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A piezo-electric pressure indicator for internal combustion engines Lind, Walter John 1935

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1 — - ; t f I mi. mk^idJmMAjifk).. ) A €6. ^61. A gIJB&0-fiiiftQ5?RI0 PRESSURE IIISlCAgQE  ffOR SERIAL COlBUSfflOI SBGI1SS hy Walter John L i n d and Ronald l e o d a r d KLinak A t h e s i s submitted f o r the Degree of MAS JEER Of APPLIED SOIBBOJS i n the Department of MEGEAfilQAL & ELECTRICAL BKG-ISffigRIl& The U n i v e r s i t y of B r i t i s h Columbia A p r i l , 19S5 < f t w ^ ' TABLE OF COKTEKTS CHAPTER IB DI GATORS INTRODUCTION Chapter Contents 1 II. HIGH SP-BED INDICATORS A. MECEAKICAL .1. Piston and Pencil Type 1 2. Optical Type Z 8. Balanced Pressure Type & B. ELECTRICAL 1. Electromagnetic Type 3 8.. Carbon Pile Type 3 3. Condenser Type 4 III. PIBZO-fiLEO.ERIO INDICATORS A. DSfSLQEEEM 1. Principle Involved 4 2. Work by Various Experimenters 5 Bi WOSK. BY TIE ASTHOSS 1. Objectives 7 2. Preparatory Charge Measurements 7 3. Design and Construction of Indicator 7 4. Testing and Specimen Results 7 : CHAPTER II I. IBTR0DUCTI01 8 i II.. THEORETICAL ASPECTS Aa CHARGE MEASUREMENTS BY J. and P. CURIE • 1* Method '" 8 2. Conclue ions 9 5. Mathematical Reletions 10 B. TEMPERATURE Ef'fECTS lo Pyro-Electrieity 11 2. Piezo-Electric Constant 13 2. El e c t r i c a l Conductivity 13 4. Conclusions 14 I I I - PRACTICAL ASPECTS •A. METHOD 15 B, TEST APPARATUS .1. Electrical.Considerations 15 2. Mechanical Considerations 17 3. Description of the Apparatus 17 C. ' CRYSTAL CLEM IK G 19 '•IT. TECBBiqUE A. ELEGTRQMBTER CALIBRATION 19 X. Vane •2. Electrometer (a) Method 20 {b} Correction for residual charges 24 B. CRYSTAL LOADIBQ 26 V. RESULTS A. SPEGBIEB TABULATION 1.. Specimen 26 2. Scope 2Q 3. Sources of Error 29 i i £>. GSI11AL fAB'OMflOB .1. Authors' Results 2. Others Results CHAPTER ; H I '. . DESCRIPTION Off JISLCATOR _ I. IlTROPgCTlOB General Requirements II. DBSIGI OOBSIDBRATIQKS A. CRYSTAL HOLDER AED LEAD 1 . Mechanical Problems 2B Electrical Problems B. AMPLIFIER 1. General Description 2. Input Circuit 3 . Compensating Circuit 4. Amplification C i r c u i t - 5 . Timing Gircuit C. GALV AB OMETER 1. General Bescrijybion 2. Magnetic Circuit 3« Electric Circuit 4. Theory (a) String (to) Harmonic analysis »; OPTICAL SYSTEM 1. General Description 2. Sweep Mechanism 3. Synchronous Shutter i i i CHAPTER I? TES f i l l 6 : ABD RESULTS I. IISTRODUUTIQI 1. Scope of Tests 2, Pressure Calibration 8. Engines II. SATISFACTORY R E S U L T S 1. Introduction 2o Cards i l l * UNSATISFACTORY RESULTS 1. Poor Performance 2 . Drifting S. High Frequency Ripple 4. Remedies 5 . Cards 6. Conclusion APPENDIX' I THEORIES Off THE P I E Z O ^ E L E O T R I O P H E H O a B M O f i H i Q,UART2 APPENDIX; II DI4PHRAM THEORY APPEIDIX III MEASUREMENT Off HIGH RESISTANCES APPEIDIX.IT HATQBMATI GAL TREATMENT Off; THE IBPUT OIROU IT; i v APPEBDIX V HAREOEIC AHALYSIS OF AM ACADEMIC PRESSURE WAVE APPlfiDIX VI LARGE SIZE DIAGRAMS BIBLIOGRAPHY v ILLUSTRATIONS • FIGURE PAGE 1 Quarts Crystal, knowing Axes 9 2 Curie Arrangement for Charge Measurement 9 ' ' 3 Authors* Arrangement for Charge Measurement 15 4 Charge Measurement Apparatus, General Arrangement 16 5 Charge Measurement Apparatus, Detail 17 6 Electrometer Arrangement 18 7 Calibration Equipment £0 8 Charge Measurement Apparatus, Diagram 21 9 Insulating Stand for Quartz Crystal 26 10 Electrometer Calibration Curve, 200 uuf. 28 11 Electrometer Calibration Curve, 600 uuf. 28 12 Crystal Holder Fitted to Lister Diesel 37 K* 13 Crystal Holder, Section 38 *^ 14 Amplifier Circuit Diagram 4-0 15 General Amplifier Characteristic 41 r* 16 Amplifier Characteristic in Working Range 41 s* 17 Measurement of Effectiv e Input Resistance 44 18 Timing Magneto f i t t e d to Lister Diesel 49 !* 19 Oscillograph Section 50 Illustrations marked ** are reproduced in Appendix 1/T to an enlarged scale. ILLffSTRATlQES EIGPRS PAGE £0 Gap flux Density Characteristics ' 51 21 Galvanometer Buspension System 52 22 Galvanometer Detail 52 23 Oscillograph Sensitivity, Theoretical and Observed 54 24 Oscillograph, General Arrangement 56 25 Sjnehromotor Wiring Diagram 57 26 Indicator Arrangement on Crossley Engine 61 CARD 1 Typical Ko-Load Card 63 8 Typical Heavy Load Card 64 9 Rapid Acceleration at ¥'ull Throttle 65 10 Rough Running During Acceleration 66 12 Multi-Exposure Card . - 6 7 13 Late Injection • 70 17 Early Injection 71 fflGURE 27 Kelvin's Model of Quartz Molecule 78 28 Model- of Quarts Molecule under Strain 80 Illustrations marked ** are reproduced in Appendix VI to an enlarged scale. v i i ILLtfSffRATIQBS FIGURE PAGE 29 Diaphram Loading Diagram 84 30 High Resistance Mesh 90 ** 31 High Resistance Measurement, Wiring-Diagram 91 02 Input Circuit Mesh 93 ** 33 Academic Pressure lave 108 v i i i A PIBZO-ELECTRIC PRESSURE INDICATOR EOR INTERNAL COMBUSTION ENGINES CHAPTER I ' 1 INDICATORS • I, : ;IN TRADUCTION ^  This chapter is devoted to a brief description and discussion of several types of high speed pressure indic-ators, an outline of the development of the piezo-electric indicator, and to an introduction to the work of the auth-ors. II. HIGH SPEED1 INDICATORS ' Commercial and laboratory instruments of the present, time may be divided broadly into two groups, as follows: v A,-;. MECHANICAL :. 1. Piston and Pencil Type: This type represents the dev^ eloped low speed indicator in which the disadvantages such as inertia and fri c t i o n of moving parts have been greatly reduced. An example of this type i s the Micro-Indicator of CQLLIES (1)4 With .this, instrument i t is possible to obtain diagrams with f a i r accuracy for speeds up to 1200 r.p.m.. , ..The natural frequency of the spring employed is ;.lg00 ^ .cycles .per second,. (1) COLLINS, W. G. , Micro-Indicator for High-Speed Engines. The Institution of Mechanical Engineers, "London. January 19-23, Vol. _1 , 127 2 2. Optical Type: In the optical indicator, the disadvan-tages of inertia and fr i c t i o n have been s t i l l further re-duced by the introduction of an oscillating optical mirror for the recording mechanism. In the WAT 8 OJS-DAL BY indicat-or, a corrugated diaphram replaces the usual piston. Al-though this has the advantage of reduced f r i c t i o n a l forces and the very important feature of continuous operation, i t introduces errors of calibration since the pressure scale is dependent on the temjjerature of the diaphram. A further error may be due to hysteresis of the diaphram* The optical indicator has, however, the advantage of giv-ing individual diagrams and with s k i l f u l operation, may be used for speedsvup to 1500 r.p.m. 3. Balanced Pressure Type: The FAREBORO' BOBBIE ECHOES indicator is an example of this type, the principle of which depends upon balancing the cylinder pressure which acts on one side of a disc-valve, by means of a known pressure on the other side. There are, therefore, no rapidly moving parts. However, although the performance of the instrument is practically independent of speed, i t has the disadvantage of giving only an average card for a series of cycles, requiring about ten seconds to obtain a complete pressure record. For a four-stroke engine running at 1500 r.p.m., this corresponds to 125 engine cycles. 3 Bo ELECTRICAL Indicators of the electrical type u t i l i z e a sens-itive galvanometer to indicate the pressure changes det-ected by the particular electrical unit employed. 1.. Electromagnetic Type: This indicator devised by TROWBRIDGE (8) has a small c o i l attached to a diaphram. One pole of an electromagnet projects into this c o i l and as the diaphram moves, an e.m.f. is set up in the c o i l which is proportional to the velocity of the diaphram. By means of a commutator on the crank shaft and an li n t - ' hoven type galvanometer, a pressure record can be taken at any part of the stroke. The instrument, therefore, gives a series of pressure ordinates upon a "time" base and in this respect resembles the PAREBORO' indicator. The instrument has the advantage of having a very compact pressure unit. However, i t also introduces errors due to the temperature and hysteresis of the diaphram. S . Carbon Pile Type: The carbon pile or variable resist-ance indicator of MARTIB and CARIS (3) employs a small diaphram connected direct to a s t i f f cantilever spring. This spring controls the pressure applied to two carbon (2) JUDGE, A. W., The Testing of High Speed Internal Combustion Engines. Page 209 (3) MART III, E* J. and. CARIS, D. E., The Electric Journal, March, 1930. Page 168 piles, which in turn control the balance of a Wheatstone bridge circu i t ; the out: of balance current passes through a sensitive galvanometer which gives the indications of the pressure fluctuations. With a galvanometer of high natural frequency, this instrument has a l l the advantages of continuous operation, "vision" diagrams, a minimum of inertia and ease of calibration. The indicator has been used by WI THROW and ROSSWEILER (4) in the Research Div-ision of General Motors. They calibrate their instrument statically at a temperature corresponding to the actual conditions of the test, and claim an accuracy of within ten percent for pressure measurements. 3. Condenser Type: Another type of electrical indicator that i s being developed at Bristol, England depends for it s operation on small changes of capacity between two insulated diaphrams, one plate of this condenser being fixed and the other subjected to the engine pressure. III. PISZO-ELECTRIC INDICATORS A. DEVELOPMENT -*•* Principle-. This instrument u t i l i z e s the property of some non-conducting crystals which become electrically polarized when subjected to pressure (5). The charge (4) WITHROw, L„, and ROSSWEILER, G. i l . , The Automobile Engineer, August, 1934. Pages 281 - 284 (5) CURIE, J. and P., Comptes Rendus, 1880, 91, 583 which is proportional to the force applied to the crystals controls the output current of a vacuum tube amplifier, which, in turn, operates an oscillograph. 2. Work by Various Experimenters: (a) S. WATAftABE (6) obtained pressure records using quartz crystals and a cathode ray oscillograph but no attempt was made to give quantitative results, the author only indicating that his results showed the method to have possibilities. (b) In 1930 KLUGE and LINGEM (7), using quartz cry-stals and a string oscillograph, obtained press-ure-time diagrams from a single cylinder 8 hp. engine running at 450 to 690 r.p.m. They give the natural frequency of the crystal unit as 100,000 cycles and that of the oscillograph as 2000 cycles per second. More recently (1933), they used a Braun tube in place of the string galvanometer, thus obviating limitations due to 6) WATAEABE, S., Scientific Papers of the Institute of Physical Chemical Research. 12: 82 - 112. 1929 7) KLUGE, J., and LIECIOi, E. E., 2eitsehrift des Vereines .deutscher. Ingenieurere vol.. 74. liov. 25, 1930. Page D O ri 6 the natural period of the string (8). A moving film was used to record the result. The engine speeds were from 750 to 2500 r.p.m. (c) WATSON, and KEYS (9) have also published results of their work using quartz crystals and a cath-ode ray oscillograph. They give the natural frequency of the detector as 100,000 cycles per second. (d) Other investigations are being carried out in the Mechanical Engineering Department of the Massachusetts Institute of Technology and at Birmingham University (10). At Birmingham, diagrams have been taken using a cathode ray tube for engine speeds up to 6000 r.p.m. (8) KLUGB and LINGER, Eorschung auf dem Gebiete des Ingenieurwesens. Vol. 4, No. 4, 1933. Pages 177 - 182 (9) WATSON, H, G. I., and KEYS, D. A., A Piezo-Elect-ric Method of Measuring-: the Pressure Variations in internal Combustion Engines. Canadian Journal of Research. Vol. 6, No. 3. March, 1932 (10) Journal of the Institute of Mechanical Engineers, February, 1935 B. . WORK BY THE AUTHORS 1. The authors o b j e c t i v e was t o develop a p i e z o - e l e c t r i c pressure i n d i c a t o r f o r l a b o r a t o r y i n v e s t i g a t i o n s having the f o l l o w i n g c h a r a c t e r i s t i c s : (a) Medium speed range (b) Continuous o p e r a t i o n {c) Adaptable to the study of t r a n s i e n t c o n d i t -ions (d) Easy c a l i b r a t i o n 2. Preparatory charge measurements were made of two quartz c r y s t a l s i n order to i n v e s t i g a t e charge leakage and the e f f e c t s of small temperature changes. 3. I n d i c a t o r u n i t s were designed and b u i l t by the authors. 4. Engine t e s t s were made on a 9 hp. Hot Surface Cross-l e y Two Stroke engine running at 550 r.p.m. CHAPTER II CHARGE MEASUR E M E K T S . 1 . INTRODUCTION This chapter describes some of the theoretical and practical aspects of the piezo-electric phenomenon in quartz crystals, and gives in detail, the methods used and the results obtained by the authors in their work on charge measurement. II, THEORETICAL ASPECTS * A. CHARGE MEASUREMENTS BY J. and P. CURIE 1. Method: In the instruments used by J. and P. CURIE to demonstrate their discovery (11) of the piezo-electric property of quartz, the quartz crystals were cut in a mode that is now known as the Curie cut. Considering a quartz crystal as a hexagonal prism, the cut is made perpendicular to one of the faces of the prism and parallel to the optic axis as illustrated in Figure .1. (11) CURIE, J . and P., Liberation of Electrical Charges by Pressure in Hemihedral Crystals with Inclined i<'aces. Comptes Rendus, 1880, 91, 294 * 1 ? 0 T s t a l l s on piezo-electric theories see Appendix I E E 0 0 T T Electric axis Optic axis Third axis Figure 1 ! The Curies coated ^ J £ the two faces perpendicular t o electric axis with t i n f o i l and applied pressure to these faces hy means of weights. Figure 2 shows the arrangement of the recording instruments. When the quartz was subjected to this load-ing, an electric charge appeared on the crystal faces connected to the quadrant elect-rometer, the latte r giving a measure of the charge liberated. 2. Conclusions: From their experiments the Curies deduced the following (12, 13) Figure 2 (12) VIGOUREUX, P. Quartz Resonators and Oscillators Page 28 (13) CURIE, J. and P., Comptes Rendus 1881, 92, 186 10 fa) "The two charges developed are equal and opposite in sign. (b) "The charge developed Is proportional to the var-iation in pressure. (c) "For a given thrust along the electric axis the charge liberated is independent of the dimensions of the piece of quartz. (d) "If the compression along the electric axis be replaced by an extension along the third axis, charges of the same sign as before w i l l be liber-ated on the same faces as before, and in the two cases the charges w i l l be equal i f the pressure per unit area is the same. (e) "Pressure in the direction of the optic axis liber-ates no electric charge." S. Mathematical Relations: If the dimensions of the plate along the electric, optic and third axes be e, o and t, the electric charge k appearing cn the faoes perpendicular to the electric axis due to a force Jf on these faces is given by = (constant)(force) - H P Assuming F to be a compressive force, then i f another compressive force i? be applied along the third axis and perpendicular to the optic axis, a charge ^ w i l l 11 appear on the same faces as in the previous case and e . .Sow suppose that a uniform pressure p be applied along a l l three axes, then the charge appearing on the ot faces due to the thrust along the electric axis is = H ( pot ) and the charge appearing on the same faces due to the thrust along the third axis is Q2 = - H F t = - ii t ( peo )•• e and Qg •= - H ( pot ) Ehen since a thrust along the optic axis produces no charge and since from the above relations we conclude that when a quartz plate of the above type is subjected to a hydrostatic pressure p , there i s no resultant charge produced. B. faifERAfURB .JgggBOTS 1. Pyro-Electricity; If, when a substance changes its temperature, there is a change in the electrical polar-ization, that substance is said to be pyro-eleetric. As crystals which are pyro-eleetric are also piezo-elect-r i c , the deformations accompanying changes in temperature give rise to polarizations of piezo-electrie origin. These false pyro-electric effects are superposed upon the true pyro-electric effects which result solely from changes of temperature, and since the false effects are generally much greater than the true, i t is d i f f i c u l t to determine the latter. A summary of a study of the subject by RIECKE, ROETGEN, Y0IG21 (14) ana LIHDMAE (15), shows the existence of a true pyro-electric effect to be in doubt and i t would seem that the sole function of temperature is to set up stresses and that no electric charges would be developed were i t possible to neutralize such stresses. More recently (1916) PERRIER (16) investigated the magnitude of the piezo-electric effect at various temperatures and considers that his results tend to prove the existence of true pyro-electricity and suggested that i t was due to a polarization existing in the quartz, independent of heat treatment or of stress. (14) VOIGT, W., Lehrbuch der Xristallphysik (15) LlKiJMAiS, K. P., 2ur Frage naeh der Existenz wahrer Pyroelektrizitat. Aimalen der Physik, Vol. 62, 1920 Page 107 (16) PERRISR, A., Hypothese de polarisations dielectri-ques spontanees et quelques-unes de ses consequence experimentales. Archives des Sciences Physiques et Haturelles. 1916, 41, 493 13 . 2. Piezo-Electric Constant; PSRRIER also made measure-ments of the variation of the piezo-electric effect with temperature, his results indicating that the phenomenon is practically independent of temperature up to 200° C., after which i t decreases until at 579° C. i t disappears entirely, reappearing at 576° C. on cooling. In 1927 DAV/SOJK (17) published results of a similar investigation. His curves indicate that the piezo-elect-r i c effect decreases gradually, but not uniformly to zero as the temperature approaches the c r i t i c a l point. It has been pointed out, however, by SCHULV'AS-SGROKIfiA (18) that results obtained by methods similar to Dawson's would necessarily be affected by the elect-r i c a l conductivity of the quarts. 3. Ele c t r i c a l Conductivity: JOPEE (12) found that the conductivity of quartz increased very rapidly with temp-erature and that i t presented strong analogies with the conductivity of a gas0 (17) DAV/SOM, L. , Piezo-Slectricity of Crystal Quartz. Physical Review, • 1.927, 29, 532 (18) SCHtflWAS-SOROKIRA, R. D., Is i t possible to det-ermine the piezo-electric constant at high temper ature by the Statical Method? Physical Review, 1929, 34, 1448 (12) VIGOUREUX, P., Quartz Resonators and Oscillators, Page 21. 14 . He expressed It in the form A <? - Be 1 where <f » Conductiv ity at T° Absolute 4 A = - 1.5 x 10" for a l l crystals For Quartz (a) B » 25000 in directions parallel to the optic axis (b) B - 1/80 in directions perpendicular to the optic axis. 4. Conclusions: (a) The piezo-electric effect is approximately constant at temperatures less than 200° C. (b) The existence of a true pyro-electric effect is s t i l l in doubt. (e) The el e c t r i c a l conductivity of quartz incr-eases rapidly with temperature. (d) Q,uartz is best as an insulator in directions perpendicular to the optic axis. (e) A static method of determining the piezo-electric constant is suitable at low temper-atures. 15 III. PRACTICAL ASPECTS A. METHOD Two quartz crystals E.5 cm. in diameter and 0.5 cm. thick, cut at right angles to the electric axis and para-l l e l to the optic axis, and tested for twinning, were ex-amined by a method very similar to that used by the Curies. A force was applied by means of weights in a direction parallel to the electric axis and perp-endicular to the faces of the — J j c r y s t a l s , thus liberating an ^ ^ ^ J H e l e c t r i c a l charge to the var-Eigure 3 iable standard a i r condenser at C in Figure 3 and the quadrant electrometer at t i , the latter giving a measure of the charge. B. TEST APPARATUS In the design and construction of the testing equip-ment the following points were considered: 1• Electrical Considerations (a) Shielding (b) Temperature control (c) Humidity control (d) Electrical insulation (e) Contact potentials (f) Surface leakage of charges 16 for Legend, see table after Figure $ 1? 2. Mechanical Considerations: (a) Method of applying a load to the c r y s t a l s (b) Instrument vi b r a t i o n 3. Description of Apparatus: The general arrangement of the charge measuring equipment i s I l l u s t r a t e d in figures 4 and 5 . Figure 5 The quadrant electrometer at S i s mounted on a concrete block set on rubber pads and Is housed i n the smaller compartment of the snield. 18 figure 6 Shielded potential lead to electrometer vane {and II) Mercury control switches A metal-lined double box used in controlling the temperature of the a i r surrounding the quartz plate under test. b t i l l air is the heat-insulat-ing medium bet?;een the two boxes and a small crucible containing phosphoric pentoxide placed in the box keeps the moisture content of the air around the quartz at a minimum. The piston that transmits the applied force to the crystals, passes through a hole in the top of the box. 19 V; Weight l i f t e r operating an eccentric cam at C L Carbon lamp with manually controlled voltage for maintaining the a i r within the shield at a des-ired temperature. She variable standard a i r condenser can be seen in the larger compartment of the shield. A l l conductors and mercury switches were insul-ated with sulphur or air. C. CRYSTAL CLEAMBG To minimize the effect cf surface leakage of the charge, the quartz crystals wwre cleaned by a method suggested to the authors by W. G. Cady *. Cleaning con-sisted of scrubbing the plates thoroughly with soap and water and then boiling them in d i s t i l l e d water, after which they were washed in alcohol and ether and allowed to dry before being placed in a dessicator, IV. TECHNIQUE ' ELBO TROMETEH • GAL IBRATIQf, 1" Vane: The mechanical and electrical zeros (M,Z. and E.Zo) of the electrometer were made to coincide by adj-ustments of the levelling screws and the position of the * V*. G. Cady, Professor of Physics, ""esleyan University 20 v a n e . The vane was main t a l l i e d at a p o s i t i v e p o t e n t i a l of 200 v o l t s . 2. E l e c t r o m e t e r : The e l e c t r o m e t e r was c a l i b r a t e d by a p p l y i n g known c h a r g e s t o t h e potential ( u n e a r t h e d ; quad-r a n t s w i t h vane v o l t s a t u^O, and o b s e r v i n g t h e d e f l e c t -I o n s , f i g u r e 7 shows a g e n e r a l a r r a n g e m e n t o f the c a l -i b r a t i n g i n s t r u m e n t s . D e t a i l e d c a l -i b r a t i o n was as f o l l o w s : 21 (a) Method 1, Residual e l e c t r i c a l charges ?<rere removed from the unearthed quadrants by c l o s i n g the ground p o t e n t i a l switch 3 { f i g u r e 8) 2. A known voltage was a p p l i e d by means of a Pye Potentiometer to the standard a i r condenser C w i t h the mercury s w i t c h S i n p o s i t i o n (1) 3* With Sg open, S was placed i n p o s i t i o n (2) and the vane d e f l e c t i o n s observed over a p e r i o d of 3 minutes. 4. Procedures 1, 2 and 3 were repeated f o r condenser s e t t i n g s of 200 and 600 micro-microfarads and the volt a g e s v a r i e d to give a f u l l s c a l e c a l i b r a t i o n of vane d e f l e c t i o n s , and recordings were made as r i n the s p e c i -men sheets T taken from m 151 of the records. pages 150 and f i g u r e 8 ** £2 Research Dec. 8, 1933 Page 150 QUANTITY CALIBRATION of ELECTROMETER Vane Volts £00 M.Z. £4.85 Room Temp. £2.6° C E.2. 25.00 STANDARD COL DEE SER SCALE READING Cap. nuf d Volts Coul. }X)iQ „ . see . P'f> Q «b V fcJ O Neg. D D 3c 200 0.550 110 00 90 180 . 2 • & S c S 0 ."2.35 2.05 25.45 48,85 48.65 49.05 200 0.480 96,0 00 90 180 25.45 5.15 5.05 45.75 45,60 45.9 200 0.410 82,0 00 120 180 8 . 1 5 8.25 7.95 25.55 42.80 42,72 42.95 200 0.350 70.0 00 120 180 25.35 10.70 10.75 10.60 25.35 39.87 40.1 200 0.280 56.0 00 120 180 25.35 13.72 13.75 13.7 25.4 37.02 36.97 37.1 200 .2050 41.0 00 120 180 25.4 16.72 16.80 16.55 25.5 33.80 33.75 33.9 200 .125C «5 a 0 00 90 180 o 3 19.87 .* 9 JS .19.8,- 25,45 30.45 30.42 30.5 200 .045 9.0 00 90 180 25.45 23.38 23.40 - S3 e 35 25,3 27.02 27.00 27.©5 SPECIMEN SHEET 23 Research Dee. 8, 1933 Page 151 . Q.TJA1 TI TY GAL I BR ATI OH of EL B C TROMB TBR Vane Volts 200 M.2. - 24.95 Room Temp. 25.4° C. E.Z. - 25.00 STANDARD CONDENSER TIME SCALE READING Cape pjif d Volts Coul /2/lC. sec. Pos. Keg, D D c D D C 600 0.310 186 00 120 180 25. 60 5.65 5.70 25.40 45.32 45.30 45.35 600 0.260 156 00 120 180 25.00 8.72 8.80 8.55 25.00 41.82 41.80 41.85 600 0,2150 129 00 120 180 25.1 11.62 11.70 11.45 25.1 38.88 38.85 38.90 600 0.1750 105 00 90 180 25.0 14. 00 14.02 13.95 25.0 36.20 56.15 600 0.135 81,0 00 90 180 25.05 16. 60 16. 62 16.65 25.2 33. 65 33.62 33.7 600 .0950 57.0 00 90 180 25.00 19.00 19.02 19.0 25.20 31.07 31.03 600 .0580 34.8 00 90 180 21.4 21.3 25.1 28.68 28.70 28.7 . 600 • .01798 10,8 00 90 180 o # IL o 23.90 23-90 23.9 25.05 26.10 26.10 26.10 600 .290 174 00 120 180 25.4 6. 92 6.95 6 * 95 25.30 43. 90 43.85 44.0 J {b) Correction for Residual Charges; Since the scale reading was not always zero (26.00) at the start of a deflection, i t was found necessary to corr-ect for small residual charges on the potential quadrants. To do this, the approximate capacity of the electrometer and leads was determined, and proportionate corrections were app-l i e d to the scale readings D . The following tabulation gives the method of calculating the electrometer capacity from the voltage sensitivity and charge relations: Voltage Calibration Applied Volts Deflections POSo & eg. E.Z. - 25.00 M/Z. - 25.00 Vane 200 v. 0.280 1.60 49.85 0.140 13.40 37.20 Erom the above, for deflections between 0 and 25, Volts per cm. _ 0.280 _ .01197 . 23.4 and for deflections between 25 and 50 Volts per cm. _ 0.260 _ ~ 24.85 01127 Since Q = (Total Capacity){Voltage on System) Quantity placed on standard condenser from Page 150 of the records (see Thesis Page 22) for Standard Condenser at 200 /anf. Rdg. Def. •E A^C em ;inf , 110 82.0 56.0 25.0 3 • 0 *5 7.95 IS.70 19.80 22.95 17.05 XX e oO 5.20 401 401 4QJ4 401 201 201 214 201 817 110 82.0 56.0 25.0 49.05 42.95 57.10 30.50 24.05 X*? o 9 5 12.10 5.50 405 405 411 404-205 205 211 204 825 Mean Electrometer Capacity = C„ _ 1642 - £05 ^ . 8 A similar calculation for the standard condenser set at 600 utif gives a value . to C £ of 218 uuf. Since the residual charge on the potential quadrants of the electrometer and leads is small, the capacity of ths electrometer and leads may be taken as approximately 200 micro-microfarads. The corrections to be made to the def-lections Dc w i l l be a constant times the recorded residual charge where the constant is .26 CRYSTAL LOADING r ^ The quartz crystal under test was placed on the insul-ating stand shown in.Figure 9 and the unit placed in the Vox Bv Figure '|>.', The remainder of the equ-• ipment was then adjusted so that when weights were applied to or removed from the crystal by r means of the cam mechanism, the resultant electric charge app~ eared on the electrometer. Readings, were taken at ,pre~det-*^ ermined time intervals and corrections were, mate f o r charge leakage,. C figure 9 V. RESULTS SPECIMEN TABULATION 1. Specimen; The specimen sheet taken from page 253 of the recordings illustrates the tabulation system used by the authors. 27 Research Jan. 25, 1934 Page 253 Crystal HlO (Quarts) C g = 600 pp,f Vane » 200.0 v. Set Temp, ; Weights D l dD1 D c 33 0. b T s On Off Sec- cm cm cm cm uuQ 8 ABCD 90 220. 150 180 X £2 6 *) X 36.42 ..36-. 42 36.41 36.40 .01 .01 36.46 198.0 9 . ABCD 90 120 ISO, l.|0 36.40 15.85 X«3 • X 0« 8 *5 15.85 15.85 198.0 20.1 20.4 IT 90 1:20' 150: 180 16.85 S © e M.,3fe .01 .02 36.39 198,0 11 IS. 90 120 150 180 36,..33 To* 72 15.73 X S 0 755 15.73 15.73 198.0 12 f! 90 120 150 180 15.73 36.31 36,30 36,50 56.28 .01 .02 36.34 198.5 13 If 90 120 150 180 36.28 15.70 '15* 71 ;i5.7i i s y v i 15.. 71 198,0 14 20,0 20.1 H 90 120 150 180 i § * 7i ; 36* 23 «^ 6. 22 & 6.22 56.21 ,01 .01 36.25 198.0 28 Symbols for Specimen Sheet m A Do dD-, (and TQ) are the temperatures in the box B and in the large shield, figure 6„ B, C and D are known weights. Scale reading at time T P D 'a Rate of leak in em. per stated time Scale reading corrected for leakage Piezo-electric effect in micro-microcoulombs, as obtained from calibration curves. Figures 10 and 11 show the general form of the calibration curves. In practice^ large detailed graphs were used. 1 'LI 1 1 * CMJBUTUM -* % BO ! | y -1 | 1 i 1 i -igure 10 Pigure 11 2. Scope: Measurements of the piezo-electric effect were made at room temperatures using weights of 5, 10, 15 and 20 pounds, and for standard condenser settings of 200 and 600 micro-microfarads. 29 3. Sources of Error: At the conclusion of the investig-ation of charge measurements, the standard air condenser was calibrated "in situ", using the Carey Foster Bridge and Wagner Earthing Device. This gave CgQQ = 185 micro-microfarads C„rt„ - 570 micro-microfarads 600 Previous results were then corrected by method of proport-ion. The calibration of the electrometer shifted from time to time, necessitating checks at frequent Intervals. A further source of error was due to non-uniform conditions of temperature, thus causing deformations of the crystal which resulted in the appearance of small charges. The polarity of these charges depended on the sign of the temperature gradient. 1. GENERAL TABULATION 1. Authors1 Results: Presented on the following pages is a summary of charge measurements for the two quartz crystals under test. CRYSTAL # 9 (Quarts) CAPACITY 2 0 0 uuf Date Page Total Sets Weight V * • Leaks em/mi Q u/iC (S)Q uuG, (S) U) Kilograms 8/12/33 1 5 2 1 8 AB 1 , 0 9 9 . 5 1 7 9 0 8 1 . 6 9/ " 1 5 8 1 2 A . 3 5 £34:« «3 6 5 4 2 7 . 2 9 / » 1 6 0 1 2 AB. = 8 1 0 4 1 2 5 0 5 4 . 4 2 1 / " 1 8 4 1 4 ABCD 1 9 6 2 7 4 0 1 2 7 2 1 / « 1 8 7 5 ABC , 7 1 4 5 7 2 5 3 4 2 1 / " 1 8 7 2 8 AB . 4 9 9 . 3 2 7 8 0 1 2 ? 2 1 / " 1 9 2 11 ABC . 7 1 4 7 1 6 2 0 7 4 . 8 6 / 1 / 3 4 2 U 7 1 4 ABC . 4 1 5 1 2 1 1 0 9 5 . 3 6 / " 2 0 9 7 AB CD . 6 2 0 1 1 4 0 7 6 3 . 5 6 / « 2 1 0 3 AB . 2 5 1 0 8 3 2 4 1 3 . 6 6 / ! T 2 1 0 2 ABC . 4 1 5 7 3 1 4 1 3 . 6 9 / " 2 2 0 1 4 A 3 C D . 3 2 0 6 2 8 8 0 1 8 7 1 0 / 18 .2 AB . . 1 5 1 0 8 2 1 6 9 . 6 1 7 / " 2 3 4 5 ABCD . 6 2 0 0 1 0 0 0 4 5 . 4 1 8 / » • -235 • 4 ABCD « *J 1 8 7 7 4 8 3 6 . 3 1 8 / " 3 AB . 1 9 7 2 9 1 1 3 . 6 1 8 / » 2 3 6 5 ABCD « 2 1 9 2 9 6 0 4 5 . 4 1 8 / " 2 3 7 7 AB . 1 9 7 6 7 9 3 1 . 7 1 9 / " 241 14 •AJ3GI) 2 1 2 2 9 7 0 1 2 7 • 1 9 . / " 2 4 3 ' AB . 1 io#. • 7 5 6 3 1 . 7 1 9 / " 2 4 4 7 ABC 1 6 1 1 1 2 7 4 7 . 6 31 Summation of ~ 27341 ;iuC Summation of (S)(?J) - 1227.3 Jtilograms CRYSTAL v-9 ((-iuartz) CAPACITY 600 mi£ Date Page :Total Sets S It eight W i i S S l C S an/ min. np-C f &)U) uuC. (S) (w) Kilograms 21/12/53 185 14 A BCD 193 2700 127 6/ 1/54 2 OS 14 ABOD 194 2720 127 9/ 1/34 818 14 ABOD ' .^10 .202. ' 2820 - 127 19/ l/i54 : 14 ABCD 0 10 209 2920 127 Summation of (S)(Q) = 11160 anC Summation, of ( S) ( w) - 508 Kilograms 52 CRYSTAL- it 10 (Quartz) CAPACITY 600 uuf Late Page Total Sets Wei glit a Leaks, cm/min. jyiC (s)( J njiC. (SHR) Kilograms 129 11 ABSB .40' 214 2360 132 17 » ,»4S 184 3130 •6/ " ; 138 . 12 ' ,40 , 217 £6.00 7/ " 145 24 « • 30 • 196 4700 22/ " 195 14 , n «2 5 220 3080 22/ " 202 7 ?7 .5 210 1470 8/ 1/34 IS ' It .4 189 2460 13/ '? 225 7 11 .4 1420 16/ 11 228 14. •. V. ' . «35 2 0 1 : 2810 16/ " 232 2 AB ' .1 103 206 20/ " 240 14 • A B 0 B ,2 198 2770 25/ " 14 it » 198 2770 Summation of (S)(Q) = 29776 njiC Summation of (S)(W) - 1360 Kilograms CRYSTAL 10 (Quartz) CAPACITY 200 mf Date Page Total Sets We ight L e s.k cm/rain n V3T, ;.i/iC ju;o.C. Kilograms 7/12/53 24 : AB . 50 98 : 2360 109 22/ ,s 198 28 .70 ' 109 1530* 65.5 8/ 1/34 2 jLX. 14 .4 102 143© 65.5 8/ " 213 14 ABO «6'- • 153 2140 O F , % 8/ 215 7 ABCD .8 197 1580 65.5 10/ " £22 'A AD .7 94 282 13.6 13/ » 223 7 w .35 108: 756 51.7 13/ » 224 7 ADC A 1110 47.6 16/ " 2&0 12 AB . . . i i . 107 1280 £4.4 16/ " 5 ABCD * . - © . 214 1070 45 . 5 20/ » 247 7 AB » « . * 107 749 31.7 20/ " 248 7 ABC .4 164 1150 47.6 24/ " 246 16 ABCD ,1 212 5590 145 25/ " 255 7 AB .1 107 749 31.7 25/ " 254 7 ABCD ,1 203 1421 65.5 25/ " 256 7 ABO .05 157 1100 47.6 Summation of (S) (ft) = 21897 juu.0 * Computed Summation of (S)(V7) = 954.5 Kilograms 34 Crystal So. Corrected Capacity Summation (S)(Q) Corrected j?or Capacity Summation (S)(W) 9 185 25300 1227 9 570 10600 508 10 185 20800 954 10 §70 28200 1360 CRYSTAL,. uuCoulom'bs per Kilogram = C C S * 6 fs, units, per dyne CRYSTAL # 10 jtyzCoulombs per Kilogram = 49000 = 21.2 2314 -8 C C S . e.s. units per dyne =. 6.5 x 10 Approx. These results compare very favorably with the following; 35900 « 20.7 1735 = 20.7 x 10" 1 2 x 5 x 10 9 981 x 1000 8 =• 6.3 z 10" Approx. 35 BlEZQ-ELEGmiG GGSStTAfgS o f QfAKfZ J„ and P. Curie lie-eke and Voigt Pockels . I j f s i Se imdre-eff, Free-tier ieksz & Jtazarnowsky (1880) 6.32 x w~a (1894) 6.47 JC 10""6 (1897) 6.29 x 10~ 8 (192?) . 6.4 x 10" 8 (1929) 6.5 x 1G~^ jSlec trestatic Coulombs per Byrne CHAPTER III DESCRIPTION OF INDICATOR I. IETRODUGTIOK This chapter describes the three component parts of a piezo-eleetric pressure indicator for internal com-bustion engines, namely; (a) A piezo-eleetric '.crystal holder (b) A vacuum tube amplifier {c) A recording oscillograph Of these, the last two have wide and diverse applications in many laboratory investigations. The three parts are designed, therefore, as separate units. The general req-uirements of the system are summarized as follows: (a) Under otherwise constant physical conditions, the crystal holder assembly must transmit to the crystals a force proportional to the cyl-inder pressure; and the resultant electric charge on the crystals must reach the amplif-ier with as l i t t l e loss as possible. (b) The amplifier must give an output current that is directly proportional to the input charge, over a wide frequency range. ( c) The oscillograph must record accurately the amplifier output. 56 37 figure 12 iriezo-eleetric c r y s t a l holder f i t t e d to L i s t e r Diesel 38 II. DiiSlGfi COIMSIDKRATIOSS A. CRYSTAL HOLDER AiiD LEAD 1. Mechanical problems: The chief mechanical problems encountered in the design of a crystal holder for eng-ines of f a i r l y large clearance volume are those of (a) Pressure pickup (b) Pressure transmission (c) Cooling MARTIE and CARIS (19) have shown that long, small diameter connecting tubes transmit to the diaphram a very distorted representation of cylinder pressure, for this reason the gos column (figure 13) has been kept as large in diameter and as short as possible. Its volume is such that i t has very l i t t l e effect on the clearance volumes of the engines to which i t has been applied. A study of the trans-mission oi pressure through a circular diaphram with clamped edges and & rigid central supp-ort has produced the interest-ing results recorded in Append-ix II. figure 13 (19) MARTM and CARIS, The Electric Journal, ..arch, 1930 Page 172 Experience that was gained during work on charge measurements indicated that temperature fluctuations in the crystals 'would introduce an undesirable d r i f t in the output charge. A water jacket is therefore incorporated in the holder (Figure 13) to keep the crystals' temperat-ure fluctuations at a minimum. £„ Electrical Problems; Leakage to ground of the charge on the insulated plate is the c r i t i c a l electrical problem. The sealed, dehydrated cartridge shown in figure 1 3 pre-vents the deposit on the quartz of dirt and moisture, which otherwise would produce a very marked detrimental effect on the surface conductivity of the crystals. Such a container gives very satisfactory service. It is rugg-ed and easy to clean, and i t maintains a very high, uni-form resistance between the crystal faces. To prevent Interference from stray electric charges in the air, the piezo-electric charge is conveyed from the holder to the amplifier on a lead that is electro-statically shielded by a grounded brass tube. The insul-ators carrying the lead are of the highest quality. Be AMPLIFIER 1. General Description: The sole purpose of the amplif-ier is to produee an output current that is at every 40 i n s t a n t a constant f u n c t i o n of the input charge, a m p l i f i e r c i r c u i t diagram Is shown In f i g u r e 14. The G h ffi 2 R R 1 f i g u r e 14 ** A m p l i f i e r S p e c i f i c a t i o n s Condenser, a i r , v a r i a b l e Rheostat, wir'n wound H tl ft Magneto Potentiometer, wire wound R e s i s t o r , ink-on-paper R e s i s t o r , wire wound, non-lnd. IT If IT II Shunts, | ampere, 60 m i l l i v o l t 180 to 2580 uuf SO ohms SO " 2000 ohms 5800 megohms 160000 ohms 160000 " Socket of a c t i v e input tube: General Radio I s o l a n t i t e 41 The general ci r c u i t arrangement is due to NOTTING-HAM (20) and the input circuit to WATSON and KEYS ( 9 ) . The unit operates as follows, with the potentiometer "P" (figure 14) set to give a minimum of bias to the grid of the active input tube t and with the balancer disconnect-ed, normal filament and plate voltages are applied. "P" is then adjusted to drive the input grid more negative. Thus the plate current and the " I R " drop through n " is reduced and the output grids, driven in the positive dir-ection, cause an increase in output current. When the output current reaches f i f t y milli&mperes, the balancer is cut in to the circuit and adjusted to bring the net output to zero. Small voltage swings on the input grid then cause the output current to vary according to the approximately linear characteristic shown in Figure 16. (20) NOTTINGHAM., Journal of the Pranklin Institute Liarch, 1930. Page 311 (9) WATSON and KEYS, Can. Jr. of Research. Loc. Git. Thus when pressure is applied to the quartz cry-stals, a. negative charge appears on the grid lead which augments the negative bias on the grid by an amount that is inversely proportional to the input capacity. The excess charge tends to leak off the grid lead through the resistor and the tube insulation, but in practice, before any appreciable amount has leaked away, the pressure on the crystals has fallen to its starting value, so that there now exists a small deficiency of charge (equal to the leakage loss) on the condenser, and leakage is in the opposite direction. Dnder steady cyclic pressure fluct-uations the grid w i l l ultimately assume, as a mean, i t s original "zero .charge input" potential, under which cond-ition the leakage off the grid lead equals the leakage on to i t . The leakage is kept small compared wi th the input charge, so that the voltage fluctuation of the grid lead ;. about i t s "zero charge input" potential resembles closely the pressure fluctuation in the engine cylinder about i t s mean pressure averaged with respect to time. Because of the linear grid voltage vs. output current characteristic of the amplifier, the output current, in responding to the grid voltage swings, thus images the enging pressures. Certain features that have contributed to accuracy •• 45 marked stability and ease of operation are discussed in the following paragraphs. 2. Input Circuit: Two features of the input charge make necessary a very careful design of the input circuit, f i r s t , the input charge i s extremely small, usually being of the order of a few hundred micro-microcoulombs per cycle. Secondly, the fundamental input frequency may be as low as five cycles per second. With this small charge and the long time interval in which to lose i t , high input resistance and good shielding are essential, further, consideration of the function of the resistor "R" (figure 14) w i l l show that to avoid constant adjustment of the potentiometer " f " , the input resistances must maintain approximately constant values over long periods of time. Selected ink-on-paper resistors, sealed in de-hydrated copper boxes have remarkably stable, high resist-ances. An application of the amplifier to the measure-ment of these high resistances is outlined in Appendix III. Using this method on the resistor nR" gave a value of 5800 megohms. The mean observed difference of potential across the resistor "R" under operating conditions is in the nei-ghbourhood of 1.4 volts, so that the normal current thr-ough "R" is -10 1.4 ~ £.4 x 10 amperes 5800 x 10° 44 The effective input resistance Re is defined as the value of an imaginary resistor which would produce, under any set of operating conditions, a charge dissip-ation identical with that produced by the actual input c i r c u i t . The effective input resistance of the amplifier is determined not by "R" (Figure 14) alone, but by the combined effect of "R", insulation resistance and certain tube characteristics* A separate analysis of these last is d i f f i c u l t and of doubtful accuracy, but fortunately i t is the lumped effective inout resistance R„ that bears e on the problem of leakage. A practical method of obtain-ing Rg is given below. Figure 17 shows the auxiliary connections on the input circuit of the amplifier, together with the addit-ional external equipment used in the test. With switches A and B in position 1, potent-iometer X. is set successively to three voltages V^, v" , and in the normal work ing range of the amplifier. These voltages, -being applied directly to the Figure 17 ** input grid, produce- milliammet-er readings A , A p and A„ respectively. Switches A and B are then placed in position 2, and Y is set to produce the least voltage, say V^, on the grid, this being ind-icated by an output current A^, B is then set on 1, and 1 is adjusted so that the milliammeter indicates an input grid bias somewhat greater than V . Switch D is 2 closed and the condenser C is charged through R. When the output current exceeds Ag, switch B i s thrown from 1 to 2, and the condenser potential starts falling. (The time required for the output meter to drop from reading Ag to Ag gives the time T that i s necessary for the f i r s t half of the excess charge on 0 to leak off. The table on Page 46 gives the results of such a test. Sote that the time T i s practically constant for the several sett-ings In the working rang©. To determine R , consider a resistor R„ and a e ' e condenser C connected in series across a source of e.m.f. E^. It i s easy to show that i f changes sharply to a new value Eg, the time T required for the condenser volt-age to reach a value "1... * 'S ±E 0.695 R£5 seconds^ i.e. R«: = 1>44 T e ,0" . _7 Taking the values T - 175 a n d 0 - 1 0 from the data on Page 46, R^  - 2490 megohms. 46 Data Pertaining to the Determination of the Effective Input Resistance R — — . — : , ,..„ e Output Rdgo Input Output Time Balanced Out Volts Rdg. X. See. 47.5 6.0 0.0 6.5 17.1 167 7,0 35.0 46.0 6.0 0.0 6.5 17„8 163 7.0 36.0 50.5 6.0 0.0 6.5 16,0 170 7.0 36.0 0 4.5 10. 6 5.0 21.0 V 182 * ) » . t ) S4..-S • 0 4. 5 10..6 5.0 t i l . . U 176 «3»t5 34.2 0 4.0 4.0 _o5~5 34.2 177 7.0 84.3 0 4.0 4.0 13«15 34.2 176 7.0' - ' :. 84.3 Capacity on charge in each ease was 0.1 microfarad 4? By subdividing the actual input c i r c u i t into two parts, i t i s also possible to show that the lumped i n s u l -ation and tube effects o f f e r a resistance of 440G megohms. Analysis of the divided c i r c u i t , which i s s i m i l a r to that given in Appendix I I I , and also the observed performance of the unit under t e s t , J u s t i f y the assumption implied i n the method, that the actual discharge i n the amplifier i s a logarithmic function. I f the charge input to the amp l i f i e r i s a known (or assumed) function of time,, and the e f f e c t i v e input resistance i s also.known, i t i s possible to deduce the proiiaJble a m p l i f i e r d i s t o r t i o n set up by charge leakage. Appendix IV' presents a mathematical analysis of t h i s problem. 4-8 3. Compensating: Circuit: KOTTIBGHAMf21} presents a detailed analysis of the operation of the balancer or !!dummy" tube. It is therefore sufficient to state here that a suitable adjustment of the resistances K and K_, « . • • 1 2 Figure 14, gives good compensation for filament voltage fluctuations on the input tubes, ho attempt was made to compensate for "B" battery fluctuations by an adjustment of R]_ and Rg. 4. Am73lification Circuit: For Infra audio frequencies the only feaaable amplification circuits are those emp-loying resistance coupling. The sise and weight of the independent "B" batteries that are required for each stage limit the desirable number of stages to two. Fig-ure 15 shows a general input voltsge vs. output current characteristic, and Figure 16 shows the very nearly l i n -ear relation over the useful portion of the eharacteristi In operation, the grid swing is limited to a suitable value by adjusting the variable a i r condenser "CtT, Fig-ure 14, and the amplifier i s caused to operate on the "straight" portion of i t s characteristic by setting the potentiometer "P" to give a proper mean bias on the input gr i d« (21) BOTTIBGH&M, Journal of the Franklin Institute, March, 1930, Page 314 49 Figure 18 \ m mm ^ 5. Timing Circuit: The input c i r c u i t of the "dummy" tub© is used to inject a timing wave into the amplifier. "Keepers" placed on the flywheel at known crank angles actuate the magneto device indicated in Figure 14 as "M" and shown In figure 18. The two timing "ripples' 7 make possible an accurate determination of crank angles on any card. 50 C. GALVANOMETER 1. General D e s c r i p t i o n : The r e s t of t h i s chapter i s a d e s c r i p t i o n of the o s c i l l o g r a p h that i s used i n recording the output current of the a m p l i f i e r . The subject f a l l s n a t u r a l l y i n t o two p a r t s , namely; (1) the galvanometer and (2) the o p t i c a l system. The galvanometer i s a two element Einthoven s t r i n g type, w i t h the magnetic c i r c u i t modified ( a f t e r Ganz) (22) to permit s h e l l type c o n s t r u c t i o n . The p r i n c i p l e of operation i s extremely simple. A f i n e wire c a r r y i n g the current to be studie d i s suspended v e r t i c a l l y under t e n s i o n i n a h o r i s o n t a l magnetic f i e l d of constant i n t e n s i t y , The i n t e r a c t i o n of the f i e l d and the c u r r e n t produce an h o r i z o n t a l displacement of the wire normal to the d i r e c t i o n of the f l u x and p r o p o r t i o n a l to the c u r r -ent. Through the microscope. Figure 19, which i e mounted a x i a l l y i n one pole-piece, i t i s p o s s i b l e to observe the d i s -placement of the wire and conseq-uent l y to gauge the current. Figure 19 ** (22) LAWS, E l e c t r i c a l Measurements, Page 637 51 2. Magnetic Olrcuiti High flux density in the air-gap i s essential to instrument sensitivity, and for the moving elements., a maximum of proteotion from external magnetic and mechanical interference is desirable* A shell type electro-magnet was designed which meets these requirements and at the same time provides easy access to the elements. The shell i s good quality grey east iron and the pole-pieces are of 2 1/8 inch (5.4 cm.) diameter mild steel, tapered at forty-five degrees to the centre line to give a gap 5/8 inch (0.95 cm.) wide,. 2 inches (5.08 em.) high and 1/52 inch (0.079 cm.) long. The two excitation coils are wound with So. 14 B & S enamel and cotton covered magnet wire, three hundred turns per c o i l ; and are operat-ed in series at 3 amperes from a 6 volt storage battery. The average flux density In the gap, as determined with a search c o i l and b a l l i s t i c galvanometer for the normal exciting current of 3 aiapereSj is 1©,200 gauss. „•.; Axial holes i n the pole-pieees which accomodate the optical sys-tem cause slightly more pronounc-ed saturation effects in the cent-figure 20 ** portion of the pole tips. Figure 20 shows flux density characteristics for (1) the 31 A 52 whole gap and (2) a r e c t a n g u l a r gap s e c t i o n 0.3 cm. wide by 2.0 cm. high, s y m e t r i c s l l y l o c a t e d w i t h respect to the gap centre l i n e s . 3. E l e c t r i c C i r c u i t : Figure 21 shows the method of sus-pending th© two tungsten wires i n the magnetic f i e l d , The current to be i n v e s t i g a t e d i s passed through one wire. The other i s used as a spare or f o r a u x i l i a r y i n d i c a t i o n s . F igure 22 As Figure 22 shows, removing h a l f the galvanometer s h e l l renders the whole bridge system eas-i l y a c c e s s i b l e . Each wire i s i n s u l -ated from the other and from the galvanometer shell, Panel-mounted voltage dividers control the inputs to the strings. 4. Theory: IRKIN (23) has shown that under the condit-ions existing in an Mnthoven galvanometer, the follow-ing equations hold: T = 4 i'Zfm A ^ ~ 1 B l z where 10 l\z T - Tension, in dynes f - Resonant frequency in cycles per second .1 a Length of wire in centimeters m - Mass of wire per centimeter of length A - Central deflection of wire in centimeters i = Current through the wire in amperes and B -. Strength of magnetic f i e l d in lines per square cm. If we take S - Galvanometer sensitivity in screen cm, per milliamp. Ii - Overall magnification of the optical system,, S . B M .. 40,000 If m- f* (23) IRWIH, Oscillographs, Pages 25 and 26 54 Taking as values B, 16,000; Ik, 155; m, 5,38 x 10" S 10.17 x 10' The theoretical sensitivities computed from this express-ion for values of " f " between 200 and 1100 cycles per second are plotted in Figure 23, together with the act-ual instrument sensitivities that were determined in the laboratory. A table of observed and calculated sensit-i v i t i e s appears on Page 55. A typical academic ; •.'pressure; wave, was analysed to ' the twenty-third harmonic (see Appendix V) to determine' .the J-., probable magnitudes of the • higher harmonies.-' IRWIf (24): " has shown that f o r an oscillo** •graph not.subjected 'to any appreciable damping, Figure 23 ** Deflection at frequency "f" _ Deflection at zero frequency (24) IRWIN, Oscillographs, Page 82 = 5 -TL 1 - [il 5^ «S Oscillograph sensitivity. .Data B©sonant Observed • lesonant : C a l c u l a t e d . Frequency S e n s i t i v i t y . Frequency Sensitivity 235 1.75 200 2.54 298 1.03 .2.50 . 1.63 0.91 300 i i« 362 0. 66 400 0. 636 416 0.51 500 0.407 501 0.375 600 0. 282 655 700 Go 208 795 0.1? 800 0,159 1160 0.09 900 0*125 1000 0,10.2 1100 0.084 1200 0.071 Sensitivities are in Screen Centimeters per Milli&mpere 56 where f = i requex^cy o l the ap p l i e d c u r r e n t and f r = frequency of resonance of the o s c i l l o g r a p h The a n a l y s i s i n d i c a t e d t h a t harmonics of higher order than the tw e n t i e t h would probably be sma l l , so that f o r an engine running a t 1000 r.p.m. th© maximum appreciable input frequency would probably be 333 c y c l e s per second, and i t s m a g n i f i c a t i o n f o r f y s 1000 would i n conseq-uence be 1.125. Thus w i t h a magnitude r a t i o of harmonic to fundamental of about 0.03, th© e r r o r introduced i n th© recorded waveform becomes n e g l i g i b l e . D. OPTICAL SYSl-Bi General D e s c r i p t i o n ; Figure £4 shows a general a r r a n -gement and Figure 19 a s e c t i o n a l view of the conventional o p t i c a l system. Only two features r e q u i r e s p e c i a l comment, namely; the synchronized sweep mechanism and the synch-ronized shutter. . Sweep Mechanism: figure 25 shows schematically the UB thod employed to obtain a small d.c. motor that runs synchronous with the crankshaft. The brushes distribute d.c. to the stator coils of the motor in such a way that each pole in turn becomes a "north" for one-third of the cycle while the opposite stat-or pole is at the same time a. "southT?. The rotating f i e l d thus set up by the stator •causes the d.*e... excited 'rotor to revolve synchronously with the distributor brushes.. The sweep period"is thus automat-i c a l l y adjusted to coincide with the engine period, i r r -espective of engine speed. Two types of time base are available, for one, a lathe-cut cam drives the mirror in one direction at a constant angular velocity and returns i t quickly to i t s starting point, imparting a "crank angle" base to the graph, for the other type, an eccentric imparts a sinu-soidal angular displacement to the mirror, giving a 'SYNCH no MOTOR" Mow. S*.TOS 58 "volume" or "out-of-phase" base to the graph. The motor shaft Is phased with respect to the crankshaft by adjust-ing the plug of the connecting cable or by rotating the distributor stator. 3. Synchronous Shuttert To obtain photographic "single shot" indicator cards from a two-stroke engine, a shutter was constructed which 1. Keeps the plate compartment in darkness until release 2. On release, initiates exposure at a pre~deter-mined crank angle 3. Continues exposure for approximately 292 deg-rees of crank angle and 4. Cuts off exposure. Synchronization and power are obtained from the mirror drive, and exposure is initiated by solenoid control. After one exposure, the device resets i t s e l f automatically, so that several selected single shot cards cay be super-imposed on one plate. To obtain a continuous exposure for visual inspection, the shutter may be looked in the open position by throwing a switch and pressing the photo-graphic release. The shutter is suitable for operation on four-stroke engines when the power is supplied through two-to-one reduction gearing. CHAPTER 11 TBSTING AND R&SPhTS I . INTRODUCTION 1 . Scope of Tests; In this chapter are presenter! the results of certain preliminary tests. They show in a very limited way the application of the instrument to the study of combustion pressures in medium speed o i l engines. Unfortunately they do not cover probable appli-cations to the study of fuel injection systems or spark ignition engines. The tests, however, make evident certain points of superiority and also certain weakness-es in the indicator, and with these the following para-graphs deal. 2. Pressure Calibration; At the time of writing, d i-rect calibration of the pressure axis has r^ ot been achiev-ed. For this purpose i t is proposed to employ a balanced-pressure electric indicator operating at two fixed press-ures. By the addition of this device, two known pressures w i l l be recorded on each individual card, A second method of calibration, involving an overall conversion factor for the indicator, would in a l l probability provide consistent but somewhat less accurate pressure calibration. Of these, 59 60 the second method would probably be the only one applic-able to work on small, high-speed engines. A further laboratory investigation is necessary before any reason-ably accurate conversion factor can be computed. For qualitative results such as are submitted herewith, calculation of the compression pressure from known engine dimensions gives a, reasonably satisfactory basis for calibration. 5. Engines: To date, the indicator has been used on two engines, one a single cylinder Crossley semi-diesel, and the other a single cylinder Lister Diesel. Specif-ications and operating conditions for these two engines appear on rage 61. A l l the cards in this thesis were taken on the Crossley engine, and a l l are on a "crank angle" base. II* SATISFACTORY RESULTS 1. Introduction: The cards submitted here present a very f a i r record of engine performance under a wide variety of conditions. For some aspects of the study of cylinder pressures, however, no series of static records can r i v a l an optical presentation. One of the chief merits of this indicator i s that i t makes possible the observation of every one of a long series of cycles, 61 Oiib£Ri.h KLGILE SPECIEICATIQLS Engine C R O i S S L E Y LISTER Type Rated Horsepower Cylinders i>peed Injection system Compression Ratio fuel Two-stroke 9 1 550 r.p.m. Crossley 6tove o i l f our-etroke 9 1 1000 r.p.m. C.A.V. - Bosch 15 to 1 "Diesol" o i l Figure 26 Indicator Arrangement Crossley showing one engine condition giving way to another. Control is extremely simple, and with one or two refine-ments in construction, the indicator would run practic-a l l y continuously. 2. Cards: The two timing waves f i x the position of top dead centre, which is marked on each card by a vertical line. The black line near the bottom of each card serves as a pressure datum, but in no case does i t represent aero pressure. The pressure scale is dependent on the {manually variable) input capacity, and. i s different for different cards. Pressure calculations are based on a compression pressure of 300 pounds per square inch, gauge, and an intake pressure of zero pounds per square inch, gauge. For a l l the cards given here, the resonant fre-quency of the oscillograph is approximately 920 cycles per second. Comments on the individual cards follow. 63 GARB fiUMBiSR DIE Engine Details Load; 2.ero t>peed; 540 r.p.m. Conditions; Normal idling Calculation Maximum pressure; 325 lb. / sq,. in., gauge Remarks This is a typical no-load card. 64 CARD LIMBER EIGHT Engine Details Load; 8.1 hp. Speed; 540 r.p.m. Condition; Steady heavy load Calculation Maximum pressure; 345 lb. / sq. in., gauge Remarks This is a typical heavy load card. 65 CARD NUMBER NIBS Engine .Details Load; Lero Speed; 500 + 50 r.p.m. Condition; Rapid acceleration at f u l l throttle Calculation Maximum pressure; 450 lb./ sq. in., gauge Remarks The sharp pressure rise and high maximum pressure are characteristic of this engine condition. 66 CARD UMBER TEN Engine Details Load; Speed; Condition; Calculation Maximum pressure; Zero 500 + 50 r.p.m. Rapid acceleration at f u l l throttle 360 lb./ sq. in., gauge frequency of ripple in expansion line; 615 to 750 cycles per second, depending on engine speed Reimrks This card shows a smooth compression curve and a rough expansion curve, from waich it may be inferred that pressure surges occurred in the cylinder after ignition. In this ease the ripple is not due to the oscillograph because the surge frequency does not coincide with the resonant frequency of the instrument. 67 CARD SOMBiiR TWELVE Engine Details Load; (a) £ero (b) 1.5 hp. opeed; 540 r.p.m. Conditions; (a) Compression wave, lo fuel injected (b) Superposed load card, steady running Remarks Illustrative of multi-exposure cards. 68 III. UESATISFACTORY.RESULTS 1. Poor Performance: Poor performance is indicated by one (or both) of two effects. The oscillograph record may " d r i f t " up and down the screen or the pressure wave may show a high frequency ripple, 2. Drift: This effect is due to an unstable input grid condition set up by commutation effects in the synchro-motor distributor and cable. D i f f i c u l t i e s from this source increase with engine speed, so that the present oscillograph drive is not suited to any but medium speed work. 3. High Frequency Ripple: Ripple effect may appear on the pressure -wave during the whole of the cycle, or at intervals, or only after fuel ignition (see Card Ten). In the f i r s t case either mechanical vibration or distrib-utor sparking may be the cause; in the second, the dis-tributor is definitely to blame even when drifting is not present; and in the third case, the pressure fluct-uations in the cylinder attain frequencies approaching the resonant frequency of the oscillograph, 4. Remedies: The d i f f i c u l t i e s caused by the sweep mechanism can be eliminated by employing either a direct mechanical drive or another type of synchronous e l e c t r i c drive, A damped galvanometer with a resonant frequency of not less than 2000 cycles•peruseeend would eliminate most of the errors introduced hy the present undamped low frequency u n i t . 5 . Cards: Cards i l l u s t r a t i n g some of the unsatisfact-ory r e s u l t s are shown on Pages 70 and 7 1 , 70 CARD hUMBER THIRTEEN Engine D e t a i l s Load; 4.8 hp. Speed; 540 r.p.m. Condition; Steady running C a l c u l a t i o n s Maximum pressure; 360 l b . / so., i n . , gauge frequency of r i p p l e ; 9 70 Cycles per second Remarks I t i s h i g h l y probable that the r i p p l e , (which i s not confined to the expansion curve i n t h i s card) occurs at the resonant frequency of th© o s c i l l o g r a p h . A t y p i c a l h a l f - l o a d card w i t h lat© i n j e c t i o n . 71 CARD LUi-BER LEVELTEBI* Engine D e t a i l s Load; About 1.4 hp. Speed; 500 + 50 r . p . m . C o n d i t i o n s ; E a r l y f u e l i n j e c t i o n and a c c e l e r a t i o n C a l c u l a t i o n s Maximum pressure ; 360 l b . / s q . i n . , gauge frequency o f r i p p l e ; 785 to 942 c y c l e s per second, depending on the engine speed Remarks A t y p i c a l e a r l y i n j e c t i o n c a r d , showing v e r y steep pressure r i s e before top dead c e n t r e . The cause of the r i p p l e i s i n t h i s case u n c e r t a i n . 72 -6. Gonelusion.: In conclusion i t is interesting to note that neither calculations nor results c a l l in question the fundamental piezo-electric principle or the method of i t s application, Further development would therefore appear to hinge on a refinement of present design. APPEllDIiL I THEORIES OP THE PIEZO-ELECTRIC PHENOMENON U QUARTS 1. The f i r s t to present an explanation of the origin of piezo-electric ity in quartz were J. and P. CURIE (13) in 1881, the year following their discovery of the phenomenon. The following extract (12) gives a clear and concise inter-pretation of their theory based on polarization of the molecules. "Curie f i r s t points out that the idea that mole-cules are polarised in the direction of the electric axis is in perfect accordance with the fact that charges of el e c t r i c i t y are liberated on the o t faces only, for i t is well known that a cylinder of molecules uniformly polarized in the direction of a generator can be replaced by a uniform charge of el e c t r i c i t y on each base. "To arrive at a more definite idea of the cause of the polarization and that of its variation, he supposes a constant difference of potential between the opposite faces of two successive layers of molecules, hueha difference of potential must produce a condensation of (IE) YIGOUREUX, P., Quartz Resonators and Oscillators, Page 171 (13) CURIE, J. and P., Comptes Rendus 1881, 93, 186 . 73 e l e c t r i c i t y , the extent of which depends upon the dist-ance between the layers. Whenever this distance is varied either by a variation of mechanical pressure or by variation of temperature, the quantity of ele c t r i c i t y varies. "As an illustration of the above he considers a number of voltaic elements, each of which is made up of a disc of copper soldered to a disc of zinc. Let a l l the elements be vertically one above the other, and at equal distances apart. Let e be the distance between the opposite faces of any two elements, s the area of a disc, and v the. contact electromotive force between zinc and copper. Connect a l l the plates to earth and then Insulate them. The quantity of electricity condensed on each of the opposite faces of two neighbouring elements is q = v e 4 TTe To a small variation de of the distance, there corresponds a variation dq = v s de 4 rn , e a of the quantity. The top and bottom discs therefore liberate equal and opposite charges v s de 4T?e2 and the equal and opposite quantities of electricity liberated in a l l the other elements neutralize each other." "The quantity of elec t r i c i t y liberated is , according to the above formula, proportional to the sur-face of the disc and to the variation of the distance between any two neighbouring elements, but does not depend on the number of elements, nor, which comes to the same thing, upon the total length of the pile. If we suppose the elements kept apart by an elastic material of modulus of elasticity E , having a l l the electric properties of air, we can calculate the total force required to produce an extension de in each gap. This force i s di' _ sB de e where., as before, s is the area of the disc. Substitut-ing for de in the f i r s t differential equation, 'we find dq _ v 1. di* "™ 4'u'e E This i s identical with the Curie equation 76 i f we write — v 1 for H ~ 4 T T e B . ... "It has been assumed that there was a constant difference of potential between the opposite faces of two neighbouring layers of molecules. This the Curies proceed to justify, at the same time pointing out that i t was only a hypothesis, not an observed fact. "Quartz being a compound, i t is conceivable that the difference of potential is due to want of homogeneity between the various parts of a molecule. It is more probable, however, that the shape of the molecules alone accounts for the phenomenon. A l l crystallographists agree in assigning to the molecules themselves the dis-symmetry which manifests Itself in the angles or faces of crystalline bodies. Crystalline quartz is hemihedral, • by which i s meant that i t has modifications on only half of i t s similar edges or angles. The Curies had shown before CIS), however, that a l l non-conducting hemihedral substances were piezo-electric, and that the signs of the charges liberated were always connected with the hemihedral form in such a way that the extremity corresp-onding to the most acute solid, angle becomes positive by contraction, 'from the analogy between the shape of the molecule and the hemihedral shape, i t may be inferred (13) Loc. Cit. 77 that the more pointed extremity of a molecule and the base of the neighbouring molecule are in the relation of zinc to copper in the "piezo-electric pi l e " described above." 8. LORD lOilVIB'S explanation of piezo-electrieity, advanced in 1893 (£5) also based on polarization of the molecules, is similar to that of the Curies., but instead of considering the molecule as a unit, he divides i t into it s component atoms. Extracts from Lord Kelvin*s illustrations are given below, "Electric eolotropy of the molecule, and nothing but electric eolotropy of the molecule, can produce the observed phenomena. The simplest kind of electric eolo-tropy which I can imagine is as follows: - Eor brevity I shall explain i t in relation to the chemical constit-ution, which, according to present doctrine, is one atom of silicon to two atoms of oxygen. The chemical molecule may be merely 3i 0 for s i l i c a in solution or i t may (£5) THOMSON, SIR WILLIAM. Mathematical and Physical Papers Vol. 5 Page 311 78 consist of several compound molecules of this type, grouped together: "but i t seems certain that, in crystal-lized s i l i c a (in order that the crystal may have the hexagonally eolotropic piezo-electric property which we know i t has) the crystalline molecule must consist of three Si Og molecules clustered together; or must be some configuration of three atoms of silicon and three double atoms of oxygen combined. As a ready and simple way of attaining the desired result, take a clust-er of three atoms of sili c o n and three double atoms of oxygen placed at equal distances of 60° in alternate order, silicon and exygen, on the circumference of a ci r c l e . W111 "The diagram (Figure 27) shows a crystalline mole-cule of this kind surrounded by six nearest neighbours in a plane perpendicular to the axis of a quartz crystal. Figure 27 Kelvin's model of quartz molecules 7 9 Each s i l i c o n atom is represented by + (plus) and each oxygen double atom by - (minus). The constit-uents of each cluster must be supposed to be held to-gether in stable equilibrium in virtue of their chemical a f f i n i t i e s . The different clusters, or crystalline molecules, must be supposed to be relatively mobile before taking positions in the formation of a crystal. But we must suppose, or we may suppose, the mutual forces of attraction (or chemical affinity),, between the s i l -icon of one crystalline molecule and the oxygen of a neighbouring crystalline molecule, to be influential in determining the orientation of each crystalline molecule, and in causing disturbance in the relative positions of the atoms of each molecule, when the crystal is strained by force applied from without. "Imagine now each double atom of oxygen to be a small negatively electrified particle, and each atom of s i l i c o n to be a particle electrified with an equal quant-ity of positive electricity.. Suppose new such pressures,, positive and negative, to be applied to the surface of a portion of crystal as shall produce a simple elongation In the direction perpendicular to one of the three sets of rows. This strain is indicated by the arrow-heads in 8 0 Figure 27 and i s realized to an exaggerated extent in Figure 28. "This second diagram shows a l l the atoms and the centres of a l l the crystalline molecules in the positions to which they are brought by the strain. Both diagrams are drawn on the supposition that the stiffness of the r e l -ative configuration of atoms of each molecule is slight enough to allow the mutual at tract I oris between the pos-i t iv e atoms and the negative atoms of neighbouring mole-cules to keep thea In lines through the centres of the molecules., as Figure 27 shows for the undisturbed condition of the system, and Figure 28 for the system subjected to the supposed elongation. Hence two of the three diameters through atoms of each crystalline molecule are altered in direct-ion, by the elongation, while the diameter through the third pair of atoms remains unchanged, as is clearly Figure 28 Kelvin.' s model of quartz mole-cules under strain 81 shown i n Figure 28 compared w i t h Figure 27. "Remark, f i r s t , t h a t the rows of atoms, i n lines through the centres of the c r y s t a l l i n e molecules, perp-e n d i c u l a r to the d i r e c t i o n of the strain, are s h i f t e d t o p a r a l l e l p o s i t i o n s with distances between the atoms i n them unchanged, hence, the atoms i n these rows con-t r i b u t e nothing to the e l e c t r i c a l e f f e c t . But, i n para-l l e l s to these rows, on each side of the centre of each molecule, we f i n d two p a i r s of atoms whose distances are diminished. "This produces an e l e c t r i c e f f e c t which, f o r great distances from the molecule, i s c a l c u l a t e d by the same formula as the magnetic e f f e c t of an i n f i n i t e s i m a l bar-magnet whose magnetic moment i s num e r i c a l l y equal to the product of the qu a n t i t y of e l e c t r i c i t y ox a s i n g l e atom i n t o the sum of the diminutions of the two distances between the atoms of the two p a i r s under consider&tion. Hence^ denoting by I the number of c r y s t a l l i n e molecules per u n i t bulk of the c r y s t a l ; by b the radius of the c i r c l e of each c r y s t a l l i n e molecule; by q the quantity of e l e c t r i c i t y on each of the s i x atoms or double-atoms, whether p o s i t i v e or negative; by S the change of d i r e c t i o n of each of the two diameters through atoms 82 which, experience change of di r e c t i o n ; and by u the e l e c t r i c moment* developed per unit volume of the c r y s t a l , by the s t r a i n which we have been considering and which is shown in figure 28; we have u s 1 q « 4 b Q cos SO0 - M . 2bq© I t i s of course understood that 9 i s a small f r a c t i o n of a radian*" I do not know i f t h i s designation has hitherto been used. I introduce i t with, precisely the same s i g n i f -icance r e l a t i v e l y to e l e c t r i c i t y , as the well-known-"magnetic moment" i n reference to magnetism. {Lord .Kelvin 1 s note) A P P J 3 H D I X H i DIAPHRAM THEORY 1. Introduction-. The following theory has been develop-ed in order to compute the probable loading on the quartz crystals of the indicator unit due to the cylinder press-ure. 2. Theory: Let 2a = Diameter of the diaphram 2b = Diameter of the end of the rod that rests on the diaphram and transmits the force to the crystals q = Uniformly distributed concentric load on the end of the rod p ==• Cylinder pressure Q = Shear force per unit length A = Deflection at a distance "x" from the centre 0 = Slope at a distance "x" from the centre D = Elexural r i g i d i t y of the diaphram = i O L . — where 12 [ 1 yu?) h = Diaphram thickness E = Young's modulus of elasticity yj- = Poisson's ratio 84 Assume Then (a) Small deflections (b) Clamped edges (c) That the load on the rod is uniformly distributed (d) No deflection at the centre d_ dx [1 d_ (x 0)1 |x dx J JSL. D (1) Figure 29 Consider two cases; (i) x 2 b (2) x = b Case (1) (2TTx) Q (q - p)Tfx z (2) Case (2) (2Tx) Q 2, . o = TTbq -l|x p lb' px (3) TIMOSHiSNXO, S., Strength of Materials, Page 490 85 for X ^ b d_ dx 1 d_ (x 0) x dx 1 D (q. - p) Integrating, d_ (x 0) dx and dx When x = 0 0 and ^ a When x — b M dx 0 h A - -D L 1 T ( q - p)x D L 1 D L D L 4 + 2 + x (4) - P)3x_ 16 + A, A2 2^ x* 0 and A2 must be zero 0 and A 3 must be zero A - -D L I f U D I p) 5b 16 P) b l 16 64 2 A, b Z (6) (?) (8) (9) for x 51 b A_ [ 1 J L U 0)1 « _ 1 •" dx dx J D qb 2x 2 Integrating, d_ (x 0) _ dx I D qb x In x 2 86 0 = A -dx 1 [ D L qb x( 2 In x - 1) 8 D ob2" x 2 (In . 8 - 1) D L 8 16 ^ E x £5* + J L l 64 T 4 ^ x + 1) gpx 16 2 B, (10) (11) (12) When x - b M » - I (2 In b + 1) _ gpb* B, B D L 8 1 £ + o v. ax, 16 b* 0. = _ 1 rab 3(2 in b - 1) _ j)b A + B J D + B T  b D i 8 16 2 b \ -<rhen I (la b - 1) ^b 4 . B, b z B In b B L 8 16 4 (IS) (14) B 3 j (15) a, a ^ _ 0' 1 gab (2 In a - 1) _ pa , B, a , B z ( 16) ° B L 8 16 2 a A o _ _ i B t qa zb z (In a - 1) _ pa 4 B. a* 8 64 4 B In a , B^  Z 3 Prom equation (17) (17) B _ aa ab*(ln a - 1) . pa* B, & B In a (18) Substituting this value into equation (15) A 1 to4"(ln b - 1) qa tb > (In a - 1) . _p(a*- bA) b ~ B L 8 8 64 B, (a z- b a) , B.ln b 1 (19) — ~. -i - <. —-4 a To solve for A , B , and B , use determinants 1 l z 87 Equating equations (7) and (IS) 4 A , _ 8 B, + 16 S4 = q( 41n b - 1 ) _ X (20) b b a b"*-' Equating equations (8) and (14) £ A. _ 8 B 15 B q( 41n b - 3 ) __ Y (21) b z b a b* Equating equations (9) and (15) 16baA, -t- 16(a*- b z ) B( - J64 In b | B? « ( 8b4-In b - 8 a a b a l n a - 9b4" 6 a z b* ) q + pa* = 2 (22) Applying determinant notation to (20), (21) and (22) gives the following expressions. 88 Denominator 8 _ 8 16 b* b2, b* 8 b* 16b* 8 b a 16(a a- b2) 16 b 4 64 In b a (16) a* (23) b 6 Numerator of A _ 8 b a _ 8 b* 16(az'-16 b* 16 b A - 64 In b a 16*rgf8a ain b . 4a* . 4 In b 5\ b^ [ j~b* a + ~~b* * a ~ j aA (24) 1 f f8b 8ln b . 4bz . 4b* In b 16 a* bh^\ q a*j pa (25) Solving for B, and Bz in the 8ame manner, B 16 r 4h«-In b _ 8b2 In a + 8b2 a a aj pa* (26) f P. 7 1 89 • ' Substituting for B, and B^ in equation (18) and simplif-ying, B, = b4; ( 5 - 4 In b )q (28) 64 Substituting for B, and B^  in equation (16) 0- _ -0 _ _1 [qfSab2 - 6b* + 8b*In b\ - Bpa3 1 so that 64 |_ I a a aj J a _•• P » (29) (32) 4a* b2- - 3b* *"'4b*lH _b a Also J? = Tfbfcq where I1 is the total load on the quartz crystals, so that j> _ TTpa* ~ 4a* - 3b a + 4b K iln b - '. a'-Substitution of Particular Values * 2a = 0.796 inches 2b = 0.127 Inches = 0.59,8^ ^ 0 # l 3 p ( 3 5 ) .796a - 3 at, .0532- + .1272- In 127 796 That i s , for every one pound per square inch of pressure in the cylinder, a force equivalent to 0.13 pounds is exerted on the quartz crystals. Dimensions taken from authors' indicator AEPBUDIX III IBAS.DRS8IEBH3? OF HIGH R&SISTAHOSS !• Theory: The application ox a high input resistance vacuum tube amplifier to the measurement of multi-megohm resistors is outlined herein. The method depends on the charging characteristic of a series circuit containing resistance and capacitance. In practice, the resistor R to be measured is so large that the insulation resist-ance of the condenser C must be taken into consideration. F Figure 30 For the simple mesh shown in Figure 30, 0 38, = Rfi, + i , ) -I- z. i . r ^ t, (R 4- r) + i, R so that £ • .. . a • *. r Substituting for i z and simplifying, d1 E r- for which the complete sol-ution i s 90 91 R r t IrO A e R + r B, G A"t t 0 , q 0 and i f d + r Pinal volts on C 1. . 3 — fc Si; G 1 t kRG XX x time f o r q to reach h a l f the f i n a l valine kSO 1.44 T kO 2. Application: To determine k , the switch B, Figure SI., is placed in position 1 to read B-p E is closed and C charges to i t s f i n a l valne. The amplifier input grid potential is adjusted so that (momentary closure of switch A in position. 1 causes ho out-r Figure 51 ** A put current variation. Switch B is opened to' re-move the internal biasing battery on the input amplifier tube, and switches A and B are 92 •closed in position 2. 7/hen 1? has heen adjusted to produce the same amplifier output current as for the condition of balance above, V reads the f i n a l condenser voltage and k ¥ The amplifier output current for an input voltage V is. determined and switches A and F are ouened. D is' 2 closed arid, the amplifier input voltage is adjusted to V . 2 volts. C is shorted instantaneously and F is closed. When switch A is closed, momentarily in position 1 after an interval of t seconds^, the amplifier output w i l l swing up or' down depending on whether the t r i a l value of t i s long or short. Repeated t r i a l s resulting in a zero output swing f i x the time T t and R «» ,1.44 ff KG For the case of the resistor R used in the amp-l i f i e r , K 8.02 : 9.05 = at>0 seconds and C = 0.1 uf. giving R 1.44 x 9.05 x £60 5800 x 10 6 ohms -7 8.02 x 10 approximately APPEMPIX IV MATIIiSuATlOAL- TRMTMEKT Of THIS IK PUT CIRCUIT I. liTRQPUCTIQl To determine the probable potentials on the grid of the "active" input tube cf the amplifier due to the variable charges from the quartz crystals, i t is necess-ary to consider the effect of charge leakage through the resistance of the input circuit. F x, i , , x^ C V A R Currents Air Condenser Instantanaous Grid Potential Battery Voltage Effective Input Resistance figure 3 2 figure 32 represents a simplified input circuit, R being e the effective Input resistance "r and C a standard air condenser. The charge appearing on the quartz crystals varies directly as the cylinder pressure and since the pressure Is a function of time = f(t) i dt £ee Chapter III, Page 44 See Appendix V 93 94 From F i g u r e 32 i = i 4 i where i = . J ^ - ±''(t) (i) d t 1 I i dt r ¥ and t h e r e f o r e C J \ z C d¥ (2) dt a e Combining e q u a t i o n s (1), (2) and (3) f 1 ( t j - - y _ E_ f G dV H R d t e e S u b s t i t u t i n g I) f o r d and a f o r 1 dt R c (J) f aitf - Ea , 1 f ' ( t ) I I I , S O L U T I O N OF THIS Jg(#JATI02* V (3) + 4 l i t ; (4) - Complementary f u n c t i o n 4 . P a r t i c u l a r i n t e g -r a l —at G * a i? 6 Where F i s a c o n s t a n t (5) I - ~ 1 Ea 4 . 1 £'(t) / 6 | L e t P, I . - ¥ 4- V 2 where- (7) 95 Since f 1 ( t ) is a sine - cosine series/ 1" write from Appendix V P Z A + A cos Ti + A, cos 2"i f — + A cos 24W + 3. sin W •• B, sin 2"? - + B sin 23?; where '\ is the angle spanned in time t Let W = wt where w is the angular velocity. Then since q. - {constant)(pressure) - K( pressure) where K i a constant depending on the diaphram of the crystal unit and the value of the piezo-electric effect, Ta Z wK - a ^ - A, sin wt - 2A asin 2wt -+ B, cos wt + 2B cos 2wt + wff (B - a) Ai ein wt 2Ag. sin 2wt * C wz+ a z i . ~~z [ 2w) + _ . Bi cos wt ZB«, cos 2wt w + a (2w) + a X | wa {(A, + B, a) cos wt + (B, - A, a) sin wi (2w)2 ("(A + B? a ^ cos 2wt * ^Bz - A t a ^ sin " {2w)% a H S w ' V 2 w ' See Appendix ? — at = O.IK -f- P.I. - F e 4- £ T V_ (10) £ II DETERMIHATICS OF PARTICULAR VALUES Value of Rg From Chapter III, page 46, R - 250© megohms e o • Value of K K = (^Coulombs per Pound Force per Crystal)(Kumber of Crystals)(Diaphram Factor) - 9.5"" x £ x 0.13** - £ .47 micro-microcoulombs per pound per square inch of cylinder pressure. Take K - £ . 5 Value of C This value w i l l be determined by the maximum desired volt swing on the grid of the "active'1 tube. Assuming no leakage, the charge <a due to a cyl-inder pressure of 600 l b . / sq. in. is given by U, 2 &(^miiX~ fvjj^) s £ . 5 x 600 nucoulombs approx. So that for a maximum grid swing of 1.20 volts, the Input capacity •C - 1250 uuf. See Chapter II, page 34 See Appendix II, page 89 Value of £ This i s the grid bias voltage at aero charge input necessary to produce a gross amplifier output of 50 milliamperes. E 2 V O l t S Minimum "Value of w Leakage w i l l produce a maxim-um detrimental effect at the minimum operating speed of the engine, and since this speed must produce sufficient persistence of vision to permit observation of the pressure phenomenon on the ground glass screen, the value of w i s limited. Taking the minimum speed as 300 r.p.m., then for a four-stroke engine, the angular velocity w s 2If (Frequency) = 2TT x 300 x 1, = 5lf radians 60 2 / see. fake w - 15 radians per second Value of a From the values of R and C, ,—_ e • a » 0.32 Value of Y Since the value a2, is small compared with wa we may write 98 V „ cos 24wt o = % I A. cos wt + A, cos 2wt + 4 A + B sin wt + B sin- 2wt + + B sis 23wt &{/A, sin wt + A,sin 2wt } - ^ B, cos wt + Bjcos 2wt — - - - - - ^ j . 0 ^t 5^ - A^j' +• £^B ( cos wt + BzcOs 2wt + - j ^ s i n wt + A zsin 2wt --^ jj (11) ¥alue of 3? At time t s 0, V = Y Q = E = 6.0 volts. ••Substituting in equation (10) o • V - 6.0 = I? e +. 6.0 Y 0 -1? z JL.\(£!i ~ A ) __a_ (B + BJJ * Bj + — + _ j | J 0 L w • 2 ' S 23 e 0.002 (-65.2 - 0.53) and • a 0.131 volts from equation (5) -at -0.32t s F e = 0.131 e and when t = 9 sec. C i 1 . - .006 volts from which we may assume that after several seconds of operation cf the amplifier input circuit, the term V Q See Appendix ¥ Table ¥ 99 -at I1 e becomes negligible and the grid potentials m a y now be calculated from ¥ 6.0 V g (12) IV PARTICULAR VALUES Off "V" 1. Let wt - 2 KTT where H is a large positive integer. Then V - 6.0 + ( .002) (-65.2 - 0.55) - 6.0 - .131 volts - 5.869 volts That i s , the grid potential at the start of the th ii cycle is 0.131 volts below i t s value for t - 0 2,. Let wt s (2B + i)TT Then V = 6.0 + ( .G02H-66.9 - 2.3) - 6.0 - .129 s- 5.871 volts There i s , therefore, a volt swing on the input ' • • • th. grid of 0.002 volts between the start of the a cycle and 'KjZ radians later. The corresponding change in cylinder pressure during this Interval Is (P,^  - PA' )*, which produces See Appendix V Table V 100 a charge Q z. 2.5 (12.1 - 12,1) - 0 , Therefore the error in voltage introduced by charge leakage over this range is ,002 volts. 3, Let wt r {21 + l)1f t s 6.0 * .002 (281.8• + 2.38) 6.0 + 0.57 volts = 6,57 volts The grid volt swing over IT radians i s 6.57 - 5.87 z 0.70 volts The corresponding charge due to the pressure change i s Q ~ 2.5 (359 - 12.1) pp. coulombs, and assuming no leakage, this would result in a voltage swing of 0.69 volts 4. Let wt s (21 + 25/24)11* ¥ = 6.0 +- .002 (524 +- 1.27) = 6.0 +- 1.04 volts r 7.04 volts The grid swing over 25/24'Tf radians Is therefore 1.17 volts The corresponding charge due to the pressure change Is Q. - 2.5 (601 - 12.1), which, with no leakage would give a swing of 1,18 volts •101 V COlQLUSIQg The derived equations and the p a r t i c u l a r values obtained by substitution indicate; 1. That the errors introduced by charge leakage vary (a) Inversely as the effective resistance R e (b) Inversely as the shunt capacity 0 Co) Inversely as the engine speed 2. The errors are of the order of one percent, f or t y p i c a l operating conditions i n t h i s indicator. APPENDIX ¥ HARMONIC ANALYSIS Off Al ACADEMIC PRESSURE WAVE I. INTRODUCTION In the following, an academic pressure wave is analysed to the 24th harmonic using a tabular system developed by the authors. II. DATA The following particulars were chosen for a four-stroke internal combustion engine; 1. Compression ratio of 5.5 2. i'or compression, p v = a constant 3. Por expansion, P If ; a constant 4. Intake pressure of 13 lb./ sq. in. absolute 5. A linear pressure rise from 10° before T.D.C. to 600 l b . / sq. in. absolute at 10° after T.D.C. 6. A constant pressure of 600 lb . / sq. in. absolute from 10° after T.D.C. to 15° after T.D.C. 7. The exhaust valve opens at 330° on the crank, and the pressure drops linearly to 20 lb./ sq. in. absolute at the end of the stroke 8. Scavenging pressure of 20 lb./ sq. in. absolute 9. Piston displacement is sinusoidal with time 102 Pressure ordinates c a l c u l a t e d from tae fore-going data f o r every 15 degrees of cranic angle appear i n Tables I I I & IV- ( P Q to P.„) I?, ffOPB-IBS SMIJSS .THEORY •. The pressure ordinates of a pressure - time wave may be given by a sine - cosine s e r i e s , P s J?( t) s A COS (0)?/ *• ,'1.^  COS W +• A o C 0 B 2W 4-0 1 a -t-A^eos RW + B-jSin :v +._„+. B R s l n R?i + — where I'"(t) i s a f u n c t i o n of time and A,„ and B_, are k R constants* I f V represents some p a r t i c u l a r value of the angle "^ 1 - ^ 0 C 0 S (0)¥ + A-^cos V + •+• A Rcos RV +• +• B,sin If + — + BgSin ffl +• -— In general t SY. - A cos (0)IV + A_ cos HY + -- A^cos RM + - o 1 R + B. s i n UV + — 4- £ sin RiJV +• — ~ JL £ . . . • • . -.where P-, Is the J3th pressure o r d i n a t e . M u l t i p l y i n g equation (2) by cos RBv" and i n t e g r a t i n g from 0 to 2 IT 104 h G 0 S m a f - , M R cos 2 RIY av + o P,. cos ai? d¥ Taking q. o r d i n a t e s ,2ir AR = - i - ) p ; <GOS REY) 27T approximately v—.2ir .2 \ _• cos R1--Y 1 / h 4 Table i l l i l l u s t r a t e s the tabular- method of s o l v i n ; O li? J^-r^ •R 105 M u l t i p l y i n g equation (2) by s i n REV and i n t e g r a t i n g from o to SIT ZTT Bj£ is .n2m \ i 5 ^ s i n RliV approximately —'o Values of i3 p appear i n Table IV S u b s t i t u t i o n s of p a r t i c u l a r values of A™ and B» i n t o equa.tion (2) appear i n Table V, the derived pressure 106 ordinates being given by PT'. where Pjr r f(t) P( t) approximately (3) Table VI shows a comparison of the derived, press-ures with the original ordinates. The maximum difference between the two Is 1.4 pounds fin 600} 107 T&BiM VI If & s P „ p i % 1 0 l ' i 3 12,1 0.9 " . 2- 13 12.4 0.6 4 . 13 . 11.8 , 1.2 4 13 12.4 0.6 8 13 12.2 0.8 10, 13 12. £ 0,8 12 . 13 12.1 0.9 14 14.1 13.0 1.1 16 . ' 17,8 16.8 1.0 18 26,5 26.0 0.5 20 46.9 46.2 0.7 22 91.0 91, 8 -0.8 kj<3 117 118.0 -1.0 . • 24 360 359 1.0 .25 600 601 -1.0 £6 472 471 1.0 28 £56 256 — 30 151 150 1.0 r/lO 104 103 1.0 34 83.8 82.8 1.0 So 52.0 55.0 -1.0 36 20.0 19.0 1.0 58 20... 0 19. 6 0.4 40 20. 0 19.0 .1.0 42 20.0 18>6 1.4 44 20.0 18. 8 ' 1.2 46 20.0 19,6. 0.4 108 Figure 35 shows the pressure wave f o r which the foregoing a n a l y s i s + w&.s c a r r i e d out. The close agree-ment between the o r i g i n a l pressures and those deriv-ed "by harmonic a n a l y s i s i n d i c a t e t h a t even i n waves having very steep grad i en t s, harmon i c e of higher order than.the 24th are small i n value. Figure 33 The authors found that i n making a d e t a i l e d a n a l y s i s of t h i s type, the t a b u l a r method indic a t e d i n t h i s Appendix provided the frequent checks that are invaluable i n l o n g c a l c u l a t i o n s . APP1BMX VI IAR0E SIZE MASEAMS T h i s Appendix contains large r e p l i c a s of those i l l u s t r a t i o n s i n the t e x t that are marked with a double s t a r .(**) 109 CMAFIGE: MEASUREMENTS I l l WATER-COOLED CRYSTAL HOLDER FIGURE 13 IIS 30 i i 1 1 N E G A T I V E I N P U T G R I D V O L T S F I G U R E 16 114 y c 3 O II 0 —(AAAwXwWW — * A A A A A A A A A A / S A A T — I I I u I 3 U J > 6 u. b. U J u. O »-Z IU 2 U J (t D < ui > O S C I L L O G R A P H F I G U R E : 19 116 £ 4 , 0 0 0 2 0 , 0 0 0 1 6 . 0 0 0 CO 0) • < > z - iti a X 3 a < 0 4 . . 0 0 0 Av E R A G E N T R A L / I Z 3 E X C I T A T I O N A M P E R E S FIGURE: £0 118 119. BIBLIOGRAPHY COLL IKS., 0. M i c r o - I n d i c a t o r f o r High-Speed Engines. She Las t i t u t i o n o f Mechanical -Engineers, London January 1925, V o l . _1__ , 127 CURIE, J. and P. Developpernent par press ion de 1 1 e l e c -t r i c i t e p o l a i r e dans l e s e r i s t a u x hemicores a. faces InclineeSe Comptes Rendus, 1880, 91, 294 CURIE, and P. Sur 1 ' e l e c t r i c i t e ^ d a n s l e s c r i s t a u x hemiedres a faces i n c l l n e e s . Comptes Rendus, 1881, 91, 385. DAWSOJB, L. P i e s o - M e c t r i c i t y of C r y s t a l Quartz. Phys-i c a l Review, 1927, 29, §32. IRV/IIv, J. T. O s c i l l o g r a p h s . Pitman & Sons, London, 1925- (Pages 25, 26 and 82) JUDGE, A. W. She Te s t i n g of High-Speed I n t e r n a l Com-b u s t i o n Engines. Chapman & Sai l . , L t d . , London, 1924. (Page 209) KLUGS, J. and LILCKH, H. E. P i e z o e l e k t r i s e h e r I n d i -c a t o r f u r schne11aufende Verbrennungsmotoren. S e i t s c h r i f t des Vereines deutscher Ingenieure, B e r l i n , 1930, 74, 887. 120 121 ILLUGE, J , and UBGKH, H». 2. P i e z o e l e k t r i s c h e Druck-messungen mit der Braunsohen Rohre. Forschung auf dem Gobiete des Ingenieurwesens, B e r l i n , 1933, 4, 177. LAWS, P. A.. E l e c t r i c a l Measurements, McGraw-Hill Book Co., Hew York, 1917. (Page 637} BlfiDMAN, K. P. Zur ffrage nach der Existenz wahrer-P y r o e l e k t r i a l t a t * Annalen, der Physik, 1920, 62, (Page 107) MARTIP, E. J. and CARIS, B. ff« An E l e c t r i c a l Engine I n d i c a t o r . Tke E l e c t r i c Journal, 1930, 27, 168 - 172 NOTTINGHAM, W. B. Measurement o f Small B. 0. Potent-i a l s and Currents i n High Resistance C i r c u i t s by-us i n g Vacuum Tubes. Journal of the f r a n k l i n I n s t i t u t e , P h i l a d e l p h i a , 1930, 209, 311 - 314. PERRIER, A. Hypothese de p o l a r i s a t i o n s d i e l e c t r i q u e s spontaneas et quelques-ones de ses consequences experimentales. Archives des Sciences Physiques et N a t u r e l l e s , 1916, 41, 493. SCHUL^AS-SOROSINA, R. B. Is i t p o s s i b l e to determine the p i e z o - e l e c t r i c constant at high temperature by the s t a t i c a l method? P h y s i c a l Review, 1929, 34, 1448 122 TIMOSfillEO, S. Strength of Materials, D. Van lostrand Co., fiew York, 1930. (Page 490) THOMSON, SIR WILLIAM Mathematical and Physical Papers, Vol. 5, University Press, Cambridge, 1911. (Page 311) VIGOURiiiUX, P. Quartz Resonators and Oscillators. K. M. Stationery Office, London, 1931, (Pages 28, 171) VOIGT, W, Lehrbuch der Kristallphysik. Druek und Verlag von B. G. Teubner, Berlin, 1910. WATAJiABE, S. A ISew Design of Cathode-Ray Oscillograph '• and Its applications to Piezo-Electric Measurements. Scientific Papers of the Institute of Physical and Chemical Research, 1929, 12, 82. ft V/ATSOE, H. G. I. and KEYS, D. A. A Piezo-Electric Method of Ileasuring the Pressure Variations in Internal CombiiBtion Canadian Journal of Research, Ottawa, 1952, 6, 322. ,71 (THROW, L. and ROSSWEILBR, G. M. A Study of Pressure Waves associated with Detonative Burning. The • Automobile Engineer, 1934, 24, 281. 


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