5.. :10. 3. At; 1.. 1.... bums. .z. 245:: _ \1 : few. I»... IPA-n «L. ufiebvmuz; . .- 4h 5.. ‘LR‘ .52.. r 1a. .35. 1 k? v I n. .9. .5 . Z .1 .. {1.2.3: ..r . .‘..u$.i.' 3....1: .1 . .r. v2.5 .551... \ nMIIaJWJJJJcnhi ‘3“...«29 54:11... . in 3&2.wa .. ‘4 3.1»): .... .c.,u..4..t Qw .In +1 2%Q75Hq0 lllllllllllllllllWWI“I IIHI ”will “BM-fa? W 3 1293 00592 3713 Michigan Stu University L This is to certify that the dissertation entitled MEASUREMENT OF APPLE FIRMNESS USING THE ACOUSTIC IMPULSE RESPONSE presented by PAUL ROBERT ARMSTRONG ' has been accepted towards fulfillment of the requirements for ‘ I Ph.D. AGRICULTURAL ENGINEERING degree in 2/4/23 é” ’ Major professofl // Date 3/3fl/gf MS U is an Affirmatiw Action/Equal Opportunity Imtitution 0-12771 PLACE IN RETURN BOX to remove this checkout from your record. To AVOID FINES return on or before date due. DATE DUE DATE DUE DATE DUE “ WV51‘ -' . J lw ‘ l . _ 1 in ii “"0 w L____——-— MSU Is An Affirmative ActionlEquel Opportunity Inditutlon MEASUREMENT OF APPLE FIRMNESS USING THE ACOUSTIC IMPULSE RESPONSE BY Paul Robert Armstrong A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY in Agricultural Engineering Department of Agricultural Engineering 1989 f) t7$390 3 [T ABSTRACT MEASUREMENT OF APPLE FIRMNESS USING THE ACOUSTIC IMPULSE RESPONSE BY Paul Robert Armstrong Non-destructive techniques that could determine fruit maturity or texture would help the producer, packer and retailer achieve a significant improvement in fruit quality. This research investigated the acoustic impulse response of -_, an apple as a non-destructive means of predicting tissue firmness. Resonant frequency modes of an apple were induced by an impulse with the resulting acoustic response being sensed by microphone. Frequency content of the response was elucidated using a Fast Fourier Transform (FFT). The repro- ducible frequency peak in the spectrum was identified as a resonant mode of the apple. A spherical resonator model, using this resonant frequency, the apple mass and the apple density, was developed to predict the modulus of elasticity. The predicted modulus of elasticity was compared with the measured firmness determined by: (l) Magness-Taylor firmness measurements of the apple, (2) Classic measurements on apple flesh from which modulus of elasticity was determined. (3) Classic measurements on apple tissue which included the core and flesh in the tissue specimen. Tests on the apples were conducted over several weeks to investigate the drop in flesh firmness. Regressing the model prediction data on the measured values of firmness show that the model has very good correlation. The r2 values (correlations) were in the range 0.774-0.803, when the modulus of elasticity measurements included the core of the apple. The model did not have as strong correlations for the Magness-Taylor firmness or for the modulus of ela- sticity determined only from the apple flesh. The knowledge gained from this research suggests that the impulse response is satifactory for non-destructive measurement of the modulus of elasticity of the apple core and surrounding flesh. The ability to predict Magness- Taylor firmness or flesh modulus of elasticity would find greater acceptance by the apple industry. Further research is required to develop the relationship between apple maturity and core strength. Approved. zyfiwé/g f2.” Co-Major Profeg ( 7 Co-Major Professor A .W pprove 1, , (agg' "_ I Department Chairman ACKNOWLEDGMENTS The author would like to express his appreciation to the following people for the encouragement and assistance they gave throughout the course of my graduate program. To Dr H. Roland Zapp, my major advisor, for his time and effort helping me academically and the hours spent editing this thesis and to Dr. John B. Gerrish, my other advisor, for his enthusiastic support and guidance. To Dr. Bernie Tennes for helping to initiate and provide assistance for this research. To Dr. Gary Burgess and Dr. James Resh for their interest and support of this research while serving on my guidance committee. To Dr. Galen K. Brown for continued interest and support. To Ed Timm for never failing to answer my questions concerning Wordstar,Plotit etc. and Dick Wolthius for providing technical support. And to my wife, Tricia, and daughters, Gillian and Claire. ii ACKNOWLEDGMENTS . LIST OF LIST OF LIST OF CHAPTER 1. TABLES. . FIGURES . SYMBOLS TABLE OF CONTENTS INTRODUCTION. . . . . . . . . . . . . . . . . 1.1 The Need . . . . . . . . . . . . . . . . Background. . . . . . . . . . . . . . . .2 1 1.3 Objectives . . . . . . . THEORY OF SPHERICAL RESONATORS. . . . . . . 2.7 Strain and Displacement. . . . . . . . . Linear Momentum and the Stress Tensor. . Stress-Strain Relationships. . . . . . . Statement of Dynamic Elasticity. . . . . The Scalar and Vector Potential Problem for a Sphere . . . . . . . . . . . . . Resonant Modes of a Sphere . . . . . . 2.6.1 2.6.2 2.6.3 Model Pure Compressional Modes. . . . . Pure Shear Modes. . . . . . . . . Mixed Modes . . . . . . . . . . . Development. . . . . . . . . . . . EXPERIMENTAL TECHNIQUES AND PROCEDURES. . . 3.1 Techniques . . . . . . . . . . . . . . . 3.1.1 Acoustic Impulse Response Measurement . . . . . . . . . . . 3.1.2 Modulus of Elasticity Measurement 3.1.3 Magness-Taylor Measurement. . . . 3.1.4 Apple Mass Measurement. . . . . . 3.1.5 Apple Storage . . . . . . . . . Procedures . . . . . . . . . . . . . . 3.2.1 Controlled Atmosphere (CA Rome Beauty . . . . . . iii PAGE ii vi vii QPJH 10 11 12 15 15 15 20 21 21 24 24 24 26 29 31 31 31 32 3.2.2 Controlled Atmosphere (CA) Law Rome. . . . . . . . . . . . .3 Paula Red . . . . . . . . . . . .4 Golden Delicious. . . . . . . 4 0 RESULTS 0 O O O O O O O O O I O O O O O O O 4.1 Magness-Taylor' Firmness. and Model Predictions. . . . . . . . . . . Elastic Modulus of Flesh and Model Predictions. . . . . . Core-Flesh Elastic Moduli and Model Predictions. . . . . . . . . . . Summary of Regression Results. . . . . 5 O CONCLUS IONS O O O O O O O O I I O O O O O O 6. RECOMMENDATIONS FOR FUTURE RESEARCH . . . . 7. SUPPLEMENTARY EXPERIMENTATION . . . . . . . \IQQQQ UlahUNl-J Water as the Acoustic Energy Carrier . Signal Noise . . . . . . . . . . . . . Repeatability of the Acoustic Response Experimentation with an Elastic Sphere Signals from an Accelerometer. . . . . APPENDIX C O O O O O O O O O O O O O O O O O O BIBLIOGRAPHY . . . . . . . . . . . . . . . . . iv 33 35 37 38 38 4O 42 52 6O 62 64 64 65 67 71 72 78 87 LIST OF TABLES TABLE PAGE 4.1 Regression results from the study. . . . . . . . . 56 7.1 Peak frequency reproducibility of five apples. . . 69 7.2 Peak frequencies obtained from different impulse and receiver orientations for five apples . . . . . . . . . . . . . . . . . . . . . . 71 7.3 Comparison of peak frequencies for two apple shapes of the same mass and the spheres from which they were made . . . . . . . . . . . . . . . 73 7.4 Ratios of peak frequencies to center frequency . . 76 LIST OF FIGURES FIGURE Spherical coordinate system for the spherical resonator. . . . . . . . . . . . . . . . . . . . Mode chart for the spherical resonator . . . . . Particle displacement for lower-order modes. . . Instrumentation and apple orientation used to measure the acoustic impulse response. . . . . The digitized acoustic impulse response of an apple detected by the microphone and the frequency spectrum obtained with a PET . . . . . Instrumentation used to measure modulus of elasticity of an apple specimen. . . . . . . . . Force versus time curve obtained for modulus of elasticity measurement . . . . . . . . . . . . . Relative location with respect to the apple where specimens were obtained for modulus of elasticity measurement . . . . . . . . . . . Apparatus used to obtain the specimens . . . . Predicted modulus of elasticity versus measured Magness-Taylor firmness for CA Rome Beauty apples . . . . . . . . . . . . . . . . . . . . . Predicted versus measured modulus of elasticity for CA Law Rome apples . . . . . . . . . . . . Drop in peak frequency versus time of 16 CA Law Rome Apples. . . . . . . . . . . . . . . . . . Predicted versus measured modulus of elasticity for Paula Red apples . . . . . . . . . . . . . . Predicted versus measured modulus of elasticity for Paula Red apples . . . . . . . . . . . . . vi PAGE 16 19 22 25 27 28 3O 34 34 39 41 43 45 46 Predicted versus measured modulus of elasticity for Paula Red apples . . . . . . . . . . . . . . Frequency squared versus measured modulus of elasticity for Paula Red apples. . . . . . . . . Predicted versus measured modulus of elasticity for Golden Delicious apples. . . . . . . . . . . Predicted versus measured modulus of elasticity for Golden Delicious apples. . . . . . . . . . . Predicted versus measured modulus of elasticity for Golden Delicious apples. . . . . . . . . . . Frequency squared versus measured modulus of elasticity for Golden Delicious apples . . . . Drop in peak frequency versus time of 10 Golden Delicious Apples . . . . . . . . . . . . . . . Original acoustic signal and its spectrum. . . DC attenuation of the acoustic signal and its spectrum . . . . . . . . . . . . . . . . . . . . Two signals and their spectra displaying multiple resonant peaks. . . . . . . . . . . . . Orientation of impulse and microphone. . . . . . Spectra from two apples and the orientation of the receiving device. . . . . . . . . . . . vii 48 49 50 51 53 54 55 66 66 68 70 75 < rt *3 XIYIZ r,O ,4! LIST OF SYMBOLS area sphere radius modulus of elasticity shear modulus of elasticity normalized frequency longitudinal phase velocity shear phase velocity = stiffness coefficients body force frequency, cycles/s denotes complex number Bessel functions of the first kind component of a unit vector subscripts Legendres polynomials displacement surface surface traction time volume cartesian coordinate axes radial Bessel function spherical coordinate axes viii >1 <3 -\ Cards; + 2,u.aaj [9] 2.4 Statement of Dynamic Elasticity Consider a body B occupying a regular region V, which may be bounded or unbounded, with interior V, and boundary 8. The system of equations governing the motion of a homogeneous, isotropic, linearly elastic body consists of the previously developed equations, [1], [6], and [9]. EN - % (LMJ +tJm) [1°] Tij,j+ ,Ofl " pUi [11] Tij - Asks. (5i; + 2118i; [12] Substituting [10] into [12] and the resulting stress expressions into [11], the following displacement equation of motion is obtained: MUM: + (MMUII + pf: - pUi [13] In the absence of body forces equation [13] becomes: MUN: + (Ml/JUN: = pl}; [141 In vector notation this can be represented as: 13 szu +(>\+,u.)VV-u - ,0 ii [15] 2 where V and V are the Laplacian and gradient operators, respectively. A decomposition of the displacement vector to scalar, Cl? , and vector potential, 41 , functions gives: u -V+-V»\lI [15] Conditions on the displacement representation to satis- fy the equation of motion are found by substitution of [16] into [15] yielding: I. V2 [V <1: + W] + (A+/1.) VV-[V Cb + vxw] 2 ,o (2.2 [v d: + vw] ”71 at Rearranging terms and using the relationships V-Vx‘i’ = O and VoV d) -V2¢ results in: V [OHZIU V243 - p315] + V'[,u.V2‘i’- pili] - O [18] The displacement representation [16] will satisfy the equa- tion of motion if: 2 1 .. V 43 - ¢ [19] —2 Cu l4 2 1 vwa—z {i} [20] where: l c. {Liz/'0]? [211 ct .[g]2 [221 Cu and Care termed the compressional (longitudinal) and shear (transverse) phase velocities, respectively. For time harmonic fields with frequency cu, equations [19] and [20] may be written, Auld (1973): 2 2 V¢+ $42-0 [231 C? Vzw fiw-ao [“1 C? Equation [16] relates the three components of the displacement vector to four other functions: the scalar potential and the three components of the vector potential. This indicates that an additional constraint is required. For an unbounded medium subjected to a distribution of body forces, with arbitrary initial conditions, Achenbach (1973) shows the following condition is sufficient to meet this requirement. 15 VAP = O [25] 2.5 The Scalar and Vector Potential Problem for a Sphere The spherical coordinate representation used in the following development is shown in figure 2.1. Solutions of the scalar potential equation [23] in spherical coordinates, as given by Stratton (1941), have the general form: ¢mn(r6¢) - 21(0) r>p'n"" (COSG) eim¢ [26] c where n = 0,1,2 .... and -n < m < n . The dependence of the function on C)is given by Legendre polynomials of the first kind. Radial Bessel func- tions describe the radial functional dependence. Similarly for the vector potential: ‘i’mntefl - ZnPLm (C056) e imd) [273 Ct 2.6 Resonant Modes of a Sphere 2.6.1 Pure Compressional Modes For a solid spherical resonator of radius a, solutions given by [26] and [27] must remain finite at r=0 thus only Bessel functions of the first kind, jn , may be used. When m=n=0, solutions for [26] and [16] are: 16 Figure 2.1 Spherical coordinate system for the spherical resonator. 17 u... - uoo -V j. (if) - F 9... jo<fl> [281 Cl ar C: where F is the radial unit vector. The strain field corresponding to this, from equation [10], has only three components: Err =J— g—Ul [29 a.] M.) r see - L P: [29 b.] M) r a» - 1 Sr [29 c.] 10) r and the traction force on the spherical surface from equations [3] and [12] is: T~F= Trr =- C11€n+C12(896+ 80¢) [30] where C11 and C12 are elements of the stiffness matrix, Auld (1973). For the assumptions governing this medium, Lame’s constants can be equated to the stiffness coeffi- cients by, A'Clz and ,LL-C44 Equations [28] to [30] lead to a stress free boundary condition of: 18 C11 i2j0<fl> + 2C12 a_jo ELF) =.O [31] dr2 (3' r 6r (3' At r = a, the substitution of an approximation for the radial Bessel function for n=0 (first kind, zero order) in (a) r) _ sir2w(:)/;/I)C.) leads to the characteristic frequency equation: (fl) ton <93) - C' [32] C: 1 on <0) O\2 4C44 C. / Specific values of a) which satisfy this equation are listed in various references, Auld (1973), Love (1949), Eringen (1974). These modes are designated Sol where 1 refers to the order of roots which satisfy [32]. Introduction of the normalized frequency, 0 , defined by: provides a common way of expressing frequencies between modes. Figure 2.2 shows the normalized frequency as a function of Poisson’s ratio. Ct can be equated to Cl by: 1 Ct - c] (1422.): [33] 2(l-V) we cl‘. NORMALIZED FREQUENCY. Q - 19 /SO 2’ 21 x540 [In /: "— /SH I30 2’5on 2 T I I I 0 0.1 0.2 0.3 0.4 0.5 POISSON'S RATIO, V Figure 2.2 Mode chart for the spherical resonator. 20 2.6.2 Pure Shear Modes Particle motion for this mode is always normal to the radial coordinate. From equations [16] and [27], particle motion is: 09 .. _L_ 23m" [34] sinC-D ac]; u. = 531’... [35] GO Bessel functions of the first kind are again only valid and the strain field from equation [10] has components which include only: See. Bonfire, 8n. Coo Traction force on the sphere from equation [3] is: T.F=O§_¢1 §U_6_£>+$C_H. [36] la) 6r r iw 6r r A wherelD and ¢ are the spherical unit vectors. For m=0,n=1 the particle field velocity from equations [27] and [16] is: um = cl) 6_ \lzm =- - {13 cosO j1<93__r.> [37] 0C) Ct Particle motion is a rigid rotation of spherical shells about the z-axis with adjacent shells moving in opposite directions. The characteristic frequency equation for this case is: 21 (“3”) ton (3)—O) .. [33] CI 1 Cr: (0)0 2 4C44 CI / Shear modes are designated Tn,l-1 where 1 refers to the order of roots which satisfy equation [38]. Figure 2.2 shows the normalized frequency, {2, as being independent of Poisson’s ratio. Frequencies are not dependent on the subscript m thus it is dropped. Note for n=1 the second mode subscript is chosen to be 1 rather than 1-1 according to common convention, Auld (1973). 2.6.3 Mixed Modes Stress-free boundary conditions at r = a result in com- plicated frequency relations for specific cases. These modes are designated Sn,l-1 and are shown in figure 2.2 for several lower-order modes. Solutions for specific cases were calculated by Sato et al. (1962). General particle dis- placement of lower-order modes for the three modes are shown in figure 2.3. 2.7 Model Development Utilizing equation [22], standard identities for elas- tic constants and the normalized frequency notation, the shear modulus, G', for a particular vibrational mode can be determined from: 2 G = (069) P [39] 22 The lowest-order torsional mode of a spherical resonator designated the T" mode. The lowest frequency mode at radial compression. 5 01 , called the breathing mode. The lowest frequency mode of e spherical resonator in a mixed mode. 3 20. called the oblote-prolate mode. Figure 2.3 Particle displacement for lower- order modes. 23 In terms of density, mass and frequency this becomes: 1/3( 2 2/3 6 :2 LG G=[p02fl) me [4o] l/3 or in terms of the Elastic Modulus, E:: 2 2/3 2 2/3 7‘) 20””? fm [41] E = [ p (6 ()2 Equation [41] provides a useful model for determining material property strengths of apple tissue utilizing the quantities of mass, density, frequency of vibration, and Poisson’s ratio. The mode of vibration is also fundamentally important. This equation will be used to predict modulus of elasticity values of apple tissue for comparison with measured values of tissue firmness. III EXPERIMENTAL TECHNIQUES AND PROCEDURES 3.1 Techniques 3.1.1 Acoustic Impulse Response Measurement Yamamoto (1980) utilized the acoustic impulse response technique to measure the resonant frequencies of apples. Although his results did not identify any dependence or independence on the variables he used in a model to predict firmness, he did have good correlations for the models used and provided insight on impulsive techniques for apples. For this study an apple was struck by a hammer which consisted of a ball of bees wax attached to the end of a steel rod. The ball of the hammer was approximately 2 cm in diameter. Acoustic emissions from the apple were sensed by a Radio Shack electret 270-090 microphone and the signal stored on a Analogic Model 6000 digitizing oscilloscope. A schematic diagram of the instrumentation and apple orienta- tion is illustrated in figure 3.1. The microphone was posi- tioned near the equator of the apple. Apples were held by hand, approximately 1 cm in front of the microphone and struck on the opposite side of the fruit. The acoustic signal emitted by the apple triggered the oscilloscope, which then sampled the signal at a rate of 25 KHz, or every 40 micro-s, for a total of 2048 points. Data were stored on floppy disk, as digitized voltage levels. A 24 25 / FLOPPY DISK DRIVE / —— BATTERY DISPLAY ' ‘—"" - N. [ :::::: + ——""°" ' IMPULSE 1.:— R u «— IIIO / T MICROPHONE HAMMER ANALOOIO 6000 OSCILLOSCOPE Z Y MICROPHONE IMPULSE LOCATION EOUATOR X Figure 3.1 Instrumentation and apple orientation used to measure the acoustic impulse response. 26 Fast Fourier Transform, FFT, of the digital signal was performed by the oscilloscope, and in some cases by a personal computer, to determine frequency content. Figure 3.2 shows a typical sampled acoustic signal from an apple and the frequency spectrum of this signal. Resolution of the FFT is determined by 1/NT where N is the number of points sampled and T is the sampling period in seconds. A sampling period of 40 micro-s, for 2048 total points results in the resolution of the FFT to be 12.207 Hz over an effec- tive range of 0-12.5 KHz. 3.1.2 Modulus of Elasticity Measurement Modulus of Elasticity measurements were obtained by subjecting a test specimen from the apple to a uniform axial compression test as shown in figure 3.3. A Daytronic 152a+50 load cell was fixed to a Chatillon HTCM crosshead. Apple sections were placed between parallel plates, one plate being attached to the load cell the other was the moving base of the Chatillon HTCM. Base plate speed was set at 0.05 cm/s for all testing. Signal output from the load cell was amplified with a Daytronic 300D amplifier before being fed to the Analogic 6000 oscilloscope. Input to the oscilloscope was sampled every 15 ms for a total of 1000 points. Load cell calibration, expressed in volts/kg, was done prior to testing and checked after test completion. Recordings of force versus time, taken by the oscilloscope, were transferred to floppy disk and analyzed on an IBM AT computer utilizing a plotting and signal analysis program MICROPHONE SIGNAL AMPLITUDE. mV. MAGNITUDE. IN. 27 -80 .03192 sec. 1000 800 903 Hz. can /- 400 200 o . - o 12.5 FREQUENCY. KHz. Figure 3.2 The digitized acoustic impulse response of an apple detected by the microphone and the frequency spectrum obtained with a FFT. 28 6250an ciao co co atoms—6.0 Co 23.23.: ocseooE 3 use: cozeacoEsbms n.n 053... magma? zofigzmaoo MAR-madame 653m: 890 QZOEE 39—: ZOE—.230 0000 0.90; _ M_ a / 1 [163.095 Wm]... .3... an 30.. 9201.53 \\ = 9.26 v.90 >LLOJL 29 developed by the author. Modulus of elasticity was esti- mated by determining the slope, expressed in N/sec, of the linear section of the plot by linear regression. The slope was used to form a line, passing through zero, which repre- sented force versus compression (expressed in meters) of the specimen. The compression of the specimen was obtained by consideration of the crosshead speed. The transformation of the slope units of N/m to stress/strain, as a result of dividing by the specimen cross-sectional area and original specimen length, yields modulus of elasticity. Figure 3.4 shows a typical plot and the linear section used in calcu- lating the modulus of elasticity. Test specimen size and the location from the apple, varied between experiments as detailed in section 3.2. 3.1.3 Magness Taylor Measurement Magness Taylor readings were performed with a Chatillon HTCM firmness tester. This was the same instrument used in modulus of elasticity measurements with a firmness testing plunger substituted for the load cell. The 11.1 mm diameter plunger was driven into the apple by a variable speed elec- tric motor to an approximate depth of 15 mm. Speed was set at approximately 10 cm/min for all tests. Skin and some flesh was removed from the apple to provide a relatively flat surface of contact for the plunger. F ORCE, N. 500 400 300 . 200 l 100. 30 LINEAR SECTION OF PLOT USED TO CALCULATE uaouws 0F ELASTICITT. 0123456789 T I 1011 I 12 13 14 Figure 3.4 Force versus time curve obtained for modulus of elasticity measurement. 15 31 3.1.4 Apple Mass Measurement Apple mass was measured by an Ohaus, Brainweight Bl500D electronic scale with a range of 0-1500 grams. Measurements were recorded to 0.1 gram. 3.1.5 Apple Storage The apples used in this study came from either con- trolled atmosphere storage or were freshly picked. During experimentation, apple batches were stored in boxes inside a cooler at a temperature of 1° C. 3.2 Procedures The purpose of the experimentation was to provide quan- titative information on the acoustic impulse response of apples and pertinent apple physical properties for use with the model given in Equation [41]. This model would be used as a predictor of flesh firmness. Measured values of flesh firmness would provide a comparison with predicted firmness. Abbott (1968) & Finney (1971) have shown that natural fre- quencies of apples are dependent on mass, as indicated by Equation [41]. Other variables that the model indicates as being important are density, and Poisson’s ratio. The effect of skin stiffening or the non-homogeneous composition of an apple cannot be predicted by this model. Experimental procedures to minimize skin stiffening, without altering the apple mass, was achieved by multiple cuts of the skin surface. Four batches of apples were used for experimentation. 32 The number of apples in each batch varied from 50 to 120. Subgroups of apples were taken from each batch and tested periodically. Testing was spread over a period of approxi- mately 6 weeks, for each batch, to allow a measurable drop in firmness within the batch. Modulus of elasticity and resonant frequency measurement techniques differed somewhat between batches. Specific techniques are given for each batch. 3.2.1 controlled Atmosphere (CA) Rome Beauty Subgroups of 20 apples for a total of 120 apples were tested on each of the dates given below. Measured variables included the acoustic impulse response, test mass and Magness-Taylor firmness readings. The subgroups were tested on the following dates: 11/2/87, 11/9/87, 11/16/87, 11/23/87, 11/30/87, 12/7/87. The total number of results from the apples tested was 118. Natural frequency measurements were conducted as out- lined in section 3.1.1. Test mass was determined just prior to impulse testing. Magness-Taylor firmness was also deter- mined as outlined section 3.1.3. Five to seven readings, depending on the size of the apple, were taken along the equator. The average value of these readings was used as an indication of apple flesh firmness. 33 3.2.2 Controlled Atmosphere (CA) Law Rome Subgroups of 10 apples were tested on the dates given below. Measured variables included the acoustic impulse response, test mass and the modulus of elasticity. The subgroups of apples were tested on the following dates: 2/2/88, 2/9/88, 2/14/88, 2/21/88, 3/7/88. A total of so apples were tested. Elastic modulus was determined as outlined in section 3.1.2 with four cylindrical specimens taken from the cheek of each apple and separately tested, (See figure 3.5 for orientation). Specimen size was 15.9 mm in diameter and 25.4 mm long. Specimens were obtained using a thin tubular cutting knife and specimen holder as shown in figure 3.6. The tube was pushed by hand into the top of the apple tra- versing to the bottom of the apple. The knife had an out- side bevel at the cutting edge. Care was taken not to ro- tate the knife while cutting as specimens could shear from torsion. To obtain parallel flat surfaces at the ends, the specimen was placed in the holder which was made from a 25.4 cm, plate plexi-glass with a hole drilled through it, see figure 3.6. The hole diameter was the same as the specimen diameter. A razor blade was used to cut the ends with the flat surfaces of the plexi-glass used as a guide. The modulus of elasticity values obtained from the four specimens were averaged and used as an indicator of the apple’s flesh strength. 34 Location of cylindrical specimen Location oi cubical specimen taken for modulus of elasticity 2 taken for modulus of elasticity measurements. measurements. Y EOUATOR x Figure 3.5 Relative location with respect to the apple where specimens were obtained for modulus of elasticity measurement. SPECIMEN TUBULAR cumnc KNIFE Alignment marks Plate slot Sae guide SPECIMEN / r / @ / £323 9 SPECIMEN HOLDER HITER BOX Figure 3.6 Apparatus used to obtain the specimens. 35 Sixteen CA Law Rome apples were measured for natural frequency and mass on the same test dates as the above CA Law Rome apples. Resonant frequency behavior for the apples as a function of time and aging was thus observed. 3.2.3 Paula Red Subgroups of 10 apples for a total of 70 apples were tested on the seven dates given below. Measured variables included the acoustic impulse response, test mass, density and the modulus of elasticity. The subgroups of apples were tested on the following dates: 9/2/88, 9/7/88, 9/12/88, 9/17/88, 9/22/88, 9/27/88, 10/3/88. The natural frequency measurements were conducted as outlined in section 3.1.1 with the following addition: apples were tested with the skin intact and with the skin cut by a multiple-bladed knife. The cuts were made lateral- ly and longitudinally over the surface of the apple, approx- imately 0.5 mm deep and separated by 5 mm. The purpose of these cuts was to negate the stiffening effect that the skin had on the apple. The mass of each apple was measured im- mediately after harvest and apples were grouped into batches of 10 with each batch having the same approximate average weight. Average weights at testing for each group ranged from 203.39 to 207.37 grams, with a standard deviation that ranged from 7.37 to 11.85 grams. The purpose of controlling weights was to establish apple groups that would have simi- lar core-to-flesh ratios and shapes. Mass was again mea- sured, for each apple, prior to its acoustic response and 36 elastic modulus measurement. The elastic modulus was determined as outlined in section 3.1.2. One cubical specimen was taken from the center of each apple and separately tested. Figure 3.5 shows the orientation of the cubical specimen with respect to the apple. The specimen size consisted of a 38 mm cube which included the core of the apple with the axis of the core emerging from opposite faces of the cube at its center. Specimens were cut from the apple using a fine blade hack saw and a specially constructed miter box as shown in figure 3.6. The saw was used for cutting, as initial attempts with a knife did not produce consistent flat surfaces. Apples were set upright in the box with the core being aligned as close as possible to centering marks, to obtain symmetric specimens with respect to the core. A side of the apple was initially cut to form a flat surface which would also be a side of the cube. The apple was then placed in the box resting on this flat surface with the core again aligned with the marks. A second side was out which was perpendi- cular to the first. A third cut was made with the apple resting on a flat side with the second flat surface against the wall of the miter box. A plate inserted into the box served as a guide for the remaining cuts. Specimens were placed in the compression tester with the core horizontal to the compression plates. Specimens were tested at a cross- head speed of 0.05 cm/s, and loaded up to a force of approx- imately 400 N. Density of each apple was determined by 37 water displacement prior to natural frequency and elastic modulus determination. 3.2.4 Golden Delicious Subgroups of 10 apples for a total of 60 apples were tested on the six dates given below. Measured variables included the acoustic impulse response, test mass, density and the modulus of elasticity. Subgroups of apples were tested every six days on the following dates: 10/8/88, 10/13/88, 10/18/88, 10/23/88, 10/28/88, 11/3/88. Experimental procedures were the same as for the Paula Red with the following exceptions: 1. 10 reference apples were measured for their acoustic im- pulse response immediately following picking and on each test date listed above. 2. The standard deviation of mass for each subgroup was in- creased to a range of 23.97 to 39.35 grams for an average mass for each subgroup from 196.5 to 201.2 grams. IV RESULTS 4.1 Magness-Taylor Firmness and Model Predictions Tests conducted on CA Rome Beauty apples utilized Magness-Taylor firmness readings primarily because of the acceptance of this measurement in the industry. Figure 4.1 illustrates the results of Magness-Taylor values versus the predicted modulus of elasticity as defined by Equation [41]. The model assumed the compressional, Sol! mode of the apple (vibration in a radial direction only) referred to hence- forth, as the breathing mode. Although the exact mode was not determined, an examination of Equation [41] reveals that for any assumed mode, and for a constant Poisson's ratio, the values predicted are linearly related. Poisson's ratio was assumed to be 0.3 for all apples. Apple density was also assumed to be constant in the model as reasonably mature apples have only moderate variations between apples. A value of 800 kg/m3 was used. The coefficient of determination, r2 , from linear regression of Magness-Taylor firmness on the predicted modulus of elasticity values is 0.265, (N=118). Thus 26.5% of the variability in the pre- dicted modulus of elasticity can be explained by a linear relationship. Clark (1973) suggested that certain modes of vibration are effected by localized material properties, ie. a pure 38 PREDICTED MODULUS OF ELASTICITY, MPa. 39 Prediction Equation E .__. l'aoo‘”(5n')”‘2(1..3)] f'm'" - 4.9955‘ s 7 . II . s . 4 . 5 '1 2 " y=.240x + 2.652 I . r2 = .265 (N=118) o 10 20 30 4o 50 60 70 so 90 MAGNESS-TAYLOR FIRMNESS. N. Figure 4.1 Predicted modulus of elasticity versus measured Magness—Taylor firmness for CA Rome Beauty apples. 4O torsional vibration of a low-order mode would be less influenced by the material properties near the core of the apple than at the circumference. As indicated by the low correlation of these results, one might suspect that Magness-Taylor properties are not directly influencing the modes of vibration induced by the methods used in this research. 4.2 Elastic Modulus of Flesh and Model Predictions Tests on CA Law Rome apples were conducted similar to CA Rome Beauty apples with the exception that apple properties were determined by compression tests, which yield modulus of elasticity, rather than Magness-Taylor firmness. This provided a more analytical approach than could be achieved from firmness readings. Measurement of modulus of elasticity from compression testing is a non-destructive measurement of the elastic properties of the apple flesh as opposed to Magness-Taylor testing which involves shearing and crushing of the apple flesh. Resonant vibrations in an elastic medium are dependent on the mediums' elastic properties and thus modulus of elasticity should provide a better determination of the flesh strength for comparison with model predictions. Predictions of the modulus of elasticity can be directly compared to the measured values which would help indicate the mode of vibration induced. Modulus of elasticity was evaluated for each apple using a cylindrical sample from the cheek as outlined in the experimental procedures section. Figure 4.2 shows predicted PREDICTED 8 7 d g 6 r.’ 9: 5 [— VI 5 4 Isl LI. 0 3 m 2 5’ 2 o o z I 0 Figure 4.2 41 Prediction Equation j E .. [aoo"’(6n')"'2(1..3)] ,‘m"' I 4.9955’ .1 ‘ y-.174x + 3.842 . r2 = .055 (N-SO) o I 2 s 4 5 6 7 II MEASURED MODULUS OF ELASTICITY. MPa. Predicted versus measured modulus of elasticity for CA Law Rome apples. 42 modulus of elasticity of the apple versus its measured value. The breathing mode, a Poisson's ratio of 0.3 and a density of 800 kg/m3 is assumed for the model. The coefficient of determination, r2 , from the regression of measured data on predicted modulus of elasticity for this case is 0.055, (N=50). The low coefficient of determination obtained contradicts the above stated argument for using this type of measurement for comparison with the model predictions. As will be seen in section 4.3, using specimens that include the core and some flesh for modulus of elasticity measurements, regression with predicted values are much improved. Sixteen CA Law Rome apples from the same source as the above tested apples were measured concurrently for their impulse response. Resonant frequencies of these apples with respect to time are shown in figure 4.3. Frequencies decreased with age, in general, except for 3 cases. 4.3 Core-Flesh Elastic Moduli and Model Predictions Due to the non-homogeneous composition of an apple and the assumption that it will vibrate in a breathing mode, core elastic modulus could have a significant effect on vibrational frequency. Measurements by Abbott et a1. (1968 a) showed flesh strength to increase then decrease toward the center of the apple. This might be expected due to the presence of seeds and cavities. Core strength was also found by Abbott (1968 a,b) to be slightly less than flesh strength and significantly less than skin strength. FREQUENCY. Hz. 43 12003 h. 1100. 10003 700 .1 TIME, days Figure 4.3 Drop in peak frequency versus time of 16 CA Law Rome Apples. 34 44 Results that included core strength in the modulus of elasticity measurements and the effect of skin stiffness were conducted on Paula Red and Golden Delicious apples. In all the predicted values of modulus of elasticity the model assumed the breathing mode. Tests on Paula Red apples were conducted as outlined in Chapter 3. Figure 4.4 shows predicted versus measured modulus of elasticity. The model incorporated measured density, mass, an assumed Poisson's ratio of 0.3, and the resonant frequency of the apple with the skin intact. The coefficient of determination from the regression of mea— sured on predicted modulus of elasticity is 0.774, (N=70). The impulse response of apples measured with the skin cut was always less than that with skin intact (uncut). It was observed that cutting the skin dropped the resonant frequencies to stable values beyond which further cutting had no effect. Resonant frequencies obtained from out and uncut apples are presented in the appendix. The purpose of cutting was to better approximate the elastic sphere model. Figure 4.5 shows predicted versus measured modulus of elasticity for the same apples used to obtain figure 4.4 but with the skin cut. The model uses an assumed Poisson's ratio of 0.3, the measured density and the measured mass. Compared to the uncut apple, cutting the apple had little effect on the coefficient of determination, r2= 0.798, (N=70), derived from the regression of measured modulus of elasticity data. The model employed in figures 4.4 and 4.5 PREDICTED MODULUS OF ELASTICITY. MPa. 45 Prediction Equation 5 .1 E - [ p"'(6n')"'2(1..3)] {mm 4.9955’ 5 . 4 3 2 .I y=.756x + .736 I - 2 r = .774 (NI-70) a . . o l 2 3 4 5 MEASURED MODULUS OF ELASTICITY, MPa. Figure 4.4 Predicted versus measured modulus of elasticity for Paula Red apples . PREDICTED MODULUS OF ELASTICITY. MPa. 46 Prediction Equation e E = [ p'”(6n')"'2(1..3)] f'm’” 4.9955’ 5 . 4 .I J .. 2 .. y=.717x + .603 I « 2 r = .798 (N=70) o , 1 , o 1 2 3 4 5 MEASURED MODULUS OF ELASTICITY, MPa. Figure 4.5 Predicted versus measured modulus of elasticity for Paula Red apples. 47 uses the measured density of individual apples. By assuming a constant density of 770 kg/m93 the moduli of elasticity predicted by the model were calculated: these and the corresponding measured values are shown in figure 4.6. The constant density value used was the average value of all apples tested in this batch. The coefficient of determination is 0.803, (N=70). The model also uses the uncut apple’s peak resonant frequency, a Poisson’s ratio of 0.3 and the apple mass. Frequency was considered as the sole predictor of firmness. Peak frequencies of the uncut apples were squared and regressed with the measured modulus of elasticity for the Paula Red apples. These results are shown in figure 4.7. The coefficient of determination is 0.769, (N=70). Golden Delicious apples tested in the same manner as the Paula Red apples displayed similar coefficients of determination from similar analyses. Figure 4.8 shows the regression of measured on predicted modulus of elasticity. The model used measured density, the uncut resonant frequency, an assumed Poisson’s ratio of 0.3 and the apple mass. The coefficient of determination for this case is 0.793, (N=60). The corresponding results from Paula Red apples analyzed in a similar manner was shown in figure 4.4. Results for cut Golden Delicious apples are shown in figure 4.9. These results, with a coefficient of determi- nation of 0.786, (N=60), were obtained in a similar manner to those for the Paula Reds (figure 4.5). PREDICTED MODULUS OF ELASTICITY, MPa. 48 Prediction Equation 5 E [77o"’(6n')"'2(1..3)] {mm 4.9955‘ 5 4 .I 5 2 ., y-.707x + .638 I - 2 r = .803 (N-70) l ,1 Q 0 r ' , I MEASURED MODULUS OF ELASTICITY, MPa. Figure 4.6 Predicted versus measured modulus of elasticity for Paula Red apples. —6 10 , 2 KHz. X FREQUENCY 1.0 .1 0.9 . 0.5 .. 0.7 - 0.6 .1 0.5 . 0.4- 0.3 - 0.2 .. 0.1 .1 49 y=.148x + .149 r = .769 (N-70) \f MEASURED MODULUS OF ELASTICITY. MPa. Figure 4.7 Frequency squared versus measured modulus of elasticity for Paula Red apples. PREDICTED MODULUS OF ELASTICITY. MPa. 50 Prediction Equation E _ l: p'”(6n‘)”’2(1..3)] (mm 7 1 4.99552 5 .I 3 «I 2 1 y-.842x -I- .953 r2 = .793 (N-ea) MEASURED MODULUS OF ELASTICITY, MPa. Figure 4.8 Predicted versus measured modulus of elasticity for Golden Delicious apples. PREDICTED MODULUS OF ELASTICITY. MPa. 51 Prediction Equation 7 . 4.99552 y-.869x + .905 . . r2 = .786 (N-GO) MEASURED MODULUS OF ELASTICITY. MPO. Figure 4.9 Predicted versus measured modulus of elasticity for Golden Delicious apples. 52 Figure 4.10 shows regression results (r2=0.790,N=60) for Golden Delicious apples with the model using a Poisson’s ratio of 0.3, the uncut apple's resonant frequency, apple mass and an assumed constant density. The constant density value used was 812 kg/m3 which is the average density of the apples in the batch. Results for Paula Red apples, for a constant density assumption, are shown in figure 4.6. Peak frequencies of the uncut Golden Delicious apples were squared and regressed with the measured modulus of elasticity, as shown in figure 4.11. The coefficient of determination is 0.544, (N=60). The change, with respect to time, of resonant frequen- cies for ten Golden Delicious apples is shown in figure 4.12. These apples were picked from the same orchard at the same time as the Golden Delicious apples discussed above and have the same test dates (except for the first date). The first test date in figure 4.12 was the date the apples were picked. The impulse response of these ten apples were recorded in the orchard. Data were recorded on cassette tape and played back to the Analogic 6000 oscilloscope for analysis. Subsequent measurements were taken in the laboratory. 4.4 Summary of Regression Results Table 4.1 is provided for easy comparison of the regression results shown in the previous figures. These results show that the model is not a good predictor of Magness-Taylor firmness (CA Rome Beauty apples) or modulus PREDICTED MODULUS 0F ELASTICITY, MPa. 53 Prediction Equation E = [812”(61r')"’ 20.45)] f'm‘” 7 l 4.9955' 5 . 5 . 4 . 3 a 2 . y=.848x + .921 1 . r2 = .790 (Na-60) 0 l 2 3 4 5 6 7 MEASURED MODULUS OF ELASTICITY. MPa. Figure 4.10 Predicted versus measured modulus of elasticity for Golden Delicious apples. 2 —6 2 54 1.4 _ . 1.2 s N I x 1.0 .. o .— 0.8 ,. 1 E; 0.6 .. 5 a 0.4 - =.197x + .157 u: E 2 r = .544 (N-60) 0.2 - l l l l l l 0 1 2 3 4 5 6 MEASURED MODULUS OF ELASTlClTY. MPa. Figure 4.11 Frequency squared versus measured modulus of elasticity for Golden Delicious apples. FREQUENCY. Hz. 1300 , 1000. 000.. 700 O N a g N O N O U N TIME. days Figure 4.12 DrOp in peak frequency versus time for 10 Golden Delicious apples. 56 of elasticity of the apple flesh (CA Law Rome apples) as indicated by the low coefficients of determination (0.265 and 0.055 respectively in table 4.1). As mentioned previously Magness-Taylor values are obtained by shearing and crushing the apple flesh. This might be compared to Brinell hardness testing of metals for which hardness values do not necessarily have linear relationships with the modulus of elasticity of the metals. Natural vibration of an apple would most likely involve flesh stresses well within the yield point of the flesh while Magness-Taylor values are obviously measuring apple flesh strength near or beyond the yield point as opposed to the flesh strength predicted by the model. Table 4.1 Regression results from the study. Result r2 N Variables Firmness Apple in model measurement Variety 1 0.265 118 m,f1 Magness-Taylor CA Rome Bty. 2 0.055 50 m,f1 M.of E.(cylinder) CA Law Rome 3 0.774 70 m,p,fl M.of E.(cube) Paula Red 4 0.798 70 m,p,f2 M.of E.(cube) Paula Red 5 0.803 70 m,f1 M.of E.(cube) Paula Red 6* 0.769 70 f2 M.of E.(cube) Paula Red 7 0.793 60 m,p,fl M.of E.(cube) G. Delicious 8 0.786 60 m,p,f2 M.of E.(cube) G. Delicious 9 0.790 60 m,f1 M.of E.(cube) G. Delicious 10* 0.544 60 f2 M.of E.(cube) G. Delicious m = apple mass p = apple density f1 = resonant frequency with the apple skin uncut f2 = resonant frequency with the apple skin cut M.of E. = modulus of elasticity(type of specimen) * Squared value of frequency was used as predictor. 57 Cylindrical specimens used to determine modulus of elasticity were small in comparison to the cubical specimens and were more difficult to prepare. Because of this the modulus of elasticity values measured using the cylindrical specimens were increasingly prone to experimental error. Specific reasons for this were: (1) Specimens were physically harder to hold. (2) Some specimens had to be discarded because: they were sheared in half, they showed visible defects of the cut surface or the specimens were not straight when taken from the plug (caused by either internal stress relief or improper cutting). Although these defective specimens were discarded, the specimens that were used may have been struc- turally altered by the cutting process. (3) Specimens contained varying amounts of vascular material (which is significantly different in strength than the surrounding flesh). Modulus of elasticity values from cylindrical and cubical specimens are of the same magnitude and one would expect good correlation between the two. Despite this the correlation results using the cylindrical specimens are quite low whereas for cubical specimens the model shows a good ability to predict modulus of elasticity. Entries 3-5,7-9, from Table 4.1 for Paula Red and Golden Delicious apples show that the model has good modulus of elasticity prediction ability. Whether the uncut or cut apple peak frequency is used in the model, correlation 58 results do not change appreciably (results 3,4 and 7,8 in Table 4.1). This is also true if measured density is used rather than an assumed density (results 3,5 and 7,9 in Table 4.1). The coefficient of determination obtained from using the squared frequency as the firmness predictor (result 10 in Table 4.1) for the Golden Delicious apples is much lower than for the Paula Red apples (result 6 in Table 4.1). This was expected since the standard deviation of the mass for Golden Delicious apples was greater than for the Paula Reds and implies the functional dependence the resonant frequency has on mass, as indicated in Equation [41]. In all the above cases the breathing mode was the assumed primary vibrational mode of the apple. Different modes would yield the same correlation results assuming a constant Poisson's ratio. Reasons for using the breathing mode were: (1) The measured values of modulus of elasticity were close to those predicted by the model (2) The breathing mode is the lowest-order mode of pure compression. (3) Torsional modes are not likely to be induced because of the method of excitation used. (4) The possibility of mixed modes exists, but higher- order modes would have to be used to obtain values of modulus of elasticity which are close to the measured values. 59 Modes which would give equivalent modulus of elasticity values would be the 821 and S40 modes. V CONCLUSIONS The fundamental objective of this research was to de- termine if the acoustic impulse response of an apple could be used to determine tissue firmness. The spherical resona- tor model, which utilized the response spectrum to predict modulus of elasticity, had good correlations with the mea- sured modulus of elasticity of tissue that included the core. Less impressive correlations were obtained when pre- dicted modulus of elasticity was regressed on Magness-Taylor firmness or the measured modulus of elasticity of flesh specimens. A list of conclusions follows. 1. The techniques used in this research for obtaining the acoustic impulse response of an apple provide an easy “W“ Iand reliable means of identifying the vibrational charac- -- -W '7“ -—-._. teristics of the apple. 2. The measured modulus of elasticity of apple speci- mens that included the core and apple flesh of the apple had good correlation, r2 > 0.773 (N=60,70), with the modulus of elasticity predicted by the spherical resonator model for Paula Red and Golden Delicious apples. 3. The measured modulus of elasticity of apple speci- mens that were taken from the cheek of the apple did not correlate well with the modulus of elasticity predicted by the spherical resonator model, r2=0.055 (N=50), for CA Law 60 61 Rome apples. 4. The Magness-Taylor firmness of an apple did not correlate well with the modulus of elasticity predicted by the spherical resonator model, r2=0.265 (N=118), for CA Rome Beauty apples. 5. Skin stiffening of the apples were apparent from the higher resonant frequencies obtained for uncut apples compared with the resonant frequencies for the cut apples. 6. Neither the use of the peak frequency for cut apples, nor the assumption of a constant density in the spherical model appreciably changed the ability of the model to predict modulus of elasticity for Paula Red and Golden Delicious apples. 7. The techniques used in this research provide a non-destructive method for firmness evaluations of apples. The method of impulsive excitation and resonant analysis could be used in research where non-destructive firmness measurements may be necessary. VI RECOMMENDATIONS FOR ’UTURB RESEARCH Based on results and experience of this research, the following recommendations for future research are suggested: 1. Improved measurement techniques to more accurately measure the firmness of the flesh part of the apple need to be developed. Measurement techniques used to determine the modulus of elasticity of the cylindrical apple specimens could be improved by using larger specimens and better cut- ting techniques. Better samples should provide better cor- relations with the model predictions. 2. Incorporation of the deviation of the apple shape from a true sphere should result in a more accurate model for the prediction of the modulus of elasticity. This was not done for the reported research except for some minor experiments with an elastic medium which was formed into an apple shape. 3. Determination of the true vibrational mode of an apple when excited by an impulse would provide a more rea- listic description of the true apple characteristics. A technique which could be tried is the strategic placement of microphones near the surface (or accelerometers on the sur- vw—h‘ \ f“ x _ gr -‘~%‘-- "F' face) of the apple and the observation of phase relation- .-~- ships of the vibrating surface. 62 63 4. Due to the sensitivity of the model to frequency, sampling techniques of the impulse response could be changed to increase the resolution of the FFT and thus a more pre- cise estimate of the resonant frequency would result. 5. A thorough understanding of the variations of tis- sue strength within an apple needs to be developed. Results from this research show that the modulus of elasticity of specimens that include the core can be reasonably predicted by the model. If a relationship exists between core strength and flesh strength the model would be more useful for non-destructive and rapid textural evaluations. Precise sample and measure techniques would require development to determine the modulus of elasticity of small apple speci- mens . VII SUPPLEMENTARY EXPERIEENTLTION The purpose of this chapter is to provide to the reader information obtained during the course of this research that is not directly related to the forgoing material but does provide additional information concerning impulse techniques and signal analysis for firmness determination in apples. 7.1 Water As The Acoustic Carrier Initial acoustic impulse response experiments were tried with the apple and a sealed microphone under water. The purpose of this was to enhance the acoustic energy transfer from the apple to the microphone and thus reduce the striking force required to produce a suitable signal. The procedure employed was similar to that outlined in the experimental techniques section. Apples were allowed to float to expose a surface for striking. Although a signifi- cant reduction in the energy required to excite vibrations was achieved and equivalent results were produced in water and air, difficulties were encountered in water due to acou- stic noise entering the apple and microphone container. The water environment itself was less desirable to work in from a practical point of view and further studies were conducted in air. 64 65 7.2 Signal Noise The acoustic signal emitted from the apple can be de- scribed as a reasonably clean, exponentially decaying perio- dic signal. In contrast, undetermined sources of noise and relative large DC offsets in the microphone signal would interfere with a frequency spectrum that would clearly de- fine a resonant mode. The Analogic 6000 was incapable of performing signal filtering, thus FFTs were sometimes per- formed by an IBM AT which could be programmed to enhance the spectral detail. A primary problem in the spectral display was the rela- tively large DC component in the spectrum which was some— times accompanied by significant frequency components in the 60-350 Hz range. The unfiltered signal and its spec- trum, obtained from the IBM FFT routine, is shown in figure 7.1. To suppress the DC component, sampled signal values were set to 0 after the primary acoustic signal had decayed significantly. The altered signal is shown in figure 7.2. Signal manipulation in this manner has effectively the same result as initially sampling for a shorter period but padding the end of the signal with zeros to enhance the resolution of the FFT (a technique commonly used with FFTs). The benefit of this can be seen in the FFT of the altered signal, shown in figure 7.2. This sampling technique generally provided enough attenuation in the DC component to make the frequency peak of interest clearly discernible. An alternative method to diminish the DC 66 N 5 a: O AA'A4- 3 mm .‘ uV. 1 04-3 coon E SPECTRUM MAGNWUOE HEMHWY Figure 7.1 Original acoustic signal and its spectrum. 120 W i'éi ‘ 40 gal; 0 VAVAVA'A'“ 3 -4o nus -ao -120 SPECTRUM MAGNWUDE uV.10-3 0+0; mammm' Figure 7.2 DC attenuation of the acoustic signal and its spectrum. 67 component would be to average the digitized signal values then subtract these from the original signal before perfor- ming the FFT. This would require more computation but would eliminate a small aliasing problem caused by zero padding. Multiple resonant peaks in the FFT were present in a few signals observed and were repeatable for different sig- nals from the same apple. Figure 7.3 shows signals in which this occurs and the spectra obtained by a FFT. Often these peaks were located close to each other and of approximately the same magnitude making it difficult to determine which peak should be used for model predictions of modulus of ela- sticity. Additional measurements were taken in these cases. The peak with the largest magnitude was always used as the desired resonance in the model. The occurrence of these peaks could be a result of the excitement of multiple reso- nant modes in the apple. 7.3 Repeatability of the Acoustic Response No distinguishable difference in impulse response was observed when holding the apple by hand as opposed to suspending the apple by the stem. Variations in striking force as the result of using a hand-held hammer did not result in any detectable difference of spectral content of a signal. Repeatability of the spectrum for an apple struck along its equator is consistent to within the resolution of the FFT. Peak frequencies determined from the impulse re- sponse of five apples, each struck eight times, are shown in 68 ‘-A-‘A‘ TIME SPECTRUM MAGNITUOE uV 1003 coo-F5 FJ FREQUENCY W 10.} 05.3 r"_."" SPECTRUM MAGNITUOE LL FREQUENCY 4b Figure 7.3 Two signals and their spectra displaying multiple resonant peaks. 69 table 7.1. Peak frequencies for the same apple are con- sistently reproduced. The receiver/impulse orientation was 180 degrees apart with the apple being struck at the equator. Table 7.1 Reproducibility of the peak frequency of five apples. Apple Impulse 1 2 3 4 5 1 1013 903 927 891 964 2 1000 903 927 891 964 3 1013 915 927 891 964 4 1013 903 927 903 964 5 1013 903 927 891 964 6 1013 903 927 891 964 7 1013 903 915 891 964 8 1013 903 927 891 964 To determine the effect the impulse location and re- ceiver orientation have on signal generation, five apples were struck with the orientations shown in figure 7.4. Two replications with random apple orientation were done for each orientation. Results, shown in table 7.2, indicate that there is a change in the peak frequency when the apple is struck on a polar region as opposed to an equatorial region. When the receiver is placed 90 degrees to the im- pulse direction, the peak frequency lies between the fre- quencies of the other two orientations with no apparent preference of one or the other. 70 POLAR IMPULSE EQUATORIAL IMPULSE Y MICROPHONE 99 ° ramronw. IMPULSE EQUATOR Figure 7.4 Orientation of impulse and microphone. 71 Table 7.2 Peak resonant frequencies obtained using different impulse locations and receiver orientations for five apples. Apple Orientation 1 2 3 4 5 Equatorial 854 866 878 854 952 Equatorial 854 866 878 854 939 Polar 878 878 927 927 939 Polar 878 878 927 927 952 90° Equatorial 854 878 878 854 976 90° Equatorial 854 878 878 854 939 7.4 Experimentation with an Elastic Sphere To verify that the experimental techniques yielded precise results, and to determine the modes of vibration excited, experimentation with a solid rubber ball was con- ducted and compared with theoretical results based on the vibrating elastic sphere model. The resonant frequencies of a 6 cm diameter rubber ball were measured in a similar man- ner used for apples. The modulus of elasticity was measured by cutting a cubical sample from the ball and subjecting it to the compression test used for apples. The spectrum from the ball was similar in appearance as that for an apple with an average peak resonant frequency of 317 Hz from four tests. The weight of the ball was 79.3 gms with a density of 594 kg/m03. Measured modulus of elasti- city of a cubical specimen cut from the ball specimen yielded a value of 0.662 MPa. Assuming Poisson’s ratios of 0.2, 0.3, and 0.4, and that the ball was resonating in 72 the breathing mode, the predicted modulus of elasticity of the ball is 0.352, 0.247, and 0.132 MPa respectively. For an oblate-prolate mode of vibration and Poisson’s ratios of 0.2, 0.3, and 0.4, the predicted modulus of elasticity is 0.817, 0.880 and 0.940 MPa respectively. These results suggest that the ball is vibrating in the oblate-prolate mode because of the smaller difference between the predicted and measured modulus of elasticity. To determine the effect that apple shape might have on resonant frequencies, two similar balls, as used above, were cut into the shape of apples. One apple shape was similar to a roundish Rome apple and the other resembled a Golden Delicious shape. Prior to shaping the balls, the resonant frequencies for each ball were determined from the average of four tests. During shaping of the balls into an apple shape, mass was kept constant for both shapes. Results from these tests, shown in table 7.3, indicate that the Golden Delicious shape has a slightly higher resonant frequency than the Rome shape. 7.5 Signals from an Accelerometer The impulse response of an apple was measured using a Vibrametrics 1009 accelerometer and a microphone for compar- ison of signal output and spectral content. The accelero- meter was attached to the apple surface at the equator, directly opposite the applied impulse and at 900 to the impulse for different measurements. The accelerometer Table 7.3 Comparison of peak frequencies for two apple shapes and the spherical balls from which they were shaped. Rome Red Delicious Test # Ref. Ball 1 Shape Ref. Ball 2 Shape 1 317 329 341 366 2 329 329 341 366 3 341 329 321 366 4 317 329 354 366 Average Frequency 326 329 339 366 1 - Rome shape obtained from Ref. Ball 1. 2 - Red Delicious shape obtained from Ref. Ball 2. 74 was attached with bee’s wax for maximum signal transfer. Measurements with the microphone were done as outlined in the experimental techniques section of this report. A second apple was also tested. The three spectra from the response signals (microphone, 180° and 900 accelerometer orientations) are shown for each apple in figure 7.5. with significant frequency components being identified. The spectral signature for both apples are very similar for the same receiver type and orientation. For simplicity, the frequency peak obtained from the microphone will be referred to as the main frequency, ie. 964 & 817 for apples 1 8 2, respectively. Spectra for the 90° accelerometer orientation has peaks at or near the main frequencies (964 and 830 Hz) for both apples, whereas the 1800 orientation does not. Spectral peaks immediately to the right and left of the main frequencies, for accelero- meter orientations, occur at similar frequencies. These frequencies may account for the double spikes observed on some spectra obtained from the microphone discussed earlier. Ratios of the main frequency, obtained from the micro- phone, to the peak frequencies of the 900 accelerometer orientation are shown in table 7.4. Within the resolution of the FFT, these ratios appear to remain constant for the apples tested. Considering the modes of vibration being induced in the apple, the oblate-prolate mode is the lowest frequency mode for a sphere and it would seem reasonable that this mode 75 6030.0 9:339. 05 .o co_3co_._o 05 one aside 03 Ea... 050on ms 053.... \ \ . 8o .. 3.: Ba 35...... III 9 mm» ..\\ Sewn “u” l\ S... I / 55:65..qu use .\ 2: |\ a \ m an .. x... ~33... IIIV “v 5 3o \ «2. m x m \ uzozaocoi «2 o2 \ 1 ‘ 1 ”13:52. l1 %. U 5 \ zo_._.<._.zm_mo N M??? — when: too BOMINOVR MOSSS 76 Table 7.4 Ratios of peak frequencies to the main frequency. Apple 1 Apple 2 Freq. Hz. Ratio Freq. Hz. Ratio 708 .734 622 .749 866 .898 732 .882 964 1.000 830 1.016 1049 1.088 903 1.088 77 would be excited by an impulse. If the above frequencies are truly resonant modes of the apple and not resonance of the accelerometer-to-apple connection, then the mode being detected by the microphone (main frequency) is a higher order mixed-mode than the oblate-prolate mode or it is the breathing mode. This conjecture assumes that an apple behaves similarly to a sphere and that pure torsional modes will not be induced to any detectable degree by an impulse. Lower order mixed modes, Sn,l-1' are relatively insens- itive to Poisson’s ratio compared with the breathing mode, 301' and higher order radial modes (refer to figure 2.2). If Poisson’s ratio varied significantly between these two apples then the presence of the breathing mode would be indicated by a change in one or all of the above ratios. This was not the case as the ratios did not change. This shows that either the breathing mode is not present or that Poisson's ratio does not change much. The latter case seems more likely. APPENDIX 78 Table A1. Data obtained from CA Rome Beauty apples. Apple Peak Resonant Magness Taylor Predicted1 Mass Frequency Firmness ME kg. Hz. N. MPa. 181.1 980 76.8 4.516 224.3 895 78.9 4.341 184.5 992 77.5 4.678 309.9 858 78.1 4.944 161.1 1013 85.3 4.463 216.0 952 76.4 4.794 195.5 964 75.6 4.592 208.3 984 77.5 4.995 169.6 1070 80.0 5.143 181.7 1000 78.0 4.702 167.3 1025 82.4 4.682 179.2 1013 80.2 4.789 207.5 939 68.7 4.534 178.9 1029 75.4 4.924 230.0 933 72.5 4.802 178.8 1000 78.6 4.650 196.1 976 83.2 4.723 164.4 1109 82.4 5.418 154.3 1066 76.8 4.798 171.2 1000 77.0 4.527 284.6 838 70.9 4.458 165.7 1000 84.6 4.421 259.8 891 78.6 4.740 195.9 1009 82.4 5.027 203.6 1000 76.2 5.076 295.4 874 77.3 4.974 182.3 976 77.5 4.496 277.6 840 64.9 4.406 184.7 1010 77.0 4.853 182.8 988 79.2 4.607 177.2 1004 75.1 4.670 138.4 1094 86.5 4.697 252.3 882 69.7 4.564 179.7 1000 83.7 4.667 198.8 964 74.9 4.639 165.9 1000 77.5 4.421 210.4 927 76.8 4.461 231.5 948 86.2 4.968 204.6 980 78.9 4.891 229.1 915 77.6 4.605 188.2 1019 82.9 5.007 178.3 1021 80.5 4.847 164.4 1090 84.6 5.234 201.5 952 73.5 4.570 169.6 1021 85.0 4.683 221.7 891 80.5 4.264 214.4 900 72.7 4.259 Table A1. 203.3 185.8 175.2 258.9 217.0 185.9 214.8 216.3 165.0 174.5 163.4 194.3 231.6 194.7 233.3 199.1 229.0 192.7 213.8 191.2 173.6 208.3 216.4 266.9 214.4 196.1 184.8 297.4 192.9 226.2 211.6 203.4 135.9 204.8 197.0 173.1 223.2 248.6 252.8 183.7 210.6 186.7 238. 263.7 216.8 202.4 224.5 224.2 261.4 164.9 185.0 270.3 continued. 976 939 984 878 903 1000 958 915 1013 1045 1037 939 909 891 854 939 903 927 915 970 897 939 878 842 842 915 952 793 970 866 884 903 1025 927 903 952 891 903 891 915 878 921 866 830 775 921 934 933 891 921 952 879 79 85.4 79.2 68.9 72.1 78.6 78.4 77.8 74.9 83.4 75.6 82.7 79.1 74.6 65.9 66.4 83.5 79.5 80.0 72.3 73.9 81.5 63.4 79.8 76.2 72.8 81.8 77.2 66.4 75.2 73.0 69.0 80.5 65.3 78.1 65.8 68.7 86.9 63.8 62.8 68.7 66.8 65.3 64.3 59.9 67.8 67.3 67.3 67.8 71.2 72.7 71.2 59.9 4.835 4.207 4.452 4.591 4.327 4.771 4.825 4.429 4.536 5.002 4.715 4.342 4.571 3.910 4.058 4.416 4.485 4.203 4.388 4.586 3.671 4.549 4.078 4.309 3.727 4.151 4.308 4.113 4.602 4.089 4.070 4.139 4.150 4.450 4.077 4.236 4.295 4.785 4.708 4.039 4.025 4.112 4.241 4.159 3.221 4.373 4.783 4.766 4.834 3.778 4.366 4.757 80 Table A1. continued. 243.2 793 57.0 3.630 205.1 903 73.7 4.190 192.6 921 62.4 4.206 203.3 884 58.4 3.986 169.6 939 57.9 3.979 207.2 866 57.4 3.863 176.3 903 62.4 3.780 229.9 866 60.9 4.145 187.0 915 53.0 4.045 184.4 909 58.4 4.005 191.3 878 64.8 3.803 188.2 921 68.2 4.089 228.3 842 57.0 3.920 207.6 921 64.8 4.365 185.5 952 71.7 4.376 251.9 854 62.4 4.289 210.8 939 58.4 4.647 206.7 842 60.4 3.623 1. Predicted modulus of elasticity by the model. The model uses measured density, mass, the uncut resonant frequency and a Poisson's ratio of 0.3. 81 Table A2. Data obtained from CA Law Rome apples. Apple Peak Resonant Measured Predicted1 Mass Frequency ME ME 239.4 878 4.506 4.365 229.6 988 4.867 5.372 231.7 927 4.588 4.755 219.3 927 4.507 4.597 235.9 915 4.873 4.689 175.5 982 5.008 4.438 221.4 939 4.872 4.743 234.5 903 4.482 4.551 180.2 1025 4.167 4.924 224.6 1025 4.581 5.696 231.8 939 3.888 4.887 206.0 988 3.925 5.000 245.5 982 4.131 5.559 227.8 939 3.998 4.822 224.7 939 3.840 4.787 232.4 933 4.013 4.835 210.1 969 3.998 4.877 265.7 878 3.611 4.675 249.4 848 3.634 4.183 192.3 976 4.012 4.661 177.6 988 4.349 4.527 219.8 933 4.325 4.659 214.9 921 3.937 4.468 213.5 939 4.894 4.620 255.0 860 4.642 4.373 204.4 958 4.821 4.676 212.3 878 4.424 4.033 219.0 915 4.616 4.471 194.6 927 5.124 4.238 231.7 933 4.834 4.826 221.0 891 4.313 4.261 189.3 1025 4.616 5.085 200.5 976 4.192 4.794 200.1 903 4.725 4.103 234.6 939 4.373 4.923 198.2 964 4.155 4.646 209.9 891 4.482 4.110 242.1 849 4.288 4.113 229.7 878 4.243 4.244 242.5 842 4.131 4.056 220.8 927 3.292 4.601 182.7 878 3.549 3.648 252.4 878 2.919 4.529 217.1 902 3.378 4.324 210.8 915 3.452 4.355 224.2 878 3.294 4.188 183.0 976 3.978 4.516 206.4 903 3.333 4.184 209.5 958 4.314 4.758 82 Table A2. continued. 1. Predicted modulus of elasticity by the model. model uses measured density, mass, the uncut resonant frequency and a Poisson’s ratio of 0.3. The 83 Table A3. Data obtained from Paula Red apples. Apple Density Freq. Freq. ME1 ME2 ME3 ME4 Mass (uncut) (cut) kg. kg/m3 Hz. Hz. MPa. MPa. MPa. MPa. 207.9 754 805 781 3.794 3.276 3.083 3.105 195.6 804 866 817 3.932 3.718 3.309 3.263 193.6 779 854 830 4.262 3.554 3.357 3.345 228.3 768 805 781 3.795 3.509 3.302 3.305 200.5 780 842 817 3.730 3.538 3.331 3.317 222.8 747 793 769 3.502 3.318 3.120 3.153 195.3 786 842 817 3.995 3.482 3.278 3.256 202.1 762 842 805 3.416 3.528 3.225 3.237 200.2 765 866 830 3.561 3.715 3.413 3.420 199.6 785 878 854 3.942 3.844 3.636 3.614 192.4 780 939 903 4.236 4.281 3.959 3.942 213.9 771 915 830 4.023 4.346 3.576 3.575 204.8 773 903 878 3.722 4.115 3.891 3.886 197.7 767 854 830 4.416 3.586 3.387 3.392 212.5 780 891 817 3.695 4.119 3.463 3.448 224.7 786 830 805 3.612 3.719 3.499 3.475 197.6 773 866 842 3.709 3.696 3.494 3.489 196.7 764 866 830 3.589 3.670 3.371 3.380 201.9 770 805 781 3.071 3.235 3.045 3.045 205.1 771 915 830 4.042 4.226 3.477 3.476 209.6 797 817 793 3.594 3.456 3.256 3.219 202.7 791 842 817 3.715 3.581 3.371 3.341 213.1 781 793 769 3.767 3.270 3.075 3.061 198.1 772 854 817 3.469 3.599 3.294 3.291 221.5 774 805 781 3.673 3.447 3.245 3.239 203.5 774 878 866 3.990 3.870 3.765 3.758 191.1 759 842 805 3.565 3.395 3.104 3.119 200.4 743 878 854 4.059 3.785 3.581 3.623 218.5 745 854 817 3.886 3.797 3.475 3.513 197.3 769 854 830 3.849 3.585 3.386 3.387 207.8 769 817 781 3.634 3.396 3.103 3.104 197.1 775 817 781 3.553 3.286 3.003 2.997 199.2 754 830 793 3.512 3.382 3.087 3.110 216.7 752 817 781 3.862 3.466 3.167 3.192 213.2 770 805 781 3.618 3.353 3.156 3.156 202.9 762 781 744 3.295 3.046 2.764 2.773 205.5 795 793 769 3.618 3.211 3.020 2.988 209.4 766 793 769 3.219 3.211 3.020 3.025 219.2 785 781 756 3.429 3.238 3.034 3.014 202.1 779 781 756 3.050 3.059 2.866 2.855 192.4 752 781 744 3.287 2.925 2.655 2.676 199.9 760 756 720 2.979 2.822 2.560 2.571 211.7 787 744 708 3.136 2.873 2.602 2.583 193.2 789 744 708 2.932 2.705 2.450 2.430 214.4 777 756 720 3.218 2.979 2.702 2.694 198.7 673 732 695 2.834 2.525 2.277 2.381 201.2 764 793 769 3.387 3.123 2.936 2.944 84 Table A3. continued. 206.8 749 732 683 3.070 2.694 2.345 2.367 214.3 799 756 732 3.038 3.003 2.815 2.781 207.1 753 756 720 2.464 2.880 2.612 2.632 205.4 788 756 720 2.860 2.909 2.639 2.618 211.3 741 756 720 2.665 2.905 2.635 2.668 196.5 759 805 769 3.130 3.162 2.886 2.900 195.8 771 756 720 2.715 2.797 2.537 2.536 206.6 779 720 695 2.689 2.638 2.458 2.449 192.2 749 720 695 2.202 2.481 2.312 2.334 216.2 763 756 720 2.886 2.978 2.701 2.709 207.9 757 756 720 2.428 2.893 2.624 2.639 213.4 730 744 708 2.661 2.818 2.551 2.597 217.2 827 720 695 2.471 2.783 2.593 2.532 205.6 783 708 671 2.617 2.547 2.288 2.275 216.9 754 695 646 2.493 2.512 2.170 2.186 195.1 771 769 732 2.830 2.887 2.616 2.614 200.4 717 683 646 2.214 2.263 2.025 2.073 211.6 791 708 683 2.416 2.605 2.424 2.403 194.4 683 720 683 2.501 2.425 2.182 2.271 194.8 772 756 720 2.803 2.789 2.530 2.527 212.2 822 756 732 2.499 3.015 2.827 2.766 205.8 719 708 683 2.450 2.478 2.306 2.359 1. Measured modulus of elasticity. 2. Predicted modulus of elasticity by the model. The model uses measured density, mass, the uncut resonant frequency and a Poisson’s ratio of 0.3. 3. Predicted modulus of elasticity by the model. The model uses measured density, mass, the cut resonant frequency and a Poisson’s ratio of 0.3. 4. Predicted modulus of elasticity by the mo e1. The model uses an assumed constant density of 770 kg/m , mass, the uncut resonant frequency and a Poisson’s ratio of 0.3. 85 Table A4. Data obtained from Golden Delicious apples. Apple Density Freq. Freq. M81 ME2 M83 M84 Mass (uncut) (cut) kg. kq/m3 Hz. Hz. MP8. MP8. MPa. MPa. 177.2 894 1135 1098 4.987 6.192 5.794 5.513 174.3 813 1025 1001 4.363 4.837 4.613 4.530 245.8 793 939 915 4.456 5.058 4.802 4.755 218.5 799 1025 1001 4.851 5.588 5.329 5.265 217.3 781 939 903 4.248 4.640 4.291 4.271 222.1 782 927 903 3.823 4.594 4.358 4.337 175.0 803 1062 1013 4.669 5.191 4.722 4.657 234.9 785 927 915 4.286 4.765 4.642 4.612 174.8 806 1098 1062 4.436 5.534 5.176 5.099 176.2 807 1147 1098 4.914 6.089 5.580 5.492 214.6 833 1013 988 4.327 5.467 5.200 5.066 222.8 799 939 903 4.885 4.747 4.390 4.337 225.6 781 952 927 4.713 4.887 4.634 4.611 223.0 811 976 927 4.676 5.170 4.664 4.584 214.1 790 976 939 4.655 4.986 4.615 4.576 174.4 809 1086 1074 4.697 5.422 5.302 5.215 176.2 822 1049 1013 4.567 5.125 4.779 4.675 174.5 817 1062 1025 4.954 5.201 4.845 4.750 175.7 803 1037 1001 4.534 4.949 4.611 4.548 174.6 817 1098 1049 4.767 5.560 5.074 4.975 180.2 799 1025 952 3.567 4.919 4.243 4.191 223.1 820 988 952 4.357 5.318 4.937 4.835 250.2 819 878 854 4.128 4.530 4.286 4.198 270.9 789 830 805 3.658 4.209 3.959 3.927 225.4 802 952 927 4.262 4.930 4.674 4.611 175.2 801 1049 1013 3.761 5.061 4.719 4.657 172.6 796 1049 1001 4.239 4.992 4.545 4.495 174.8 812 1110 1062 3.936 5.671 5.190 5.099 154.5 809 1062 1025 4.121 4.779 4.451 4.379 172.4 804 1049 1013 4.119 5.009 4.671 4.604 180.8 804 988 976 3.363 4.579 4.468 4.405 239.7 810 866 842 3.685 4.262 4.028 3.961 236.9 797 842 830 3.691 3.974 3.861 3.816 244.0 822 891 866 4.296 4.595 4.341 4.248 225.2 806 939 927 4.051 4.805 4.683 4.611 172.4 796 964 939 3.554 4.217 4.000 3.956 158.6 798 976 964 3.437 4.087 3.987 3.940 158.8 810 1025 1013 3.772 4.531 4.425 4.351 177.8 805 879 854 3.145 3.586 3.384 3.335 176.6 807 939 915 3.793 4.081 3.875 3.814 222.3 802 830 817 3.289 3.714 3.598 3.550 238.2 789 878 866 3.837 4.330 4.212 4.178 238.4 805 854 830 3.376 4.124 3.895 3.838 241.6 811 817 775 3.395 3.816 3.433 3.374 175.1 801 921 903 3.567 3.901 3.750 3.701 153.9 813 1062 1025 3.806 4.766 4.439 4.360 226.8 809 854 839 3.562 3.991 3.851 3.789 86 Table A4. continued. 153.0 817 1025 1013 3.576 4.447 4.343 4.258 173.3 800 1013 1001 4.253 4.681 4.571 4.513 181.4 802 878 854 2.542 3.627 3.431 3.385 194.2 789 866 854 2.732 3.676 3.574 3.545 178.7 805 775 756 2.674 2.798 2.663 2.623 154.8 811 878 854 3.191 3.269 3.093 3.040 231.2 801 756 744 2.248 3.163 3.063 3.023 219.0 813 775 756 2.684 3.224 3.067 3.012 192.0 809 815 775 2.901 3.260 2.948 2.900 227.4 804 775 744 2.148 3.290 3.031 2.988 223.7 817 756 732 2.861 3.110 2.915 2.858 189.3 800 854 830 3.127 3.529 3.333 3.291 1. 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