A new shaker for fruit and nut trees

J. agric. Engng Res. (1989) 44, 53-66

A N e w Shaker for Fruit and Nut Trees H. A. AFFELDT JR*; G. K. BROWNt; J. B. GERRlSH:~ Bark damage at the point of shaker attachment has become a major concern with the widespread use of mechanical harvesters for fruits and nuts. The dynamic displacements of a commercial trunk shaker when clamped to three sizes of Montmorency cherry trees were monitored for damaging effects. Maximum displacements were found to be 2-5 times greater during start-up and shut-down than at steady-state. Relative displacements between the shaker and the trunk were also excessive and can exceed tolerable bark strength limits. Subsequently, attempts were made to eliminate potentially damaging displacements through shaker redesign. A controllable variable-eccentric mass (VEM) was designed and retrofitted into the commercial shaker in place of the original fixed-mass. The design successfully eliminated excessive vibration resulting from low natural frequencies and shaker inertia while retaining the desired motion necessary for fruit removal. 1. Introduction Machines for the shake-harvesting of tree fruits have been proposed for use in US fruit and nut crops since the early 1920s. 1 The need to reduce labour and improve economic efficiency have stimulated efforts to mechanize the harvesting of fruit and nut crops used for processing (almonds, apples, apricots, cherries, citrus, olives, peaches, pears, plums, prunesa). With the introduction of trunk shakers in the early 1960s, bark d a m a g e at the area of shaker attachment on fruit and nut trees became a serious concern, a'3 Large forces transmitted during clamping and shaking were found to split, crush, or shear bark and internal tree tissues. In cherry trees, shear stress and strain imposed on tree bark, parallel to the clamp pads, from the shaking action and excessively high or low clamping pressures can cause the phloem underneath the epidermis to rupture without epidermis rupture, thus causing bark damage to remain hidden. 4 Trees w e a k e n e d by bark d a m a g e , particularly young trees with active cambium from rainfall and irrigation, may begin to decline. Loss of vigour and yield necessitates early replacement of the orchard. The decline may be accelerated by agents such as cold injury, borers, n e m a t o d e s , viruses, fungi, bacteria, etc. Before the era of mechanical harvesting, normal productive life of a cherry orchard averaged 40 years. The era of trunk shaker harvesting has reduced productive tree life to half its original potential, s Serious bark d a m a g e initiated by stress at the shaker clamping points has remained a prominent issue despite previous research and r e c o m m e n d a t i o n s on bark strength, shaker design, shaker pads, and static clamping forces, s Clamping pressures which caused no damage in the static situation were later found to be much too high to avoid c a m b i u m damage in a dynamic state. 7 The bruising of the c a m b i u m layers was initiated by dynamic forces which were only 75% of the same static force required to cause damage. It b e c a m e * Instrumentation Research Laboratory, USDA-Agricultural Research Service, Beltsville, Maryland, USA t Fruit and Vegetable Harvesting Research, USDA-Agricultural Research Service, East Lansing, Michigan, USA :l: Agricultural Engineering Department, Michigan State University, East Lansing, Michigan, USA Received 1 June 1988; accepted in revised form 28 March 1989 Paper presented at AG ENG 88, Paris, France, 2-6 March 1988 53

54

SHAKER

FOR FRUIT

AND

NUT TREES

clear that recommendations made from static measurements were not necessarily valid for the dynamic state. Research on various tree crops resulted in specifications of frequency and amplitude of shake which would minimize the deleterious effects on the bark. Various shaker designs have been developed to control the shaking motion of the tree. These shaker designs were based on recommendations to shake trunks of tart variety cherry trees at 10 to 24 Hz with 20 to 40 mm strokes, and sweet cherry tree trunks at 12 to 24 Hz with 12 to 16 mm strokes for satisfactory fruit removal, s Significantly, these frequencies are well above the first natural frequencies (about 1 Hz) of a tart cherry tree. s Harrett 1° developed a shaker consisting of an adjustable eccentric employing pitman arms. Fridley 11 developed a mechanism to create any desired shaking pattern by having a variable offset mass on a common shaft with a fixed offset mass, chain linked for a fixed phase relationship. Gould and Richter 12 varied their shaker's eccentricity by varying the rotational velocity of a hollow cylindrical shell into which they introduced a flowable heavy matter (such as lead shot or sand). The combination of rotational velocity and mass of matter introduced determined the eccentric force of the shaker. H o o d et al.13 created a unique trunk shaker by using an eccentric mass on a sun gear which "walked" around the inside of a planet gear. As the eccentricity of the mass was capable of being partially offset by the offset of the "walking" sun-gear shaft, various geometric paths (shake patterns) were traced out by the shaker during vibration. Unfortunately, the eccentricity generated by many of these designs could not be adjusted during shaker operation; a criterion desirable for a shaker used to harvest different crops. The objectives of the research report here were: (1) to measure the accelerations and displacements of a trunk shaker attached to various size tree trunks to identify and calculate forces from those measurements which may exceed tree bark strength and co,lsequently, induce hidden bark damage; (2) to estimate dynamic compressive and shear stresses imposed on the trunk of young cherry trees by using a second-order, single degree-of-freedom vibration model; and (3) to develop a shaking mechanism through which vibration amplitude and frequency could be independently modulated during tree shake, isolating vibration which may exceed bark strength limits or initiate tree decline. 2. Vibration

2.1. Instrumentation and equipment A Friday C-clamp trunk shaker (Friday Tractor Co., Hartford, MI) was mounted on the loader frame of a 4 2 p t o kW tractor with three hanger links provided by the manufacturer (S1, $2 and $3 in Fig. 1). Shaker vibrations were isolated from the tractor by incorporating the manufacturer's rubber bushings between the end washers on the hanger links and the shaker and tractor body. A single hydraulic cylinder (C1) linearly controlled the movement of the outer pad P1). The operator was required to manoeuvre the shaker to position the inner pad (P2) next to the tree. The retraction of cylinder C1 compresses the tree between the two pads; the force of compression being proportional to the cylinder pressure and the contact area of the pad. Two contra-rotating eccentric masses (MA, MB) generate vibration in the shaker body. Each mass consists of a semicircular steel shell (radius = 200 mm, thickness = 90 mm) filled with lead having a mass of 40 kg. An auxiliary pto driven hydraulic system was mounted on the rear of the tractor to provide the required oil flow for the rotating eccentric masses. Each mass was driven by a separate, independent hydraulic motor (MA1, MA2). Each motor was regulated with a single, continuously variable, pressurecompensated flow control valve. The hydraulic system was open-centred (without

H. A. A F F E L D T E T A L .

55

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53

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145

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Fig. I. Dimensional plan view of C-clamp trunk shaker showing accelerometer and proximity sensor locations (all dimensions in mm). Key: A 3 - A 4, A ccelerometers at shaker centre of gravity; A 5 - A 6, Accelerometers at shaker pad, PSA,PSB, Proximity sensors on rotating mass shafts

feedback) so that the mass position and velocity at any instant were unknown. The operation of one mass alone would cause the shaker to vibrate in a circular motion. Operation of both masses would generate various shaker vibration patterns, depending on the instantaneous velocities of the two masses. A nitrile-covered sling was bolted to the shaker body and encircled the Kilby clamp pads in order to hold the pads in the shaker clamp (Kilby Manufacturing Co., Inc., Gridley, CA). A flap of the same material hung loosely down over each sling and made contact with the tree trunk. Heavy gear oil was periodically applied to the mating surfaces between the sling and flap (standard procedure) to promote slip, in an attempt to reduce shear force at the trunk bark. Clamping circuit pressure 14 was set to limit peak compressive pressures to 2070 kPa. On small trees, however, contact between the two pads (P1, P2) encircling the tree caused insufficient gripping force to be placed on the trunk to prevent slip. On large trees, the gripping action which resulted from the recommended clamping pressure forced the pads to conform firmly around the tree, constraining the flaps in place and preventing their movement relative to the slings. Consequently, though shear was reduced between the trunk and the pad, in some cases, the complex interaction between the clamping pressures, the pad conformity around the tree and the gripping force limited the amount of slip possible between the flap and sling, converting that energy into shear force on the trunk's surface. The shaker was instrumented with four piezoelectric accelerometers in order to characterize planar motion by integrating the acceleration measurements to give displacements (Fig. 1). Pad compression was defined as the relative displacement between the shaker and the tree in the X direction while pad shear was defined as the relative displacement in the Y direction. Hall-effect proximity sensors were placed at the shaft of each rotating mass to monitor mass position and velocity.

56

SHAKER

FOR

FRUIT

AND

NUT TREES

Three similar accelerometers were attached to the trunk to characterize planar motion. Two accelerometers were placed at 90° to one another (TA1, TA2) on a steel block which was fixed to the trunk at clamp height along the X axis with a lag bolt (Fig. 1). A third accelerometer (TA3) was similarly fixed at 90° around the trunk from TA1 and TA2 in the Y direction at clamp height. Trunk accelerations were integrated to give displacements for comparison with shaker displacements. Two linear variable differential transformers (LVDTs) were used to verify trunk vibration patterns and phase angles with the displacement patterns calculated from the accelerometers mounted on the tree. During free shake tests (no tree in the clamp), accelerometers and LVDTs were connected to a 50 mm × 100 mm board (610 mm long) placed in the shaker clamp. All transducer signals were amplified, then recorded in analogue form for post-processing and analysis. 2.2. Field tests Displacement tests were conducted on Montmorency tart cherry trees, P r u n u s cerasus. Shaker frequencies of 9 Hz and 16 Hz were employed separately on three trees in each of three size groups (65, 110 and 165 mm trunk dia.). These frequencies were within the recommended range of 10 to 24 Hz for sweet and tart cherries. 8 However, the maximum frequency attainable with the Friday shaker was 16 Hz. Free shake tests at each frequency were also conducted. Using standard practice, the shaker clamp was centred orthogonal to the tree trunk at 250 to 300 mm above the soil surface. Each shake test lasted 9 to 16 s, which allowed for start-up and shut-down transients and a full-power, steady-state shaking period of 4 to 8 s. 2.3. Data analysis LVDT signals, measuring trunk displacement in the X and Y directions, were converted from voltage to length units using linear calibration equations. Hall-effect sensor signals were converted to frequency and position, then smoothed with a look-ahead routine. 15 Integration of digital accelerometer signals into displacement produced unrealistic results for displacement because: (1) integration of low frequencies (often amplifier drift) produced very large unrealistic displacement traces which masked the higher frequency, lower magnitude shaker vibration of interest; and (2) large numerical values resulting from integration of these low frequencies usually reduced the numerical accuracy of high frequency information (due to loss of significant digits in the computer). To circumvent this problem, integration of the accelerometer data into displacement was performed by decoding the stored acceleration data from the data logger's internal format into a contiguous array of voltage data, converting these voltages into acceleration units, and then converting this acceleration vs time information into the frequency domain (magnitude and phase vs frequency) using a Decimation-In-Time (DIT) Cooley-Tukey "Fast Fourier Transform" (FFT) algorithm, is Double integration (integration of acceleration once into velocity, then integration of velocity into displacement) was then performed in the frequency domain by dividing complex frequency components (real and imaginary values) by the radian frequency squared (2s~f)2. Very low frequencies whch resulted from amplifier drift and which were obscuring the true trunk and shaker displacements were removed by multiplying the integrated frequency-domain data with a Hanning (cosine squared) window (equivalent to convolution in the time-domain). ~s The frequencies needed to filter the data were determined from the frequency spectra of uncontaminated (no amplifier drift) acceleration signals and the LVDT displacement traces.

H. A. A F F E L D T

ET AL.

57

After integration, the frequency-domain displacement spectra were converted back to the time-domain (displacement vs time) with an inverse Fourier transform; a routine which uses the above FFT algorithm with the sign of the exponent reversed and divides final coefficients by N (the number of points). 2.4. Results and discussion In free shake (no tree in the shaker clamp), unintended transients (short duration, large magnitude shaker displacements exceeding the design, operating, safe or steady-state limits) occurred during start-up and shut-down. It is important to identify the frequencies of these transients for if they occur at frequencies within the range of frequencies used for tree vibration (up to 24 Hz), then the tree may resist this large amplitude resonant motion of the shaker and hence, encounter larger vibration forces than the bark is capable of withstanding. Furthermore, recommendations in the literature indicate that large displacements typical of resonance phenomena, can damage tree bark even if the tree attempts to follow the shaker displacements. These shaker transients may result from excitation of system resonance, instability at specific frequencies or excitation of undesired vibration modes. Transients on start-up, resulting from sudden power application, have exceeded steady-state displacement values by a factor of 2-5, often reaching 25 mm amplitudes while steady-state is normally 10 to 19 ram. Oscillations in both the X and Y directions require several cycles to settle, indicating an underdamped system. Double-peaked maxima and zero displacement values signalled rapid changes in shake direction at frequencies around 1-5 to 2.0 Hz with initial excitation near 3-0 to 4.0 Hz. When attached to a 65 mm dia. trunk, transients occurred during start-up (0.5 to 4.0 s after the start of shake) and shut-down (11.0 to 14.0s after the start of shake). These transients were often of larger amplitude than the free shake displacement indicating that an interaction between the tree and shaker takes place which amplifies the displacement to values greater than would ordinarily be exhibited by the shaker alone (Fig. 2). Some of these transient vibrations are excited at a frequency of 2-0 Hz which coincides with the natural frequency of the shaker suspension system (1.5 to 2-0 Hz) as well as the natural frequency of a small tree TM (1-0 to 3-0 Hz). When the frequency of the shaker masses passes through these low frequencies on start-up and shut-down, which induce resonance, amplification of shaker or tree displacements may create very high reactive forces between the tree and shaker, particularly if the tree and shaker attempt to vibrate in non-coincident directions at the same time. Table 1 summarizes steady-state and peak displacements (maximum displacement during a shaking operation) under different shaking conditions with two mass operation (necessary to remove fruit suspended from limbs non-parallel with the direction of shaker attachment to the trunk). During the shaking of all sizes of Montmorency cherry trees, with both the conventional fixed-eccentricity masses operating in the shaker, it was observed that the majority of fruit was removed when vibration began at start-up (fruit with a very low stem attachment force) and then later during the higher frequency steady-state operation (fruit with high stem attachment forces). Irrespective of the quantity of cherries remaining on the tree, very few were detached during shut-down, even though tree and shaker displacements reached maxima. Consequently, the largest displacements may cause damaging stress in the tree bark yet remove few, if any, fruit. Potentially more harmful than absolute displacement, relative displacement may also induce bark stress and strain. Relative displacement was calculated as the difference between absolute shaker and tree displacements at a particular instant in a given direction. X direction relative displacements are typically larger during mass acceleration

58

SItAKER

E E ~E

3O 2O tO

~,

o

o~

FOR

FRUIT

AND

NUT

TREES

~_ -~0 -~ - 2 0 X -30 E E

~-

3O

20 o -sO

~'

-20 -30 0

2

~

6

8

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[4

16

Time, S 30 (c) 20

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-30

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--~,0 - 2 0

--I0

0

2r" displacement,

I0

i i i i i

20

30

mm

Fig. 2. Displacement of the trunk with both masses operating at 16 Hz on a 65mm dia. trunk: (a) X displacement; (b) Y displacement; (c) planar (X vs Y) displacement (X, Y directions correspond to Fig. 1)

than during deceleration. The relative displacement frequency spectra (not shown) discloses the maximum amount of vibration energy from 3 to 6 Hz; frequencies where the shaker and tree have opposing absolute displacements (increasing phase difference due to tree and shaker resonance). Force-deformation constants for the pads, referred to as pad deflection constants (PDC), were reported by Frahm et al. TM for the pads and clamping force used in the present experiments. Our observed X direction relative steady-state displacement of 3 mm, which is absorbed in pad deformation, adds a 4200 N force [(PDC = 1400 N / m m ) x 3 mm] to the resisting trunk side, translating to 1000 kPa for a 50 mm dia. trunk (contact area for 50 mm dia. trunk = 4195 mm2). Similarly, measured X direction relative transient displacements of 8 mm may add 11 200 N or 2670 kPa. By using a ratio of peak-average pressure from Frahm's pad pressure distribution plots for our clamp pads, we calculated that our pad could reach a peak pressure of 2760 kPa. Therefore, the large transient relative X displacements of 8 m m can cause the recommended pressure limit TM of 2070kPa to be exceeded. PDCs increase approximately 25% on 110 and 165 mm dia.

59

H. A. A F F E L D T E T A L .

Table 1 Steady-state (SS) and peak (PK) displacements at the shaker clamp for free shake (no tree in the clamp) and tree shake using the Friday C-clamp fixed-mass inertial shaker (mm displacement) Conventional X direction

9 Hz rotational Free shake Tree shake 65 mm dia. 110 mm dia. 165 mm dia.

Y direction

SS

PK

SS

PK

19

39

17

35

22 24 23

36 33 25

24 20 19

30 26 22

18

44

18

25

26 22 16

52 46 42

20 19 12

45 41 38

frequency

trunk trunk trunk

16 Hz rotational frequency Free shake Tree shake 65 mm dia. trunk 110 mm dia. trunk 165 mm dia. trunk

trunks while pad contact area increases 400 to 650% respectively, thereby reducing average contact pressures on larger trees and hence, imparting less stress on larger trees with the clamp pressure employed in these experiments. Effective mass and stiffness coefficients were 16 kg and 12.8 N / m m , respectively, for a typical Montmorency cherry tree with a 65 mm dia. trunk. 17 A first estimate of force levels on the trunk bark from vibratory excitation, calculated using our measured peak X displacements (Table 1) and a second-order, single degree-of-freedom vibration model 18 resulted in a force of 6278 N from acceleration and 381 N from tree stiffness F = m £ + cYc + k x

(1)

where: F = force; m = e f f e c t i v e mass; c = e f f e c t i v e damping; k = e f f e c t i v e stiffness; = acceleration; k = velocity; and x = displacement. In the X or compression direction, only one pad (P2) is effective in transmitting vibration to the trunk at any instant. Using the contact area of 4195 mm 2 for our pads clamped around a 5 0 m m dia. trunk, the average contact pressure over the pad becomes 1590 kPa, which is less than both the peak pressure limit for a bark stress of 2070 kPa and the peak pressure developed from relative displacements of 2760 kPa. Consequently, forces generated while inducing tree motion should not induce bark damage. Contact area estimates for a larger tree with a 65 mm dia. trunk (semicircular surface area) may reduce this to 700 kPa, much less than the 2070 kPa peak pressure limit. Similarly, employing measured absolute peak Y displacements (Table 1) in the above model resulted in a force from acceleration of 5500 N and a force from spring reaction of 305 N. In the Y or shear direction, however, both pads P1 and P2 contact the trunk simultaneously. Therefore, the total pad contact area of 8390 mm 2 for a 50 mm dia. trunk would develop a shear stress of 690 kPa. Relative Y displacements measured as pad deflection in the Y direction, may also be used to calculate potential shear force. Y relative displacements of 4 mm generate 5600 N of force (PDC = 1400 N / m m , assumed constant for small deflections), or 667 kPa for a pad contact area of 8390 mm 2. Assuming that some slip takes place between the flap

60

S H A K E R FOR F R U I T A N D NUT T R E E S

contacting the tree and the sling supporting the pads when well lubricated, actual shear stress absorbed by trunk bark will be a mere fraction of the potential total stress. Without slip, however, the shear stress of 667 kPa exceeds the acceptable threshold reported by Brown et al. 19 of 300 kPa for sectioned bark, though intact bark (not separated from surrounding bark) is expected to resist greater shear stress. Acceptable stress and strain values for fruit tree bark have customarily been reported by researchers from forces which were imposed only once on the trunk, with the effect measured immediately thereafter (single cycle or static values). In contrast, a typical commercial shake of 3 to 5 s at 16 Hz will theoretically impose upon the trunk bark 90 to 150 cycle peaks in each of the X and Y directions. Therefore, in the dynamic state, bark damage from cyclic fatigue may occur at stress levels much lower than in single cycle tests.

3. Methods of eliminating transients Our experimental results on trunk shaker vibration have shown that the low natural frequencies of the tree, the shaker, and the tree-shaker system can cause unstable, unproductive, and potentially damaging vibrations when the system is excited near these frequencies. To circumvent vibration transients, customary methods of isolating or changing the natural frequencies of a mechanism were investigated. One approach which was practical to construct and economical for orchard operations was a method to isolate vibration near the low resonant frequencies of the tree-shaker system and deliver shaking energy near higher shaker frequencies. Two concepts are practical to achieve this goal: (1) phasing of multiple exciters; and (2) varying unbalance of the eccentric mass. A solution employing the latter was selected. Force (F) generated by an eccentric is proportional to its mass (m), eccentricity (e) and rotational velocity (co): F = m e c o 2.

(2)

It is desirable to vary ca since it has the greatest effect on force. However, on start-up and shut-down with a fixed-eccentricity mass, co would pass through and thereby generate some force at the low natural frequencies of the tree and shaker, which contradicts the objective of avoiding these frequencies during vibration. Adjustment of the mass necessitates mass transfer to and from the eccentric shell such as in the shaker design of Gould and Richter. la Systems involving a mass or force transfer are difficult to implement and usually require an auxiliary absorber for the parameter being isolated. Furthermore, mass transfer systems are typically dependent on physical phenomena such as centrifugal and gravitational force and thus defy continuous positive control, often necessitating mass transfer at the same time for each run. Alternatively, eccentricity of the mass can be manipulated to control force. If e ~ 0 when ca is small, near the natural resonances, then F ~ 0 and no motion would occur. Then, when co is large, near the desired shake frequency, eccentricity would be increased to generate the required shaking forces and undesirable transients would theoretically be avoided.

4. Variable-eccentric mass (VEM) 4.1.

Design

A prototype variable-eccentric mass (VEM) was designed, constructed and mounted on the Friday C-clamp trunk shaker. For simplicity of construction, positive control over eccentricity, and independent amplitude and frequency control, we selected a design

H, A. A F F E L D T E T A L .

61

21

22

10

i

Fig. 3. Variable-eccentric mass design: (a) top view; (b) exploded view

consisting of a hydraulically activated mass pivoted about a primary rotating shaft from a balanced position (e - 0, F ~ 0) to a fully unbalanced position (e = max, F = max). Flow control valves were retained on the original shaker to provide infinite adjustment of mass rotational velocity. The conventional, fixed-eccentric mass consisted of a 40 kg, semicircular, lead-filled steel shell welded to a 49 mm dia. steel shaft. An eccentricity of 99 mm generated shaker vibrations during shaft rotation. The VEM design, Fig. 3, employs a similar steel shell (10) appropriately cut in the centre for the passage of the vertical rotating drive shaft (14) through the proper arc. The shell was filled with molten lead and cooled, thus forming the mass. A top retaining plate (12) and a bottom retaining plate (11) were welded to the vertical shaft. One end of the mass (axial end) is mounted between these plates by pin (16). A second pin (18) passes through a mounting backplate (19) on the 76mm x 7 6 m m hydraulic cylinder (17) to form an axis of rotation for the cylinder. The opposite end of the mass, free to move between the plates, is connected by a pin (13) to the piston rod (15) for positive position control. Two canals (21, 22) internal to vertical shaft (14) are aligned with a union plate (23) and a rotating union (24) for hydraulic fluid passage. Suitable flexible hydraulic hoses (25, 26) transmit hydraulic fluid from the vertical shaft to the actuating hydraulic cylinder. During harvesting, shaking force can be varied by changing the position of the centre of gravity of the mass with respect to the centre of rotation of the vertical shaft (14), thus changing the eccentricity. Various shaker patterns can be developed by adjusting the number, relative size, direction, phase, and frequencies of these individual masses. 4.2. Field tests The prototype VEM design for shaker control was field tested using the same experimental protocol as with earlier commercial shaker vibration tests. High-speed

62

SHAKER

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FRUIT

AND NUT TREES

photographic methods a° were employed to validate displacement traces for the modified shaker. Eccentricity engagement rate and position curves when shaking a 65 mm trunk were analysed in order to determine the effect of engagement rate (from 0 to 175 mm/s maximum) on transient shaker behaviour and mass rotational velocity. The rate which provided the minimum operating time and yet did not excite transient shaker displacements when the mass was engaged was then selected for further design validation.

4.3. Results and discussion The ability to control frequency and amplitude independently provided the means necessary to pass through the low first natural frequency of the shaker (1-5 to 2-0 Hz) and of small trees (1-0 to 3-0 Hz) with no excitation energy. Furthermore, though time to steady-state vibration was slightly longer than conventional (0-5 vs 0-3 s), time from steady-state vibration to zero vibration was considerably less with the modified design than with the conventional fixed-mass design (0-8 s vs 3 to 8 s), thus enabling shorter times between clamping and unclamping. Rapidly engaging the modified mass from a balanced position to an unbalanced (eccentric) position instantaneously decreased the rotational frequency of the mass more severely than did slow engagement of mass eccentricity, thus requiring more time for the mass to speed up and settle to its pre-engagement rotational velocity. This was attributed to the power drawn from the hydraulic system and the inertia involved in moving the mass. Patterns of mass rotation varied insignificantly with tree size or within free shake tests. All factors considered, rapid mass engagement was chosen as the standard to maintain harvesting efficiency. Free shake displacements were equivalent to the steady-state value of the conventional shake (10 to 12 mm). A low frequency waveform (0.8 to 1.0 Hz), of the order of half the conventional transient magnitude, was superimposed on the steady-state frequency, however, near the first natural modes of the shaker suspension (1.0 to 2 . 0 H z ) . It seems likely that this was initiated by rapid mass engagement. Settling from this excitation required several cycles. X and Y trunk displacements of a 65 mm dia. tree when using the modified shaker (Fig. 4) show that motion starts linearly and reaches a steady-state value equivalent to that of a conventional shake of similar trunk size and frequency (Fig. 2). No transient or resonant motion is evident with the modified shaker design on start-up or shut-down in either the X or Y direction, with only minor overshoot at mass engagement ( - 1 mm at time = 2 s) evidenced in the X direction (Fig. 4). This overshoot appears to be proportional to mass engagement velocity and was not affected by tree size. Table 2 summarizes displacements incurred by operating the V E M desgin in both the fixed-mass mode and the variableeccentricity mode. Contrary to spectra for the fixed-mass shaker which exhibit an abundance of low frequency energy (Fig. 5a, b), VEM spectra exhibit very little energy loss due to inertial and resonant reaction forces (Fig. 5c, d). Low frequency oscillations in the fixed-mass design not only contribute to peak displacement amplitudes for high stress levels in the bark, but may also provide a mechanism for shaker rotation, thereby imparting highly damaging torsion on the bark. The V E M design eliminates this broad band of vibration and allows the shaker frequency to be precisely defined. X relative displacements for a 65 mm dia. trunk shaken at 16 Hz ranged from 1 to 3 mm; well below the 8 mm transients reported with the fixed-mass shaker. Relative displacement spectra indicate total energy domination at the shaking frequency. In agreement with absolute displacements, the shaker and tree are nearly in-phase for the

H.

A.

AFFELDT

63

ET AL. E E

8: 6i

.,.r

4 l

(0)

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6I

~.. - - 8 L . . . . 0 2

4

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Fig. 4. Displacement of the trunk with fast engagement of variable-eccentricity operating at 16 Hz on a 65mm dia. trunk: ( a ) X displacement; (b) Y displacement; (c)planar (X us Y)displacement (X, Y directions correspond to Fig. I)

entire shake period (characteristic spring reaction) and evade low frequency resonance (characteristic dashpot, mass reaction). Utilizing the PDCs of Frahm et al., 14 the observed X relative displacements translate into a 1000 kPa contact pressure for a 50 mm dia. trunk. At absolute X peak displacements, acceleration was 14 g and displacement reached 12 mm. The second-order vibration model [Eqn (1)] predicts contact pressures of 540 kPa on the same trunk. Contact area estimates for a 65 mm dia. trunk (semicircular surface area) may reduce this to 270 kPa. These pressures are well below the limit of 2070 kPa. Absolute peak Y displacements reached 13 mm for small trunks where acceleration was approximately 16g. Around a 5 0 m m dia. trunk, shear stress may reach 310kPa. Lubrication of the sling-pad interface to reduce shear may be less effective on small trunks due to the pad-to-pad contact around the trunk which resists pad slippage. Corresponding Y relative displacements ranged from 0-5 to 1-5 mm, capable of a force of 2100 N, resulting in an acceptable stress limit of 250 kPa. Clamping force, pad properties, pad and sling lubrication, localized pressure zones 1 4 and pad relaxation effects~ 1 may change clamping characteristics.

64

SHAKER

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FRUIT

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NUT TREES

Table 2 Steady-state (SS) and peak (PK) displacements at the shaker clamp for free shake (no tree in the shaker clamp) and tree shake using the variable-eccentricity mass shaker design in a Friday C-clamp inertial shaker (mm displacement) Conventional, mass extended X

Slow engage, 70 m m / s

Y

X

Fast engage, 175 m m / s

Y

X

Y

SS PK SS PK SS PK SS PK SS PK SS

PK

9 Hz rotational frequency Free shake Tree shake 6 5 m m dia. t r u n k l l 0 m m dia. t r u n k 1 6 5 m m dia. t r u n k 16 Hz rotational frequency Free shake Tree shake 6 5 m m d i a . trunk ll0mmdia, trunk 165mmdia. trunk

9

31

8

17

10

13

9

13

10

13

9

I1

12 13 9

22 21 11

11 9 13

24 16 16

10 10 10

* * *

11 11 14

* * *

12 11 10

* * *

11 12 13

* * *

II

30

10

17

11

13

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15

11

13

11 11 8

19 20 12

12 13 12

23 19 15

11 11 9

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11 12 14

* * *

* Less t h a n 1 m m d e v i a t i o n f r o m s t e a d y - s t a t e at a n y t i m e

4.4. Practical achievements The VEM design exhibited an improved trunk shaking motion by eliminating fixed-mass vibration resonance phenomena upon start-up and shut-down, believed to be damaging to the bark system. Since shaking force and amplitude are independent, continuous rotation of the VEM at shake frequency is possible for the duration of the entire harvest, thereby eliminating the time and power required for acceleration and deceleration of the masses at each tree. Furthermore, continuous shaft rotation reduces component wear due to acceleration forces and eliminates the need for the operator to reset the shaker frequency at each tree. Steady-state vibration amplitudes, equivalent to the fixed-mass system, were maintained. Independence of shaking amplitude and frequency gives the operator improved shake harvesting control in the field, varying eccentricity and thus, shaker displacement, frequency, and pattern, in a simple, quick manoeuvre. This advantage also provides easy adaptability to further intelligent controller design such as an on-board computer for sequencing shaker masses to achieve predetermined patterns. 5. Conclusions

(1) Displacement resonance phenomena occurred during start-up and shut-down when shaking tart cherry trunks of 65, 110 and 165 mm dia. at 9 and 16 Hz with a commercial C-clamp trunk shaker. Displacement during resonance exceeded steady-state displacement by a factor of 2.5. (2) A second-order, single-degree-of-freedom vibration model indicated total dynamic compressive stress values of 700 to 1590 kPa on 65 mm dia. trunks. Relative displacements between the trunk shaker and a 65 mm dia. trunk resulting from large acceleration forces and resonance ranged from 3 to 8 mm and appeared to significantly contribute to bark stress and strain.

H.

A.

AFFELDT

65

ET AL.

F

161 c

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1-2~

o8I

E 0.4 ~ ' ~ 0. . . . .

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~oi

i

0

20

40

60

80

I00

~ 3.o

120 (c)

2

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f.oi: 0

........... 20

40

' . . . . . . . . . . 60 80 I00

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Frequency, Hz

Fig. 5. Spectral content of vibration when shaking a 65mm dia. trunk at 16 Hz: (a) X magnitude in conventional fixed-mass; (b) Y magnitude in conventional fixed-mass; (c) X magnitude with rapid eccentricity engagement (d) Y magnitude with rapid eccentricity engagement (X, Y directions correspond to Fig. 1)

(3) A variable-eccentric mass (VEM) design successfully eliminated displacement transients caused by low frequency resonance during start-up and shut-down of a trunk shaker. (4) Steady-state displacements of IU to 12 mm were maintained by the V E M at shaking frequencies of 9 and 16 Hz, corresponding to steady-state displacements of the conventional shaker. (5) The absolute and relative steady-state displacements of the VEM do not generate shear or compressive stresses exceeding bark strength limits reported by previous researchers. (6) The VEM design provided independent control of shake frequency and displacement in a quick and simple manoeuvre, providing great flexibility for operator use and future implementation of intelligent control. References

1 Abildgaard, W. Fruit and nut harvester. US Patent No. 1 472 262, 1923 2 Brown, G. K. Harvest mechanization status for horticultural crops. ASAE Paper No. 80-1532. ASAE, 2950 Niles Rd, St Joseph, MI 49085, 1980 3 Fridley, R. B.; Brown, G. K.; Adrian, P. A. Strength characteristics of fruit tree bark. Hilgardia 1970, 40(8): 205-223

66

SHAKER

FOR

FRUIT

AND NUT TREES

4 Diener, G. R.; Levin, J. H.; Tennes, B. R. Directional strength properties of cherry, apple, and peach bark and the influence of limb mass and diameter on bark damage. Transactions of the ASAE 1968, 11(6): 788-791 s Burton, C. L.; Schulte-Pason, N. L.; Brown, G. K.; Marshall, D. E. Influence of mechanical harvesting on cherry tree decline. ASAE Paper No. 86-1559. ASAE, 2950 Niles Rd., St Joseph, MI 49085, 1986 • Timm, E. J.; Brown, G. K.; Segerlind, L. J.; Van Ee, G. R. Slipbelt and lubrication systems for trunk shakers. Transactions of the ASAE 1988, 31(1): 40-46 7 Adrian, P. A.; Fridley, R. B.; Chaney, D. H.; Uriu, K. Shaker-clamp injury to fruit and nut trees. California Agriculture 1965, 19(8): 8-10 a O'Brien, M.; Cargill, B. F.; Fridley, R. B. Principles and Practices for Harvesting and Handling Fruits and Nuts. Westport, CT: AVI Publishing Co., 1983 g Halderson, J. L. Fundamental factors in mechanical cherry harvesting. Transactions of the ASAE 1966, 9(5): 681-684 lo Harrett, E. F. Method and apparatus for removing fruit from trees. US Patent No. 3 084 967, 1963 11 Fridley, R. B. Trunk shaker for attachment to a tree. US Patent No. 3 540 486, 1970 12 Gould, R. D.; Richter, J. E. Variable inertia weight for tree shaker. US Patent No. 3 564825, 1971 la Hood, C. E.; AIper, Y,; Webb, B. K. Tree shaker. US Patent No. 4 170 100, 1979 14 Frahm, J. R.; Brown, G. K.; Segerlind, L. J. Mechanical properties of trunk shaker pads. ASAE Paper No. 83-1078. ASAE, 2950 Niles Rd, St Joseph, MI 49085, 1983 is Affeldt, H. A. Spectral analysis for optimal design of a variable eccentricity trunk shaker harvester system. Ph.D. Dissertation. Mich. State Univ., E. Lansing, MI 48824, 1987 is Stanley, W. D.; Dougherty, G. R.; Dougherty, R. Digital Signal Processing. Reston, VA: Reston Publishing Co., 1984 17 Esch, T. A. Personal communication. Michigan State University, E. Lansing, MI 48824, 1986 18 Thompson, W. T. Theory of Vibration with Applications. Englewood Cliffs, N J: Prentice-Hall, 1981 19 Brown, G. K.; Frahm, J. R.; Segerlind, L. J.; Cargill, B. F. Shaker damage to cherry trees--causes and cures, in Fruit, Nut and Vegetable Harvesting Mechanization. Special Publication 5-84. ASAE, 2950 Niles Rd., St Joseph, MI 49085, 1984 20 Marshall, D. E. Determining motion of mechanical harvesting systems with photographic techniques. ASAE Paper No. 86-1556. ASAE, 2950 Niles Rd, St Joseph, MI 49085, 1986 21 Affeldt, H. A. Digital analysis of the dynamic response within trunk shaker harvester systems. M,S. Thesis, Michigan State University, E. Lansing, MI 48824, 1984