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Stresses and vibrations in bandsaw blades Eschler, Andreas 1982

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c,  STRESSES AND  VIBRATIONS  BANDSAW  IN  BLADES  by  ANDREAS M.A.SC  ESCHLER  , 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 THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE (Department  We  of M e c h a n i c a l  accept t h i s to  thesis  the required  Engineering)  as c o n f o r m i n g standard  THE UNIVERSITY OF BRITISH COLUMBIA October  (cp  Andreas  1982  Eschler,  1982  OF  I  II  In  presenting  requirements of  B r i t i s h  i t  freely  agree for  this for  an  available  that  I  understood  that  financial  by  his  or  at  the  of  DE-6  (3/81)  ZZ.  reference  and  study.  I  extensive be  her or  shall  copying  granted  by  the  of  publication  not  be  allowed  of  Columbia  this  It  this  without  make  further  head  representatives.  /TecticrspScaf £r<f?<?//7-e<?  fp  University shall  The U n i v e r s i t y o f B r i t i s h 1956 M a i n M a l l Vancouver, Canada V6T 1Y3  Date  the  Library  permission.  Department  of  the  may  copying  gain  degree  fulfilment  that  for  purposes  or  p a r t i a l  agree  for  permission  scholarly  in  advanced  Columbia,  department  for  thesis  thesis  of  my  i s thesis my  written  ABSTRACT  Due  to r i s i n g  important  lumber c o s t s i t has become more  to  optimize  bandsaws  as  they  industry.  One  important  torsional thickness  deflections  of  industrial  the  of  the  behaviour  forest  blade  to  bandsaw  were  performed  the  assess  the  parameters  of t h e s t a t i o n a r y  and  are  measurements  compared  with  with  of  results  on t h e on  the  and t h e r u n n i n g a  fullsize  p r o d u c t i o n bandsaw. The e x p e r i m e n t a l  the s t r e s s - s t r a i n  and  minimize  to  blade  of  products  the l a t e r a l  tries  v a r i o u s t y p i c a l bandsaw  sawblade. Experiments  sawblade  in  more  performance  aim i s t o reduce  d i s t r i b u t i o n i n the  vibrational  for  used  cutting  of t h e c u t . T h i s s t u d y  influence stress  are  the  and  the from  results  stationary theoretical  solutions. Vibration  measurements o f t h e s t a t i o n a r y  and o f t h e  r u n n i n g b l a d e a r e compared t o v a l u 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  for for  lateral  deflection  the  the s t a t i c  analytically  influencing axial  stress  prestress,  The  results  presented  measurements a g r e e  predicted  the s t r e s s  solution  [21]  and w i t h ALSPAUGH'S [ 2 ] s o l u t i o n  torsional vibrations.  that  and KANAUCHI'S  results.  distribution in  stresses  very w e l l Major  the  due t o b e n d i n g  show with  factors  blade:  the  of t h e b l a d e  over the  t h e bandsaw w h e e l s , and s t r e s s e s due  to t i l t i n g  of  t o p bandsaw wheel were e x a m i n e d . A c o m p a r i s o n o f t h e  experimental measurements good  and  f o r the  agreement  while  the  natural  mode  sawblade  lateral  the  showed  natural  natural  than  of the v i b r a t i o n  frequencies,  frequencies analytically  could  be  of the running  very  were  predicted  observed  for  the  blade.  shapes of the s t a t i o n a r y sawblade a t the  frequencies  modeshapes  the  results  frequencies  The natural  for  higher  Similar  results  stationary  torsional  considerably values.  analytical  were m e a s u r e d .  consisted  tiltstress differences.  of  coupled  I t was  found  modes  that  for  the most  V  TABLE OF  CONTENTS  Chapter  Page  Abstract  I l l  List  of T a b l e s  VIII  List  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 research  3  2. E x p e r m e n t a l s e t up  5  2.1  Bandsaw f a c i l i t i e s  2.2  Instrumentation  5  and  data  acquisition  system 3. T h e o r e t i c a l  5 stress  e v a l u a t i o n f o r a bandsaw  blade 3.1  20 Fundamental calculation  3.2  Static  theory  of  stress  of a bandsaw b l a d e  stresses  for  the  20  stationary  blade 3.2.1  21 Axial  p r e s t r e s s due  prestressing  force  t o the  axial 21  VI  3.2.2  Bending of  3.2.3  t h e bandsaw  Stress the  Stress  3.2.5  Stress of  wheels  due t o t h e  bandsaw  3.2.4  3.2.6  s t r e s s due t o t h e r a d i u s  crown  up  of  wheels  as a f u n c t i o n due  22 of t h e t i l t  t o the notch  Stress  due t o  23  pretensioning  of  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  idling  24  S t r e s s due t o c e n t r i f u g a l f o r c e s  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 3.4.1  Stress  3.4.2  Stress  cutting  due t o t h e c u t t i n g f o r c e s due  to  Experiments  4.2  Stress-strain different  4.3  temperature  measurements  27 27  measurements  for  tiltangles  Stress-strain  31  measurements a r o u n d t h e  bandsaw 5. Dynamic  5.1  40  vibration  stationary  measurements  with  a  blade  48  Experimental bandsaw  5.2 L a t e r a l  .....24  25  stress-strain  4.1  24 24  changes 4. S t a t i c  22  factor  the blade t e e t h  the  3.3.1  21  set  up  and t h e o r e t i c a l  blade models and  torsional  48 natural  VII  frequencies  of  t h e b l a d e between t h e  guides  63  5.3 T r a n s m i s s i b i l i t y 5.4 Dynamic  of the blade  vibration  78  measurements w i t h  a  moving b l a d e  94  6. C o n c l u s i o n s  102  REFERENCES  105  APPENDIX I  Stress  as  a  function  tiltangle APPENDIX I I  Wheel  APPENDIX I I I E r r o r APPENDIX IV  support  the 105  s t i f f n e s s Ks  calculation  Computer  of  programs  formulae  111 112 113  VIII  L I S T OF  TABLES  Table I  Page Parameter  list  sawblade u s e d la  List  of  II  Average inside  III  strain of  the  Change of  torsional  and  errors fL,T  tiltstress  of two  the  lowest  stationary lateral  frequencies differences  and for and  prestresses  related  69  72  tiltstress  for  experimental  blade  and  frequencies  the  natural  Values  and  39  relative  of  19  and  TSD  sawblade a t t h e  VI  the o u t s i d e  natural frequencies  function  differen  equipment  a t pos.E  natural  the  the 10  theoretical  Transmissibility  axial  at  blade  and  experiments  a b s o l u t e and  difference V  data  for  related  a  saw  i n s t r u m e n t a t i o n and  Values  as  the  i n the  experimental  IV  of  88 theoretical  natural errors  and  frequencies for  the  and  running 101  IX  L I S T OF FIGURES  FIGURES  Page  1  Bandsaw s e t up  2  Straining  3  D i m e n s i o n s o f t h e bandsaw  4  Straingage blade  5  system and t i l t a n g l e  location  7 8  on t h e  blade  and  support  loadcell  system  LC  under  of the  a  press  E n g i n e e r i n g UBC)  Calibration excitation  9  for  (mechanical 6  motor  dimensions  Calibration wheel  6  of  12  loadcell  f o r the  f o r c e 'of t h e e l e c t r o  magnet  with weights 7  Calibration  13 o f a #300  eddy-current  Bentley  displacement  Nevada  transducer  with a feelergage 8  Calibration  16  o f a #300  eddy-current  Bentley  displacement  Nevada  transducer  with a feelergage  17  9  Measurement c h a i n  18  10  Straingage  11  Average  positions  tensile  around  strain  direction  around  tiltangle  TA=0.06°  the  t h e saw  variation saw  28  i n x-'  for  a 32  X  12  Average  compresed  y-direction  13  14  15  TA=0.06°  Average  stress around  tiltangle  TA=1.33°  Average  strain  17  18  19  20  the  stress  variation  in x-direction  across  positions  a  between  between  = 0.60°, p o s i t i o n  different  TA  =  TA  = 0.06°, p o s i t i o n  A  prestresses  = 0.00°  42 across around  and  the blade the  saw,  C  43 across  positions  in x-direction  saw,  C  in x-direction  different  the blade  around the  positions  at  saw, 41  positions  1.33°, p o s i t i o n  position  around the  across  in x-direction  at  the blade  C  in x-direction  TA  TA  for  37  different  axial  x-  C and D  at  at  in  36  = 0.06°, p o s i t i o n  Stress  saw  variation  TA  Stress  a  34  different  Stress  for  33  at  Stress  saw  in  C and D  Average  Stress  the  distribution  direction  position 16  around  tiltangle  position  strain variation  the blade  around the  saw,  G  44 across E  the b l a d e  for different  SIG0(x),  tiltangle 45  XI  21a  Position  of  vibration 21b  Definition  RMS  of  the  and r e l a t e d  spectra  49  for  tiltstressstresses  24  function  of  sawblade  (magnetic  excitation  and  transfer  the  imaginary  Shift  of  different  natural  Tiltstress  54  for  RO*  55  sawblade a t 56 of  the  as a f u n c t i o n  of 60  RO*  differences  TSD  Lowest  lateral  different  lowest  and for  prestresses  2nd  the  sawblade  lateral  and v a r i o u s 31  sawblade  tiltangle  Lowest  for  of  difference  frequencies  30  the  frequencies  stationary  29  of  frequencies  axial prestresses  Transmissibility  the  52  53  26  27  )  function  Coherence of the s t a t i o n a r y  natural  51  stationary  part  25  27  and  sawblade  Transfer  Real  49  excitation  response of the s t a t i o n a r y 23  for  measurements  difference 22  instrumentation  torsional  natural  different  and v a r i o u s  axial  tiltstress 64  natural axial  frequencies prestresses  fL1 RO*  TSD natural  65 frequency  fL2 f o r .  XII  different various 32  Lowest for  axial  34  35  torsional  natural axial  lowest  fT2  for  RO*  and v a r i o u s  different  2nd  different  TSD  36 • 2nd  lateral  a function  prestress  as  39  of  frequencies  .the  and for 72  frequency•fL1  TSD  for  lateral natural  axial  o f t h e TSD  frequency for axial 74  natural  of  the  f r e q u e n c y fT1  TSD  for  axial  RO*  75  2nd  lowest  fT2  as a f u n c t i o n  torsional  natural  frequency  o f t h e TSD  for axial  RO*  76  transmissibility  for  torsional  73  a function  sawblade  68  natural  torsional  prestress  prestresses  RO*  prestress 38  axial  frequency  RO*  lowest  Lowest  natural  and RO*  fL2- as a f u n c t i o n  37  RO*  lowest  natural  prestress  prestresses  TSD  lateral  Lowest  fT1  67  torsional  and  frequency  TSD  2nd  as  and 66  different  1st  RO*  TSD  and v a r i o u s 33  prestresses  of  (measurement  f L 1 ) as  a  the  stationary  a t the  function  of  toothside RO*  for  XIII  different 40  for  for  for  for  for  fT1)  different 45  for  fT2)  different  of RO* f o r  of  the  stationary  a t the t o o t h s i d e  function  of RO* f o r 82  of  (measurement a  the  stationary  a t the backside  function  of  RO*  for  TSD  83 of  (measurement a  the  stationary  at the t o o t h s i d e  function  of  RO*  for  TSD  84 of  (measurement as  a  the at the  function  stationary backside of RO* f o r  TSD  85  transmissibility sawblade  46  a  transmissibility sawblade  backside  TSD  fT1) as  different 44  as  transmissibility sawblade  at the  function  (measurement  fL2) as  different  stationary  81  transmissibility sawblade  the  TSD  fL2)  different  43  a  transmissibility sawblade  of  (measurement  f L l ) as  different  42  80  transmissibility sawblade  41  TSD  of  (measurement as  a  the  stationary  at the t o o t h s i d e  function  of RO* f o r  TSD  transmissibility  . .86 of  the  stationary  XIV  sawblade for  (measurement  fT2) as  different  a  at the  function  of  backside RO*  for  TSD  87  47  Mode s h a p e s o f t h e s t a t i o n a r y sawblade  48  Natural blade RO*,  49  for different c = 40.7  Natural blade RO*,  50  Natural  R0*,  frequencies  fL1 of t h e axial  running  prestresses 96  frequencies  fL2 of the axial  running  prestresses 97  frequencies for different  c = 40.7  Natural blade  fT1 of t h e axial  running  prestresses  m/s  98  frequencies  for different  f T 2 of t h e axial  running  prestresses  c = 40.7 m/s  Non  uniform  the  blade  tiltangle 53b  prestresses  c = 40.7 m/s  blade  53a  running  95  for different  Natural  R0*,  axial  the  c = 40.7 m/s  RO*,  52  of  m/s  for different  blade  51  frequencies  Change  a  function  across of  the  TA  of s t r a i n  tiltangle  99  stress distribution as  TA  90  110 as a f u n c t i o n of  the 110  NOMENCLATURE  A  = cross  section  of the blade  BO  = width of the blade  B  = total  Bw  = w i d t h o f bandsaw  wheel  Bs  = distance  between  straingage  Bt  = distance  center  from t o o t h  gullet  to backside  width of blade  tiltangle  l o c a t i o n SG1 a n d SG7  o f t o p wheel t o p o i n t o f  rotation  cO  = wave v e l o c i t y  c  = sawblade v e l o c i t y  D  = band  fL1  = 1. l a t e r a l  natural  frequency  fL2  = 2. l a t e r a l  natural  frequency  fTl  = 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  flexural  Fvert=vertical  rigidity  modulus cutting  3  2  v  of e l a s t i c i t y force  cutting  =(EH /12(1- ))  (in x-direction)  Flat  = lateral  force  ( i n z-direction)  Fhor  = horizontal cutting  fc  = height  G  = s h e a r modulus  g  = gravitational acceleration  H'  = band  Ks  = wheel s u p p o r t  L  = band l e n g t h  force  (in y-direction)  o f crown of e l a s t i c i t y  thickness system  between  stiffness guides  Lw  = distance  between c e n t e r  of  rotation  of  saw  wheels  n  = number of  2R0  = total  RO*  = axial  r  = radius  rc  = crown  s  = standard  data  axial  samples  prestressing  force  prestress of  saw  wheels  radius deviation  SIGO(x) = axial  prestress  SIGb(x) = bending  stress  due  to  r  stress  due  to  crown  SIGc(y) = bending SIGf(x) = stress  due  to c e n t r i f u g a l  due  to  due  to  = stress  due  to  = stress  in  forces  SIGn(x) = stress  the  notch  factor  at  the  teeth SIGr(x) = stress  pretensioning  SIGta(x) the  tiltangle  SIG(x) x-direction  SIGtemp(x) = s t r e s s  due  to  temperature  changes  blade  XVII  SIGw(x) = stress  due  to  cutting  T  =  transmissibility  t  =  temperature  TA  =  tiltangle  u  =  feedspeed  u  = mean v a l u e  Z  = tooth  a  = temperature  v  = Poison's  K  = wheel  p  =  n  = support  of  forces  n data values  x  spacing  gradient  ratio  support  stiffness  factor  density stiffness  constant  (H = 1 K ) -  1  1 INTRODUCTION  1.1  Background  Due  to  the  products  industry  of  influence  the  cutting  rising  cost  o f lumber  i n the f o r e s t  t h e need  of a  thorough  understanding  of  performance  the of  governing parameters  the  bandsaw  has  on t h e  become  a  necessity. To  achieve  laboratory  was  Engineering consisting together and  this  s e t up a t t h e  at of  with  objective,  the a  Department  University  vertical  i n 1981 a w o o d c u t t i n g  5  of  of  Mechanical  British  foot  Columbia,  production  a s p e c i a l l y designed log carriage  a sophisticated  instrumentation  bandsaw system  and d a t a a c q u i s i t i o n  system. The  parameters  governing  the  performance  of  bandsaw c a n be s e p a r a t e d i n t o t h r e e d i f f e r e n t g r o u p s :  a) human i n f l u e n c e operator  factors  chooses  parameters  ( i . e . The bandsaw  certain  bandsaw  by e x p e r i e n c e )  b) d e s i g n p a r a m e t e r s  established  by t h e bandsaw  designer c) s t o c h a s t i c  influence  inhomogenities  i n the  f a c t o r s (e.g. lumber,  a  temperature changes, The of  objective  of  study  parameters c h a r a c t e r i z e d  stress  distribution  vibrational  1.2  first  stationary  and  the  tiltangle around  the  The of  the  part  and  axial  The  prestress of the  (Figure  the  measured  sawblade,  lowest  and  on  the  The the  strain  were  measurements  of  which  , the  blade around  of  were  tiltangle  the  the  of  saw.  top  The wheel  v i b r a t i o n measurements  excited and  w i t h an  torsional  for various  different tiltstress  tiltangle  experiments  SIGO(x)  lateral  were m e a s u r e d  at  sawblade  3).  stationary  quantities.  the  rotation  consisted  the  on  parameters  axial  differences  a different representation for  1.b)  parts:  sawblade.  z-axis  frequencies  and  the  c o n s i s t s of  describes  two  1.a)  influence  saw.  second part  magnet. The  RO*  the  major  position  TA  the  objective  part  c h a n g e d were the TA  under  in of  this  i n t o three  The  i s t o examine t h e  aims  achieve  divided  the  behaviour  Experimental  To  and  this  etc.)  f o r the  were c h o s e n  transmissibility previously  to of  axial  the  identified  natural  prestresses  TSD.  allow  electro  In  this  prestress normalized blade  was  natural  frequencies  for  tiltstress  differences  The t h i r d vibration different stiffness  1.3  different  of  THUNELL  In 1971  in this  in  to  a  solutions.  measured  wheel  support  have  covered  [19]  PORTER  In 1972  results. effect  In  experimental the  e a c h o t h e r . He  1981 study  of  also  blades  to  in  idling  a  and  experiments  his results [13,14]  blades  wheel  [21]  stresses  behaviour^  1970  and  with  analysed compared  In 1977 KIRBACH and BONACH  TANAKA on  In  stresses  did stress  PAHLITSCH  s t r e s s e s i n bandsaw  the  study.  calculate  on t h e n a t u r a l f r e q u e n c i e s  sawblade.  at  publication . various  s a w b l a d e and compared  them t o e x p e r i m e n t a l  these  done  t o t h e g e o m e t r y of t h e saw,  the d i f f e r e n t  of  The  sawblade  researchers  summarized  with a stationary  comparing  RO*.  various  formulae  cutting.  tensioning  running  measured.  experiments  [22,23]  s a w b l a d e due  [7]  and  research  the  analytical  free  (MOTE [ 9 ] ) was  mathematical  to  of a  prestresses  Over t h e y e a r s some  RO*  p a r t of t h e r e s e a r c h p r o g r a m c o n s i s t e d o f  axial  Previous  prestresses  TSD.  measurements  Ks  axial  of f i v e  examined the for stationary  in  tilting of did  a  and  stationary  an  extensive  bandsaw  different vibrational  saw  blades  blades  with  behaviour  and r u n n i n g c o n d i t i o n s  and  compared them t o a n a l y t i c a l In  the  presented natural  20  analytical  the  vibrations  of  a  experimental  model  analytical were  used.  a  solutions  solutions,  KANAUCHI'S  ALSPAUGH'S  years  analytical  frequencies  compare  and  last  solutions. number to  running data  of  lateral  solution  researchers  t r y to p r e d i c t the bandsaw  MOTE'S f l e x i b l e for  of  this  blade. study  band s o l u t i o n vibrations  [2]  for  To with [9]  [ 2 1 ] and torsional  2 EXPERIMENTAL SET  2.1  Band saw  For  Figure  facilities  the  vertical  5  1).  straining  experiments  production  The  saw  prestressing  the  be  region,  2R0  tilted can  a l o g by the  is  bandmill  equipped  =  by an be  the  saw.  idling  was  with  study  used a  Above  blade  (see  an  axial The  is  below  guided  cutting  top  ( F i g u r e 2)  towards a c a r r i e r and  by  the blade  a  hydraulic  provide  e l e c t r o motor  and  this  45000 N t o 90000 N.  positioned  bandsaw  guides. During  in  ( F i g u r e 2) w h i c h can  force  whole saw  passes  presented  foot  system  wheel can  UP  and which  the  cutting  two  pressure  i s cooled  by  waterjets. The blade  saw  w i t h an  dimensions and  and  equipped  unknown  with  internal  the chosen  the b l a d e a r e  listed  2.2  was  in Table  shown  arm  temperature  transducer  will  stress  bandsaw  distribution.  i n F i g u r e s 3 and  The  f o r the  4 and  are  saw also  I.  Instrumentation  the h y d r a u l i c  pretensioned  c o o r d i n a t e system  and  data a c q u i s i t i o n  To measure t h e a x i a l in  a  straining  prestressing system  was  force  2R0,  equipped  compensated  straingage  be  t o as  referred  system link  with a  bridge.  "loadcell"  a  or  4-  This "LC".  top guide  instrumentation frame electromagne 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 MOTOR  SYSTEM  AND  TILTANGLE  8  FIGURE 3 DIMENSIONS OF THE  BANDSAW  Bo -  H = 1.651  J  ~  B  mm  Z =44.375 mm B = 242.  mm  B = 260.  mm  a  FIGURE  4  STRAINGAGE  LOCATION ON THE  BLADE  10  AO = 398.7  mm  cross-section  BO = 241.5 mm  width to  B  = 260 mm  area  of the blade  of the blade from  backside  gullet.  total  width  Bw = 228.6 mm  width  o f wheel  Bs  = 222 mm  distance  between SG1 a n d SG7  Bt  = 222.3  distance  between LC a n d c e n t e r  mm  of  wheel  blade  m/s  of blade  velocity  c  =40.7  D  = 86347  E  =  fc  = 0.102 mm  G  = 80000 N/mm  modulus o f e l a s t i c i t y  H  = 1.651 mm  t h i c k n e s s of blade  Ks  = 825  support  L  = 762 mm  flexural  Nmm  2.1*l0 N/mm 5  2  N/mm  Lw = 2464  Young's modulus height  2  blade  o f crown  stiffness  l e n g t h between g u i d e s  distance  mm  regidity  between saw w h e e l  r  = 762.5 mm  radius  o f bandsaw  rc  = 64 m  radius  o f bandsaw crown  t  = 19 mm  overhang  Z  = 44.23  Table I  tooth  mm  Parameter used  list  wheels  of pressure  spacing  f o r t h e saw  i n the experiments  guides  axes  The  calibration  curve  standard  deviation  confidence  value  The with  factor  /degree  digits/degree below a r e  and  the  error  o f t h e t o p wheel  calibrated  calibration digits  s  LC i n c l u d i n g bounds  of 95% a r e shown i n F i g u r e  tiltangle  a  f o r the l o a d c e l l  digital of  counter  the  tilt,  could  instrumentation  in  be  used  in  9  measured  counter  a standard  Figure  a  5.  and  is  675  d e v i a t i o n of 59  f o r n=lO. The measurement c h a i n s  shown  for  ( s e e F i g u r e 2 ) . The  tiltangle  with  the  the  described  equipment  and  the experiments are l i s t e d i n  Table l a . To two  measure s t a t i c  different  and  dynamic  as w e l l  measurement  strain  as  dynamic  s y s t e m s were u s e d . F o r  measurements,  9  c e m e n t e d on t h e o u t s i d e of t h e b l a d e some 1,4  experiments and  7  on  quantities,  straingages (see F i g u r e  the  inside  of  the  blade.  f o r these  NEFF  signal  c o n d i t i o n e r which p r o v i d e d  as  supply  individual  into  a NEFF  and b r i d g e  bridge  simultaneously.  The  fixed  digital  conversion  values  for  conditioned converter  were t h e n  each  up  to  64  as w e l l channels  s i g n a l s were then f e d and  channel.  multiplexed  constant  resistors  amplifier  and programmable a m p l i f i c a t i o n for  data  s t r a i n g a g e s c o n s i s t e d of a  completion  balancing  620/100 A/D  provided  data  4). For  The  system  voltage  were  3 s t r a i n g a g e s were mounted a t p o s i t i o n  acquisition 620/300  static  and  The sent  and  which analog  digitalized from  the.  0  5  10  15  20  25  30  35 LOAD  FIGURE  5  CALIBRATION S Y S T E M UNDER  FOR L O A D C E L L A PRESS  LC  OF  40 C  3  3  THE  CMECHANICAL  45  50  N> WHEEL  SUPPORT  ENGINEERING  UBO  55  60  0  10  20  30  40 LOAD  FIGURE  6  CALIBRATION  OF  ELECTROMAGNET  LOADCELL WITH  FOR  WEIGHTS  50  60  70  CN> THE  EXCITATION  FORCE  OF  THE  laboratory  through  a  NEFF  t o a PDP  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  intelligent  on  allowed  digital  plotter.  to  make  scanning  program  dimensional straingage  these  blade  and t h e  compiles  calibration  with  a  r a t e and s t o r e s  using  the  in  static  two-  blade  from  around  the  the  positions  from  p r o g r a m DYN c a l c u l a t e s  t h e s t r a i n g a g e s on t h e previously  established  the s t r e s s  distribution  from  straingage readings  during  a  chosen  duration. For  vibration  measurements  acquisition  s y s t e m was u s e d .  an  magnet. The e x c i t a t i o n  by  n channels  files.  distribution  loadcell,  a  a r e documented i n  calculates  the data  on  factors.  the blade  time  data  results  system, v a r i o u s  and s a m p l i n g  readings at d i f f e r e n t  It  in  STRAIN  stress  saw.  The  frequency  in user-specified  The  graphing  hardcopies  To r u n t h i s  APPENDIX I V . The p r o g r a m NEFF2 s c a n s  the data  The  through  one t o view t h e e x p e r i m e n t a l  FORTRAN p r o g r a m s were d e v e l o p e d ;  chosen  processing.  t o t h e PDP 11-34. S o f t w a r e  the T e k t r o n i x screen and  connected  data  T e k t r o n i x 4051 t e r m i n a l i n t h e l a b o r a t o r y  w h i c h was i n t e r f a c e d facilities  for  processing  unit  an  11-34 computer  620/500 c o n t r o l  electro  a B r u e l and K j a e r  power a m p l i f i e r  The b l a d e  frequency  and f e d i n t o  a  different  data  was e x c i t e d  with  c u r r e n t was  generator, the  electro  generated  amplified  by a  magnet.  The  magnet  was  dimensional between was  guides.  measured  with  by  error  bounds  Figure  6.  Vibrations  curves and  Dual  and  amplifier.  95%  response  signals  deviation value  and  the  i s shown i n  Their  were  to accept  2 non  calibration  fed  into  then  the necessary  calculate  the  the  two  a  660A  method o f d o c u m e n t a t i o n frequency  analyser  the T e k t r o n i x  and  into  to  function,  the  coherence  R e s u l t s c o u l d be  out onto  was  calibration  transfer  channels.  on a s c r e e n and be p l o t t e d  plotter.  curve  C h a n n e l F r e q u e n c y A n a l y z e r . The a n a l y s e r  between  them o u t w i t h  The c a l i b r a t i o n  i n F i g u r e 7 and 8. B o t h t h e e x c i t a t i o n  function  the  and  transducers.  spectrum  from  blade  o f t h e s a w b l a d e were m e a s u r e d w i t h  RMS  second  the  loadcell  confidence  transmissibility,  shown  behind  a three-  f o r c e o f t h e magnet  i t s standard a  be programmed  factors  o f t h e magnet  piezo-electric  eddy-current  the blade  could  with  a r e shown  Nicolett  a  for  a frame w h i c h a l l o w e d  The e x c i t a t i o n  a charge  the l o a d c e l l  contacting  in  positioning  the  amplified of  mounted  a hard  enter  copy. A  the  data  t h e PDP11-34 and p l o t  terminal  and  the  digital  ,1 /  SENSITIVITY-  0 . 3 4 4 mm/V  IN  FROM  THE RANGE  1mm TO 2 . 7 5 m m  P R O B E #1 I  = DATA RANGE FOR A CONFIDENCE RANGE O F 95%, n = 3 I~ ~  1  2  M ENT  OF #399  PROBE WITH A  ~  3 GAP  CALIBRATION  ~  ! 4  "  ~  — " I 5  6  CMM?  BENTLEY  NEVADA  FEELERGAGE  EDDY--CURRENT  DISPLACE-  10  P  R 0 X I M I T 0 R  0 U T P U T  8  J  6  J  S E N S I T I V I T Y = - 0 . 3 6 mm/V  4 J  I N THE RANGE FROM 1mm TO 2 . 7 5 TO 2.75mm  2  PROBE #2  J  0 0  1  2  I  « DATA RANGE FOR A CONFIDENCE RANGE OF 95%, n «= 3  T 3  T  4  5  6  GAP CmnO FIGURE 8  C A L I B R A T I O N OF # 3 0 0 B E N T L E Y NEVADA MENT PROBE WITH A F E E L E R G A G E  EDDY-CURRENT  DISPLACE-  /  Signal Conditioner  ©  /  7—  /  Sample and Hold A/0 Converter  ®  Main frame Computer  FIGURE  9  MEASUREMENT  amplifier  Data  I/O  System  CHAINS I—'  oo ••  1  f o u r arm s t r a i n g a g e EA-06-125AD-120,  loadcell,  K=2.065,  120Ohms  2  piezo-electric  loadcell,  3  9 straingages,  Kiowa KFC-5-c1.11, K=2.10  4  2 non-contacting Bentley  eddy c u r r e n t  2 proximitors, Bentley  6  electro  7  NEFF 620/300 s i g n a l  8  NEFF 620/100 a m p l i f i e r  9  NEFF 620/500 d e m u t i p l e x o r  Nevada  conditioner a n d A/D  converter  and d a t a  storage  11/34 m a i n f r a m e c o m p u t e r Terminal  12 TEKTRONIX  digital  4051 plotter  13 s i n e - r a n d o m g e n e r a t o r , 14 660A d u a l  channel  15 c h a r g e a m p l i f i e r  Ia  probes,  magnet  11 TEKTRONIX  Table  + Kjaer  Nevada  5  10 PDP  Bruel  L I S T OF  4662  Bruel + Kjaer  analyser, 504D,  Nicholet  Kistler  INSTRUMENTATION AND  EQUIPMENT  3 THEORETICAL STRESS EVALUATION FOR  3.1  Fundamental  bandsaw  different  blade  stresses  while  c u t t i n g . To  and  prestress  in  bandsaw  during  wheels  top  to  wheel  to  t h e b l a d e , non  of  the  the  pre-tensioning  concentration During  force  tiltangle  cutting  to c e n t r i f u g a l f o r c e s ,  stresses  r e s u l t i n g from  in  stresses the  acting  following  static  during  by This  of  idling on  the axial  forcing  the  force  results  the  blade.  across  e x i s t due  of  to the  the w h e e l s ,  done t o t h e b l a d e  a t t h e g u l l e t of and  variety  stress d i s t r i b u t i o n across  subject  The  2R0.  stresses  (rolling)  idling  a  s t i f f n e s s an  the blade  t h i s constant  wheels,  blade  distribution  constant  to  keep t h e b l a d e p o s i t i o n e d  increase  stress  subject  i t is stationary,  upwards w i t h a  a constant  the  is  SIGO i s imposed on  Additional  of  stress calculation for a  blade  The  and  t h e o r y of  A BANDSAW BLADE  the  t h e amount and  stress  teeth.  the blade  furthermore  temperature  the c u t t i n g  crown  stresses  is and  forces.  i n a bandsaw b l a d e can  be  classified  way:  stresses - a x i a l s t r e s s SIGO(x) due t o a x i a l p r e s t r e s s i n g f o r c e 2R0 - b e n d i n g s t r e s s S I G b ( x ) due t o b e n d i n g of t h e blade over the wheels - s t r e s s S I G c ( y ) due t o crown of t h e w h e e l s - s t r e s s S I G t a ( x ) due t o t h e t i l t a n g l e of t h e t o p wheel  21  - s t r e s s S I G n ( x ) due t o t h e n o t c h f a c t o r o f the b l a d e t e e t h - s t r e s s S I G r ( x ) due t o p r e - t e n s i o n i n g of t h e blade additional stresses during idling - s t r e s s S I G f ( x ) due t o c e n t r i f u g a l  forces  additional stresses during cutting - s t r e s s SIGw(x) due t o t h e c u t t n g f o r c e s - s t r e s s SIGtemp(x) due t o t e m p e r a t u r e c h a n g e s  3.2 S t a t i c 3.2.1  stress"for  Axial  prestress  prestressing  The 2R0.  the s t a t i o n a r y  force  SIGO(x) due t o t h e a x i a l  2R0  axial prestress  Using  the cross  SIGO(x) i s c a u s e d  section  axial  gullet  and  prestress  H  is  2R0  bandsaw  the backside  to  the t h i c k n e s s of the blade, the from:  1 B0*H  stress  S I G b ( x ) due t o t h e r a d i u s  r of the  wheels  The blade  force  * 2  3.2.2 B e n d i n g  from  SIGO(x) c a n be c a l c u l a t e d  SIGO(x) =  by t h e  a r e a A0=B0*H o f t h e b l a d e ,  where BO i s t h e w i d t h o f t h e b l a d e the  blade  stress  over  SIGb(x),  the  resulting  cylindrical  w h i c h c a n be c a l c u l a t e d E  from: H  SIGb(x) =  * 1-v  2  2r  from b e n d i n g  wheels r e s u l t s  in a  of  the  stress  W i t h E=Young's modulus, v = P o i s o n ' s the  bandsaw  For  the  r a t i o and r - r a d i u s of  wheels.  saw  used  in  these  experiments  this  stress  component amounts t o : SIGb(x)  3.2.3  2  Stress Under  crown  = 250N/mm  S I G c ( y ) due t o crown o f t h e w h e e l s the  follows  assumption  that  the  a c i r c u l a r a r c of radius  S I G c ( y ) c a n be c a l c u l a t e d  curvature  of the  r c , the  stress  from:  H 1 v * - (-—+ — ) 2 1-v 2 rc r E  SiGc(y)  =  with  r c = r a d i u s o f crown,  Again  f o r o u r saw t h i s  results  '1*2. 1*1u N/mm 5  SIGc(y) =  1-0.3  2  i n a 'maximum stress:  1.675mm: 2  2  2  _1 1  .  0.3 ) = 79 N/mm  2  64*10 mm 3  3.2.4  Stress Using  support  762.5mm  SIGta(x) as a f u n c t i o n  of the t i l t  the geometric r e l a t i o n s h i p  and the t i l t  system  of the  top  wheel  ( s e e APPENDIX I ) t h e s t r e s s  SIGta(x)  due  position  can  to be  the  tiltangle  caculated  (straingage  of  L w = d i s t a n c e between wheel  3.2.5  S t r e s s S I G n ( x ) due  blade  teeth  Photoelastic  can  [19])  reach  authors  1.3  to the  2.0  KRILOV for  gullets factor  by  other  [8] c i t e s  a value  f a c t o r of  of  1.35  for  tension.  S I G r ( x ) due  to p r e t e n s i o n i n g  measurement  i n t o a blade  during  Therefore  the  deflected  blade  in  pretensioning.  of  the  the  x and  the  pretensioning the  blade stresses  process  is  shape  of  y - d i r e c t i o n i s measured  a measure of  Nevertheless  some r e s e a r c h e r s .  of  inplane  i n many s a w m i l l s  ( l i g h t - g a p method) t o o b t a i n  by  Studies  reports a stress concentration  direct  taken  shaped  results:  difficult.  been  elliptical  the  t o 2.5.  Stress  the  f a c t o r of  2.0  very  of  notch  a m a g n i t u d e of  while  and  axes.  stress concentration  t o 2.5  induced  (degrees)  the  [22]  The  topwheel  show t h a t  b e n d i n g and  3.2.6  the  s t u d i e s of  show s i m i l a r  .SUGIHARA  position)  Lw  TA=tiltangle  (PORTER  straingage  *TA*E* 180  where'  each  from:  IT SIGta(x) =  for  KRILOV  the  influence  measurements have [8]  reports  that  the  stress  70N/mm  SIGr(x)  while  2  SIGr=65N/mm Of  BAJKOWSKJ with  2  up t o 550N/mm  2  3.3  Additional  3.3.1  Stress The  during  reaches  (PAHLITSCH  centrifugal  forces  result  w i t h p =mass d e n s i t y  of  a  o f 30 t o  tensile  compressive  stress  stress zones  [13]).  during  idling  which  forces  a c t on  the  blade  in a stress:  SIGf(x) = P * c  the  measures  intermittend  stresses  tensile level  S I G f ( x ) due t o c e n t r i f u g a l  running  During  a  2  of t h e blade  experiments  c = 40.7m/s, w h i c h  t h e bandsaw r a n w i t h a v e l o c i t y  results  in  a  stress  SIGf(x)  =  15.8N/mm . 2  3.4  3.4.1  Additional  Stress Up  to  stresses  and  that  cutting  SIGw(x) due t o t h e c u t t i n g date  very  been done c o n c e r n i n g reports  during  little  forces  experimental  the c u t t i n g  forces.  under e x t r e m e c o n d i t i o n s  d e p t h o f c u t i s 300mm) a c u t t i n g  r e s e a r c h has  FEOKTISKOV [ 1 3 ]  (c=45m/s, force  u=1m/s  Flat=900N can  be  reached.  unfavorable neglible axial  calculated  conditions  compared  to  pretensioning  blade  over  stresses  SIG(x)  the  force  [ 1 3 ] ) . KRILOV  stresses  The  such  stresses  are  r e s u l t i n g from t h e bending  same  forces  the c u t t i n g  of the  c a n be s a i d f o r  [8] d e t e r m i n e s  from  under  Flat  that  and Fhor  the  forces  stress  can reach  o f up t o 7N/mm  2  Stress  average cutting  SIGtemp(x) due t o t e m p e r a t u r e  temperature  MOVI  change  difference  (1953 [ 2 2 ] ) shows  speed  (assuming  r e s u l t i n a temperature SIGtemp =  changes an  i n t h e b l a d e of 45° C d u r i n g  m o i s t wood w i t h a f e e d  temperature  would  resulting  .  A s t u d y by SAITO a n d  a  even  2R0 a n d from  the wheels.  resulting  levels  the  that  r e s u l t i n g from t h e c u t t i n g  (PAHLITSCH  3.4.2  He  o f u=0.47m/s. rigid  Such  wheelsupports)  stress of:  E*at*(t2-t1) 11 *1 0 = 2. 1*1u N/mm * *45deg = l04N/mm deg 6  5  with  at=linear  coefficient  (t2-t1)=temperature  This  shows t h a t  significant  change  2  of expansion, i n the blade  a temperature  influence  2  change  i n t h e b l a d e has a  on t h e sum o f t h e a x i a l  stresses  acting in a bandsaw blade.  4 STATIC STRESS-STRAIN  MEASUREMENTS WITH A STATIONARY SAWBLADE  4.1  Experimental  Using chapter were  the  2,  procedure  instrumentation  strain  measurements  taken,  while  changing  i)  axial  p r e s t r e s s SIGO  ii)  tiltangle  iii)  position  of  location  around  the  to  N.  a r e shown To  of  t h e f o l l o w i n g saw p a r a m e t e r s :  the  position  saw  i n Figure the  x  +  v e  y  straingage  b y r o t a t i n g the  The c h o s e n  stresses  law was u s e d  ( e  the  straingage  10 and a r e l a b e l l e d  P l a t e s " [24])  a  of  was a c h i e v e d  t h e bandsaw.  calculate  measurements Hooke's  x and y - d i r e c t i o n s  t o t h e bandsaw  change  positions  in  o f t h e s t r a i n g a g e s on t h e b l a d e  The  by hand a r o u n d  in  described  o f t h e t o p wheel  relative  blade  set-up  }  from  the  (TIMOSHENKO,  from A strain "Theory  /  FIGURE  10 STRAINGAGE  POSITIONS AROUND THE SAW  All and  measurements  represented  s t r e s s e s w h i c h were imposed  straingages  to  configuration  of the blade  straining  determine  onto the blade  the i n i t i a l (due  e t c . of the blade)  the  to  accurately,  before  e a c h e x p e r i m e n t . T h i s was done  common mode v o l t a g e  stress  welding,  straingages  strains had t o be to  on  the  balanced  minimize  the  i n t h e NEFF  To  could  be  signal  during  each experiment. 2R0  direction experiment bending  to  strains  the  straingage  that  experiment  exist,  preload  of  the  a t p o s i t o n E would d e f l e c t  i n y-  and once  the  experiments,  had t o be i d e n t i c a l f o r that without  shape This  i n the straingages  identical  the  axial  experiment.  readings,  of  any  deflected  straingages  change  the g u i d e s ) .  repeatable  I t was o b s e r v e d  the  the  E (between  of the blade  the blade  and  for  an e x p e r i m e n t . The s t r a i n g a g e s  t o perform  conditions  preload  used  at position  be a b l e  inital  of t h e s t r a i n g a g e  before  range of t h e a n a l o g / d i g i t a l c o n v e r t e r  were b a l a n c e d  axial  in-plane  so t h a t t h e  system  assure  these  signal  straingage  of  a f t e r the  rolling,  measure  blade  100  strains  w h i c h were p r e s e n t  e x p e r i m e n t s were done. To  whole  reflect  were a p p l i e d . I t i s n o t p o s s i b l e from  measurements  the  here only  in  blade  conditions blade  was  2R0=2700N/mm  2  vary  deflection during  results the  would  the  an is  from  induces balancing  e r r o r of the strained.  To  experiment t o  prestrained before  from  with  balancing.  an This  procedure  results  in identical  initial  t h e b a l a n c i n g of t h e  straingages  While  strain  the  average  experiments it  does  i s not reduce  distribution During  by  this  slope  of  a c r o s s the b l a d e  due  the  the  for  level  effected  experiments  conditions during each  of t h e b l a d e  between  prestraining  force,  the  it  experiment.  measured  strain  to a t i l t a n g l e  change.  was  found  that  the  average  strain  measured on  t h e o u t s i d e of t h e b l a d e  a factor  of  higher  the c o r r e s p o n d i n g  level  1.3  calculated  experiments the  inside  measured smaller  by  mounted on performed position  the  were of  the  a  even  loadcell  and  strain  on  factor  of  from  the  inside position  LC.  E  an  saw).  of  the  blade  (between the  from  found  inside than  the  w i t h a p r e l o a d of  to  was  Experiments  of  ( a t t h e back of  although  straight.  the  readings  prestrain LC.  The  s t r a i n g a g e s mounted  it  1.1  s t r a i n g a g e s , there are  blade  with  blade  level  at L  the  repeated  average  prestrain  that  from  than  was  that  on the  the blade  was  corresponding  with  straingages  could  only  the g u i d e s ) These  be  and  results  at  show  2700 N d u r i n g b a l a n c i n g of  still  observer  bending  effects  in  the b l a d e appears  the to  be  31  4.2  Stress-strain  measurements w i t h a  stationary  sawblade  In  F i g u r e 11  outside  and  12  of the b l a d e  positions  around  the  i n x and the  straingages  position  L the average  of  t h e b l a d e have  been  between  the  (straight  b l a d e ) and  in  bending  409  =1125  bending  of  for  over  bending  1187  the p o s i t i o n s ,  where t h e  the  0.60°  The  microstrain  and  have  1.33°.  respectively  or a  inside  difference E  and  L  blade to  is  1534  -  3.2.2  difference for  differences  microstrains  and  experimental  the  For  repeated  strain  1168  out.  chapter  been  The  the  s t r a i n value for  t h e w h e e l s from  1191  and  amounts  theoretical  the wheels a r e  microstrain  the results  and  differences are  1.9%  0.3%. The  average  s t r e s s - d i s t r i b u t i o n in x-direction  t h e o u t s i d e of t h e b l a d e the of  wheels  measurements  between t h e o r e t i c a l and  position  strains  i n a v a l u e of  of  s t r a i n l e v e l s on  at  over  tiltangles  plotted  strain  average  These  been  the  over  The  microstrain.  5.5%.  have  on  for different  averaged  added.  of t h e b l a d e o v e r  results  levels  y-direction  saw,  corresponding E and  strain  s t r a i n data axial  over  the  stress saw  i n F i g u r e 13  i n F i g u r e 11 the b l a d e wheels.  and  12 and  undergoes, As  is calculated  described  shows t h e while  on  from  change  travelling  in chapter  3 the  2000  T E N S I L E M I C R 0 S T R A I N  1750 1500  * — * BLADE OUTSIDE Q BLADE INSIDE  J  PRESTRESS SIG0Cx>»e57.dN/mm2 RESTRAIN MEPSCx>«322 £ H  J  1250 A  1000 J H  C  ll  •E  750  J  +  •0  /  500 J  MEPSCX} 250  J  B  A  0  FIGURE 1 1  T 0  —r-  c  T  1  D E F  -  1 —  6  H — j —  T  -  L  K  T  POS.  M  N  j —  2000  6000 8000 4000 , i STRAINGAGE POSITION AROUND THE SAW Cmm> AVERAGE TENSILE STRAIN VARIATION IN X-DIRECTION AROUND FOR A TILTANGLE TA«0.06° 00  2080 C 0 M P R E S S I  1750  _  1500  _  1250  _  1000  _  750  „  V  E M I C R 0 S T R A I  N  500  A  A  BLADE  OUTSIDE  PRESTRESS PRESTRAIN  SIG0Cx>=67.6N/mm2 MEPSCx ) = 3 2 2 ^ £  POS. A  B  D  E  F  H  L  M  N  250  0  J  T 0  2000  4000 STRAINGAGE  FIGURE  12  AVERAGE AROUND  COMPRESSIVE  STRAIN  6000  8000  P O S I T I O N AROUND VARIATION  T H E SAW F O R A T I L T A N G L E  IN  T H E SAW  CmiO  Y-DIRECTION  TA=0.06° U)  (jO  500  A  —  Q  A  400  S T R E S S  <  B L A D E OUTSIDE BLADE INSIDE B C D E F  PRESTRESS S I G 0 < x » = 6 7 . 6  A  i  i  1—i—i  G  1  H  I  i  i  J  i  K  N/mm  L  i  2  M  i  N  «  •  300  200  CN/mm^V 100  0  n  ; 0  r  1  2000  1  4000  13  AVERAGE FOR  STRESS DISTRIBUTION  A TILTANGLE  OF  TA=0.06°  1  6000  STRAINGAGE FIGURE  ;  IN  POSITION  8000  AROUND  X-DIRECTION  1  T H E SAW CmnO  AROUND  T H E SAW  stress  in  consists  the  blade  mainly  passing  over  the  o f t h e sum o f t h e s t r e s s e s  SIGb(x).  The s t r e s s  amounts  to  values  while  c h a n g e s between  255N/mm  f o r bending  over  t h e wheels  SIGO(x) a n d  position  which agrees  2  well  wheels  E  and  A  with the s t r e s s  from  chapter  3.2.2 o f  250N/mm  2  Figure changes away  on  from  the  TA=0.60°.  of the  damaging position  outside  the  which  direction  is  slightly  Going  from  direction  geometric  of 15  Figure  14.  reached  are  the  D  t o C3, i t r e a c h e s  -  o f 19  at  the  the  position  strain  i n xthen  guide. i n x-  microstrain/mm.  The  At  increases with a values  in  strain  data  in  in x-direction  drops  at a  from  stress  upper  C3 t h e s t r a i n  in y-direction  o f 5N/mm /mm w h i l e t h e b l a d e 2  that  C3,  microstrain/mm.  While  t h e b l a d e and  a c o n s t a n t v a l u e which  at a rate  calculated  l o c a t i o n of  i n F i g u r e 6. C3  between  C1 t o p o s i t i o n  the s t r a i n  0.61  from  up t o p o s i t i o n  decreases  Figure  C1  away  position  same t i m e  rate  without  The  has almost  raises  rate  performed  straingages.  35mm  a  on t h e  be  I t c a n be o b s e r v e d  for  strains  not  the exact contact point  strain  i t travels  zone  could  t h e bandsaw w h e e l .  the  of  C1 t o C5 and X1 t o X7 a r e shown  represents  C5,  contacting  Measurements  blade  r e s u l t s of  of the blade while  the wheel-blade  tiltangle inside  14 shows t h e e x p e r i m e n t a l  the  stress  travels  a minimum o f 85N/mm  2  from  position  a t p o s i t i o n X4  2000  1750  J  . B  ~* TENSILE STRAIN IN X - D I R E C T I O N , BLADE OUTSIDE BCOMPRESSIVE STRAIN IN Y - D I R E C T I O N , BLADE OUTSIDE  1500 M I C R 0 s T R A I N  1250  J AXIAL  PRESTRESS  SIG0Cx!>=70N/W  1000  750  J  500  250  C5  XI  X2 A  X3 A  X4  X5 —-a*>  -B-  -B-  XS A  X7 A  -B-  -B-  D  J  •0"  -B-  -B  0 0  100  200  300  STRAINGAGE FIGURE  14  STRAIN  VARIATION  Z O N E AND G U I D E } ,  400  POSITIONS  T  T  T  500  603  700  BETWEEN P O S .  BETWEEN P O S I T I O N TILTANGLE  C AND D  C AND D  800 (mm)  CBETWEEN  CONTACT  TA=0.60° U)  580  400  J A  C  S T R E S S  300  J  200  J  1  B  — * STRESS B STRESS  IN IN  AX.  X-DIRECTION , Y-DIRECTION , PRESTRESS  BLADE BLADE  OUTSIDE OUTSIDE  SIG0<x>=70.0N/mm  2  CN/mm > 2  100  C5  XI  X2  X3  X4  A  A  A-  X5 X6 -h —h  D -A  X7 A—  SIGOCx) 0  J 0  FIGURE  15  • 100  200  -.  B  300 400 500 600 700 800 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)  AVERAGE  STRESS  CONTACT  ZONE  VARIATION  AND G U I D E ; ,  BETWEEN TILTANGLE  POSITION TA  =  C AND D  0.60°  CBETWEEN  compared The  t o an  stress  blade  in  from  a  direction  and  position  E  blade  y-direction  of  thin  having and  plate free  experiments bounds a r e  2  one  edges  on  i n the  t i l t a n g l e s at  shown  standard  in Table I I .  two  the  the  expect sides  to  i n x-  y-direction.  have been  a t t h e back o f t h e b l a d e . The with t h e i r  zero after  would  supported  L the experiments  for 4 d i f f e r e n t and  70N/mm .  approaches  l e a v e s t h e c o n t a c t zone as  happen  times  axial prestress  repeated  front data  deviations  At  of  3  the  from  these  and  error  39  1  2  tiltangle  3 average  TA  LC  (degrees)  4 strain  straingages outside  from on  5 average  blade  3 and 4  inside  '(ye)  (ye)  (ye)  (ye)  0.00  332  402  278  340  0.33  320  408  291  349  0.60  319  404  280  342  1.30  319  398  276  337  320  403  281  342  average  strain  from  (ye) r  >?.standard deviation s  6.7  14.0  13.5  11.6  -+4.3  +8.9  +8.6  +  (ye) error  bounds  (ye)  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 bounds 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 95%.  Table  II  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 and t h e the blade a t p o s i t i o n E  inside  of  4.3 S t r a i n locations and  measurements a c r o s s around  t h e saw f o r d i f f e r e n t  at different  axial  prestresses  tiltangles  Figure across  16,  the  position  17  blade  undergoes  250N.mm  2  tiltangles  E (between t h e g u i d e s ) and p o s i t i o n a n d saw w h e e l ) . P o s i t i o n  70 mm a p a r t . T h e  blade  a n d 18 show t h e s t r e s s - d i s t r i b u t i o n for different  zone between b l a d e are  the blade  results  the  total  - due t o b e n d i n g  velocity  of  c=40m/s  show t h a t  (as  C1  change o f  For  later  in  stress  change  in  the  slope  of  distribution can  not  axial  across  preload  the blade  of local  2700N/mm  the s t r e s s -  due t o a t i l t a n g l e  before  2  change  balancing  stresses resulting  of the  from a t i l t a n g l e  a t i l t a n g l e o f T A = 0 . 0 6 ° t h e above  repeated  at  position  the  stress-distribution  is  50%  less  conditions tiltangle top  happens  reduced. For  were  of  blade  be measured a c c u r a t e l y , b e c a u s e by a p p l y i n g an  straingages, are  change  a  t h e dynamic  this  The  C5  stress  e x p e r i m e n t s ) t h i s means t h a t 1.7ms.  and  70 mm t h e  t h e wheel.  used  C (contact  i n these  average  over  between  wheel  than  which on  across  the slope shows  G (Figure  1 9 ) . The s l o p e o f  the blade  at position  that  the  measurements  at position  C5 f o r t h e same  influence  the s t r e s s - d i s t r i b u t i o n  of  i s greater  than a t t h e bottom wheel. T h i s  G5  i s due  the  at the to the  500  A  S T R E S S  400  J  300  J  200  J  ApQS.  B — a pos. «—»POS. *POS. o — ® POS, v POS .  E CI C2 C3 C4 C5  AXIAL  PRESTRESS  BLADE  OUTSIDE  SIS0Cx^~67.6N/mm  2  CN/mm2>  100  SIG0Cx> 0 0  50  1  1  1  100  150  200  STRAINGAGE FIGURE  16  STRESS  IN  CCONTACT  POSITION  X - D I R E C T I O N ACROSS ZONE),  TILTANGLE  ACROSS  THE BLADE  TA«.06°  AT  1  1  250 THE BLADE POSITION  (mm) C  500  400  J  A—POS . E B — e p o s . Ci *~"*POS. C2 *--*POS. C3 Q POS. C4 V— VPOS. C5  AVERAGE  PRESTRESS  SIG0Cx)=70N/mm'  BLADE OUTSIDE  G  y  J¥ S T R E S S  300  J  200  J  100  J  C N / mm  SIG0CX) 0  ~ r  0  50  1  r  100  150  STRAINGAGE F I G U R E 17  STRESS  IN  CCONTACT  X-DIRECTION ZONE),  POSITION ACROSS  TILTANGLE  ACROSS  1 200 THE BLADE  THE BLADE  r™  250 (mm)  AT P O S I T O N  C  TA=0.6° it*  500  *— POS. 0—BPOS. -^POS. * PCS. A  400  J  °—°POS.  *POS.  S T R E S S  E Cl C2 C3 C4 C5  AVERAGE PRESTRESS SIG<x)=66N/mm 2  BLADE OUTSIDE  300  200  J  100  J  CN/mm ) 2  SIG0Cx> 0 0  100 STRAINGAGE  FIGURE  18  STRESS  IN  CCONTApT  150 POSITION  X-DIRECTION ZONED,  ACROSS  TILTANGLE  200  ACROSS THE  THE  BLADE  250  BLADE AT  CmirO  POSITION  C  TA=1.33° U)  500  A  400  J  —  <s> G  v— S T R E S s  300  A  POS .  & pos . *POS. OpQS. v pos  E G1 G2 G3 G4 G5  AXIAL  PRESTRESS  BLADE  SIG0Cx)=67.6N/mm  2  OUTSIDE ¥  J  200  CN/mm^}  100  J SIG0Cx>  0 0 •  1  1  1  50  100  150  STRAINGAGE FIGURE  19  STRESS  IN  <CONTACT  POSITION  1 —  200  ZONED,  TILTANGLE  AT  r ~ ~ —  250  ACROSS THE  X - D I R E C T I O N ACROSS THE BLADE  I  BLADE  POSITION  CmmD S  TA=0.06<> 4^  500 BLADE  400  OUTSIDE  J  POS. S T R E S S  A  300  200  J  CN/mm ) 2  A *SIGCX!>= 5 0 B—B IGCX>=60 ^ - ^ S I G C X ) = 70 + SIGCX^= 7 6 © e S I G C X ) - 86 S  N/mm N/mm N/mm N/mm N/mm  2 2 2 2 2  100  0 0  FIGURE  20  50  STRESS FOR  IN  100 150 STRAINGAGE P O S I T I O N ACROSS X-DIRECTION  INCREASING  ACROSS  AX.PRESTRESSES  200 THE BLADE  THE BLADE SIGOCx),  250 (mm)  AT P O S . A AND E TILTANGLE  TA=0.0° it*  fact  that  during  only  a  remains  the  tiltangle  different  Figure  20.  The  l e v e l s of  the  the  loadcell  LC  stress  changes  position of  influence  of  stress  A  z-axis  bottom  wheel  top  at  stress-distribution  A.  While  PAHLITSCH  at  stress-distribution and  simultaneously  bent  in  due  x-direction  d i a m e t e r and  i s due over to  the  to  the  at  the  to  .  The  to  the  stress show  the  that  stress  stress-distribution linear, a  been  fact  wheels  two  guides)  5  the  parabolic (one  tooth g u l l e t ) . A has  due  outside  examine  results  follows  curvature  in y - d i r e c t i o n  the  is nearly  A  blade  the  straingage position the  the  i s to  i s equal  E  with system  wheel)  on  The  the  position  b l a d e away from  [13]  A. E  in  in  steps.  straining  top  series  position  c u r v e w i t h a maximum a t  parabolic  E and  five  (between t h e  the  position  at  E  shown  performed  increases  position  blade  the  of  in  s e t - u p on  were  position  are  measured  x-direction  straingage  at  (on  position  the  in  prestress at  raised  into  experiments  increase  at  was  t h i s experimental  distribution  increase  the  locations,  objective  across  the  experiments  the  b l a d e . The  different  of  incorporated  measured w i t h  across  the  were  were  the  while  around  axial prestresses  the  at  change,  series  while  and  rotates  axial prestress  The  the  wheel  stationary.  A  of  top  third  similar  measured  that  the  by  blade  is  i n two  directions,  of  bandsaw  the  the  crown  of  -  wheel the  wheel.  The  stress  with the geometric  maximum location  across  the wheel  of t h e h i g h e s t  coincides  peak  of  the  crown o f t h e w h e e l . This results higher  parabolic  i n maximum s t r e s s than  tiltangle at  of  SG  18.5% h i g h e r across  that  the s t r e s s  subject parabolic fatigue this  in  to  the a x i a l  blade.. chapter  3  distribution  across  f a c t has t o be t a k e n  a  stress  65.6N/mm  2  averaged  over a l l  theoretical  stress  the  f o r the f a c t blade,  and t o b e n d i n g  c u r v e arid h a s t h e r e f o r e calculations  is  do n o t a c c o u n t  an a x i a l p r e s t r e s s  limit  A t h e maximum  stress  The  considerably  the blade. For the  the f i v e experiments  than  the  calculations  across  TA=0.00° a t p o s i t i o n over  at position A  v a l u e s which a r e  the average s t r e s s  SG5 a v e r a g e d  or  stress-distribution  maximum  while  follows value.  a If  f o r sawblades a r e performed  into  consideration.  5 DYNAMIC VIBRATION MEASUREMENTS WITH A STATIONARY BLADE  5.1  Experimental  To  measure  stationary  away to  of the from  the  a  span  electro  from  was  force  the  Hz.  a  excitation The  signals  excitation  two  to  to the t o o t h s i d e  two  non  at the  process. contacting  same h e i g h t  toothside,  the  and  the other  as on  electro  generator  which  sawblade,  ranging  excitation  force  c o u l d be  measured  force  well  as  response  (deflections)  channel  frequency  as  FFT  analyser  and  (excitation)  i n t o t h e b l a d e and  transfer  t h e b l a d e . B e s i d e s many o t h e r i n p u t and  output  the  of t h e b l a d e were f e d i n t o a  the  the  the g u i d e s ,  the top guide  frequency  displayed  of  of  (see F i g u r e 2 1 a ) . The  to  the  loadcell.  The  dual  connected  the  the  inside  of the c u t t i n g  blade  on  the  between  were s i t u a t e d  magnet, one  of  r e g i o n (between  mounted on  influence  of  probes  a broad  0-200  with a  cutting  position  t h e b a c k s i d e of t h e b l a d e  supplied  frequencies  l e n g t h L down from  outside  displacement  magnet  bandsaw m o d e l s  t h e c e n t e r of t h e b l a d e o v e r  the  the  natural  in  at  s i m u l a t e the  On  theoretical  e l e c t r o magnet was  sawblade  thirds  the  blade  g u i d e s ) an the  s e t up and  which  function output  calculated between  ( d i s p l a c e m e n t ) of  f u n c t i o n s the  signal,  input  the coherence  RMS  values  (a measure  49  back side of the blade  top guide  electromagnet  d isplacemenf tr ansdu cers  bottom guide  POSITIONING FOR  OF  INSTRUMENTATION  VIBRATION  MEASUREMENTS  TSD = SIG/-SIG1 = 2SIGt  FIGURE  21  b  DEFINITION  OF THE  DIFFERENCE  AND  TILTSTRESS RELATED  STRESSES  of  the  data),  linear and  between  the  interest  and  the and  functions w i l l means o f an  recorded. (.234, for  explained  22  the  electro The  RMS  numerical ...)  blade  (see 23  d e g r e e s and  values  values  represent B over The  this  is  of  the  special These  in  more  the  excitation force  blade  inside  the  p h a s e and  the  Hz  detail  by  Figure  of  the a  Scale)  RMS  the  values  of  The  frequency.  the The  can  be  in  the  part  Figure of  of  90  same i n f o r m a t i o n  a  indication  magnitude  of  a  p l o t t e d . A s i g n change  24).  shift  for  imaginary  imaginary  from  displayed  are  an  (log.  function  natural  function  function,  frame  around  phase  numerically  Hz).  and  A  i f the  (Figure  graph  transmissibility  transfer  obtained  frequency  the  the  display.  indicates  real  values  are  27).  (peak) i n  (61  response  intervals  ratio  magnitude are  frequency  RMS  channel A give  a maximum  function  peak  values  displayed.  the  the  10  analyser  transfer  of  and  shows a t y p i c a l  frequency  chosen  output  RMS  b l a d e ) were  later  magnet  frequencies.  Figure the  case  c a l c u l a t e d and  c h a n n e l A and  the  i n our  could  be  the  pf  of  c h a n n e l B d i v i d e d by of  data,  (ratio  and  example.  .137,  natural  output  input  stiffness  be  In F i g u r e the  between  transmissibility  input  i n v e r s e of  from  relationship  the  parts  of  i n the indicate  25  the real  transfer part  and  a  natural  shows t h e  coherence  linear  cause/effect  56.50000 66.50000 RMS SPECTRUM CH. A CEXClt) CN)  HZ HZ  R0*= 28L;.0 , TSD= +15.7 N/mm  2 3 4 . - 0 3 RMS 1 3 7 . - 0 3 RMS  L G  2  RS  RMS SPECTRUM CH.B CBLADERESPONSE) Cmm)  FIGURE  22  :FREQUENCY CHz) 200 RMS SPECTRA FOR EXCITATION AND RESPONSE OF THE STATIONARY SAWBLADE •  R0*= ; 28.6 TSD= -1.5 .,7N/mm  1 4 5 . 8  2  6 1 . 0 0 0 0 0  TRANSFER FUNCTION  +  1 . 5 4 + 0 0  H Z  1  L G  E  +  + J  1^  LAJ  CDEGREES  i T F  D G  .54  +  CMH/N>  FIGURE  FREQUENCY CHO 2 0 TRANSFER FUNCTION OF THE STATIONARY SAWBLADE CMASNETIC EXCITATION} 23  :  0 Ln  R0*««  28.0  TSD= + 1 5 . 7 N/mm  2  61.00000  HZ  1.27+00 866.-03  E E  L N  REAL PART  R Cmm/N)  IMAG. ^ PART Cmm/N)  FIGURE  24  FREQUENCY CHz) REAL AND IMAGINARY PART OF THE TRANSFER FUNCTION  200  158.0000 61.00000 R0*=28.0,  521.-83  HZ HZ  TSD=15.7N/MM  2  T  COHERENCE  L N  H  H  rrt  h  1  »1  ft  F  T2  COH + fL2  r-rri 0 FIGURE  H 25  h  ^  H  1  h  FREQUENCY (Hz)  COHERENCE OF THE STATIONARY SAWBLADE  H  h  200  TILTANSLE =1.2°  3.1 6 + 0 0  E  LG  TSD= +15.7N/MM  2  FIGURE  26  FREQUENCY  SHIFT OF NATURAL FREQUENCIES FOR DIFFERENT AXIAL PRESTRESSES RO*  R0*=  28.8  TSD=Ht5.7N/mm  61.00000  2  2.13+00  E  L G  HZ  TRANSMISSIBILITY Cmm/N>  4-  TM +  FIGURE  27  ^  '  FREQUENCY CHz)  TRANSMISSIBILITY OF THE SAWBLADE AT NATURAL FREQUENCIES  200  relationship  between  transmission coherence addition and  factor  of  1.  A  only  Non  and c h a n n e l  26 t h e s h i f t  natural  linearities  transfer axial  function  prestressing  as w e l l  Linear  yield  a  or inputs i n  f a c t o r s between. 0  of t h e v a r i o u s  frequencies  B.  by c h a n n e l A  t o channel A produce coherent  torsional  the  systems e x c i t e d  1. In F i g u r e  the  channel  l a t e r a l and  as the  change  of  m a g n i t u d e due t o an i n c r e a s e o f force  2R0  (RO* = f (2R0)) c a n  be  seen. To  obtain  factors and To  general  typical  independent  of  f o r o u r bandsaw, t h e a x i a l  the t i l t a n g l e describe  values  TA were  the i n f l u e n c e  geometric  prestress  2R0  normalized.' of  the  axial  prestress  the  normalization: / 2R0 R0*=  (  I  was u s e d [24]).  L  '  2  *  2  )  B*D  (TIMOSHENKO 1959, " T h e o r y o f P l a t e s In  case  of  the  variety  of  possibilities  authors  on  bandsaw  formulae  t o take  TA  into  ratio  TSR  were  vibrations  of the t i l t a n g l e a  considered.  .  ULSOY  TSR:  = (SIG7 / SIG1) - 1  Different  have s u g g e s t e d  the e f f e c t of changes of the  consideration  tiltstress  influence  and S h e l l s "  [25]  various  tiltangle  defined  the  SIG7  i s stress  at location  of s t r a i n g a g e  7  at location  of s t r a i n g a g e 1  (toothside) SIG1  i s stress  (backside)  This  y i e l d s a value  [7]  defines  tilt)  t o 0,  o f TSR = 0 i f SIG7 =  the t i l t s t r e s s r a t i o no  tension  SIG1.  as r a n g i n g  stress  at  SG1.  KIRBACH  from  1.0  TANAKA  (no [21]  def i n e s :  TSR = SIG7 / SIG1  In  contrast  t o 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 fact  problem that  function the  the  these  to a l l these d e f i n i t i o n s  tiltstress  tilting  system  but  also  are  a function  To f i n d a d e f i n i t i o n w h i c h  t h e t i l t a n g l e and t h e tilting  tiltangle  ratios  o f t h e t i l t a n g l e and t h e g e o m e t r i c  prestress. of  inherent  individual  system t h e f o l l o w i n g  difference  TSD = SIG1  TSD was  not  i s the only  s i t u a t i o n of of t h e a x i a l  i s only a  function  characteristic  formulae d e s c r i b i n g  used:  - SIG7  TSD = MSIGO + S I G t  - (MSIGO  a  - S I G t ) = 2SIGt  of a  59  For  a definition  21b.  Because  of  the  TSD  v a l u e s a s compared experimental tensioned Figure  with  confidence The natural bandsaw  is  t o TSR,  relationship  blade  28  the d i f f e r e n t  used  the  value  difference  i t i s not between TSD  in these  of  solution  frequencies in a  f o r c e 2R0,  A  saw  the  theoretical derived  stationary  amplitudes  c,  solutions Mote's  for  the  i s shown i n  bounds  for  a  by  Mote's  and  KANAUCHI  data  (1-K  2LjpA  Kanauchi's  )  RO (1 + O - e )  axial  2  ) RO  are  used  with  the  solutions with  are  small  boundary c o n d i t i o n s a t  2  pAc  [21]  obtained  solution  1  L,  such  The  and  b [RO  moving  researchers.  supported  band  a  in  various  are:  flexible  lateral  area  in transverse vibrations  simply  the  cross section  pA*c fL=  The  TA  span l e n g t h  x =+L. The  free.  and  experimental  data.  and  stress  (as a f u n c t i o n of  density  blade)  f o r a band  and  that predict  s o l u t i o n s d e r i v e d by MOTE [9] and t o compare  two  dimension  error  have been d e r i v e d  prestressing the  of  Figure  95%.  p a r a m e t e r s as bandsaw v e l o c i t y  of  see  experiments  corresponding  mathematical  blade  a  stresses  20  CN/mm ) 2  -0.2  0  0 . 2 0 . 4  0.6  TILTANGLE FIGURE  28  TILTSTRESS  0.8  1.2  1.4  CDEGREES)  D I F F E R E N C E OF THE THE  1  SAWBLADE  AS A FUNCTION  OF  TILTANGLE o  with  the  definition  of  the  wave v e l o c i t y  cO  RO cO = —  1  • pA we c a n  write:  1 fL  - K  c0  =—*c0  :  2L  1+(  The v e l o c i t y solution the  will for  c = 0 is the -1  2L,pA  In c o m p a r i s o n the  wheel  support  (the  is  wheel  equal  support  Kanauchi's  1)  c  of  or h y d r a u l i c  f L ( c = 0) = 2L  IpA  1  and  - a measure  the all  b  = —*c0 2L  the is  production  strain  are  when  support  systems  a stationary  solutions [RO  defines  2  Mote  (0<K<1). K = 0  stiffness  b  only  2  cO  2L  and K = 1 when  and M o t e ' s  here  ) *c0  Appendix II)  For  band  solution:  b  RO  .  6 while  ) =—*(1  stiffness  rigid  to  following  (see  flexible  interest.  Kanauchi's solution,  equipped with a i r or  Motes  in chapter  of  *(1  value K  uses  support  to  of  pAc2  b JRO  =  :  part  be examined  developed  fL  c0  dependent  solution  Kanauchi  1-K)  the  wheel flexible  bandmills is  sawblade  identical:  of  close Cc = 0)  The  experimental  frequencies analytical  data  were  for  compared  solution  the with  developed  torsional the  natural  results  by A l s p a u g h  from t h e  [2]:  b c f T = *( 1 ) *c0 2L cO 2  2  H =4*—*  G  2  with  cO  2  B He  derived this  p  2  formula  speed  is  simply  to  be  P  fora  moving a t a c o n s t a n t assumed  SIGO(x) +  supported  a t x=±L a s f o r example,  fixed  rollers  a  strip  The s t r i p  t o r s i o n a l ] ^ a t two  band  running  between  supports.  the s t a t i o n a r y  torsional  rectangular  i n the x - d i r e c t i o n .  lines  For  thin  sawblade t h e a n a l y t i c a l  solution for  natural frequencies i s : b H G SIG(x) b =—*4 * —+ = *c0 2  f T ( c = 0)  2L Experiments observed. shape  showed t h a t However  to  2  p  p  in general the  2L coupled  p u r p o s e of t h i s  i n which t h e t o o t h s i d e and b a c k s i d e  deflected called  B  into  lateral  which t h e  t h e same d i r e c t i o n s  along  of  modes  were  work a mode the  blade  t h e z - a x i s were  n a t u r a l f r e q u e n c i e s a n d a mode shape i n  toothside  and  the  backside  dc e a lf ll ee dc t et do r si in ot no a lo p p n oa st iu trea l d if rr ee cq tu ie on nc si e as l. o n g  of  the  blade  t h e z - a x i s were  63  5.2  L a t e r a l and t o r s i o n a l  blade  two  frequencies prestress  lowest  plotted  RO*  each  a better  increasing  for different  frequencies  The  the  by . i t s e l f  with  RO*  the  axial  have  frequency  through  linearly  been scales  33.  a l l measured  increase  With  natural  but  with  from Mote's K a n a u c h i ' s and  s o l u t i o n s a r e added 30  formulae III  natural  i n APPENDIX f o r two  frequencies Ilia  axial  and  a  axial  difference  d i f f e r e n c e corresponds  the  running  sawblade. Examining  it  becomes e v i d e n t well with  that  whole measurement  errors  f o r the  are  summarized  in  RO* s p a n n i n g t h e prestress  values  TSD=-40.7N/mm . 2  to the  tiltangle  the r e s u l t s  the l a t e r a l  the values  results  data  a r e c a l c u l a t e d from  prestresses  and  tiltstress  and r e l a t i v e  and e x p e r i m e n t a l  range of t h e experimental  tiltstress  to the experimental  t o 33. The a b s o l u t e  total  the  30  natural  differences are  frequencies expanded  results  the a n a l y t i c a l  agree very  torsional  tiltstress  four  prestress  theoretical  different  Table  and  resolution i n Figure  essentially  Figures  four  of the  slopes.  Alspaugh's  between  29. T h e s e  axial  different  lateral  o f t h e sawblade a s a f u n c t i o n o f  shown i n F i g u r e  in  frequencies  between t h e g u i d e s  The  for  natural  natural  This for  i n Table I I I frequencies  p r e d i c t e d by t h e o r y  for  r a n g e o f RO*. From t h e F i g u r e s 30  200  175 _ N  22  24  26  28  AXIAL FIGURE  29  LOWEST AXIAL  L A T E R A L AND T O R S I O N A L PRESTRESSES  R0*  30  PRESTRESS R0*  NATURAL  FREQUENCIES  FOR  AND T I L T S T R E S S - D I F F E R E N C E S  TSD  DIFF.  4^  90  N A T U  80  _  R  A  22  24  26  28 AXIAL  FIGURE 30  LOWEST  LATERAL  PRESTRESSES  NATURAL  FREQUENCY  30  PRESTRESS R0* f  u  FOR D I F F E R E N T  R 0 * AND T I L T S T R E S S - D I F F E R E N C E S  AXIAL  TSD Ln  148  22  24  26  28 AXIAL  FIGURE  31  2 n d LOWEST AXIAL  LATERAL  PRESTRESSES  NATUREL  30  PRESTRESS R0*  FREQUENCY  f  L  2  FOR  DIFFERENT  R 0 * AND T I L T S T R E S S - D I F F E R E N C E S  TSD  90  N A T U R A L  80  J  70  J  60  J  50  J  r  R E Q U E N C I E S f  T  1  A—*TSD=-95.6 B B ysrj»=-47 . 9 « ^TSD=-40.7 *"~*TSD=»-12.9 0 ©JSD= 2 2 . 0  CHz?  40  ~T~ 24  22  _  j  T  26  FIGURE  32  LOWEST AXIAL  TORSIONAL  NATURAL  FREQUENCY  2  2  2  p  28 AXIAL  CN/MM ) CN/MM } CN/MM^ CN/MM^} CN/MM }  30  PRESTRESS R0* f  T  1  FOR  DIFFERENT  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  TSD  22  24  26  28 AXIAL  FIGURE  33  2 n d LOWEST AXIAL  TORSIONAL  PRESTRESSES  NATURAL  30  PRESTRESS R0*  FREQUENCY  f  J  2  FOR  R 0 * AND T I L T S T R E S S - D I F F E R E N C E S  DIFFERENT TSD CO  RO*  fLl t h e o r . exp. (Hz) (Hz)  23  51.4  51.5  31  69.0  68.0  RO*  .2  absolute error (Hz) 0.3 -1.0  absolute error (Hz)  rel. error (*) 0.6 -1.4  rel. error  theor. (Hz)  exp. (HZ)  23  102.3  101.6  -0.7  -0.7  31  137.9  135.4  -2.5  -1.8  RO*  r ri t h e o r . exp. (Hz) (Hz)  absolute error (Hz)  (%)  rel. error (%)  23  57.0  74.4  17.4  30.5  31  72.4  85.2  12.8  17.7  RO*  f " r2 t h e o r . exp. (Hz) (Hz)  absolute error (Hz)  rel. error (%)  23  114.1  147.2  33.1  29.0  31  144.8  173.2  28.4  19.6  I  Table  III  V a l u e s f o r t h e o r e t i c a l and 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 , 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 errors  to  33 i t c a n be  between  f o r the  different  between Later  in  this  or  The on  experimental  differences  chapter  i t will  of about  that the  2  while  fora  lateral  f o r higher  n a t u r a l f r e q u e n c i e s of the blade a r e  average values  29.7%  higher  f o r lower  decreases  t h e modes a r e c o u p l e d .  than  axial  f o r higher  blade  theoretical  theoretical  study  by ULSOY  frequencies  pretension  rise  i n the blade  distribution  in  stress  the  while  by  frequencies  the blade  than the torsional  show a good  p r e d i c t e d frequency  levels. A  [ 2 5 ] shows t h a t t h e t o r s i o n a l linearly  (assuming blade).  distribution  with a  the l e v e l of  parabolic  He c a l c u l a t e s with  a  a t t h e t o o t h s i d e and t h e b a c k s i d e a n d a minimum  experiments  a r e 9 t o 17% h i g h e r  values,  theoretical  (R0*=23).  prestresses  natural  f r e q u e n c i e s f o r an u n t e n s i o n e d  agreement w i t h  theoretical  axial  t o 18.7%. S i m i l a r  pretensioned  comparable  the  prestresses  of  parabolic  increases.  seen  -40.7N/mm  [ 2 1 ] show t h a t t h e t o r s i o n a l  natural  the d e v i a t i o n  values be  TANAKA  SIG(x)*  2  modeshapes a r e u n c o u p l e d ,  (R0*=31) on t h e a v e r a g e  value  TSD=-40.7N/mm .  torsional  error  natural  reaches a  differences  predicted  a  values  tiltstress  and e x p e r i m e n t a l  difference  tiltstress  the  This  calculated  difference  difference  torsional lower  and  the  tiltstress  theoretical  tiltstress and  that  theoretical  minimum For  seen  stress  that  maximum  fora stress  o f t h e b l a d e of  s t r e s s value at the center  of the  blade the  of  blade  with  a  SIG(x)*/2,  the lowest  i s 17Hz h i g h e r uniform  than  stress  distribution  uniform  stress  the  experimental these  square  data  and  function axial  values  blade,  the t h e o r e t i c a l  A first  order  natural  34 t h r o u g h a  parabolic  torsional  difference natural  TSD  of  different  than  the  blade  were TSD  a  =-26.7  used  using the  plotted for  2  IV  tiltstress  i n the  frequencies  maximum  N/mm  at  while  shows  f o r the  that  differences  frequencies.  sign  as i t s e f f e c t  on t h e t o r s i o n a l  The a b s o l u t e a n d r e l a t i v e  natural  frequencies  are  formulae  i n Appendix  Illb.  calculated  changes according  the the  the  on t h e  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  opposite  as a  various  a r e shown  fT1 has a minimum  . Table  in  experimental  natural  with  frequency  same t i l t s t r e s s d i f f e r e n c e influence  lateral  curve  for  polynominal  These r e s u l t s  38. B o t h  values  lower  frequencies  RO*.  different  b u t assumes a  f i t t i n g method was f i t t o t h e  the  tiltstress  of  consider  are  blade  across the blade.  of the t i l t s t r e s s d i f f e r e n c e  follow  lateral  the  frequency of  untensioned  f o r the pretensioned  prestresses  Figures  across  not  frequencies  experiments.  least  does  distribution  torsional  f o r an  distribution  Because Alspaugh's theory stress  torsional  and  natural of  the  t o the  200  N A T U R A L F R E Q U E N C I E S  175  J  150  J  ^ m i m ^ •h-  9  7 — —0  B  • -—4$  •  -B A  125  J  —v  •e—  — 0  G -<=>  100  •e-  J  •B  •B-  •  -A  75  50  25  J * R0*=23 0 — B R0*=2S . 0 * R0*=26 . 5 * — * R0*=27 . 9 Q £>R0*=29.3 ^ R0*=30.6  J  0  ^ -100  -80  -60  [  j  1  I  -40  -20  0  20  TILTSTRESS-DIFFERENCE FIGURE  *  34  1st  AND 2 n d L O W E S T  FOR D I F F E R E N T  L A T E R A L AND T O R S I O N A L  TILTSTRESS-DIFF,  TSD  TSD  NATURAL  AND A X .  CN/mm ) 2  FREQUENCIES  PRESTRESSES R0*  80  N A T U R A L F R E Q U E N C Y f  L 1  CHz>  70  J  60  J  50  J  40  J  A—* R0*=23.4 0—SR0*«25.0 4 * R0*«26.5 *—*R0»«27.9 o — © R0*=29.3 V—V R0**»30 . 6  30  T  T -80  -100  •60  -40  -20  0  TILTSTRESS-DIFFERENCE FIGURE  35  LOWEST L A T E R A L NATURAL F R E Q U E N C Y THE  TILTSTRESS-DIFFERENCE  TSD  f  u  TSD  20  CN/mm } 2  AS A FUNCTION  FOR A X I A L  PRESTRESSES  OF R0*  3  -100  -80  -60  -40  0  R9*=29 . 3  -20  0  TILTSTRESS-DIFFERENCE FIGURE  36  2 n d LOWEST THE  LATERAL NATURAL  TILTSTRESS-DIFFERENCE  FREQUENCY  TSD  f  L  FOR A X I A L  2  TSD  29 CN/mm } 2  AS A FUNCTION PRESTRESSES R0*  OF  100  N A T U R A L F R E Q U E N C Y  90  0  V  9€>  80  J  <•>  B-—  0  70  J  60  J  A A R0*=23 . 4 B-~-0 R0*=25 . 0 3 ©• R 0 * = 2 6 . 5 *-—A R 0 * = 2 7 . 9 9 ©R0*=29 . 3 R0*«30 .6  T1  50 -100  -80  -60  T  T  -40  -20  T 0  TILTSTRESS-DIFFERENCE FIGURE  37  LOWEST THE  TORSIONAL  NATURAL FREQUENCY  TILTSTRESS-DIFFERENCE  TSD  f , T  FOR A X I A L  TSD  20 CN/MM } 2  AS A FUNCTION  OF  PRESTRESSES R0*  180  N A T U R A L F R E Q U E N C Y f  T ;  ,CHz}  170  J  160  150  140  3  0  J  A A R0*=23. 4 0 — B R0*=25 . 0 4 »R0*=26.5 *R0*=27.9 0 €> R 0 * = 2 9 . 3 7 - - - V R0*=*30 . 6  -  120 -80  -5 00  FIGURE  38  -60  TORSIONAL  0 TSD  -40 -20 TILTSTRESS-DIFFERENCE  2nd  LOWEST  NATURAL FREQUENCY  THE  TILTSTRESS-DIFFERENCE  TSD  FOR A X I A L  f  J 2  20 CN/WO  AS A FUNCTION  P R E S T R E S S E S RO*  OF  absolute R0+  TSD (N/mm ) 2  26.7 to 95.6  29.3  AfLl  AfL2  change AfTl  (Hz)  (Hz)  (Hz)  (Hz)  -4.8  -7.6  +3.3  +0.4  relative R0+  TSD (N/mm ) 2  26.7 to 95.6  29.3  Table  IV  1  AfT2  change  AfLl  AfL2  AfTl  AfT2  (*)  (%)  '(%)  {%)  -7.8  -3.1  3.9  0.2  Change o f the natural  frequencies  as a  function of the t i l t s t r e s s difference  TSD  78  5.3  Transmissibility Beside  the  t h e S t a t i o n a r y Sawblade  t h e e v a l u a t i o n of  associated  Therefore  of  mode  the  shapes  were of  the t r a n s m i s s i b i l i t y  t o o t h s i d e and  at  the  backside  T of of  and  plotted.  The  experimental  21a.  The  was  excited  the  blade  blade  response  transducers, the  other  at  represents signal  one  values  at  of  the  was  more  promising  repeated  from  results.  at  over  value  and  was for  was  then a  again  signal.  measuring  10 Hz of  value  the  these  and  interval the  RMS  natural  The of  data  each  data  yielded  frequency, with  the  band w i d t h  one  three times  averaged.  confidence  is  approach  to y i e l d  The  although  readings  second  a  blade,  response  established  the c e n t e r  repeated  the  the  Around each n a t u r a l  r e a d i n g s were a v e r a g e d  procedure  of  results, 32  while  contacting  transmissibility  3 times. A  frequency  This  bounds  the  in Figure  transmissibility  excitation  inconsistent  v a l u e s were a v e r a g e d  32  the  non  value  previously  averaged  value  then  The  of t h e b l a d e . E x p e r i m e n t s  were  natural  of  i s shown  two  the  were measured  t o o t h s i d e of  of t h e RMS  value  f r e q u e n c i e s gave  RMS  the  at  e l e c t r o magnets,  backside.  value  right  values  the  interest.  blade  the blade setup  frequencies  special  the  measured w i t h  ratio  t o t h e RMS  stiffness  by  l o c a t e d at  the  the  reciprocal  was  natural  data  value.  f o r each average 95%  and  for  data error the  transmissibility  data  shown  in  this  chapter  were  +0.048mm/N. These experiments to  arrive  39  through  fit  then  h a d t o be r e p e a t e d  a t the t r a n s m i s s i b i l i t y t o F i g u r e 46. A f i r s t  through  the curves  transmissibilities experimental  for  range)  data  order  128 t i m e s  shown i n F i g u r e polynominal  was  from  F i g u r e 39 - 46 a n d t h e n t h e  RO*  =  were  26.0 used  (midpoint in  of the  the following  discussion. Figure  39 a n d 40 show t h e t r a n s m i s s i b i l i t y  stationary backside  blade  f o r fL1  respectively  prestress  as  for different  t h e cha*nge o f t h e a x i a l on  the  slope  tiltstress  of  a t the t o o t h s i d e and a t t h e a  tiltstress  the curves,  difference at  0.62mm/N  413% w h i l e  effect in  by  of  633%.  little  increase  i s s m a l l e r - from  of  the  transmissibility  from  tiltstress  difference.  effect the the  0.15mm/N  relatively  effect  to  little  c a n be o b s e r v e d  that  the  absolute  0.19mm/N  at the o r by  a t f L i n c r e a s e s f o r an  tiltstress  at f T decreases  While  increases  0.03mm/N t o  the t r a n s m i s s i b i l i t y  axial  in  t h e magnitude of t h e t r a n s m i s s i b i l i t y  While  increase  the  differences.  having  F i g u r e 41 a n d 42 f o r f L 2 , o n l y  toothside  the  an  toothside  a t the backside. A similar  change  of  greatly  transmissibility or  function  p r e s t r e s s has very  the  of the  difference,  the  f o r t h e same change o f  In F i g u r e  43  the  torsional  0.8  0.7 T R A N S M I S s I B I L I T Y  0.6  0.5  J  0.4  J  .  *r  <5  0.3 0  B  -  -a  -  0.2  •  CMM/N} 0  A  0  ;  22  24  — * T S D = ~ 8 t . 8 CN/MM - 4 7 . 9 CN/MM *> T S D = 1 3 . 7 C N / M M L4 .^_„CHZM«_ I  26  28  AXIAL FIGURE  39  TRANSMISSIBILITY THE  TOOTHSIDE  OF THE  FOR F . ) L  2 2 2 2  ) ) ) X 30  PRESTRESS R0*  STATIONARY  S A W B L A D E C M E A S U R E D AT  AS A FUNCTION  OF  R 0 * FOR D I F F .  TSD 30 3  0.8  T R A N S M I S s I B I L I T Y  0.7  J  0.6  J  0.5  J  0.4  J  * — * T S D — 8 1 . 8 CN/MM j B—B TSD=-47 . 9 CN/MM ^--^ TSD—13.7 CN/MM * — * T S D « 1 4 . 0 CN/MM  2 2 2 2  ) } } }  0.3  0.2  J  0. 1  J  CMM/N}  0  T 22  24  26  28 AXIAL  FIGURE  40  TRANSMISSIBILITY BACKSIDE  FOR f  OF }  THE  STATIONARY  AS A F U N C T I O N OF  30  PRESTRESS  SAWBLADE R 0 * FOR  R0*  C M E A S U R E D AT DIFF.  TSD  THE  0.8  T R A  0.7  J  0.6  J — * TSD=-81 . 8 CN/MM H E3 T S D — 4 7 . 9 C N / M M T S D — 1 3 . 7 CN/MM * — * T S D » 1 4 . 0 CN/MM A  N  S M  I S S I B I L I T Y  153  0.5  J  0.4  J  2 2 2  ) ) ) )  0.3  0.2  J  0.1  J  CMM/N)  ,  +  B-  -  —G--  0  ^  22  24  41  26  TRANSMISSIBILITY TOOTHSIDE  FOR f  L  OF THE 2  )  2  j  A  28 AXIAL  FIGURE  2  STATIONARY  AS A FUNCTION  T~ 30  PRESTRESS R 0 * S A W B L A D E CMEASURED AT  OF  R 0 * FOR D I F F .  TSD  THE CO  to  0.8  0.7 T R A N S M I S s I B I L I T Y  J  0.6  0.5  J — TSD=-81.8 B— TSD=-47.9 »TSD=-13.7 * - — * TSD= 1 4 . 0  A  0.4  A  B  0.3  J  0.2  J  0. 1  J  CN/MM2> CN/MM2> CN/MM ? CN/MM2> 2  CMM/N?  0 22  26  24  28 AXIAL  FIGURE 42  TRANSMISSIBILITY BACKSIDE  FOR f  L  2  OF T H E 5  STATIONARY  AS A FUNCTION  OF  30  PRESTRESS R0*  SAWBLADE -CMEASURED R0«  FOR  AT  THE  DIFF.TSD 00 OJ  0.8  T R  0.7  J  0.6  J  0.5  J  A N S M  B-  •B-  I S S  0.4  I B  I L I T Y  0.3  J  0.2  J  ^—*TSD=-81.8 B — B TSD*=~47.9 * »TSD«-13.7 *~-*TSD= 14.0  CMM/N)  0.1  CN/MM ) CN/MM ) 2  2  CN/MM ) 2  CN/MM ) 2  J  0 22  24  26  28 AXIAL  FIGURE  43  TRANSMISSIBILITY THE  TOOTHSIDE  FOR  OF f  THE T  i )  STATIONARY  30  PRESTRESS R0* SAWBLADE  A S A F U N C T I O N OF  CMEASURED  R 3 * FOR  DIFF.  AT TSD CO 4^  0.8  0.7 T R 0.6 A N S 0.5 M I S S 0.4 I B I 0.3 L I T CMM/N? 0 . 2  0. 1  -A  J  J a*  J *— TSD=-8I .8 B 0TSD=—47.9 ^-^TSD=-13.7 * — -*TSD= 1 4 . 0 A  J  J  C N/MM 2 ? CN/MM2? CN/MM2) CN/MM } 2  0 22  24  26  28 AXIAL  riGURE 44  TRANSMISSIBILITY BACKSIDE  OF THE  STATIONARY  FOR f , ? A S A F U N C T I O N T  OF  30  PRESTRESS R0*  S A W B L A D E C M E A S U R E D AT R 0 * FOR D I F F .  THE  TSD CO Ul  0.8  T R A N S M I S S I B I L I. T Y  0.7  J  0.6  J  0.5  J  A—*TSD=-81.8 B — H TSD=-47 .9 * * TSD=~13.7 *—*TSD= 14.0  0.4  0.3  J  0.2  J  0.1  J  CN/MM CN/MM CN/MM CN/MM  2 2 2 2  ) ) ) )  CMM/N) B-  0 22  26  28 AXIAL  FIGURE  45  TRANSMISSIBILITY BACKSIDE  FOR f  J  2  OF ) AS  THE  PRESTRESS  STATIONARY  A FUNCTION  OF  SAWBLADE R 0 * FOR  30 RP* CMEASURED DIFF.TSD  AT  TH  0.8  T R A N S M I S S I B I L I T Y  0.7  J  0.6  J A—AjSD= B---B T S D = « » TSD= TSD-  0.5  0.4  J  0.3  J  0.2  J  0.1  J  81.8 47.9 13.7 14.0  CN/MM } CN/MM2? CN/MM } CN/MM ? 2  2  2  CMM/NO  0  1 26  24  22  28 AXIAL  FIGURE  46  TRANSMISSIBILITY TOOTHSIDE  FOR  f*> i 2  OF  THE  r  STATIONARY  AS A FUNCTION  OF  30  PRESTRESS  SAWBLADE R 8 * FOR  R0*  C M E A S U R E D AT DIFF.  THE  TSD 00  TSD (N/mm )  to othside T L 1 (mm/N) RO* RO* 26 237  -81.8 -47.9 -13.7 14.0  .18 .26 .37 .58  ?  .15 .26 .39 .62  RO* 29  backside T L 1 (mm/N) RO* RO* 23 26  RO* 29  .12 .26 .42 .65  .33 .34 .27 .24  .31 .27 .32 .27  .32 .30 .29 .25  -  TSD (N/mm ) ?  -81.8 -47.9 -13.7 14.0 TSD (N/mm ) ?  -81.8 -47.9 -13.7 14.0 TSD (N/mm ) ?  to othside T T 1 (mm/N) RO* RO* f RO* 23 26 29 .74' .74 .74 .47 .53 .58 .32 .41 .50 .18 .26 .34  backside T T 1 (mm/N) RO* RO* 23 26  RO* 29  .46 .39 .34. .21  .66 .55 .53 .47  toothside T L 2 (mm/N) RO* RO* 23 26  RO* 29  backside T L 2 (mm/N) RO* RO* 23 26  RO* 29  .04 .14 .18 .27  .02 .07 .09 .12  .07 .10 .08 .06  .07 .05 .05 .04  RO* 29  backside T T 2 (mm/N) RO* RO* 23 26  RO* 29  .18 .10 .11 .07  .08 .09 .04 .05  .08 .10 .11 .08  .03 .10 .14 .19  toothside T T 2 (mm/N) RO* RO* 23 26  .56 .47 .43 .34  .07 .08 .06 .05  •  -81.8 -47.9 -13.7 14.0  .11 .09 .06 .03  Table 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 sawblade a t the two.lowest l a t e r a l and t o r s i o n a l natural frequencies f o r different tiltstress differences a n d a x i a l p r e s t r e s s e s RO*  .14 .10 .08 .05  .08 .09 .08 .06  transmissibility is  lowered  (from  increasing  f o r fT1 a t t h e t o o t h s i d e 0.74mm/N t o 0.26mm/N o r by  tiltstress  transmissibility decreases  of the blade  differences,  while  at the backside of the  from  0.14mm/N  to  280%)  blade  0.05mm/N  with the  f o r fT1  or  by 36%  (Figure 44). In F i g u r e  45 a n d 46 t h e t r a n s m i s s i b i l i t i e s  f o r the  toothside  a n d t h e back s i d e a t f T 2 a r e r e c o r d e d .  Similar  to  transmissibilities  natural  the  frequencies,  t h e change  transmissibility the  toothside  f o r the  of  lateral  the amplitude  a t f T 2 i s much s m a l l e r  than  of  the  f o r f T 1 . At  t h e change o f t h e t r a n s m i s s i b i l i t y  function  of  0.14mm/N  t o 0.05mm/N o r c h a n g e s by 36%. A t t h e b a c k s i d e  the  tiltstress  transmissibility  0.07mm  /N  increase effect the  the  or  by  f o r fT2 changes 9%.  of the a x i a l onto  the  difference  as a  While  from  prestress  only  0.08mm/N  has a  very  as well  backside  raises  prestress  from R0*=23 t o R0*=29. F o r a b e t t e r  of  the t r a n s m i s s i b i l i t y  axial  prestress  tiltstress In sawblade  RO*  values these  to  little  of the blade,  at the toothside  considerably  from  f o r f L 1 , f L 2 a n d f T 2 an  transmissibility  transmissibility  ranges  a t fT1  as a t the  f o r a change o f t h e a x i a l  as values  a  comparison  function averaged  of the over t h e  d i f f e r e n c e s a r e shown i n T a b l e V.  Figure at  47  four  t h e modeshapes natural  of  frequencies  the  stationary  f o r R0*=23 a n d  90  1st LATERAL MODESHAPE  2nd. LATERAL MODES HAPE  TSD =TSD=  Figure  47  81.8  N/mm  1st. TORSIONAL MODESHAPE  2  U.N/mm  2  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 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  2nd. TORSIONAL MODESHAPE  R0*=29 a n d  f o r TSD=-81.8N/mm  shown.  the  At  transmissibility increase  lowest  2  and  lateral  TSD=14.ON/mm  are  2  natural  a t the toothside raises  frequency the f o r the  from TSD=-81.8N/mm t o 14.ON/mm 2  stated  by 0.4mm/N f o r  2  R0*=23 a n d by 0.53mm/N f o r R0*=29, w h i l e a t t h e b a c k s i d e the  transmissibility  i s lowered  0.04mm/N f o r t h e c o r r e s p o n d i n g  by  0.09mm/N  changes  of  the  a n d by axial  p r e s t r e s s RO*. At of  t h e second  the  transmissibility  tiltstress to  lowest  difference  lateral  frequency  f o r t h e r e p o r t e d change  i n the  amounts t o 0.23mm/N f o r R0*=23 a n d  O.lOmm/N f o r R0*=29 a t t h e t o o t h s i d e  while  the increase  of  the  blade,  a t 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 t h e 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 a n d by 0.03mm/N f o r R0*=29. These has  a  results  show t h a t  the  f a r greater influence  lateral  natural  tiltstress  difference  on t h e modeshapes f o r t h e  f r e q u e n c i e s , than  a change o f t h e  axial  prestress. At 8l.8Nmm  fT1 a c h a n g e to  2  i n the t i l t s t r e s s  14.ON/mm  2  reduces  difference  from -  the t r a n s m i s s i b i l i t y at  t h e t o o t h s i d e o f t h e b l a d e by 0.56mm/N f o r R0*=23 a n d by 0.40mmN  f o r R0*=29. A t t h e b a c k s i d e t h e t r a n s m i s s i b i l i t y  decreases R0*=29.  by 0.25mm/N f o r R0*=23 The  equivalent  transmissibility  and  by  0.19mm/N f o r  values f o r the decrease  a t fT2 a t  the  toothside  of the  amounts  to  0.08mm/N f o r R0*=23 a n d t o 0.11mm/N f o r R0*=29, w h i l e a t the for  backside  the t r a n s m i s s i b i l i t y  decreases  by 0.03mm/N  R0*=23 a n d by 0.Omm/N f o r R0*=29. From  these  increase  in  effect  on  results  the  the  natural little high  frequencies. effect  prestress  the blade.  i t decreases  for a  small  tiltstress  the  toothside  low  and  and  natural  while  the  natural  at the torsional p r e s t r e s s has  a t f L 1 . At fL2 a of the  axial  on t h e t o o t h s i d e  tiltstress  frequencies  difference  the  An i n c r e a s e  transmissibility  the backside  there  an i n c r e a s e o f  the t r a n s m i s s i b i l i t y at  at the backside.  raises at  an  changes i n t h e t r a n s m i s s i b i l i t y .  d i f f e r e n c e lowers  prestress  While  at the l a t e r a l  the t r a n s m i s s i b i l i t y  while  the  difference,  of  that  h a s m a i n l y an  A change o f t h e a x i a l  the t o r s i o n a l  toothside  difference  d i f f e r e n c e a n d an i n c r e a s e  lowers  a r e only  axial  concluded  on t h e t r a n s m i s s i b i l i t i e s  considerably,  At  be  at the toothside  increases,  tiltstress  there  tiltstress  toothside  transmissibility frequencies  i t can  i svery  f o r a high  little  of t h e at the  tiltstress  change a t  a low  tiltstress difference. Figure  47  also  lateral  and t o r s i o n a l  For  special  a  8l.8N/mm  2  and  shows natural  tiltstress  t h e modeshapes  frequencies difference  TSD=14N/mm )  u n c o u p l e d . Some o t h e r  that  2  the  researchers  are  coupled.  (between  modeshapes  for  TSD=become  have t h e o r e t i c a l l y a n d  experimentally  examined  modeshapes o f bandsaw study H,  free  edge l o a d  b l a d e s . PAHLITSCH  span Fhor  in y-direction  functon  a  o f an edge l o a d F h o r .  study  function  further done.  analysis  of  study  did  p r e s t r e s s RO*  a  on  the  and  teeth.  on c o u p l e d modes a s a  The a u t h o r  i s n o t aware of  or e x p e r i m e n t a l  difference.  the here  torsional  [16,17]  acting  of modeshapes - t h e o r e t i a l of the t i l t s t r e s s  and  of the blade t h i c k n e s s  l e n g t h L, t h e a x i a l  SOLER [ 2 6 ] d i d a t h e o r e t i c a l  any  lateral  on modeshapes a s a f u n c t i o n  the  an  the  as  Therefore  no  p r e s e n t e d modeshapes  was  94  5.4 Dynamic v i b r a t i o n  measurements w i t h a moving  To measure t h e n a t u r a l blade  the  repeated.  same A  experiments  di fferent  experiments.  frequencies  It  as  blade  had  no  blade  due  used  i n the s t a t i o n a r y  c = 40.7 m/s  Mote'  support  data and the  error  are  not  f o r the  be  The  varied.  lateral  these  the  width  stiffness  Ks had  The  to  analytical  prestress  the value  be  of  s s o l u t i o n s a r e added  R0*=26  Mote a n d K a n a u c h i  to  theoretically deviation  natural  predicted  amounts  Similar  are  to  R0*=31  differ  t o the  of  the a n a l y t i c a l  o n l y by 0.13 Hz t o  on t h e a v e r a g e frequencies.  stationary  Mote' s,  V. F o r t h e r a n g e  51  they  The l a t e r a l  lower  For  t o 9.9% a n d f o r R0*=31 the  (see  the r e l e v a n t data  t h e r e f o r e r e p r e s e n t e d o n l y by one c u r v e . frequencies  the  of the  evaluated  results  i n Table  velocity  frequencies  Hz o r by 0.3% t o 0.18% . In F i g u r e s 49 t o  natural  across  compare  natural  i n F i g u r e 49 t o 51, w h i l e  from  were  in  blade To  band s o l u t i o n ,  bounds a r e shown  axial  that  5.2  stress distribtion  experiments.  s and Alspaugh'  1  so  flexible  II).  plots  results 0.10  s  system  APPENDIX Kanauchi  data  used  running  p r e t e n s i o n i n g compared t o t h e b l a d e  could  experimental with  to  a  chapter  was  teeth  B0=B=260mm, b u t had a s i m i l a r the  in  of  blade  than t h e  R0*=26  the  i t i s 11.2%.  sawblade t h e t o r s i o n 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  175 J  A T U  R A L F R  150 J 125 J  E Q  100 J  E  75 J  I E S  50 J  U  N C  CHz)  A—AFLi  25 J  •—EJ P L 2 *—*FT2  0 25 FIGURE 48  —T 27  ~1  1  1  29 30 31 32 AXIAL PRESTRESS R0* NATURAL FREQUENCIES f AND f FOR THE RUNNING BLADE FOR DIFFERENT AXIAL PRESTRESSES R0*, c « 40.7 m/s 26  28  L  T  Ul  80  J  70  J  60  J  N  A T U R  A L  F R E Q U E N C Y  50  40  J  i AXAIL FIGURE 49  NATURAL  LATERAL  DIFFERENT  AXIAL  FREQUENCY  r  1 29  28  f  30  PRESTRESS R0*  OF  THE  PRESTRESSES R 0 * .  «  L 1  RUNNING 40.7  ^/s  BLADE  FOR cn  I  1  1  1  1  1  !  25  26  27  28  29  30  31  AXIAL FIGURE  50  NATURAL  LATERAL  DIFFERENT  AXIAL  FREQUENCY  f  L  2  PRESTRESS R8*  0F  PRESTRESSES R 0 » ,  THE o -  RUNNING  SAWBLADE FOR  4 0 . 7 m/s  1  32  80  Y 40  _  CHZ?  25  26  27  28  29 AXIAL  FIGURE 51  NATURAL TORSIONAL DIFFERENT  AXIAL  FREQUENCY  fTl  30  31  32  PRESTRESS R0* OF  PRESTRESSES R 0 * , c  THE  RUNNING BLADE  FOR  = 4 0 . 7 m/s 00  150  26  27  28  29  30  31  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  32  100  theoretically  predicted  average d i f f e r e n c e  amounts t o 32.5%  17.9%.  These d i f f e r e n c e s  for  stationary  the  frequencies.  are  stress  blade  analytical  used  their  i n these  in a parabolic  and  t o the  distribution  e x p e r i m e n t s was stress  solutions  fact  Alspaugh  the  which the  is  -like  across  , while  across  the  it  that  and  RO/A  pretensioned  distribution  R0*=26  f o r R0*31  s a w b l a d e - Mote, K a n a u c h i  assume a c o n s t a n t in  due  For  the blade  results  blade.  fl .1  RO*  absolute error (Hz)  rel. error (%)  theor. (Hz)  exp. (Hz)  26  45.6  41  31  58.7  52  -6.7  -11.4  exp. (Hz)  absolute error (Hz)  rel. error (*)  f .2  RO*  26  theor. (Hz) -  31  RO*  --4.6  -10.1  91.2  82.4  -8.8  -9.6  117.4  104.5  -12.9  -11.0  f" n theor. (Hz)  exp. (Hz)  absolute error (Hz)  rel . error (%)  26  52.5  70.5  18.0  34.3  31  64.3  77.0  12.7  19.8  RO*  f" T2 theor. (Hz)  exp. (Hz)  absolute error (Hz)  rel. error (%)  26  105.0  137.2  32.2  30.7  31  128.6  149.0  20.4  15.9  T a b l e VI  V a l u e s f o r t h e o r e t i c a l and 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 and 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 blade  CONCLUSIONS Strain show  measurements f o r t h e  that  direction the  in  the  increase  axial  free  prestressing  w h e e l s t h e measured  of  the  bending local  in fatigue incremental  resulted  across  the straingage  stresses  limit  g u i d e s showed t h a t  increase  change  the t i l t s t r e s s  of  quadratic  with  and  f a c t has  t o be  of the s t r e s s  span  of  i n x-  of the p o s i t i o n  length,while  the  blade  zero.  t h e b l a d e between t h e and  torsional  the a x i a l difference  fL2 at  2R0  t h e saw. The s t r e s s i n  r e l a t i o n s h i p f o r the natural  a maximum f o r fL1  . The  i n two d i r e c t i o n s  independent  lateral  frquencies  )  of the a x i a l preload  l o c a t i o n around  the  (due t o t h e  t h a n a mere a d d i t i o n o f  increase  measurements  over  consists  t h e wheel  away from t h e w h e e l s a p p r o a c h e s  Vibration  bending  of  calculations.  increase  the blade,  i n x-  a n d t h e s t r e s s e s due  suggests. This  y - d i r e c t i o n at the free  travels  of  blade  increase  x-direction  of the blade  i n an e q u i v a l e n t  direction  an  i n x and y - d i r e c t i o n  theoretical stresses  An  the  of  saw  stresses  RO*. D u r i n g in  r a n d t h e crown  i n higher  considered  of  stress  of the blade  radius  combination  the  force  sum o f t h e a x i a l p r e s t r e s s  to bending  results  length  proportionally with  the  wheel  span  stationary  natural  prestress  RO*. A  resulted  in a  frequencies  TSD =-26.7N/mm  2  with  and a  minimum a t t h e same t i l t s t r e s s torsional lateral of  natural  freuencies.  and t o r s i o n a l n a t u r a l  the  difference  tiltstress  The s l o p e s  frequencies  difference  f o r an optimum t i l t s t r e s s  drawn  this.  A  comparison  theoretical  the  solutions derived  and  Alspaugh  for  the l a t e r a l  with  of  [2] showed t h a t  these  natural  frequencies  from A l s p a u g h ' s Alspaugh  distribution used  in  across  these  pretensioning with higher  of the  and  at  than  s o l u t i o n . This  assumes  stresses  prestress  i n the  14N/mm , 2  natural  the lowest  tiltstress  predicted  i s due t o t h e stress  was  pretensioned.  The  stress distribution  a t t h e edges of t h e b l a d e .  of  mode s h a p e s o f t h e  showed t h a t little  the  difference  maximum  the  t h e b l a d e w h i c h was  RO* has v e r y  frequency  well  while  the transverse  deflections  the  with  very  a • constant  b l a d e between t h e g u i d e s  normalized  lateral  higher  the blade,  of  data  be  [ 9 ] , Kanauchi [21]  agreed  results in a parabolic  tensile  the a x i a l  change  by Mote  experiments  Measurements stationary  experimental  can  r e s u l t s . The t o r s i o n a l n a t u r a l  were c o n s i d e r a b l y  that  function  the t h e o r e t i c a l p r e d i c t i o n s  frequencies  fact  as a  difference  frequencies  experimental  f o r both the  were s i m i l a r so t h a t no  conclusion from  f o r the lowest  torsional natural  influence  blade while  on  fora  between-81.8N/mm  deflections  could  a change  be l o w e r e d frequency  at by  2  the lowest 413%  and  by 280%. T h i s  shows t h a t axial to  at the n a t u r a l  p r e s t r e s s RO*  achieve  an  promises Another  at  the  the  little  stress  far better interesting  lateral  consisted  very  optimum s t r e s s  t h r o u g h a change of blade  has  frequencies  of  and  a  raise  effect,  distribution  of  while  trying  i n the  distribution  the  across  blade the  results. fact  torsional  coupled  modes  f o r the  running  errors  between  was  that  t h e mode s h a p e s  natural for  frequencies  most  tiltstress  di fferences. The  results  relationships theoretical sawblade.  and data  v a l u e s as  sawblade the  observed  showed  similar  experimental f o r the  and  stationary  105  REFERENCES [1]  ALLEN, F . E . " H i g h s t r a i n - t h i n K e r f " , Volume 1 o f t h e s a w m i l l c l i n i c l i b r a r y . C o p y r i g h t 1973 by M i l l e r Freeman Pub. I n c . , Howard street, 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 o f a moving band" J . F r a n k l i n I n s t . Volume 2 8 3 ( 4 ) : 3 2 8 - 3 3 8 , 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 o f a m u l t i b l e span moving Bandsaw" Western F o r e s t p r o d u c t l a b o r a t o r y , F i s h e r i e s and E n v i r o n e m e n t C a n a d a . V a n c o u v e r B.C.  [4]  KIRBACH, E.;BONACH, T. "An e x p e r i m e n t a l study on the lateral natural frequencies o f bandsaw blades" E n v i r o n m e n t Canada, W e s t e r n F o r e s t e r y Production L a b o r a t o r y , 1977  [6]  CLOUGH, R.W. McGraw H i l l ,  [7]  KIRBACH, E . "The e f f e c t o f t e n s i o n i n g and wheel t i l t i n g on t h e t o r s i o n a l a n d l a t e r a l fundamental f r e q u e n c i e s o f bandsaw b l a d e s " Environment o f Canada, Western Forest Product Laboratory  [8]  KRILOV, A. " E i n i g e A s p e k t e d e r K o n s t r u k t i o n von Bandsaege- maschinen m i t hoher B l a t t s p a n n u n g " Holztechnologie 2, J a h r g a n g 16, June 1975, p a g e s 109-111  [9]  MOTE, C.C. "Some dynamic characteristics of bandsaws" Forest Product J o u r n a l , V o l . XV, No. 1, J a n u a r y 1965a  "Dynamics o f s t r u c t u r e s " 1975  [10]  MOTE, C D . "A S t u d y o f 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, C D . , ULSOY, A.G. "Analysis of Vibration" 6th, 1979, Woodmachine Seminar, F o r e s t L a b o r a t o r y , Richmond/ C a l i f o r n i a  Bandsaw Product  [12] MOTE, C D . "Dynamic S t a b i l i t y o f an Axially M o v i n g Band". Journal o f t h e 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 L o a d i n g of Bandsaw B l a d e s : S t r e s s e s a n d S t r e n g t h F a c t o r s " Holz Roh-Werkstoff 30, Pages 165-174, 1972 [14] PAHLITSCH, G., PUTTKAMMER, " I n v e s t i g a t i o n s on t h e S t i f f n e s s o f Bandsaw B l a d e s " H o l z , Roh-Werkstoff 31, p a g e s 161-167, 1975 [15] PAHLITSCH, G., PUTTKAMMER, "Beurteilungskriterion fuer die Auslenkung 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 ; H o l z 32 [16] PAHLITSCH, G. , " B e u r t e i l u n g s k r i t e r ion fuer die Bandsaegeblaettern" Zweite Mitteilung: Berechnung der H o l z 32  PUTTKAMMER, Auslenkung  K.  K. von 1974 -K, von  A u s l e n k u n g e n ; 1974  [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 die 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 H o l z 34 [18] Primer" McGraw H i l l  PERRY, C.C., LISSNER, H.R. Book Company, s e c o n d  "The  edition,  Straingage  1955  [19] PORTER "Some E n g i n e e r i n g C o n s i d e r a t i o n s o f H i g h S t r a i n Bandsaws" F o r e s t P r o d u c t J o u r n a l , A p r i l 1971, Volume 21 #4 [20] RHODES, J.E., Jr. "Parametric Self E x c i t a t i o n of a B e l t i n t o T r a n s v e r s e V i b r a t i o n " J o u r n a l o f A p p l i e d M e c h a n i c s , December 1980, T r a n s a c t i o n of t h e ACME:1055- 1060 [21] TANAKA, C. " E x p e r i m e n t a l S t u d i e s on Bandsaw B l a d e V i b r a t i o n s " Wood S c i e n c e T e c h n o l o g y 15, p a g e s 145159, 1981 [22] THUNELL, B. "The S t a b i l i t y of the Blade" Holz/Roh-Werkstoff, 9 8 ( p a g e s 343-348), 1970  Bandsaw  [23] Blade" paperi  THUNELL,  j a p u i No.  B.  "The  Stresses  in  a Bandsaw  11, 1972  [24] TIMOSHENKO " T h e o r y McGraw H i l l , 1959  of P l a t e s  and S h e l l s "  [25] ULSOY, A.G. "Vibration and S t a b i l i t y of Bandsaw B l a d e s : A t h e o r e t i c a l and e x p e r i m e n t a l s t u d y " Technical R e p o r t #10, U n i v e r s i t y o f C a l i f o r n i a , O c t o b e r 1979 [26] SOLER, A. "Vibrations M o v i n g 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,  and  Stabilty  No.4 O c t . 1968  of  a  108  APPENDIX I  Stress a  function  Due tilting  variation of  to of  the  the  tiltangle  the  geometry  top  wheel  stress-distribution This  stress  two  of  the  distribution  SIGta.  across  the be  prestressing  SIGtO+SIGt between  the  tiltangle derive  due  the  called formula  for  as  system  Figure  into  the  uniform  2R0  plus  The  From  stress  53a).  sum  of  stressstress-  incorporated  stress  due  1  and  Figure SIGta  into  to  the  stress  the  stresses difference  7 due 53b  for a  to we  any can  tiltangle  TA  tan  TA  w i t h TA  = AL/Bs = TA*H/180° in  ,  A L=n*TA*Bs/l80°  *E  = II * y t * E * T A / ( 180°  degrees  and  SIGta  = 2*SIGt  =£*E = A L / L w  a  uniform  triangular  locations  the  blade  non  (see  the  tiltangle.  2*SIGt.  a  divided  loadcell LC,  force  straingage  is  the  to  blade  the  s t r a i n i n g system measures  axial  in  the  and The  the  tiltangle  results  stress-distributions, SIGtO  across  TA  d i s t r i b u t i o n can  distribution  the  in x-direction  *  Lw)  The  uniform  part  any t i l t a n g l e  S i g t O of  the  stress distribution  TA can be c a l c u l a t e d  for  from:  t a n TA = A L / ( B t - B s / 2 ) = H * T A / 1 8 0 ° or  AL  =n*(Bt-Bs/2)*TA/l80°  and SIGtO =e*E = E*A L / L = n * ( B t - B s / 2 ) * E * T A / ( L w * l 8 0 ° )  The  additional  loadcell consists  LC of  SIGtta  stress i n the  the  S I G t t a which straining  is  measured  s y s t e m due t o  sum:  = S I G t O + S I G t a / 2 = SIGtO+SIGt  a  by  the  tiltangle  110  -0 T  FIGURE  53 a  straingage position  ® — © — © — © — < Z )  T  T  T  I  I  NON UNIFORM STRESS DISTRIBUTION ACROSS THE BLADE AS A FUNCTION OF THE TILTANGLE TA  w =w +  !  l  (Bf-B^j 2  FIGURE  53 b  CHANGE OF THE  OF STRAIN AS A TILTANGLE TA  FUNCTION  APPENDIX I I  Calculation  In  of t h e wheel s u p p o r t  the p u b l i c a t i o n  Band Saws" C D . MOTE to  describe  stiffness  the  Ks on  introduces calculated  a  "Some Dynamic C h a r a c t e r i s t i c s o f  [9] develops  influence  the  s t i f f n e s s Ks  a  mathematical  o f t h e wheel  lateral  natural  nondimensional  factor  model  support  system  frequencies. which  He  can  be  from: 1  n=1-K=  1+  Lw*Ks 2A*E  Experiments system  showed  Ks=825N/mm. formula  with  static that  loading the  Substituting  of t h e t o p wheel  wheel this  support  value  into  yields: 1  n=1  -K=  1+ 2*398.7mm *2.1*l0 N/mm 2  or  K=0.988  = 0.012  :  2 464mm*825N/mm 5  2  support  stiffness the  above  APPENDIX I I I a)  Error calculation absolute rabs  - t h e o r . Data  Data v a l u e  - t h e o r . Data v a l u e )  theor.data  b)  Fomula  value  error:  (exp.  =  data  error:  = exp. Data v a l u e  relative rrel  for stress  for calculation  value  of the a b o l u t e  change 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 of  the t i l t s t r e s s - d i f f e r e n c e  fabs  = f(TSD=95.6N/mm )  -  2  f(TSD=95.6N/mm ) 2  f=frequency  Formula for  SG  function  TSD: 2  f(TSD=26.7N/mm ) 2  + 2  f(TSD=95.6N/mm ) 2  v a l u e (Hz)  f o r the c a l c u l a t i o n  s t r a i n g a g e and l o a d c e l l  rrel= rrel  a  = f(TSD=26.7N/mm )  c)  and r e l a t i v  f(TSD=26.7N/mm ) -  2  frel  * 100  ( SG - LC = relativ  error  data:  )*100/LC error  = change o f a v e r a g e from  of the r e l a t i v e  seven  stress across  the blade  s t r a i n g a g e s SG  LC  = change o f a x i a l  LC  = absolute  maximum  p r e s t r e s s from axial  l o a d c e l l LC  p r e s t r e s s from LC  113  PROGRAM NEFF  "  THIS PROGRAM SCANS SELECTS THE NUMBER CHANNELS AND THEIR CHANGED BY EDITING  "V  NEFF CHANNELS IN HANDSHAKE MODE. THE USER OF SAMPLES > THE SAMPLING RATE ? THE NUMBER OF ADDRESSES AND GAINS. THESE PARAMETERS ARE THE PARAMETER F I L E > 'PAR.DAT'.  C C C C C  NOTE: MAXIMUM CLOCK RATE IS 40000 HZ. FOR MULTI-CHANNEL SCANSv THE CLOCK RATE SHOULD BE LIMITED TO 22000 HZ.  C C C C  THIS PROGRAM INCLUDES EXTERNAL SCAN START.  THE MAXIMUM SAMPLE SIZE IS 4096.  SYSTEM LIBRARY ROUTINES EXTERNAL WTQIO EXTERNAL GETADR EX TERN Air.. ASNLUN DATA  ARRAYS  DIMENSION LIST(4096) DIMENSION I DAT(4096) DIMENSION IBUFF(1) C C  C C  C C  QIO PARAMETER DIMENSION  ARRAY  IPARM<6>  QIO STATUS ARRAY DIMENSION I STAT(2)  C C C  C C C C C C C C C C C C C C C C C C C 1.11  DINP STATUS ARRAY DIMENSION  I0SBC2)  BYTE HQ, ANS» ANS2> YES DATA NO/78/> YES/89/ ASSIGN NIO: TO LU 3 CALL ASNLUN < 3 y'NI'» 0) GET STARTING AND ENDING LIST INDEX IF NOT GOOD DO AGAIN  THE FOLLOWING ROUTINE TO ALLOW EXTERNAL SCAN INITIATION CAN BE INSERTED INTO THE PROGRAM BY REMOVING THE FOLLOWING 'GO TO' INSTRUCTION. GO TO 595 DECIDE IF SCAN WILL BE STARTED EXTERNALLY. WRITE<5»111) FORMAT (1X» 'WILL SCAN BE INITIATED EXTERNALLY? Y/N '»$)  114  222 C 393 C  READ(5y222) ANS FORMAT(A5) CONTINUE CALL. ASSIGN<1»'PAR.DAT')  C C C: C C C 901 551 532 C C C C C C  C 560 C C  C  590 570 580 C C C  321 1234 C C C C C C C 303 C C  READ PARAMETERS FROM F I L E 'PAR.DAT'. IWCT=SAMPLE SIZE PER CHANNEL. NCHAN=NUMBER OF CHANNELS. CLOCK=NEFF SAMPLING RATE PER CHANNEL. READ (1,901) J.UICT » NCHAN FORMAT ( 215) READ(1»S51> CLOCK FORMAT(F16.5) READ(1»552) LIST (1) y L I S T ( 2 ) FORMAT(06) IF (NCHAN. EC1.1) GO TO 590 FOR TWO OR MORE CHANNELSy USE SAMPLE/HOLD MODE. CLOCK RATE AND SCAN LIST SIZE ARE MULTIPLIED TO GIVE DESIRED SAMPLING RATE AND SAMPLE SIZE FOR EACH CHANNEL. 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> ( L I S T ( I ) y 1 = 3 y NCHAN+2) DO 560 1 = 2 y(IUCT-NCHAN+1) LIST(I+NCHAN+1)=LIST(I) CONTINUE GO TO 580 FOR SINGLE CHANNELy  USE SAMPLE MODE ONLY.  DO 570 I=2yIWCT-l LIST(I+1)=LIST(I) CONTINUE CONTINUE SET PROGRAMMABLE CLOCK. DWELL=1./CLOCK HERTZ=1./XRATE(DUELL»IRATE»IPRSET»1) WRITE(Sy321> CLOCKy HERTZ FORMAT (IX, 'CLOCK= ',615.5. ' HERTZ= 'G12.5) CALL CLOCKB(IRATE»IPRSETt1tINDy 1) WRITE(5y1234) IND FORMAT(IX»'IND CODE= ' r I 3 ) RESET SERIES 500 BUS BYTE COUNT = 2 IPARM 1 = IDATA ADDRESS FUNCTION = 1002 OCTAL IPARM(2)=2 CALL GETADR(IPARM(1) yIDAT) CALL WTQIO("1002 ,3, 10 y yISTATyIPARMyIDS) PRINT COMPLETION  MESSAGE  115  c WRITE(5*905) 905  F0RMAT(1X*/*1X»'SERIES WRITE(5*906)  906  500  BUS  RESET!'*/)  I S T A T U ) * I S T A T ( 2 ) * I D S  FORMAT(IX*'DRIVER *  *1X*'LAST  *  FIX.'DIRECTIVE  COMPLETION  RESPONSE STATUS  CODE  ='»06*'  (OCTAL)'*/  ='*06*'  ( O C T A D ' F /  =',06*'  (OCTAL)'*/)  C C  WRITE  DATA  TO  RAM*  READ  BACK  AND.  CHECK  C C  CONVERT  C  IPARM(3)=RAM  WORDS  C  IPARM(1)=LIST  C  FUNCTION  TO  BYTES  STARTING  ADDRESS  ADDRESS  C0DE=400  OCTAL  C IPARM(2)=IWCT*2 IPARM(3)=1 CALL  GETADR(IFARM(1)*LIST(1))  CALL  WTQIO("400,3*10*,ISTAT,IPARM*1DS)  C C  READ  C  LOCATIONS  C C C C  IPARM(1)=IDAT ADDRESS IPARM(2) AND IPARM(3> UNCHANGED FUNCTION CODE--1000 OCTAL CALL CALL  DATA  BACK IN  FROM  ARRAY  RAM  INTO  CORRESPONDING  I DAT FROM  GETADR(IPARM(1)*IDAT<1)) WTC4I0( " 1 0 0 0 * 3 * 1 0 * , 1 S T A T » I P A R M *  ABOVE  IDS)  C C  PRINT  ANY  ERRORS  C  :I:ERR=O DO  400  1= 1 *IWCT  IF(I DAT(I),EQ.LIST(I)) IERR=IERR+1 WRITE(5*920) 920 400 C C  GO  TO  400  L I S T ( I ) » I D A T ( I )  FORMAT(IX*'RAM  ERROR  -  OUTPUT  =  '*05*'  »  READ  BACK  =  ',05,/)  CONTINUE PRINT  ERROR  COUNT  C URITE(5*921) 921  IERR  FORMAT(IX*'WRITE WRITE(5*906)  TO  RAM  AND  READ  BACK  COMPLETE'*14  ISTAT(l)*ISTAT(2).IDS  C C 354  CONTINUE  C C  TO  C  REMOVE  ACTIVATE THE  THE  EXTERNAL  FOLLOWING  'GO  SCAN TO'.  C GO  TO  345  IF  (ANS.EO.NO)  C GO  TO  345  .C "c  EXTERNAL  START  C C  WAIT  FOR  SIGNAL  TO  START  CALL  DINP(0*0*IOSB,INPUT)  C 10  IF  (INPUT.EQ.O)  GO  TO  346  C 345  CONTINUE  GO  TO  10  SCAN.  START  OPTION*  *'  ERRORS  '*/)  116  c C  C 654 346 C C C C C C C C  C C C C C  MANUAL  WRITE<5,654> F O R M A T ( I X , ' T O START R E A D < 5 , 2 2 2 ) CR CONTINUE EXECUTE  922 C C C  930  444 445 935 450  924 C C C -C 302 112 211  800 902 804  FROM  RAM  SCAN,  ENTER  RETURN' , $)  HANDSHAKE  FUNCTION C0DE=3001 OCTAL I P A R M ( 1 ) = I D A T ADDRESS IPARM<2)==BYTE COUNT IPARM(3)=RAM S T A R T I N G ADDRESS CALL GETADR(IPARM<1),IDAT<1)) IPARM<2)=IUCT*2 IPARM<3)=1 C A L L WTQIO< "30011-3,10, , I S T A T , I P A R M , I D S )  R E P E A T L A S T F E U DATA P O I N T S U N T I L THE P O I N T S EQUALS 'IWCT', A POWER OF 2. DO  888 C  START  TOTAL  NUMBER  OF  DATA  888  I=IWCT, IWCT+NCHAN+1 ID A T ( I ) = ID A T < I -- N C H A N -1) CONTINUE  WRITE(5,922) FORMAT < I X , ' E X E C U T E  FROM  STORE  SELECTED  DATA  IN USER  RAM  IN HANDSHAKE  MODE',/)  FILES.  DO 4 5 0 J=3,NCHAN+2 CALL F I L E S ( J ) I F < NCHAN.EH . 1 ) GO TO 444 WRITE ( 2 ,930 ) INT ( F L O A T ( I W C T ) / F L O A T (NCHAN+1) ) , H E R T Z / F L O A T (NCHAN+1) FORMAT(I5,F16.5) WRITE ( 2 , 9 3 5 ) ( F L O A T ( I DAT < I ) ) / 3 2 7 6 8 . , I = ..l, IWCT+NCHAN+1 , NCHAN + 1 ) GO TO 4 4 5 W R I T E ( 2 , 9 3 0 ) IWCT,HERTZ WRITE(2,935)(FLOAT(I DAT(I))/32768.,I=J,IWCT+NCHAN+1) CONTINUE FORMAT(6E13.5) CALL C L 0 S E ( 2 ) CONTINUE WRITE(5,906) I S T A T ( 1 ) , I S T A T ( 2 ) , I D S WRITE<5,924) F O R M A T ( I X , / , I X , ' F I N I S H E X E C U T I N G FROM RAM',/) GO TO 8 0 2 THE FOLLOWING OPTION ALLOWS SCAN TO BE R E P E A T E D USING THE SCAN L I S T STORED IN N E F F RAM. WRITE(5,112) FORMAT <1X,'DO YOU WISH TO R E P E A T SCAN? ',$) R E A D ( 5 , 2 1 1 ) ANS2 FORMAT(A5) I F ( A N S 2 . E Q . Y E S ) GO TO 3 5 4 GO TO 8 0 4 WRITE(5,902) F O R M A T ( I X , ' # * * * * I N V A L I D DATA *****',/) STOP END  117  c C C C  140 150  SUBROUTINE F I L E S ( J ) FOR DATA STORAGE.  ALLOWS USER TO CHOOSE F I L E  SUBROUTINE F I L E S ( J ) BYTE BUF<80> WRITE(5,140) J-2 F O R M A T d X , 'ENTER CHANNEL I >' ) F I L E READ<5,150) (BUF(I)»I=1»80) FORMAT(80A1) L=LENGTH(BUF 180) BUF(L+1)=0 CALL ASSIGN(2,BUF) RETURN END  NAMES  NAME ',$>  1  C C C C C  100 200  FUNCTION LENGTH F I N D S LENGTH OF ALPHANUMERIC DATA S T R I N G . THE F I R S T 'BLANK' CHARACTER I N D I C A T E S THE END OF THE S T R I N G . INTEGER FUNCTION L E N G T H ( B U F tN) BYTE B U F ( 1 ) t B L INTEGER N DATA B L / 3 2 / DO 100 I = N , 1 y - 1 I F ( B U F < I ) . N E . B L ) GO TO 2 0 0 CONTINUE LENGTH-I RETURN END  118  C C C C C C  " S T R A I N " READS STRAINGAGE-DATA FOR ONE L O A D C E L L AND 9 S T R A I N GAGES FROM F I L E S . I T C A L C U L A T E S THE A X I A L PRELOAD TUOROCN3, THE S T R A I N S AND S T R E S S E S DUE TO L O A D C E L L R E A D I N G S y S T R A I N S AND S T R E S S E S AND MEAN VALUES DUE 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 . "S6" MEANS STRAINGAGE . L C " M E A N S L O A D C E L L . STG MEANS S T R E S S EPS MEANS S T R A I N INTEGER I . J , E . I W C T » E X P N O . N . M . K REAL C A L L C » C A L S G X . 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. E P S < 5 . 1 0 . 1 0 > . S I G ( 5 . 1 0 . 1 0 ) . D A T A < 5 » 1 0 . 1 0 ) REAL E P S X ( 5 > 1 . 10 >_. S I O Y < 5 . 1 » 1 0 > . S I G X < 5 » 1 . 1 0 ) REAL M S I G S G ( I O ) . M S I G L C ( 1 0 ) > M E P S L C ( 1 0 ) » M E P S S G ( 1 0 ) y M 2 R 0 ( 1 0 ) y NUM 0  C C C C  C C 71 72 C C  37 C C 700  701  150  111 112 C  ?12 211 91 81 C C  BYTE I B U F ( 8 0 ) A S S I G N P R I N T E R T T 5 TO L A B E L CALL A S S I G N ( 1 . ' T T 5 ' ) CALLC=1.9264E5 CALSGX=146.32 CALSGY=415.8 Y0UNG=210000.0 A-398.7  "1"  EXPNO I S AMOUNT OF E X P E R I M E N T S DONE WRITE ( 5 y 7 1 ) FORMAT ( I X . 'ENTER AMOUNT OF E X P E R I M E N T S DONE J'y *) READ ( 5 y 7 2 ) EXPNO FORMAT ( 1 4 ) • M I S #0F E X P E R I M E N T S y N I S tfOF STRAINGAGES USED y K I S NUMBER SAMPLES BEEN TAKEN DO 81 M = l y EXPNO WRITE ( 5 . 3 7 ) M FORMAT ( I X y ' E X P E R I M E N T NUMBER'.14) READ DATA FROM F I L E SG(My N)y *0 OF SCANNS IWCT AND SCANNING FREQUENCY HERTZ WRITE(5.700) F O R M A T ( I X . ' E N T E R F I L E N A M E y WHERE S T R A I N G A G E DATA ARE  *.*>  OF  STORED:'  READ ( 5 . 7 0 1 ) <IBUF( J ) » J - ~ l y 80 ) FORMAT(80A1) L=LENGTH ( I B U F . 8 0 ) DO 91 N = l » 1 0 I B U F <L+1)=59 I F ( N . G E . 8 ) GOTO 150 IBUF(L+2)=N+48 ' I B U F ( L + 3)=0 GOTO 111 IBUF(L+2)=49 IBUF(L+3)=N-8+48 IBUF(L+4)=0 CALL ASSIGN (2.IBUF) READ ( 2 . 1 1 2 ) IWCTyHERTZ FORMAT ( I 5 . F 1 6 . 5 ) READ DATA FROM F I L E SG(M.N) S I G N A L V A L U E S DO 211 K = l y ( I W C T - l ) READ ( 2 . 2 1 2 ) DATA(M.N y K ) FORMAT ( 6 E 1 3 . 5 ) CONTINUE CALL C L 0 S E ( 2 ) CONTINUE CONTINUE NOW A L L DATA FOR M E X P E R I M E N T S DATA(M y N.K) DO 213 K = l y ( I W C T - 1 )  ARE READ  INTO  IWCTy  HERTZ  AND  119  C C  58  311 C  411 C C  611 511 C  911 811 C C  C A L C U L A T E A B S . V A L U E S ! TUOROySTRAIN AND S T R E S S FOR L O A D C E L L READINGS DO 58 N = l y l O DATA<1»NrK)=(DATA<1yNyK)+DATA<2yNyK>)/2 CONTINUE DO 3 1 1 M = 3 » E X P N 0 DATA < M r 1 1 K ) = D A T A < My1>K)-DATA < 1 , 1 1 K ) TWORO(M y1y K ) = D A T A ( M y1y K ) # ( C A L L C / O . 8 3 5 + 8 5 8 8 . 7 ) * 1 . 1 9 EPS(My 1yK)=TWORO(My1yK>/C2*A*Y0UNG> SIG(My1yK)=EPS<My1yK)*YOUNG CONTINUE C A L C U L A T E V A L U E S FOR SGX5 ABS.y STRAINSGX DO 5 1 1 M=3yEXPNO DO 411 N = 2y8 DATA< M y N y K )=DATA(M y Ny K)-DATA<1y N y K) E P S ( M y N y K)=DATA < M tN,K)/CALSGX CONTINUE CALCULATE DO 611 N = 9 » 1 0 DATA(M y N y K)=DATA < M y N y K ) - D A T A ( 1 y N y K) EPS < M y N y K >=DATA(M y N y K >/CALSGY CONTINUE CONTINUE C A L C U L A T E S T R E S S SGX DO 8 1 1 N==2y8 DO 9 1 1 M=3yEXPN0 S I G ( M y N y K ) = 2 3 0 7 6 9 . 2 * ( E P S ( M y N y K) *+0.15*(EPS(My9yK)+EPS(My10yK))) CONTINUE CONTINUE CALCULATE  S T R E S S SGY  DO 9 1 2 M=3yEXPN0 DO 9 1 3 N==2y8 C E P S X ( M y l y K ) I S SUM OF S T R A I N V A L U E S IN C X-DIRECTION. E P S X ( M y1y K ) =EPSX(M y1y K > +EPS < M y N y K) 913 CONTINUE S I G Y ( M y l y K ) = < E P S X ( M y1y K ) * 0 . 3 / 7 . 0 + 0 , 5 * ( E P S < M » 9 y K) *+EPS(My10yK)))*230769.2 912 CONTINUE C C A L C U L A T E THE AVERAGE FOR TWORO FOR A L L M E X P . DO 9 2 3 M=3.EXPN0 M 2 R 0 ( K ) = M 2 R 0 ( K ) + T U O R O ( M y1y K) 923 CONTINUE M2R0 ( K ) =M2R0 ( K ) / ( EXPN0--2 ) C C A L C U L A T E AVERAGE L O A D C E L L - S T R E S S "MSTRESSLC FOR A L L E X P . DO 9 2 4 M=3yEXPN0 M S I G L C ( K ) = M S I G L C ( K ) + S I G ( M y1y K) 924 CONTINUE MSIGLC(K)=MSIGLC < K)/(EXPNO-2) C C A L C U L A T E THE AVERAGE S T R E S S D I S T R I B U T I O N FROM STRAINGAGE 2-8 C * ACROSS THE BLADE DO 9 2 1 M=3yEXPN0 ' DO 9 2 2 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 C A L C U L A T E AVERAGE S T R A I N FOR L C AND SGX ACROSS THE BLADE FOR A L L C . * M E X P E R I M E N T S IN MICROSTRAIN DO 9 2 5 M = 3y EXPNO  120  MEPSLC(K)=MEPSLC(K)+EPS(M,1,K) MEPSSG(K)=MEPSSG< K ) + E P S X ( M , 1 , K ) /7.0 925 213  CONTINUE MEPSLC < K)=MEPSLC < K ) / ( E X P N O - 2 5 * 1 . 0 E 6 MEPSSG(K)=MEPSSG(K)/<EXPNO-2)*1.0E6 CONTINUE  C  DO  928 C  C C C C  52 51 9 C  11 12 13 C 14  15  16  22  23  24  9 2 8 M=3yEXPNO TILTRA=TILTRA+SIG(M,2, l)/SIG(My8y 1 > CONTINUE TILTRA=TILTRA/(EXPNO-2) *************  *****************  ******************************  ONLY VALUES F O R K = l ARE BEING PRINTEDy BUT A L L VALUES FOR K = l TO * ( I U C T - 1 ) ARE STORE I N ARRAYS DATAy E P S , S I G K =l WRITE A L L DATA ON SCREEN AND PRINTER F I R S T M U L T I P L Y A L L S T R A I N S BY 1.0E6 TO GET M I C R O S T R A I N UNITS DO 51 M-=3 y EXPNO DO 52 N = l , 1 0 E P S ( M y N y K)=EPS< M , N , K ) * 1,0E6 CONTINUE CONTINUE WRITE<1,9) WRITE(5,9) FORMAT('l') WRITE 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 PAPER WRITE ( 5 , 1 1 ) FORMAT<1X,'ENTER B L A D E P O S I T I O N (A TO X ) : ' , $ > READ<5,12) POS FORMAT(A3) W R I T E C 1 y 1 3 ) POS W R I T E ( 5 , 1 3 ) POS F O R M A T ( I X y'BLADE P O S I T I O N J ' , A 2 ) WRITE(5,17) WRITE<1,17> WRITE AVER. A X I A L PRELOAD FROM LC FOR M E X P . WRITE ( 5 , 1 4 ) M 2 R 0 ( K ) WRITE<1y14) M2R0(K) FORMAT <IX y'AVERAGE A X I A L PRELOAD FROM LOADCELL FOR M EXPERIMENT *Sy M2R0=',F12.2, ' CN3') WRITE ( 5 , 1 5 ) M S I G L C ( K ) WRITE ( 1 , 1 5 ) M S I G L C ( K ) FORMAT ( I X , ' A V E R A G E A X I A L P R E S T R E S S FROM LOADCELL * M S I G L C = ' , F 1 2 . 2 , ' CN/MM"23') 'WRITE ( 5 , 1 6 ) M S I G S G ( K ) WRITE ( 1 , 1 6 ) M S I G S G ( K ) FORMAT ( I X , ' A V E R A G E A X I A L STRESS FROM SG2-SG10 FOR M E X P E R I M E N T S * MSIGSG=' , F 1 2 . 2 , ' t:N/MM"2J') WRITE(5,17) WRITE(lyl7) WRITE(5,22> MEPSLC(K) WRITE(1,22) MEPSLC(K) F O R M A T ( I X , ' A V E R A G E A X I A L P R E S T R A I N FROM LOADCELL ' y l S X y *'MEPS1.C==' , F 1 2 . 2 , ' CMICR0STRAIN3 ' ) WRITE(5y23) MEPSSG(K) WRITE(1,23) MEPSSG(K) F O R M A T C I X y ' A V E R A G E A X I A L S T R A I N FROM SG2-SG8'>23X > * 'MEPSGX=',F12.2,' LMICR0STRAIN3') WRITE(5,17) WRITE(1,17) WRITE(5,24) TILTRA WRITE(1,24) TILTRA F O R M A T ( I X , ' T I L T S T R E S S R A T I O FOR M EXPERIMENTS =',F4.2) WRITE(1,17)  121  WRITE<1»17) WRITE(1F17) WRITE(1F17) WRITEC5,17) WRITE(5yl7) W R I T E ( 5 F 17) 17 C C  18 C  19  FORMAT('  ')  PRINT T A B L E PRINT HEADLINE WRITE (5F18) WRITE(1F18) FORMAT < 1X F ' EXP ' F 17X F 'STRAIN *ESS X CNMM"23'F21XF'STRESS Y')  XCE--6II' , 13X F ' S T R A I N  YCE-63 ' F!6X»  SECOND H E A D L I N E WRITE (5F19) WRITE ( I F 19) FORMAT(2XF'#'F4XF'SG2'F3XF'SG3'F3XF'SG4'F3XF'SG5'F3XF'SG6'F3XF *'SG7'F3XF'SG8'F4XF'SG9'F3XV'SG10' * F 4 X F ' L C I ' F 4X v ' S G 2 ' » 3 X F ' S G 3 ' y 3X y'SG4'y 3X y ' S G 5 ' F 3X F ' S G 6 ' F 3 X F  20 C  21  25 C C C  *'SG7 ? 3X F S G 8 ' F 4X F ' S G 9 y 1 0 ' ) WRITE(5F20) WRITE(ly20) F O R M A T ( ' ') WRITE D A T A B L O C K DO 25 M=3yEXPNO W R I T E ( 5 F 2 1 ) (M-2> y(INT(EPS(M»NFK)+0.5)yN==2y10)yINT(SIG * ( 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 ( I N T ( E P S ( M y N y K ) + 0 . 5 ) F N = 2 F 1 0 ) t #INT(SIG(MF1FK)+0.5)y *(INT(SIG(MFNFK)+0.5)FN=2F8)FINT(SIGY(MF1yK)+0.5) FORMAT(2XFI2F2XFI4F2XFI4F2XFI4y2XyI4F2XFI4F2XFI4F2XFI4F4XF13F *3X F13y 5X y13y 4X 113F3X F 1 3 y3X y13 y 3X y13 y 3X,13 y 3 X F 1 3 t 3 X F 1 3 F 4 X y 1 3 ) CONTINUE  c  C  + + + + • • » • •  *  + •  + • • •  + + + • • • • • • • • • • • • • •  + *  + • • •  STOP END INTEGER F U N C T I O N BYTE B U F ( l ) INTEGER N B Y T E BL DATA B L / 3 2 / DO  10 20  I=Nyly-l IF(BUF(I ) CONTINUE LENGTH=I RETURN END  LENGTH(  BUFy  N)  10  .NE.  BL  ) GO  TO  20  + • •  + • + + • • • • • •  + • •  + + +  <•*•  'STR  122  C  "DYN"  READS  C  GAGES  FROM  C  THE  C  STRESSES  STRAINGAGE-DATA FILES.  STRAINS  C  "SG"  C  EPS  AND  AND  MEANS  IT  FOR  ONE  LOADCELL  CALCULATES  THE  AXIAL  STRESSES  MEAN  VALUES  STRAINGAGE  MEANS  STRAIN.  DSG2-SG8  TO  LOADCELLREADINGS;  TO  9  "LC"MEANS VALUES  VALUE  INTEGER  I» J ? E »IWCT >EXPNO»N»M ? K .POS.NCHAN CALSGX.  FILE  OF  CALSGY .  STRAINS  AND  READINGS.  MEANS  STRESS  LOCATIONS.  SAMPLES)  =512!!  TUORO(1.1.513),  AFYOUNG.HERTZ»TILTRA  VIRTUAL  EPS(1.9.513). SIG(1»8,513).DATA(3.9.513)  VIRTUAL  EPSX(1F1F513)FSIGY(1F1.513)»SIGX(1.1F513)  REAL  MSIGSG<513>FMSIGLC(I)FMEPSLC(513)FMEPSSG(513)FM2RO<1)FNUM BYTE  C  (NO  S T R A I N •TWOROTNIIF  LC  AN  IWCT  AT  LOADCELL. SIG  FOR  9  STRAINGAGE  MAXIMUM  FOR  STORED  SINGLE  C  CALLC.  BE  DUE DUE  C  REAL  CAN  .  STRESS  AND  PRELOAD  ASSIGN CALL  IBUF(80)  PRINTER  TTS  TO  LABEL  "1"  ASSIGN(IF'TTS')  CALLC=1.9264E5 CALSGX=166.32 C A L S G Y = 4:I.5,8 Y0UNG=210000.0 A=398.7 C C  M  C  SAMPLES  IS  »0F  C  NCHAN  IS  WRITE 71 72  37  NUMBER  81  OF  <IX»'ENTER  (5F72)  FORMAT DO  N  IS  #OF  STRAINGAGES  USED.  K  IS  NUMBER  IWCT  AND  OF  TAKEN CHANNELSBE1NG  SCANNED  (5.71)  FORMAT READ  EXPERIMENTS. BEEN  #OF  CHANNELS  BEING  SCANNED:'.$)  NCHAN  (14)  f3  M=l.  WRITE (5.37) M FORMAT (IX.'EXPERIMENT  C  READ  c  DATA  NUMBER'.14)  FROM  SCANNING  FILE  FREQUENCY  SG(M.N).  »0  OF  SCANNS  HERTZ  WRITE(5.700)  700  FORMAT(IX F'ENTER  FILENAME.  WHERE  STRAINGAGE  DATA  ARE  STORED 5  *»* ) READ 701  (5.701)  (IBUF(J).J=1.80)  FORMAT(80A1) L=LENGTH DO  91  IBUF IF  (IBUF.80)  N=l,NCHAN (L+l)=59  (N.GE.8)  X  GOTO  150  IBUF(L+2)=N+48 IBUF(L+3)=0 GOTO 150  111  IBUF(L+2)=49 IBUF(L+3)=N-8+48 IBUF(L+4)=0 CALL ASSIGN (2.IBUF) READ (2.112) IWCT.HERTZ FORMAT (I5.F1A.5)  111 112  c  READ  DATA  READ  (2.212)  212  FORMAT CALL  91 81 C C  FROM  FILE  SG(M.N)  SIGNALVALUES  (DATA(M.N.K).K=1.IWCT  )  (6E13.5)  CL0SE(2)  CONTINUE CONTINUE NOW  ALL  DATA  FOR  M  EXPERIMENTS  ARE  READ  INTO  IWCT.  HERTZ  AND  DATA(M.N»K) DO  213  K'=1,IUCT  C  CALCULATE  C  READINGS DO 6 5 N=1FNCHAN  ABS.  VALUES:  TWORO.STRAIN  AND  STRESS  FOR  LOADCELL-  123  DATA(1 y N y K ) = (DATA(1 y N y K)+DATA(2 y N yK))/2 65  CONTINUE D A T A < 3 f1fK)=DATA  <1y11K)  < 3 y1yK)-DATA  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 EPS(1,1yK)=TWORO(1t1>K)/(2*A*Y0UNG) SIG(1y1fK)=EPS(1y1rK)*YOUNG 311  CONTINUE IF  C  (NCHAN.  CALCULATE  EQ.  1)  VALUES  DO  GOTO FOR  411  900  SGXJ  ABS  STRAINSGX  N=2y(NCHAN-1) DATA(3 y N yK)=DATA(3 y N yK)-DATA(1 y N yK ) EPS(1yNyK)=DATA(3yNyK)/CALSGX  411  CONTINUE  C C  CALCULATE 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 ) EPS(1y NCHAN y K)=DATA(3 y NCHAN y K ) / C A L S G Y  611  CONTINUE  C  CALCULATE DO  811  STRESS  SGX  N==2y ( N C H A N - 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  CONTINUE  C C  CALCULATE  STRESS  DO  913  SGY  N=2y(NCHAN-1)  C  EPSX(lylyK)  C  IS  SUM  OF  STRAIN  VALUES  IN  X-DIRECTION. E P S X ( 1 y1 y K ) =EPSX ( 1 y1 y K ) + E P S ( 1 y N y K >  913  CONTINUE 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 NCHAN yK) *))*230769.2  C  CALCULATE  THE AVERAGE  FOR  C  CALCULATE  THE AVERAGE  S T R E S S D I S T R I B U T I O N FROM  C  *  ACROSS  THE DO  TWORO  FOR  ALL  M EXP. STRAINGAGE  2-8  BLADE 922  N=2y(NCHAN-1> SIGX(1y1yK)=SIGX(1ylyK)+SIG(lyNyK>  922  CONTINUE MSIGSG(K)=SIGX(1y1yK)/(NCHAN-2)  C C  CALCULATE •  *  M  AVERAGE  EXPERIMENTS  IN  STRAIN  FOR  LC  AND  SGX  ACROSS  THE BLADE  FOR  ALL  MICROSTRAIN  M E P S L C ( K ) = M E P S L C ( K > +EPS(1y1y K) MEPSSG(K)=MEPSSG(K)+EPSX(1y1y  K>/(NCHAN-2)  MEPSLC(K >=MEPSLC(K)*1.0E6 MEPSSG <K)=MEPSSG(K)*1.0E6 213  CONTINUE  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 C C  ONLY *  VALUES  (IWCT-1) WRITE  ARE  ALL  FOR  K=l  STORE  DATA  ON  ARE IN  BEING  ARRAYS  SCREEN  AND  PRINTEDy DATAy  BUT  EPSy  ALL  VALUES  S I G  PRINTER  WRITE(ly9) WRITE(5y9> 9  FORMAT('l')  C  WRITE  SCREEN:  BLADEPOSITION  AND  900 11  WRITE (Syll) FORMAT( lXy ' E N T E R R E A D ( 5 y12) P O S  BLADEPOSITION  (A  12  13  ON  FORMAT(A3) WRITE(lyl3)  POS  WRITE(5yl3)  POS  FORMAT(lXy'BLADE WRITE(5yl7)  POSITION:'yA2)  PRINT TO  ON  XK'yU)  PAPER  FOR  K=l  TO  124  17 C  16  14  15  24 C 901 57  58 C C 51  53 50 C56  54 902  52  WRITE(1,17) FORMAT < ' ') 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) CONTINUE M2R0(1)==M2R0(1)/IUCT MSIGLC <1)=MSIGLC <1)/IWCT WRITE (5,14)M2R0(1) WRITE(1,14> M2R0(1> 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) 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 FORMAT(IX»'TILTSTRESSRATIO FOR M EXPERIMENTS =',F4.2) ASSIGN FILENAME TO OUTPUT F I L E FOR STRESS DATA LC WRITE (5,57) FORMAT (IX,'ENTER FILENAME, WHERE LC STRESS VALUE fcSHALL BE STORED:' ,*) CALL FILES WRITE (4,58) (SIG(1,1,K),K=1,IUCT) FORMAT (6F9.2) CALL CLOSE (4) IF (NCHAN.EQ.l) GOTO 902 ASSIGN FILENAME TO OUTPUT F I L E FOR STRESS DATA SG2--SG8 WRITE SG STRESS VALUES FROM SGI - SG(NCHAN-1) TO F I L E DO 50 N=2,(NCHAN-1) WRITE (5,51) N 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) FORMAT (6F9.2) CALL CLOSE (4) CONTINUE WRITE AVERAGE STRESS FOR ALL (NCHAN-1) SG INTO F I L E WRITE (5,56) FORMAT (IX,'ENTER FILENAME, WHERE AVERAGE SG STRESS- VALUES tSHALL BE STORED:',*) CALL FILES WRITE (4,54) (MSIGSG(K),K=1»IWCT) FORMAT (6F9.2) CALL CLOSE (4) STOP END SUBROUTINE FILES BYTE IBUF (80) READ (5,52) ( I B U F ( J ) , J = l , 8 0 ) 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» BYTE B U F ( l ) INTEGER N BYTE BL DATA B L / 3 2 / 10 I=N»1»-1 IF(BUF<I) CONTINUE LENGTH=I RETURN END  N)  DO  .NE. BL ) GO TO 20  C C C C C C  "FREQ" E N T E R S DATA FOR A T I M E S C A L E INTO A F I L E C A L L E D "FREQ.DAT". THE DATA R E P R E S E N T THE T I M E A X I S IN A X-Y PLOT AND ARE NEEDED TO PLOT DATA A C Q U I S I T I O N E D WITH THE " N E F F " PROORAMM. THE T I M E A X I S DATA ARE INCREMENTS OF THE R A T I O I U C T / H E R T Z — ( S A M P L E S TAKEN/SCANNING F R E Q U E N C Y ) . IWCT AND HERTZ DEPEND ON THE E Q U I V A L E N T V A L U E S IN "PAR.DAT".  C C  11  12 13  14  15  16  REAL H E R T Z , T I M E ( 5 1 2 > ' INTEGER IWCTvN WRITE ( 5 , 1 1 ) FORMAT ( I X , ' E N T E R #OF SAMPLES BEING TAKEN (IWCT FROM " P A R . D A T " ) : *',*> READ ( 5 , 1 2 ) IWCT FORMAT ( 1 4 ) WRITE ( 5 , 1 3 ) FORMAT ( I X , ' E N T E R SCANNING FREQUENCY ( H E R T Z FROM "PAR.DAT") * DO NOT FORGET THE !!DECIMAL-POINT!! :',*) READ ( 5 , 1 4 ) HERTZ FORMAT ( F 1 0 . 3 ) DO 15 N=1,IWCT TIME'(N)=TIME(N-1 ) + l / H E R T Z CONTINUE CALL ASSIGN (2,'FREQ.DAT') WRITE ( 2 , 1 6 ) ( T I M E ( N ) , N = l , I W C T ) FORMAT ( 6 F 1 2 . 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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