4 0 - 2 0 0 2 0 T I L T S T R E S S - D I F F E R E N C E T S D C N / W O F I G U R E 3 8 2 n d LOWEST T O R S I O N A L N A T U R A L F R E Q U E N C Y f J 2 A S A F U N C T I O N OF T H E T I L T S T R E S S - D I F F E R E N C E TSD FOR A X I A L P R E S T R E S S E S R O * R0+ T S D (N/mm 2) A f L l ( H z ) a b s o l u t e A f L 2 ( H z ) 1 c h a n g e A f T l ( H z ) A f T 2 ( H z ) 2 9 . 3 2 6 . 7 t o 9 5 . 6 - 4 . 8 - 7 . 6 +3.3 +0.4 R0+ T S D (N/mm 2) A f L l (*) r e l a t i v e A f L 2 (%) c h a n g e A f T l '(%) A f T 2 {%) 2 9 . 3 2 6 . 7 t o 9 5 . 6 - 7 . 8 - 3 . 1 3.9 0.2 T a b l e I V C h a n g e o f t h e n a t u r a l f r e q u e n c i e s a s a f u n c t i o n o f t h e t i l t s t r e s s d i f f e r e n c e T S D 7 8 5.3 T r a n s m i s s i b i l i t y of the S t a t i o n a r y Sawblade Beside the e v a l u a t i o n of the n a t u r a l f r e q u e n c i e s the a s s o c i a t e d mode shapes were of s p e c i a l i n t e r e s t . T h e r e f o r e the t r a n s m i s s i b i l i t y T of the blade at the t o o t h s i d e and at the backside of the blade were measured and p l o t t e d . The experimental setup i s shown in F i g u r e 21a. The blade was e x c i t e d by the e l e c t r o magnets, while the blade response was measured with two non c o n t a c t i n g t r a n s d u c e r s , one l o c a t e d at the t o o t h s i d e of the blade, the other at the b a c k s i d e . The t r a n s m i s s i b i l i t y r e p r e s e n t s the r a t i o of the RMS value of the response s i g n a l to the RMS value of the e x c i t a t i o n s i g n a l . The r e c i p r o c a l value of the t r a n s m i s s i b i l i t y i s the s t i f f n e s s of the blade. Experiments measuring these RMS v a l u e s r i g h t at the p r e v i o u s l y e s t a b l i s h e d n a t u r a l f r e q u e n c i e s gave i n c o n s i s t e n t r e s u l t s , although data values were averaged from 32 readings and each data value was repeated 3 times. A second approach y i e l d e d more promising r e s u l t s . Around each n a t u r a l frequency, RMS values were averaged over a 10 Hz i n t e r v a l with the n a t u r a l frequency at the c e n t e r of the band width and then 32 readings were averaged to y i e l d one data v a l u e . T h i s procedure was repeated three times f o r each data value and was then again averaged. The average e r r o r bounds f o r a c o n f i d e n c e value of 95% f o r the t r a n s m i s s i b i l i t y data shown i n t h i s chapter were +0.048mm/N. These experiments then had to be repeated 128 times to a r r i v e at the t r a n s m i s s i b i l i t y data shown i n F i g u r e 39 through to F i g u r e 46. A f i r s t order polynominal was f i t through the curves from F i g u r e 39 - 46 and then the t r a n s m i s s i b i l i t i e s f o r RO* = 26.0 (midpoint of the experimental range) were used i n the f o l l o w i n g d i s c u s s i o n . F i g u r e 39 and 40 show the t r a n s m i s s i b i l i t y of the s t a t i o n a r y blade f o r fL1 at the t o o t h s i d e and at the backside r e s p e c t i v e l y as a f u n c t i o n of the a x i a l p r e s t r e s s f o r d i f f e r e n t t i l t s t r e s s d i f f e r e n c e s . While the cha*nge of the a x i a l p r e s t r e s s has very l i t t l e e f f e c t on the slope of the curves, an i n c r e a s e i n the t i l t s t r e s s d i f f e r e n c e g r e a t l y i n c r e a s e s the t r a n s m i s s i b i l i t y at the t o o t h s i d e from 0.15mm/N to 0.62mm/N or by 413% while having r e l a t i v e l y l i t t l e e f f e c t at the backside. A s i m i l a r e f f e c t can be observed in F i g u r e 41 and 42 f o r fL2, only that the abs o l u t e change of the magnitude of the t r a n s m i s s i b i l i t y at the t o o t h s i d e i s s m a l l e r - from 0.03mm/N to 0.19mm/N or by 633%. While the t r a n s m i s s i b i l i t y at f L i n c r e a s e s f o r an inc r e a s e of the t i l t s t r e s s d i f f e r e n c e , the t r a n s m i s s i b i l i t y at fT decreases f o r the same change of the t i l t s t r e s s d i f f e r e n c e . In F i g u r e 43 the t o r s i o n a l 0 . 8 T R A N S M I S s I B I L I T Y CMM/N} 0 . 7 0 . 6 0 . 5 J 0 . 4 J 0 . 3 0 . 2 0 0 2 2 2 4 . <5 *r 0 B - - -a • A — * T S D = ~ 8 t . 8 C N / M M 2 ) - 4 7 . 9 C N / M M 2 ) 1 3 . 7 C N / M M 2 ) ; L 4 I . ^ _ „ C H Z M « _ 2 X 2 6 2 8 A X I A L P R E S T R E S S R 0 * *> TSD= 3 0 F I G U R E 3 9 T R A N S M I S S I B I L I T Y OF THE S T A T I O N A R Y S A W B L A D E C M E A S U R E D AT T H E T O O T H S I D E FOR F L . ) A S A F U N C T I O N OF R 0 * FOR D I F F . T S D 30 3 0 . 8 T R A N S M I S s I B I L I T Y CMM/N} 0 . 7 J 0 . 6 J 0 . 5 J 0 . 4 J 0 . 3 0 . 2 J 0 . 1 J F I G U R E 4 0 0 2 2 * — * T S D — 8 1 . 8 CN/MM j 2 ) B — B T S D = - 4 7 . 9 C N / M M 2 } ^ - - ^ T S D — 1 3 . 7 C N / M M 2 } * — * T S D « 1 4 . 0 C N / M M 2 } T 2 4 2 6 2 8 3 0 A X I A L P R E S T R E S S R 0 * T R A N S M I S S I B I L I T Y OF THE S T A T I O N A R Y S A W B L A D E CM E A S U R E D AT T H E B A C K S I D E FOR f } A S A F U N C T I O N OF R 0 * FOR D I F F . T S D 0 . 8 T R A N S M I S S I B I L I T Y C M M / N ) 0 . 7 J 0 . 6 J 0 . 5 J 0 . 4 J 0 . 3 0 . 2 J 0 . 1 J 0 2 2 A — * T S D = - 8 1 . 8 C N / M M 2 ) H E3 TSD 1 5 3 —47 . 9 C N / M M 2 ) T S D — 1 3 . 7 C N / M M 2 ) * — * T S D » 1 4 . 0 C N / M M 2 ) B- + , —G-- - 2 A 2 4 ^ j T ~ 2 6 2 8 3 0 A X I A L P R E S T R E S S R 0 * F I G U R E 41 T R A N S M I S S I B I L I T Y OF T H E S T A T I O N A R Y S A W B L A D E C M E A S U R E D AT T H E T O O T H S I D E FOR f L 2 ) A S A F U N C T I O N OF R 0 * FOR D I F F . T S D CO t o T R A N S M I S s I B I L I T Y CMM/N? 0 . 8 0 . 7 J 0 . 6 0 . 5 J 0 . 4 0 . 3 J 0 . 2 J 0 . 1 J 0 F I G U R E 4 2 2 2 A — A T S D = - 8 1 . 8 CN/MM2> B — B T S D = - 4 7 . 9 CN/MM2> » T S D = - 1 3 . 7 C N / M M 2 ? * - — * TSD= 1 4 . 0 CN/MM2> 2 4 2 6 2 8 3 0 A X I A L P R E S T R E S S R 0 * T R A N S M I S S I B I L I T Y OF T H E S T A T I O N A R Y S A W B L A D E -CMEASURED AT THE B A C K S I D E FOR f L 2 5 A S A F U N C T I O N OF R 0 « FOR D I F F . T S D 00 OJ T R A N S M I S S I B I L I T Y CMM/N) 0 . 8 0 . 7 J 0 . 6 J 0 . 5 J 0 . 4 0 . 3 J 0 . 2 J 0 . 1 J 0 2 2 B- •B-^ — * T S D = - 8 1 . 8 C N / M M 2 ) B — B TSD*=~47.9 C N / M M 2 ) * » T S D « - 1 3 . 7 * ~ - * T S D = 1 4 . 0 C N / M M 2 ) C N / M M 2 ) 2 4 2 6 2 8 3 0 F I G U R E 4 3 A X I A L P R E S T R E S S R 0 * T R A N S M I S S I B I L I T Y OF T H E S T A T I O N A R Y S A W B L A D E C M E A S U R E D AT THE T O O T H S I D E FOR f T i ) A S A F U N C T I O N OF R 3 * F O R D I F F . T S D CO 4^ 0 . 8 0 . 7 T R A N S M I S S I B I L I T CMM/N? 0 . 2 J 0 . 1 J 0 . 6 0 . 5 J 0 . 4 J 0 . 3 J 0 2 2 -A a * * — A T S D = - 8 I . 8 C N/MM 2 ? B 0 T S D = — 4 7 . 9 CN/MM2? ^ - ^ T S D = - 1 3 . 7 C N / M M 2 ) * — - * T S D = 1 4 . 0 C N / M M 2 } 2 4 2 6 2 8 3 0 r i G U R E 4 4 A X I A L P R E S T R E S S R 0 * T R A N S M I S S I B I L I T Y OF T H E S T A T I O N A R Y S A W B L A D E CM E A S U R E D AT T H E B A C K S I D E FOR f T , ? A S A F U N C T I O N OF R 0 * FOR D I F F . T S D CO Ul 0 . 8 T R A N S M I S S I B I L I. T Y CMM/N) 0 . 7 J 0 . 6 J 0 . 5 J 0 . 4 0 . 3 J 0 . 2 J 0 . 1 J 0 2 2 A — * T S D = - 8 1 . 8 C N / M M 2 ) B — H T S D = - 4 7 . 9 C N / M M 2 ) * * T S D = ~ 1 3 . 7 C N / M M 2 ) * — * T S D = 1 4 . 0 C N / M M 2 ) B -2 6 2 8 3 0 F I G U R E 4 5 A X I A L P R E S T R E S S R P * T R A N S M I S S I B I L I T Y OF T H E S T A T I O N A R Y S A W B L A D E C M E A S U R E D AT TH B A C K S I D E FOR f J 2 ) A S A F U N C T I O N OF R 0 * FOR D I F F . T S D T R A N S M I S S I B I L I T Y CMM/NO 0 . 8 0 . 7 J 0 . 6 J 0 . 5 0 . 4 J 0 . 3 J 0 . 2 J 0 . 1 J 0 2 2 A—AjSD= B---B TSD= « » TSD= T S D -- 8 1 . 8 C N / M M 2 } - 4 7 . 9 C N / M M 2 ? 1 3 . 7 C N / M M 2 } 1 4 . 0 C N / M M 2 ? 2 4 2 6 1 r 2 8 3 0 A X I A L P R E S T R E S S R 0 * F I G U R E 4 6 T R A N S M I S S I B I L I T Y OF THE S T A T I O N A R Y S A W B L A D E C M E A S U R E D AT THE T O O T H S I D E FOR f * > A S A F U N C T I O N OF R 8 * FOR D I F F . T S D i 2 00 T S D ? (N/mm ) t o T L RO* o t h s i d e 1 (mm/N) RO* RO* b T L RO* a c k s i d e 1 (mm/N) RO* RO* 2 3 7 26 29 23 26 29 - 8 1 . 8 - 4 7 . 9 - 1 3 . 7 1 4 . 0 .18 .26 .37 .58 .15 .26 .39 .62 .12 .26 .42 .65 .33 .34 .27 .24 .32 .30 .29 .25 .31 .27 .32 .27 -T S D ? (N/mm ) t o T T RO* o t h s i d e 1 (mm/N) RO* f RO* b T T RO* a c k s i d e 1 (mm/N) RO* RO* 2 3 26 29 23 26 29 - 8 1 . 8 - 4 7 . 9 - 1 3 . 7 14.0 .74' .47 .32 .18 .74 .53 .41 .26 .74 .58 .50 .34 .46 .39 .34. .21 .56 .47 .43 .34 .66 .55 .53 .47 T S D ? t o o t h s i d e b a c k s i d e (N/mm ) T L 2 (mm/N) T L 2 (mm/N) • RO* RO* RO* RO* RO* RO* 2 3 26 29 23 26 29 - 8 1 . 8 .04 .03 .02 .07 .07 .07 - 4 7 . 9 .14 .10 .07 .10 .08 .05 - 1 3 . 7 .18 .14 .09 .08 .06 .05 1 4 . 0 .27 .19 .12 .06 .05 .04 T S D ? t o o t h s i d e b a c k s i d e (N/mm ) T T 2 (mm/N) T T 2 (mm/N) RO* RO* RO* RO* RO* RO* 2 3 26 29 23 26 29 - 8 1 . 8 .11 .14 .18 .08 .08 .08 - 4 7 . 9 .09 .10 .10 .09 .09 .10 - 1 3 . 7 .06 .08 .11 .04 .08 .11 1 4 . 0 .03 .05 .07 .05 .06 .08 T a b l e V T r a n s m i s s i b i l i t y o f t h e s t a t i o n a r y s a w b l a d e a t t h e t w o . l o w e s t l a t e r a l a n d t o r s i o n a l n a t u r a l f r e q u e n c i e s f o r d i f f e r e n t t i l t s t r e s s d i f f e r e n c e s a n d a x i a l p r e s t r e s s e s RO* t r a n s m i s s i b i l i t y f o r fT1 at the t o o t h s i d e of the blade i s lowered (from 0.74mm/N to 0.26mm/N or by 280%) with i n c r e a s i n g t i l t s t r e s s d i f f e r e n c e s , while the t r a n s m i s s i b i l i t y at the backside of the blade f o r fT1 decreases from 0.14mm/N to 0.05mm/N or by 36% (Figure 44). In F i g u r e 45 and 46 the t r a n s m i s s i b i l i t i e s f o r the to o t h s i d e and the back s i d e at fT2 are recorded. S i m i l a r to the t r a n s m i s s i b i l i t i e s f o r the l a t e r a l n a t u r a l f r e q u e n c i e s , the change of the amplitude of the t r a n s m i s s i b i l i t y at fT2 i s much smaller than f o r fT1. At the t o o t h s i d e the change of the t r a n s m i s s i b i l i t y as a f u n c t i o n of the t i l t s t r e s s d i f f e r e n c e ranges from 0.14mm/N to 0.05mm/N or changes by 36%. At the backside the t r a n s m i s s i b i l i t y f o r fT2 changes from 0.08mm/N to 0.07mm /N or by 9%. While f o r fL1, fL2 and fT2 an incr e a s e of the a x i a l p r e s t r e s s only has a very l i t t l e e f f e c t onto the t r a n s m i s s i b i l i t y of the blade, at fT1 the t r a n s m i s s i b i l i t y at the t o o t h s i d e as w e l l as at the backside r a i s e s c o n s i d e r a b l y f o r a change of the a x i a l p r e s t r e s s from R0*=23 to R0*=29. For a b e t t e r comparison of the t r a n s m i s s i b i l i t y values as a f u n c t i o n of the a x i a l p r e s t r e s s RO* these values averaged over the t i l t s t r e s s d i f f e r e n c e s are shown i n Table V. In F i g u r e 47 the modeshapes of the s t a t i o n a r y sawblade at four n a t u r a l f r e q u e n c i e s f o r R0*=23 and 90 1st LATERAL 2nd. LATERAL 1st. TORSIONAL 2nd. TORSIONAL MODESHAPE MODES HAPE MODESHAPE MODESHAPE TSD =- 81.8 N/mm 2 TSD= U.N/mm2 F i g u r e 47 M o d e s h a p e s o f t h e s t a t i o n a r y s a w b l a d e a t t h e two l o w e s t l a t e r a l a n d t o r s i o n a l n a t u r a l f r e q u e n c i e s R0*=29 and f o r TSD=-81.8N/mm2 and TSD=14.ON/mm2 are shown. At the lowest l a t e r a l n a t u r a l frequency the t r a n s m i s s i b i l i t y at the t o o t h s i d e r a i s e s f o r the s t a t e d i n c r e a s e from TSD=-81.8N/mm2 to 14.ON/mm2 by 0.4mm/N f o r R0*=23 and by 0.53mm/N f o r R0*=29, while at the backside the t r a n s m i s s i b i l i t y i s lowered by 0.09mm/N and by 0.04mm/N f o r the corresponding changes of the a x i a l p r e s t r e s s RO*. At the second lowest l a t e r a l frequency the in c r e a s e of the t r a n s m i s s i b i l i t y f o r the re p o r t e d change i n the t i l t s t r e s s d i f f e r e n c e amounts to 0.23mm/N f o r R0*=23 and to O.lOmm/N f o r R0*=29 at the t o o t h s i d e of the blade, while at the backside of the blade the t r a n s m i s s i b i l i t y decreases f o r the change i n the t i l t s t r e s s d i f f e r e n c e by 0.0lmm/N f o r R0*=23 and by 0.03mm/N for R0*=29. These r e s u l t s show that the t i l t s t r e s s d i f f e r e n c e has a f a r g r e a t e r i n f l u e n c e on the modeshapes f o r the l a t e r a l n a t u r a l f r e q u e n c i e s , than a change of the a x i a l p r e s t r e s s . At fT1 a change i n the t i l t s t r e s s d i f f e r e n c e from -8l.8Nmm2 to 14.ON/mm2 reduces the t r a n s m i s s i b i l i t y at the t o o t h s i d e of the blade by 0.56mm/N f o r R0*=23 and by 0.40mmN f o r R0*=29. At the backside the t r a n s m i s s i b i l i t y decreases by 0.25mm/N for R0*=23 and by 0.19mm/N f o r R0*=29. The e q u i v a l e n t v a l u e s f o r the decrease of the t r a n s m i s s i b i l i t y at fT2 at the t o o t h s i d e amounts to 0.08mm/N f o r R0*=23 and to 0.11mm/N f o r R0*=29, while at the backside the t r a n s m i s s i b i l i t y decreases by 0.03mm/N for R0*=23 and by 0.Omm/N f o r R0*=29. From these r e s u l t s i t can be concluded that an in c r e a s e i n the t i l t s t r e s s d i f f e r e n c e has mainly an e f f e c t on the t o o t h s i d e of the blade. While the t r a n s m i s s i b i l i t y at the t o o t h s i d e at the l a t e r a l n a t u r a l f r e q u e n c i e s i n c r e a s e s , i t decreases at the t o r s i o n a l n a t u r a l f r e q u e n c i e s . A change of the a x i a l p r e s t r e s s has l i t t l e e f f e c t on the t r a n s m i s s i b i l i t i e s at f L 1 . At fL2 a high t i l t s t r e s s d i f f e r e n c e and an inc r e a s e of the a x i a l p r e s t r e s s lowers the t r a n s m i s s i b i l i t y on the t o o t h s i d e c o n s i d e r a b l y , while f o r a low t i l t s t r e s s d i f f e r e n c e there are only small changes i n the t r a n s m i s s i b i l i t y . At the t o r s i o n a l n a t u r a l f r e q u e n c i e s an inc r e a s e of the t i l t s t r e s s d i f f e r e n c e lowers the t r a n s m i s s i b i l i t y at the t o o t h s i d e and at the backside. An i n c r e a s e of the a x i a l p r e s t r e s s r a i s e s the t r a n s m i s s i b i l i t y at the t o o t h s i d e and at the backside f o r a hi g h t i l t s t r e s s d i f f e r e n c e , while there i s very l i t t l e change at a low t i l t s t r e s s d i f f e r e n c e . F i g u r e 47 a l s o shows that the modeshapes f o r l a t e r a l and t o r s i o n a l n a t u r a l f r e q u e n c i e s are coupled. For a s p e c i a l t i l t s t r e s s d i f f e r e n c e (between TSD=-8l.8N/mm2 and TSD=14N/mm2) the modeshapes become uncoupled. Some other r e s e a r c h e r s have t h e o r e t i c a l l y and e x p e r i m e n t a l l y examined the l a t e r a l and t o r s i o n a l modeshapes of bandsaw blades. PAHLITSCH [16,17] d i d a study on modeshapes as a f u n c t i o n of the blade t h i c k n e s s H, the f r e e span l e n g t h L, the a x i a l p r e s t r e s s RO* and an edge lo a d Fhor i n y - d i r e c t i o n a c t i n g on the t e e t h . SOLER [26] d i d a t h e o r e t i c a l study on coupled modes as a functon of an edge lo a d Fhor. The author i s not aware of any study of modeshapes - t h e o r e t i a l or experimental as a f u n c t i o n of the t i l t s t r e s s d i f f e r e n c e . Therefore no f u r t h e r a n a l y s i s of the here presented modeshapes was done. 94 5.4 Dynamic v i b r a t i o n measurements with a moving blade To measure the n a t u r a l f r e q u e n c i e s of a running blade the same experiments as i n chapter 5.2 were repeated. A d i f f e r e n t blade was used i n these experiments. I t had no t e e t h so that the width B0=B=260mm, but had a s i m i l a r s t r e s s d i s t r i b t i o n a c r o s s the blade due to p r e t e n s i o n i n g compared to the blade used i n the s t a t i o n a r y experiments. The blade v e l o c i t y c = 40.7 m/s c o u l d not be v a r i e d . To compare the experimental data f o r the l a t e r a l n a t u r a l f r e q u e n c i e s with Mote' s f l e x i b l e band s o l u t i o n , the value of the support system s t i f f n e s s Ks had to be ev a l u a t e d (see APPENDIX I I ) . The a n a l y t i c a l r e s u l t s of Mote' s, Kanauchi 1 s and Alspaugh' s s o l u t i o n s are added to the data p l o t s i n F i g u r e 49 to 51, while the r e l e v a n t data and e r r o r bounds are shown i n Table V. For the range of the a x i a l p r e s t r e s s R0*=26 to R0*=31 the a n a l y t i c a l r e s u l t s from Mote and Kanauchi d i f f e r only by 0.13 Hz to 0.10 Hz or by 0.3% to 0.18% . In F i g u r e s 49 to 51 they are t h e r e f o r e represented only by one curve. The l a t e r a l n a t u r a l f r e q u e n c i e s are on the average lower than the t h e o r e t i c a l l y p r e d i c t e d f r e q u e n c i e s . For R0*=26 the d e v i a t i o n amounts to 9.9% and fo r R0*=31 i t i s 11.2%. S i m i l a r to the s t a t i o n a r y sawblade the t o r s i o n a l n a t u r a l f r e q u e n c i e s are. c o n s i d e r a b l y higher than the 200 N A T U R A L F R E Q U E N C I E S C H z ) 175 J 150 J 125 J 100 J 75 J 50 J 25 J 0 FIGURE 48 25 A—AFLi •—EJ P L 2 *—*FT2 26 —T 27 ~1 1 1 28 29 30 AXIAL PRESTRESS R0* 31 32 NATURAL FREQUENCIES f L AND f T FOR THE RUNNING BLADE FOR DIFFERENT AXIAL PRESTRESSES R0*, c « 40.7 m/s Ul 8 0 J N A T U R A L F R E Q U E N C Y 7 0 J 6 0 J 5 0 4 0 J F I G U R E 4 9 i 1 r 2 8 2 9 3 0 A X A I L P R E S T R E S S R 0 * N A T U R A L L A T E R A L F R E Q U E N C Y f L 1 O F T H E R U N N I N G B L A D E F O R D I F F E R E N T A X I A L P R E S T R E S S E S R 0 * . « 4 0 . 7 ^/s cn I 1 1 1 1 1 ! 1 2 5 2 6 2 7 2 8 2 9 3 0 31 3 2 A X I A L P R E S T R E S S R 8 * F I G U R E 5 0 N A T U R A L L A T E R A L F R E Q U E N C Y f L 2 0 F T H E R U N N I N G S A W B L A D E FOR D I F F E R E N T A X I A L P R E S T R E S S E S R 0 » , o - 4 0 . 7 m / s 8 0 Y 4 0 _ CHZ? 2 5 2 6 2 7 2 8 2 9 3 0 31 3 2 A X I A L P R E S T R E S S R 0 * F I G U R E 5 1 N A T U R A L T O R S I O N A L F R E Q U E N C Y f T l OF T H E R U N N I N G B L A D E FOR D I F F E R E N T A X I A L P R E S T R E S S E S R 0 * , c = 4 0 . 7 m / s 00 1 5 0 2 6 2 7 2 8 2 9 3 0 31 3 2 AXIAL PRESTRESS R0* FIGURE 5 2 NATURAL TORSIONAL FREQUENCY f j 2 OF THE RUNNING BLADE FOR DIFFERENT AXIAL PRESTRESSES R0*, c » 40.7 m/s 100 t h e o r e t i c a l l y p r e d i c t e d f r e q u e n c i e s . For R0*=26 the average d i f f e r e n c e amounts to 32.5% and f o r R0*31 i t i s 17.9%. These d i f f e r e n c e s are due to the f a c t t h at - l i k e f o r the s t a t i o n a r y sawblade- Mote, Kanauchi and Alspaugh assume a constant s t r e s s d i s t r i b u t i o n RO/A a c r o s s the blade i n t h e i r a n a l y t i c a l s o l u t i o n s , while the blade used i n these experiments was p r e t e n s i o n e d which r e s u l t s i n a p a r a b o l i c s t r e s s d i s t r i b u t i o n across the blade. RO* f l t h e o r . ( H z ) .1 e x p . ( H z ) a b s o l u t e e r r o r ( H z ) r e l . e r r o r (%) 26 31 4 5 . 6 5 8 . 7 41 52 - - 4 . 6 - 6 . 7 - 1 0 . 1 - 1 1 . 4 RO* f t h e o r . ( H z ) .2 e x p . ( H z ) a b s o l u t e e r r o r ( H z ) r e l . e r r o r (*) 26 -31 9 1 . 2 1 1 7 . 4 8 2 . 4 1 0 4 . 5 - 8 . 8 - 1 2 . 9 - 9 . 6 - 1 1 . 0 RO* f" t h e o r . ( H z ) n e x p . ( H z ) a b s o l u t e e r r o r ( H z ) r e l . e r r o r (%) 26 31 5 2 . 5 6 4 . 3 7 0 . 5 7 7 . 0 1 8 . 0 1 2 . 7 3 4 . 3 1 9 . 8 RO* f" t h e o r . ( H z ) T2 e x p . ( H z ) a b s o l u t e e r r o r ( H z ) r e l . e r r o r (%) 26 31 1 0 5 . 0 1 2 8 . 6 1 3 7 . 2 1 4 9 . 0 3 2 . 2 2 0 . 4 3 0 . 7 1 5 . 9 T a b l e V I V a l u e s f o r t h e o r e t i c a l a n d e x p e r i m e n t a l n a t u r a l f r e q u e n c i e s a n d r e l a t e d e r r o r s f o r t h e r u n n i n g b l a d e CONCLUSIONS S t r a i n measurements f o r the s t a t i o n a r y saw blade show that i n the f r e e span l e n g t h s t r e s s e s i n x-d i r e c t i o n i n c r e a s e p r o p o r t i o n a l l y w i t h an i n c r e a s e of the a x i a l p r e s t r e s s i n g f o r c e RO*. During bending over the wheels the measured s t r e s s i n x - d i r e c t i o n c o n s i s t s of the sum of the a x i a l p r e s t r e s s and the s t r e s s e s due to bending of the blade i n x and y - d i r e c t i o n (due to the wheel r a d i u s r and the crown of the wheel ) . The combination of bending of the blade i n two d i r e c t i o n s r e s u l t s i n higher l o c a l s t r e s s e s than a mere a d d i t i o n of the t h e o r e t i c a l s t r e s s e s suggests. T h i s f a c t has to be con s i d e r e d i n f a t i g u e l i m i t c a l c u l a t i o n s . An incremental i n c r e a s e of the a x i a l p r e l o a d 2R0 r e s u l t e d i n an e q u i v a l e n t i n c r e a s e of the s t r e s s i n x-d i r e c t i o n across the blade, independent of the p o s i t i o n of the str a i n g a g e l o c a t i o n around the saw. The s t r e s s i n the y - d i r e c t i o n at the f r e e span length,while the blade t r a v e l s away from the wheels approaches zero. V i b r a t i o n measurements of the blade between the guides showed that the l a t e r a l and t o r s i o n a l n a t u r a l f r q u e n c i e s i n c r e a s e with the a x i a l p r e s t r e s s RO*. A change of the t i l t s t r e s s d i f f e r e n c e r e s u l t e d i n a qu a d r a t i c r e l a t i o n s h i p f o r the n a t u r a l f r e q u e n c i e s with a maximum f o r fL1 and fL2 at TSD =-26.7N/mm2 and a minimum at the same t i l t s t r e s s d i f f e r e n c e f o r the lowest t o r s i o n a l n a t u r a l f r e u e n c i e s . The slopes f o r both the l a t e r a l and t o r s i o n a l n a t u r a l f r e q u e n c i e s as a f u n c t i o n of the t i l t s t r e s s d i f f e r e n c e were s i m i l a r so that no c o n c l u s i o n f o r an optimum t i l t s t r e s s d i f f e r e n c e can be drawn from t h i s . A comparison of the experimental data with t h e o r e t i c a l s o l u t i o n s d e r i v e d by Mote [ 9 ] , Kanauchi [21] and Alspaugh [2] showed that the t h e o r e t i c a l p r e d i c t i o n s f o r the l a t e r a l n a t u r a l f r e q u e n c i e s agreed very w e l l with these experimental r e s u l t s . The t o r s i o n a l n a t u r a l f r e q u e n c i e s were c o n s i d e r a b l y higher than the p r e d i c t e d f r e q u e n c i e s from Alspaugh's s o l u t i o n . T h i s i s due to the f a c t t h at Alspaugh assumes a • constant s t r e s s d i s t r i b u t i o n across the blade, while the blade which was used i n these experiments was p r e t e n s i o n e d . The p r e t e n s i o n i n g r e s u l t s i n a p a r a b o l i c s t r e s s d i s t r i b u t i o n with higher t e n s i l e s t r e s s e s at the edges of the blade. Measurements of the t r a n s v e r s e mode shapes of the s t a t i o n a r y blade between the guides showed that a change of the a x i a l p r e s t r e s s RO* has very l i t t l e i n f l u e n c e on the normalized d e f l e c t i o n s of the blade while f o r a change i n the t i l t s t r e s s d i f f e r e n c e between-81.8N/mm2 and 14N/mm2, the maximum d e f l e c t i o n s at the lowest l a t e r a l n a t u r a l frequency c o u l d be lowered by 413% and at the lowest t o r s i o n a l n a t u r a l frequency by 280%. Th i s shows that at the n a t u r a l f r e q u e n c i e s a r a i s e of the a x i a l p r e s t r e s s RO* has very l i t t l e e f f e c t , while t r y i n g to achieve an optimum s t r e s s d i s t r i b u t i o n i n the blade through a change of the s t r e s s d i s t r i b u t i o n a c r o s s the blade promises f a r b e t t e r r e s u l t s . Another i n t e r e s t i n g f a c t was that the mode shapes at the l a t e r a l and t o r s i o n a l n a t u r a l f r e q u e n c i e s c o n s i s t e d of coupled modes f o r most t i l t s t r e s s d i f f e r e n c e s . The r e s u l t s f o r the running sawblade showed s i m i l a r r e l a t i o n s h i p s and e r r o r s between the experimental and t h e o r e t i c a l data values as observed f o r the s t a t i o n a r y sawblade. 105 REFERENCES [1] ALLEN, F.E. "High s t r a i n - t h i n K e r f " , Volume 1 of the sawmill c l i n i c l i b r a r y . Copyright 1973 by M i l l e r Freeman Pub. Inc., Howard s t r e e t , San F r a n c i s c o [2] ALSPAUGH, D.W. " T o r s i o n a l v i b r a t i o n s of a moving band" J . F r a n k l i n I n s t . Volume 283(4):328-338, 1967 [3] ANDERSON D.L. "Natural Frequenciey of L a t e r a l V i b r a t i o n s of a m u l t i b l e span moving Bandsaw" Western F o r e s t product l a b o r a t o r y , F i s h e r i e s and Environement Canada. Vancouver B.C. [4] KIRBACH, E.;BONACH, T. "An experimental study on the l a t e r a l n a t u r a l f r e q u e n c i e s of bandsaw blades" Environment Canada, Western F o r e s t e r y P r o d u c t i o n Laboratory, 1977 [6] CLOUGH, R.W. "Dynamics of s t r u c t u r e s " McGraw H i l l , 1975 [7] KIRBACH, E. "The e f f e c t of t e n s i o n i n g and wheel t i l t i n g on the t o r s i o n a l and l a t e r a l fundamental f r e q u e n c i e s of bandsaw blades" Environment of Canada, Western F o r e s t Product Laboratory [8] KRILOV, A. " E i n i g e Aspekte der Ko n s t r u k t i o n von Bandsaege- maschinen mit hoher Blattspannung" H o l z t e c h n o l o g i e 2, Jahrgang 16, June 1975, pages 109-111 [9] MOTE, C.C. "Some dynamic c h a r a c t e r i s t i c s of bandsaws" F o r e s t Product J o u r n a l , V o l . XV, No. 1, January 1965a [10] MOTE, C D . "A Study of Bandsaw V i b r a t i o n s " J . F r a n k l i n Institute,279(63):430:444,1965 [11] MOTE, CD., ULSOY, A.G. " A n a l y s i s of Bandsaw V i b r a t i o n " 6th, 1979, Woodmachine Seminar, Fore s t Product Laboratory, Richmond/ C a l i f o r n i a [12] MOTE, C D . "Dynamic S t a b i l i t y of an A x i a l l y Moving Band". J o u r n a l of the F r a n k l i n I n s t i t u t e , V o l . 285, Number 5, May 1968 [13] PAHLITSCH, G., PUTTKAMMER, K. "The Loading of Bandsaw Blades: S t r e s s e s and Strength F a c t o r s " Holz Roh-Werkstoff 30, Pages 165-174, 1972 [14] PAHLITSCH, G., PUTTKAMMER, K. " I n v e s t i g a t i o n s on the S t i f f n e s s of Bandsaw Blades" Holz, Roh-Werkstoff 31, pages 161-167, 1975 [15] PAHLITSCH, G., PUTTKAMMER, K. " B e u r t e i l u n g s k r i t e r i o n fuer d i e Auslenkung von Bandsaegeblaettern" E r s t e M i t t e i l u n g : Systematik der B e l a s t u n g s f a e l l e ; 1974 Holz 32 [16] PAHLITSCH, G. , PUTTKAMMER, -K, " B e u r t e i l u n g s k r i t e r ion fuer d i e Auslenkung von Bandsaegeblaettern" Zweite M i t t e i l u n g : Berechnung der Auslenkungen; 1974 Holz 32 [17] PAHLITSCH, G., PUTTKAMMER, K. " B e u r t e i l u n g s k r i t e r ion fuer d i e Auslenkung von Bandsaegeblaettern" D r i t t e M i t t e i l u n g : E r m i t t l u n g der Gesamtseitenauslenkung G e s a m t s t a e t i g k e i t : 1976 Holz 34 [18] PERRY, C.C., LISSNER, H.R. "The Straingage Primer" McGraw H i l l Book Company, second e d i t i o n , 1955 [19] PORTER "Some En g i n e e r i n g C o n s i d e r a t i o n s of High S t r a i n Bandsaws" F o r e s t Product J o u r n a l , A p r i l 1971, Volume 21 #4 [20] RHODES, J.E., J r . "Parametric S e l f E x c i t a t i o n of a B e l t i n t o Transverse V i b r a t i o n " J o u r n a l of A p p l i e d Mechanics, December 1980, T r a n s a c t i o n of the ACME:1055- 1060 [21] TANAKA, C. "Experimental S t u d i e s on Bandsaw Blade V i b r a t i o n s " Wood Science Technology 15, pages 145-159, 1981 [22] THUNELL, B. "The S t a b i l i t y of the Bandsaw Blade" Holz/Roh-Werkstoff, 98(pages 343-348), 1970 [23] THUNELL, B. "The S t r e s s e s i n a Bandsaw Blade" p a p e r i j a p u i No. 11, 1972 [24] TIMOSHENKO "Theory of P l a t e s and S h e l l s " McGraw H i l l , 1959 [25] ULSOY, A.G. " V i b r a t i o n and S t a b i l i t y of Bandsaw Blades: A t h e o r e t i c a l and experimental study" T e c h n i c a l Report #10, U n i v e r s i t y of C a l i f o r n i a , October 1979 [26] SOLER, A. " V i b r a t i o n s and S t a b i l t y of a Moving Band" F r a n k l i n I n s t i t u t J o u r n a l , Vol.286, No.4 Oct. 1968 108 APPENDIX I S t r e s s v a r i a t i o n i n x - d i r e c t i o n a c r o s s the blade as  a f u n c t i o n of the t i l t a n g l e TA Due to the geometry of the t i l t a n g l e system a t i l t i n g of the top wheel r e s u l t s i n a non uniform s t r e s s - d i s t r i b u t i o n a c r o s s the blade (see F i g u r e 53a). T h i s s t r e s s d i s t r i b u t i o n can be d i v i d e d i n t o the sum of two s t r e s s - d i s t r i b u t i o n s , the uniform s t r e s s -d i s t r i b u t i o n SIGtO and the t r i a n g u l a r s t r e s s -d i s t r i b u t i o n SIGta. The l o a d c e l l L C , i n c o r p o r a t e d i n t o the s t r a i n i n g system measures the s t r e s s due to the a x i a l p r e s t r e s s i n g f o r c e 2R0 p l u s the s t r e s s e s SIGtO+SIGt due to the t i l t a n g l e . The s t r e s s d i f f e r e n c e between the s t r a i n g a g e l o c a t i o n s 1 and 7 due to any t i l t a n g l e i s c a l l e d 2*SIGt. From F i g u r e 53b we can d e r i v e the formula f o r the s t r e s s SIGta f o r a t i l t a n g l e TA tan TA = A L/Bs = TA * H/180° , A L = n * T A * B s / l 8 0 ° with TA i n degrees and SIGta = 2*SIGt =£*E = A L / L w *E = II *yt*E*TA/( 180° * L w ) The u n i f o r m p a r t S i g t O of the s t r e s s d i s t r i b u t i o n for any t i l t a n g l e TA can be c a l c u l a t e d from: tan TA = A L / ( B t - B s / 2 ) =H * T A / 1 8 0 ° or AL = n * ( B t - B s / 2 ) * T A / l 8 0 ° and SIGtO =e*E = E*A L / L = n * ( B t - B s / 2 ) * E * T A / ( L w * l 8 0 ° ) The a d d i t i o n a l s t r e s s S I G t t a which i s measured by the l o a d c e l l LC i n the s t r a i n i n g system due t o a t i l t a n g l e c o n s i s t s of the sum: S I G t t a = SIGtO+SIGta/2 = SIGtO+SIGt 110 -0 ® — © — © — © — < Z ) straingage T T T T I I position FIGURE 53 a NON UNIFORM STRESS DISTRIBUTION ACROSS THE BLADE AS A FUNCTION OF THE TILTANGLE TA !w =lw + (Bf-B^j 2 FIGURE 53 b CHANGE OF STRAIN AS A FUNCTION OF THE TILTANGLE TA APPENDIX II C a l c u l a t i o n of the wheel support s t i f f n e s s Ks In the p u b l i c a t i o n "Some Dynamic C h a r a c t e r i s t i c s of Band Saws" C D . MOTE [9] develops a mathematical model to d e s c r i b e the i n f l u e n c e of the wheel support system s t i f f n e s s Ks on the l a t e r a l n a t u r a l f r e q u e n c i e s . He intr o d u c e s a nondimensional f a c t o r which can be c a l c u l a t e d from: 1 n = 1 - K = Lw*Ks 1+ 2A*E Experiments with s t a t i c l o a d i n g of the top wheel support system showed t h a t the wheel support s t i f f n e s s Ks=825N/mm. S u b s t i t u t i n g t h i s value i n t o the above formula y i e l d s : 1 n = 1 - K = : = 0.012 2 464mm*825N/mm 1 + 2*398.7mm2*2.1*l05N/mm2 or K=0.988 APPENDIX III a) E r r o r c a l c u l a t i o n f o r s t r e s s data absolute e r r o r : rabs = exp. Data value - theor. Data value r e l a t i v e e r r o r : (exp. Data value - theor. Data value) * 100 r r e l = theor.data value b) Fomula f o r c a l c u l a t i o n of the abolute and r e l a t i v change of the n a t u r a l f r e q u e n c i e s as a f u n c t i o n of the t i l t s t r e s s - d i f f e r e n c e TSD: fabs = f(TSD=95.6N/mm2) - f(TSD=26.7N/mm2) f(TSD=95.6N/mm2) - f(TSD=26.7N/mm2) f r e l = f(TSD=26.7N/mm2) + f(TSD=95.6N/mm2) 2 f=frequency value (Hz) c) Formula f o r the c a l c u l a t i o n of the r e l a t i v e e r r o r fo r s t r a i n g a g e and l o a d c e l l data: r r e l = ( SG - LC )*100/LC r r e l = r e l a t i v e r r o r SG = change of average s t r e s s a c r o s s the blade from seven s t r a i n g a g e s SG LC = change of a x i a l p r e s t r e s s from l o a d c e l l LC LC = ab s o l u t e maximum a x i a l p r e s t r e s s from LC 113 PROGRAM NEFF " "V THIS PROGRAM SCANS NEFF CHANNELS IN HANDSHAKE MODE. THE USER SELECTS THE NUMBER OF SAMPLES > THE SAMPLING RATE ? THE NUMBER OF CHANNELS AND THEIR ADDRESSES AND GAINS. THESE PARAMETERS ARE CHANGED BY EDITING THE PARAMETER FILE > 'PAR.DAT'. C NOTE: MAXIMUM CLOCK RATE IS 40000 HZ. FOR MULTI-CHANNEL SCANSv C THE CLOCK RATE SHOULD BE LIMITED TO 22000 HZ. C C THE MAXIMUM SAMPLE SIZE IS 4096. C C THIS PROGRAM INCLUDES EXTERNAL SCAN START. C C SYSTEM LIBRARY ROUTINES C EXTERNAL WTQIO EXTERNAL GETADR EX TERN Air.. ASNLUN DATA ARRAYS DIMENSION LIST(4096) DIMENSION I DAT(4096) DIMENSION IBUFF(1) C C QIO PARAMETER ARRAY C DIMENSION IPARM<6> C C QIO STATUS ARRAY C DIMENSION I STAT(2) C C DINP STATUS ARRAY C DIMENSION I0SBC2) BYTE HQ, ANS» ANS2> YES DATA NO/78/> YES/89/ C C ASSIGN NIO: TO LU 3 C CALL ASNLUN < 3 y'NI'» 0) C C C GET STARTING AND ENDING LIST INDEX C IF NOT GOOD DO AGAIN C C C C C C THE FOLLOWING ROUTINE TO ALLOW EXTERNAL SCAN INITIATION C CAN BE INSERTED INTO THE PROGRAM BY REMOVING THE FOLLOWING C 'GO TO' INSTRUCTION. C GO TO 595 C C DECIDE IF SCAN WILL BE STARTED EXTERNALLY. C WRITE<5»111) 1.11 FORMAT (1X» 'WILL SCAN BE INITIATED EXTERNALLY? Y/N '»$) 114 READ(5y222) ANS 222 FORMAT(A5) C 393 CONTINUE C CALL. ASSIGN<1»'PAR.DAT') C C READ PARAMETERS FROM FILE 'PAR.DAT'. C: IWCT=SAMPLE SIZE PER CHANNEL. C NCHAN=NUMBER OF CHANNELS. C CLOCK=NEFF SAMPLING RATE PER CHANNEL. C READ (1,901) J.UICT » NCHAN 901 FORMAT ( 215) READ(1»S51> CLOCK 551 FORMAT(F16.5) READ(1»552) LIST (1) y LIST(2) 532 FORMAT(06) IF (NCHAN. EC1.1) GO TO 590 C C FOR TWO OR MORE CHANNELSy USE SAMPLE/HOLD MODE. C CLOCK RATE AND SCAN LIST SIZE ARE MULTIPLIED C TO GIVE DESIRED SAMPLING RATE AND SAMPLE SIZE C FOR EACH CHANNEL. C IWCT=IWCT*(NCHAN+1) IF((IWCT.GT.4096).OR.(IUCT.LE.O)) GO TO 800 CLOCK-CLOCK*(NCHAN+1> IF ((CLOCK.GT.40000.>.OR.(CLOCK. L.T.O.)) GO TO 800 READ(ly552> (LIST(I)y 1 = 3 y NCHAN+2) C DO 560 1 = 2 y(IUCT-NCHAN+1) LIST(I+NCHAN+1)=LIST(I) 560 CONTINUE GO TO 580 C C FOR SINGLE CHANNELy USE SAMPLE MODE ONLY. C 590 DO 570 I=2yIWCT-l LIST(I+1)=LIST(I) 570 CONTINUE 580 CONTINUE C C SET PROGRAMMABLE CLOCK. C DWELL=1./CLOCK HERTZ=1./XRATE(DUELL»IRATE»IPRSET»1) WRITE(Sy321> CLOCKy HERTZ 321 FORMAT (IX, 'CLOCK= ',615.5. ' HERTZ= 'G12.5) CALL CLOCKB(IRATE»IPRSETt1tINDy 1) WRITE(5y1234) IND 1234 FORMAT(IX»'IND CODE= 'rI3) C -C C RESET SERIES 500 BUS C BYTE COUNT = 2 C IPARM 1 = IDATA ADDRESS C FUNCTION = 1002 OCTAL C 303 IPARM(2)=2 CALL GETADR(IPARM(1) yIDAT) CALL WTQIO("1002 ,3,10 y yISTATyIPARMyIDS) C C PRINT COMPLETION MESSAGE 115 c W R I T E ( 5 * 9 0 5 ) 9 0 5 F 0 R M A T ( 1 X * / * 1 X » ' S E R I E S 5 0 0 B U S R E S E T ! ' * / ) W R I T E ( 5 * 9 0 6 ) I S T A T U ) * I S T A T ( 2 ) * I D S 9 0 6 F O R M A T ( I X * ' D R I V E R C O M P L E T I O N C O D E = ' » 0 6 * ' ( O C T A L ) ' * / * * 1 X * ' L A S T R E S P O N S E = ' * 0 6 * ' ( O C T A D ' F / * F I X . ' D I R E C T I V E S T A T U S = ' , 0 6 * ' ( O C T A L ) ' * / ) C C W R I T E D A T A TO RAM* R E A D B A C K AND. C H E C K C C C O N V E R T WORDS TO B Y T E S C I P A R M ( 3 ) = R A M S T A R T I N G A D D R E S S C I P A R M ( 1 ) = L I S T A D D R E S S C F U N C T I O N C 0 D E = 4 0 0 O C T A L C I P A R M ( 2 ) = I W C T * 2 I P A R M ( 3 ) = 1 C A L L G E T A D R ( I F A R M ( 1 ) * L I S T ( 1 ) ) C A L L W T Q I O ( " 4 0 0 , 3 * 1 0 * , I S T A T , I P A R M * 1 D S ) C C R E A D D A T A B A C K F R O M RAM I N T O C O R R E S P O N D I N G C L O C A T I O N S I N A R R A Y I D A T C I P A R M ( 1 ) = I D A T A D D R E S S C I P A R M ( 2 ) AND I P A R M ( 3 > U N C H A N G E D F R O M A B O V E C F U N C T I O N C O D E - - 1 0 0 0 O C T A L C C A L L G E T A D R ( I P A R M ( 1 ) * I D A T < 1 ) ) C A L L WTC4I0( " 1 0 0 0 * 3 * 1 0 * , 1 S T A T » I P A R M * I D S ) C C P R I N T ANY E R R O R S C :I:ERR=O DO 4 0 0 1 = 1 * I W C T I F ( I D A T ( I ) , E Q . L I S T ( I ) ) GO TO 4 0 0 I E R R = I E R R + 1 W R I T E ( 5 * 9 2 0 ) L I S T ( I ) » I D A T ( I ) 9 2 0 F O R M A T ( I X * ' R A M E R R O R - O U T P U T = ' * 0 5 * ' » R E A D B A C K = ' , 0 5 , / ) 4 0 0 C O N T I N U E C C P R I N T E R R O R C O U N T C U R I T E ( 5 * 9 2 1 ) I E R R 9 2 1 F O R M A T ( I X * ' W R I T E TO RAM AND R E A D B A C K C O M P L E T E ' * 1 4 *' E R R O R S '*/ ) W R I T E ( 5 * 9 0 6 ) I S T A T ( l ) * I S T A T ( 2 ) . I D S C C 3 5 4 C O N T I N U E C C TO A C T I V A T E T H E E X T E R N A L S C A N S T A R T O P T I O N * C R E M O V E T H E F O L L O W I N G 'GO T O ' . C GO TO 3 4 5 C I F ( A N S . E O . N O ) GO TO 3 4 5 .C "c E X T E R N A L S T A R T C C W A I T F O R S I G N A L TO S T A R T S C A N . C 1 0 C A L L D I N P ( 0 * 0 * I O S B , I N P U T ) I F ( I N P U T . E Q . O ) GO T O 1 0 GO TO 3 4 6 C 3 4 5 C O N T I N U E 116 c C MANUAL START C WRITE<5,654> 654 FORMAT(IX,'TO START SCAN, ENTER RETURN' , $) READ<5,222) CR 346 CONTINUE C C EXECUTE FROM RAM HANDSHAKE C C FUNCTION C0DE=3001 OCTAL C IPARM(1)=IDAT ADDRESS C IPARM<2)==BYTE COUNT C IPARM(3)=RAM STARTING ADDRESS C CALL GETADR(IPARM<1),IDAT<1)) IPARM<2)=IUCT*2 IPARM<3)=1 CALL WTQIO< "30011-3,10, ,ISTAT,IPARM,IDS) C C C REPEAT LAST FEU DATA POINTS UNTIL THE TOTAL NUMBER OF DATA C POINTS EQUALS 'IWCT', A POWER OF 2. C DO 888 I=IWCT, IWCT+NCHAN+1 ID A T ( I ) = ID A T < I -- N C H A N -1) 888 CONTINUE C WRITE(5,922) 922 FORMAT <IX,'EXECUTE FROM RAM IN HANDSHAKE MODE',/) C C STORE DATA IN USER SELECTED F I L E S . C DO 450 J=3,NCHAN+2 CALL F I L E S ( J ) IF < NCHAN.EH . 1 ) GO TO 444 WRITE ( 2 ,930 ) INT (FLOAT (IWCT) /FLOAT (NCHAN+1) ) , HERTZ/FLOAT (NCHAN+1) 930 FORMAT(I5,F16.5) WRITE (2, 935) ( FLOAT ( I DAT < I ) )/32768. , I = . . l, IWCT+NCHAN+1 , NCHAN + 1 ) GO TO 445 444 WRITE(2,930) IWCT,HERTZ WRITE(2,935)(FLOAT(I DAT(I))/32768.,I=J,IWCT+NCHAN+1) 445 CONTINUE 935 FORMAT(6E13.5) CALL CL0SE(2) 450 CONTINUE WRITE(5,906) I S T A T ( 1 ) , I S T A T ( 2 ) , I D S WRITE<5,924) 924 FORMAT(IX,/,IX,'FINISH EXECUTING FROM RAM',/) GO TO 802 C C THE FOLLOWING OPTION ALLOWS SCAN TO BE REPEATED C USING THE SCAN L I S T STORED IN NEFF RAM. -C 302 WRITE(5,112) 112 FORMAT <1X,'DO YOU WISH TO REPEAT SCAN? ',$) READ(5,211) ANS2 211 FORMAT(A5) IF(ANS2.EQ.YES) GO TO 354 GO TO 804 800 WRITE(5,902) 902 FORMAT(IX,'#**** INVALID DATA *****',/) 804 STOP END 117 c C SUBROUTINE F I L E S ( J ) ALLOWS USER TO CHOOSE F I L E NAMES C FOR DATA STORAGE. C SUBROUTINE F I L E S ( J ) BYTE BUF<80> WRITE(5,140) J-2 140 FORMATdX, 'ENTER CHANNEL I >' ) F I L E NAME ',$> READ<5,150) (BUF(I)»I=1»80) 150 FORMAT(80A1) L=LENGTH(BUF 180) BUF(L+1)=0 CALL ASSIGN(2,BUF) RETURN 1 END C C FUNCTION LENGTH FINDS LENGTH OF ALPHANUMERIC C DATA STRING. THE FIRST 'BLANK' CHARACTER INDICATES THE C END OF THE STRING. C INTEGER FUNCTION LENGTH(BUF tN) BYTE BUF(1) tBL INTEGER N DATA BL/32/ DO 100 I=N,1y-1 IF(BUF <I).NE.BL) GO TO 200 100 CONTINUE 200 LENGTH-I RETURN END 118 C "STRAIN" READS STRAINGAGE-DATA FOR ONE LOADCELL AND 9 STRAIN-C GAGES FROM F I L E S . IT CALCULATES THE AXIAL PRELOAD TUOROCN3, C THE STRAINS AND STRESSES DUE TO LOADCELLREADINGS y STRAINS AND C STRESSES AND MEAN VALUES DUE TO 9 SINGLE STRAINGAGE READINGS. C "S6" MEANS STRAINGAGE . 0LC"MEANS LOADCELL. STG MEANS STRESS C EPS MEANS STRAIN INTEGER I . J , E . I W C T » E X P N O . N . M . K REAL CALLC» CALSGX. CALSGYy T W O R O < 5 , 1 , 1 0 ) . A » Y O U N G , H E R T Z . T I L T R A REAL POS. EPS<5.10.10> . S I G ( 5 . 1 0 . 1 0 ) . D A T A < 5 » 1 0 . 1 0 ) REAL EPSX(5>1. 10 >_. SIOY < 5.1»10 > .SIGX<5»1.10) REAL MSIGSG(IO).MSIGLC(10)> MEPSLC(10)» MEPSSG(10)y M2R0(10)y NUM C C C BYTE IBUF(80) C ASSIGN PRINTER TT5 TO LABEL "1" CALL ASSIGN(1.'TT5') CALLC=1.9264E5 CALSGX=146.32 CALSGY=415.8 Y0UNG=210000.0 A-398.7 C C EXPNO IS AMOUNT OF EXPERIMENTS DONE WRITE (5 y 71) 71 FORMAT ( I X . 'ENTER AMOUNT OF EXPERIMENTS DONE J'y *) READ (5y72) EXPNO 72 FORMAT (14) • C M IS #0F EXPERIMENTS y N IS tfOF STRAINGAGES USED y K IS NUMBER OF C SAMPLES BEEN TAKEN DO 81 M = l y EXPNO WRITE (5.37) M 37 FORMAT (IXy'EXPERIMENT NUMBER'.14) C READ DATA FROM F I L E SG(My N)y *0 OF SCANNS IWCT AND C SCANNING FREQUENCY HERTZ WRITE(5.700) 700 FORMAT(IX.'ENTER FILENAME y WHERE STRAINGAGE DATA ARE STORED:' *.*> READ (5.701) <IBUF( J ) » J - ~ l y 80 ) 701 FORMAT(80A1) L=LENGTH (IBUF.80) DO 91 N = l » 1 0 IBUF <L+1)=59 IF (N.GE.8) GOTO 150 IBUF(L+2)=N+48 ' IBUF(L + 3)=0 GOTO 111 150 IBUF(L+2)=49 IBUF(L+3)=N-8+48 IBUF(L+4)=0 111 CALL ASSIGN (2.IBUF) READ (2.112) IWCTyHERTZ 112 FORMAT (I5.F16.5) C READ DATA FROM F I L E SG(M.N) SIGNALVALUES DO 211 K = l y ( I W C T - l ) READ (2.212) DATA(M.N y K ) ?12 FORMAT (6E13.5) 211 CONTINUE CALL CL0SE(2) 91 CONTINUE 81 CONTINUE C NOW ALL DATA FOR M EXPERIMENTS ARE READ INTO IWCTy HERTZ AND C DATA(M y N.K) DO 213 K=ly(IWCT-1) 119 C CALCULATE ABS. VALUES! TUOROySTRAIN AND STRESS FOR LOADCELL-C READINGS DO 58 N=lylO D A T A < 1 » N r K ) = ( D A T A < 1 y N y K ) + D A T A < 2 y N y K > ) / 2 58 CONTINUE DO 311 M= 3 » E X P N 0 DATA < M r11K)=DATA < My1>K)-DATA <1,11K) TWORO(M y1y K)=DATA(M y1y K)#(CALLC/O.835+8588.7)*1.19 EPS(My 1yK)=TWORO(My1yK>/C2*A*Y0UNG> SIG(My1yK)=EPS<My1yK)*YOUNG 311 CONTINUE C CALCULATE VALUES FOR SGX5 ABS.y STRAINSGX DO 511 M=3yEXPNO DO 411 N = 2y8 DATA< M y N y K )=DATA(M y Ny K)-DATA<1y N y K) EPS(M y N y K)=DATA < M tN,K)/CALSGX 411 CONTINUE C C CALCULATE DO 611 N=9»10 DATA(M y N y K)=DATA < M y N y K)-DATA(1y N y K) EPS < M y N y K >=DATA(M y N y K >/CALSGY 611 CONTINUE 511 CONTINUE C CALCULATE STRESS SGX DO 811 N==2y8 DO 911 M=3yEXPN0 SIG(M y N y K)=230769.2*(EPS(M y N y K) *+0.15*(EPS(My9yK)+EPS(My10yK))) 911 CONTINUE 811 CONTINUE C C CALCULATE STRESS SGY DO 912 M=3yEXPN0 DO 913 N==2y8 C EPSX(MylyK) IS SUM OF STRAIN VALUES IN C X-DIRECTION. EPSX(M y1y K ) =EPSX(M y1y K > +EPS < M y N y K) 913 CONTINUE SIGY(MylyK) = < EPSX(M y1y K)*0.3/7.0 + 0,5*(EPS < M » 9 y K) *+EPS(My10yK)))*230769.2 912 CONTINUE C CALCULATE THE AVERAGE FOR TWORO FOR ALL M EXP. DO 923 M=3.EXPN0 M2R0(K)=M2R0(K)+TUORO(M y1y K) 923 CONTINUE M2R0 ( K ) =M2R0 ( K ) / ( EXPN0--2 ) C CALCULATE AVERAGE LOADCELL -STRESS "MSTRESSLC FOR ALL EXP. DO 924 M=3yEXPN0 MSIGLC(K)=MSIGLC(K)+SIG(M y1y K) 924 CONTINUE MSIGLC(K)=MSIGLC < K)/(EXPNO-2) C CALCULATE THE AVERAGE STRESSDISTRIBUTION FROM STRAINGAGE 2-8 C * ACROSS THE BLADE DO 921 M=3yEXPN0 ' DO 922 N=2y8 SIGX<Mr1yK)=SIGX<My1yK)+SIG(M,NyK> 922 CONTINUE MSIGSG(K)=MSIGSG<K)+SIGX(My1yK)/7.0 921 CONTINUE MSIGSG(K)=MSIGSG(K)/(EXPN0-2) C CALCULATE AVERAGE STRAIN FOR LC AND SGX ACROSS THE BLADE FOR ALL C . * M EXPERIMENTS IN MICROSTRAIN DO 925 M = 3y EXPNO 120 MEPSLC(K)=MEPSLC(K)+EPS(M,1,K) MEPSSG(K)=MEPSSG< K ) +EPSX(M,1,K) /7.0 925 CONTINUE MEPSLC < K)=MEPSLC < K)/(EXPNO-2 5*1.0E6 MEPSSG(K)=MEPSSG(K)/<EXPNO-2)*1.0E6 213 CONTINUE C DO 928 M=3yEXPNO TILTRA=TILTRA+SIG(M,2, l ) / S I G ( M y 8 y 1 > 928 CONTINUE TILTRA=TILTRA/(EXPNO-2) C * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * C ONLY VALUES F O R K=l ARE BEING PRINTEDy BUT ALL VALUES FOR K = l TO C * ( I U C T - 1 ) ARE STORE IN ARRAYS DATAy EPS, SIG K = l C WRITE ALL DATA ON SCREEN AND PRINTER C FIRST MULTIPLY ALL STRAINS BY 1.0E6 TO GET MICROSTRAIN UNITS DO 51 M-=3 y EXPNO DO 52 N=l,10 EPS(M y N y K)=EPS< M,N,K)* 1,0E6 52 CONTINUE 51 CONTINUE WRITE<1,9) WRITE(5,9 ) 9 FORMAT('l') C WRITE ON S C R E E N : BLADEPOSITION AND PRINT ON PAPER WRITE (5,11) 11 FORMAT<1X,'ENTER BLADEPOSITION (A TO X):',$> READ<5,12) POS 12 FORMAT(A3) WRITEC1y13) POS WRITE(5,13) POS 13 FORMAT(IX y'BLADE POSITION J',A2) WRITE(5,17) WRITE<1,17> C WRITE AVER. AXIAL PRELOAD FROM LC FOR M EXP. WRITE (5,14)M2R0(K) WRITE<1y14) M2R0(K) 14 FORMAT <IX y'AVERAGE AXIAL PRELOAD FROM LOADCELL FOR M EXPERIMENT *Sy M2R0=',F12.2, ' CN3') WRITE (5,15) MSIGLC(K) WRITE (1,15) MSIGLC(K) 15 FORMAT (IX,'AVERAGE AXIAL PRESTRESS FROM LOADCELL * MSIGLC=',F12.2,' CN/MM"23') 'WRITE (5,16) MSIGSG(K) WRITE (1,16) MSIGSG(K) 16 FORMAT (IX,'AVERAGE AXIAL STRESS FROM SG2-SG10 FOR M EXPERIMENTS * MSIGSG=' ,F12.2, ' t:N/MM"2J') WRITE(5,17) W R I T E ( l y l 7 ) WRITE(5,22> MEPSLC(K) WRITE(1,22) MEPSLC(K) 22 FORMAT(IX,'AVERAGE AXIAL PRESTRAIN FROM LOADCELL ' y l S X y *'MEPS1.C==' ,F12.2, ' CMICR0STRAIN3 ' ) WRITE(5y23) MEPSSG(K) WRITE(1,23) MEPSSG(K) 23 FORMATCIXy'AVERAGE AXIAL STRAIN FROM SG2-SG8'>23X > * 'MEPSGX=',F12.2,' LMICR0STRAIN3') WRITE(5,17) WRITE(1,17) WRITE(5,24) TILTRA WRITE(1,24) TILTRA 24 FORMAT(IX,'TILTSTRESSRATIO FOR M EXPERIMENTS =',F4.2) WRITE(1,17) 121 W R I T E < 1 » 1 7 ) W R I T E ( 1 F 1 7 ) W R I T E ( 1 F 1 7 ) WRITEC5,17) WRITE(5yl7) W R I T E ( 5 F 17) 17 FORMAT(' ') C PRINT T A B L E C PRINT HEADLINE WRITE (5F 1 8 ) W R I T E ( 1 F 1 8 ) 1 8 FORMAT < 1X F ' EXP ' F 17X F 'STRAIN XCE--6II' , 13X F ' STRAIN YCE-63 ' F!6X» 'STR *ESS X CNMM"23'F21XF'STRESS Y') C SECOND HEADLINE WRITE (5F 1 9 ) WRITE ( I F 19) 19 FORMAT(2XF'#'F4XF'SG2'F 3 XF'SG3'F3XF'SG4'F3XF'SG5'F 3 XF'SG6'F3XF * ' S G 7 ' F 3 X F ' S G 8 ' F 4 X F ' S G 9 ' F 3 X V ' S G 1 0 ' * F 4 X F ' L C I ' F 4X v'SG2'»3X F'SG3'y 3X y'SG4'y 3X y 'SG5'F 3X F'SG6'F3XF *'SG7 ? 3X F SG8'F 4X F'SG9 y10') W R I T E ( 5 F 2 0 ) WRITE(ly20) 20 F O R M A T ( ' ') C WRITE DA TABLOCK DO 25 M=3yEXPNO W R I T E ( 5 F 2 1 ) (M-2> y ( I N T ( E P S ( M » N F K ) + 0 . 5 ) y N = = 2 y 1 0 ) y I N T ( S I G * ( M y1y K)+0.5) y * ( I N T ( S I G ( M y N y K)+0.5)y N = 2F 8 ) y I N T ( S I G Y ( M y1F K)+0.5 ) WRITECI.y21) (M-2) F ( INT(EPS(MyNyK)+0.5) F N = 2 F 1 0 ) t # I N T ( S I G ( M F 1 F K ) + 0 . 5 ) y * ( I N T ( S I G ( M F N F K ) + 0 . 5 ) F N = 2 F 8 ) F I N T ( S I G Y ( M F 1 y K ) + 0 . 5 ) 21 F O R M A T ( 2 X F I 2 F 2 X F I 4 F 2 X F I 4 F 2 X F I 4 y 2 X y I 4 F 2 X F I 4 F 2 X F I 4 F 2 X F I 4 F 4 X F 1 3 F *3X F13y 5X y13y 4X 113F3X F13 y3X y13 y 3X y13 y 3X,13 y3XF13 t3XF13F4X y13) CONTINUE + + + + • • » • • + • + • • • + + + • • • • • • • • • • • • • • + * + • • • + • • + • + + • • • • • • + • • + + + < • * • STOP END INTEGER FUNCTION LENGTH( BUFy N) BYTE B U F ( l ) INTEGER N BYTE BL DATA BL/32/ DO 10 I = N y l y - l I F ( B U F ( I ) .NE. BL ) GO TO 20 CONTINUE LENGTH=I RETURN END 25 C C C c C * 10 20 122 C "DYN" R E A D S S T R A I N G A G E - D A T A F O R O N E L O A D C E L L AND 9 S T R A I N •-C G A G E S F R O M F I L E S . I T C A L C U L A T E S T H E A X I A L P R E L O A D TWOROTNIIF C T H E S T R A I N S AND S T R E S S E S D U E TO L O A D C E L L R E A D I N G S ; S T R A I N S AND C S T R E S S E S A N D MEAN V A L U E S D U E TO 9 S I N G L E S T R A I N G A G E R E A D I N G S . C " S G " M E A N S S T R A I N G A G E . " L C " M E A N S L O A D C E L L . S I G M E A N S S T R E S S C E P S M E A N S S T R A I N . S T R E S S V A L U E S F O R L C C AN D S G 2 - S G 8 C A N B E S T O R E D A T F I L E L O C A T I O N S . C M A X I M U M V A L U E F O R I W C T ( N O O F S A M P L E S ) = 5 1 2 ! ! I N T E G E R I » J ? E » I W C T > E X P N O » N » M ? K . P O S . N C H A N R E A L C A L L C . C A L S G X . C A L S G Y . T U O R O ( 1 . 1 . 5 1 3 ) , A F Y O U N G . H E R T Z » T I L T R A V I R T U A L E P S ( 1 . 9 . 5 1 3 ) . S I G ( 1 » 8 , 5 1 3 ) . D A T A ( 3 . 9 . 5 1 3 ) V I R T U A L E P S X ( 1 F 1 F 5 1 3 ) F S I G Y ( 1 F 1 . 5 1 3 ) » S I G X ( 1 . 1 F 5 1 3 ) R E A L M S I G S G < 5 1 3 > F M S I G L C ( I ) F M E P S L C ( 5 1 3 ) F M E P S S G ( 5 1 3 ) F M 2 R O < 1 ) F N U M B Y T E I B U F ( 8 0 ) C A S S I G N P R I N T E R T T S TO L A B E L " 1 " C A L L A S S I G N ( I F ' T T S ' ) C A L L C = 1 . 9 2 6 4 E 5 C A L S G X = 1 6 6 . 3 2 C A L S G Y = 4:I.5,8 Y 0 U N G = 2 1 0 0 0 0 . 0 A = 3 9 8 . 7 C C M I S » 0 F E X P E R I M E N T S . N I S #OF S T R A I N G A G E S U S E D . K I S NUMBER O F C S A M P L E S B E E N T A K E N C N C H A N I S NUMBER O F C H A N N E L S B E 1 N G S C A N N E D W R I T E ( 5 . 7 1 ) 7 1 F O R M A T < I X » ' E N T E R # O F C H A N N E L S B E I N G S C A N N E D : ' . $ ) R E A D ( 5 F 7 2 ) N C H A N 7 2 F O R M A T ( 1 4 ) DO 8 1 M=l. f3 W R I T E ( 5 . 3 7 ) M 3 7 F O R M A T ( I X . ' E X P E R I M E N T N U M B E R ' . 1 4 ) R E A D D A T A F R O M F I L E S G ( M . N ) . » 0 O F S C A N N S I W C T AND S C A N N I N G F R E Q U E N C Y H E R T Z W R I T E ( 5 . 7 0 0 ) F O R M A T ( I X F ' E N T E R F I L E N A M E . WHERE S T R A I N G A G E D A T A A R E S T O R E D 5 * » * ) R E A D ( 5 . 7 0 1 ) ( I B U F ( J ) . J = 1 . 8 0 ) 7 0 1 F O R M A T ( 8 0 A 1 ) L = L E N G T H ( I B U F . 8 0 ) DO 9 1 N = l , N C H A N I B U F ( L + l ) = 5 9 X I F ( N . G E . 8 ) G O T O 1 5 0 I B U F ( L + 2 ) = N + 4 8 I B U F ( L + 3 ) = 0 G O T O 1 1 1 1 5 0 I B U F ( L + 2 ) = 4 9 I B U F ( L + 3 ) = N - 8 + 4 8 I B U F ( L + 4 ) = 0 1 1 1 C A L L A S S I G N ( 2 . I B U F ) R E A D ( 2 . 1 1 2 ) I W C T . H E R T Z 1 1 2 F O R M A T ( I 5 . F 1 A . 5 ) R E A D D A T A FROM F I L E S G ( M . N ) S I G N A L V A L U E S R E A D ( 2 . 2 1 2 ) ( D A T A ( M . N . K ) . K = 1 . I W C T ) F ORMAT ( 6 E 1 3 . 5 ) C A L L C L 0 S E ( 2 ) 9 1 C O N T I N U E 8 1 C O N T I N U E C NOW A L L D A T A F O R M E X P E R I M E N T S A R E R E A D I N T O I W C T . H E R T Z A N D C D A T A ( M . N » K ) DO 2 1 3 K ' = 1 , I U C T C C A L C U L A T E A B S . V A L U E S : T W O R O . S T R A I N AND S T R E S S F O R L O A D C E L L -C R E A D I N G S DO 6 5 N = 1 F N C H A N C c 7 0 0 c 2 1 2 123 D A T A ( 1 y N y K ) = ( D A T A ( 1 y N y K ) + D A T A ( 2 y N y K ) ) / 2 65 C O N T I N U E D A T A < 3 f1fK)=DATA < 3 y 1 y K ) - D A T A <1y11K) TWORO < 1 , 1 1 K ) = D A T A ( 3 y 1 1 K ) * ( C A L L C / 0 . 8 3 5 + 8 5 8 8 . 7 > *1.19 E P S ( 1 , 1 y K ) = T W O R O ( 1 t 1 > K ) / ( 2 * A * Y 0 U N G ) S I G ( 1 y 1 f K ) = E P S ( 1 y 1 r K ) * Y O U N G 3 1 1 C O N T I N U E IF ( N C H A N . EQ. 1) GOTO 900 C C A L C U L A T E V A L U E S F O R S G X J A B S S T R A I N S G X DO 411 N=2y(NCHAN-1) D A T A ( 3 y N y K ) = D A T A ( 3 y N y K ) - D A T A ( 1 y N y K ) E P S ( 1 y N y K ) = D A T A ( 3 y N y K ) / C A L S G X 411 C O N T I N U E C C C A L C U L A T E D A T A (3 y N C H A N y K > ==DATA (3 y N C H A N y K ) - D A T A (1 y N C H A N y K ) E P S ( 1 y N C H A N y K ) = D A T A ( 3 y N C H A N y K ) / C A L S G Y 611 C O N T I N U E C C A L C U L A T E S T R E S S S G X DO 811 N==2y (NCHAN-1) S I G <1y N y K ) = 2 3 0 7 6 9 . 2 * ( E P S <1y N y K ) * + 0 . 3 0 * ( E P S <1y N C H A N y K ) ) ) 811 C O N T I N U E C C C A L C U L A T E STRESS S G Y DO 913 N=2y(NCHAN-1) C E P S X ( l y l y K ) IS SUM OF S T R A I N V A L U E S IN C X - D I R E C T I O N . E P S X ( 1 y 1 y K ) = E P S X ( 1 y 1 y K ) + E P S ( 1 y N y K > 913 C O N T I N U E S I G Y ( 1 y 1 y K ) = ( E P S X ( 1 y 1 y K > #0.3/(NCHAN-2) + ( E P S ( 1 y N C H A N y K ) * ) ) * 2 3 0 7 6 9 . 2 C C A L C U L A T E T H E A V E R A G E F O R TWORO F O R ALL M E X P . C C A L C U L A T E T H E A V E R A G E S T R E S S D I S T R I B U T I O N F R O M S T R A I N G A G E 2-8 C * A C R O S S T H E B L A D E DO 922 N=2y(NCHAN-1> S I G X ( 1 y 1 y K ) = S I G X ( 1 y l y K ) + S I G ( l y N y K > 922 C O N T I N U E M S I G S G ( K ) = S I G X ( 1 y 1 y K ) / ( N C H A N - 2 ) C C A L C U L A T E A V E R A G E S T R A I N F O R LC AND S G X A C R O S S T H E B L A D E F O R ALL C • * M E X P E R I M E N T S IN M I C R O S T R A I N M E P S L C ( K ) = M E P S L C ( K > + E P S ( 1 y 1 y K ) M E P S S G ( K ) = M E P S S G ( K ) + E P S X ( 1 y 1 y K > / ( N C H A N - 2 ) M E P S L C ( K > = M E P S L C ( K ) * 1 . 0 E 6 M E P S S G < K ) = M E P S S G ( K ) * 1 . 0 E 6 213 C O N T I N U E C T I L T R A = T I L T R A + S I G ( 1 y 2 y 1 ) / S I G <1y 8 y1) C O N L Y V A L U E S F O R K=l A R E B E I N G P R I N T E D y B U T ALL V A L U E S F O R K=l TO C * ( I W C T - 1 ) A R E S T O R E IN A R R A Y S DATAy EPSy S I G C W R I T E ALL D A T A ON S C R E E N AND P R I N T E R W R I T E ( l y 9 ) W R I T E ( 5 y 9 > 9 F O R M A T ( ' l ' ) C W R I T E ON S C R E E N : B L A D E P O S I T I O N AND P R I N T ON P A P E R 900 W R I T E ( S y l l ) 11 F O R M A T ( lXy ' E N T E R B L A D E P O S I T I O N (A TO X K ' y U ) R E A D ( 5 y12) P O S 12 F O R M A T ( A 3 ) W R I T E ( l y l 3 ) P O S W R I T E ( 5 y l 3 ) P O S 13 F O R M A T ( l X y ' B L A D E P O S I T I O N : ' y A 2 ) W R I T E ( 5 y l 7 ) 124 WRITE(1,17) 17 FORMAT < ' ') C WRITE AVER. AXIAL PRELOAD FROM LC FOR M EXP. DO 16 K=1,IWCT M2R0(1)=M2R0(1)+TW0R0(1,1,K) MSIGLC(1)=MSIGLC(1)+SIG(1,1,K) 16 CONTINUE M2R0(1)==M2R0(1)/IUCT MSIGLC <1)=MSIGLC <1)/IWCT WRITE (5,14)M2R0(1) WRITE(1,14> M2R0(1> 14 FORMAT (IX»'AVERAGE AXIAL PRELOAD FROM LOADCELL FOR M EXPERINENT *S, M2R0=',F12.2,' L"NJ') WRITE (5,15) MSIGLC(l) WRITE (1,15) MSIGLC(l) 15 FORMAT (IX,'AVERAGE AXIAL PRESTRESS FROM LOADCELL * MSIGLC=',F12.2,' CN/MM"2IT > IF <NCHAN.EQ.l) GOTO 901 WRITE(5vl7> WRITE(1,17> WRITE<5,24) TILTRA WRITE<1,24) TILTRA 24 FORMAT(IX»'TILTSTRESSRATIO FOR M EXPERIMENTS =',F4.2) C ASSIGN FILENAME TO OUTPUT FILE FOR STRESS DATA LC 901 WRITE (5,57) 57 FORMAT (IX,'ENTER FILENAME, WHERE LC STRESS VALUE fcSHALL BE STORED:' ,*) CALL FILES WRITE (4,58) (SIG(1,1,K),K=1,IUCT) 58 FORMAT (6F9.2) CALL CLOSE (4) IF (NCHAN.EQ.l) GOTO 902 C ASSIGN FILENAME TO OUTPUT FILE FOR STRESS DATA SG2--SG8 C WRITE SG STRESS VALUES FROM SGI - SG(NCHAN-1) TO FILE DO 50 N=2,(NCHAN-1) WRITE (5,51) N 51 FORMAT (IX,'ENTER FILENAME, WHERE STRESS VALUE FROM SG',I1,' KSHALL BE STORED:' ,$) CALL FILES WRITE (4,53) (SIG(1,N,K),K=1,IWCT) 53 FORMAT (6F9.2) CALL CLOSE (4) 50 CONTINUE C- WRITE AVERAGE STRESS FOR ALL (NCHAN-1) SG INTO FILE WRITE (5,56) 56 FORMAT (IX,'ENTER FILENAME, WHERE AVERAGE SG STRESS- VALUES tSHALL BE STORED:',*) CALL FILES WRITE (4,54) (MSIGSG(K),K=1»IWCT) 54 FORMAT (6F9.2) CALL CLOSE (4) 902 STOP END SUBROUTINE FILES BYTE IBUF (80) READ (5,52) (IBUF(J),J=l,80) 52 FORMAT (80A1) L=LENGTH(IBUF,80) IBUF(L+1)=46 IBUF(L+2)=68 IBUF(L+3)=65 IBUF(L+4)=84 IBUF(L+5)=0 CALL ASSIGN (4,IBUF) RETURN END INTEGER FUNCTION LENGTH< BUF» N) BYTE B U F ( l ) INTEGER N BYTE BL DATA BL/32/ DO 10 I=N»1»-1 IF(BUF<I) .NE. BL ) GO TO 20 CONTINUE LENGTH=I RETURN END C "FREQ" ENTERS DATA FOR A TIME SCALE INTO A F I L E C CALLED "FREQ.DAT". THE DATA REPRESENT THE TIMEAXIS IN A X-Y PLOT C AND ARE NEEDED TO PLOT DATA ACQUISITIONED WITH THE "NEFF" C PROORAMM. THE TIME AXIS DATA ARE INCREMENTS OF THE RATIO C IUCT/HERTZ — ( S A M P L E S TAKEN/SCANNING FREQUENCY). IWCT AND HERTZ C DEPEND ON THE EQUIVALENT VALUES IN "PAR.DAT". C C REAL HERTZ,TIME(512> ' INTEGER IWCTvN WRITE (5,11) 11 FORMAT (IX,'ENTER #OF SAMPLES BEING TAKEN (IWCT FROM "PAR.DAT"): *',*> READ (5,12) IWCT 12 FORMAT (14) WRITE (5,13) 13 FORMAT (IX,'ENTER SCANNING FREQUENCY (HERTZ FROM "PAR.DAT") * DO NOT FORGET THE !!DECIMAL-POINT!! :',*) READ (5,14) HERTZ 14 FORMAT (F10.3) DO 15 N=1,IWCT TIME'(N)=TIME(N-1 )+l/HERTZ 15 CONTINUE CALL ASSIGN (2,'FREQ.DAT') WRITE (2,16) (TIME(N),N=l,IWCT) 16 FORMAT (6F12.8) CALL CLOSE (2) STOP END •;'bye HAVE A GOOD AFTERNOON 27-SEP-82 1 2 M 3 TT5: LOGGED OFF 

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