A model to predict damage to horticultural produce duringtransport

J. agric. Engng Res. (1991) 50, 259-272

A Model to Predict Damage to Horticultural Produce During Transport C. S. JONES;* J. E. HOLT;* D. SCHOORLt * Department of Mechanical Engineering, The University of Queensland, 4072, Australia t Department of Primary Industries, G.P.O. Box 46, Brisbane 4001, Australia (Received 5 November 1990; accepted in revised form 17 March 1991)

A model of the road-vehicle-load system has been developed to enable prediction of mechanical damage in loads of horticultural produce during transport. The elements of the system are the road profile, the tyres, suspension and chassis of the vehicle and the produce, packaging and cushioning which constitute the load. The model used a force-characteristic description of the vehicle and load elements to calculate the energy absorbed by the produce. The energy absorbed in turn was used to calculate physical damage to the produce, in this case bruise volumes in apples. The model was simulated on an IBM compatible 386 PC. A predictor-corrector numerical solution technique was adopted. A parametric study, in which bruise volumes were predicted for apples transported in bulk bins at different locations on a hypothetical truck, traversing bumps over a range of velocities, showed that the model gave results in accord with practice. It may be concluded that this approach to predicting damage during transport has considerable potential.

1. Introduction D a m a g e during transport is a m a j o r cause of quality deterioration during distribution of the fresh fruit and vegetables. O ' B r i e n et al.1 reported that in loads of cling peaches on a road journey of 260 km, up to 40% of the fruit was damaged. M o r e recently, Maindonald and Finch 2 measured bruising in apples contained in bulk bins at various locations on two different trucks, and found appreciable d a m a g e in up to 16% of the fruit. The basic mechanisms involved seem to be impact or vibration experienced by individual items of produce as the vehicle traverses abrupt changes in road profile. In both cases it is the r o a d - v e h i c l e - l o a d interaction which determines the mechanical damage to the produce, a This p a p e r is concerned with modelling those interactions so that the d a m a g e in loads of fruit and vegetables under various transport scenarios can be predicted. This in turn leads to the capacity to manage better distribution to reduce quality deterioration by the judicious choice of transport parameters. The p a p e r begins with the formulation of an overall r o a d - v e h i c l e - l o a d system, identification of the essential elements and definition of the links between these elements. The individual parts are then modelled in detail in terms of force-characteristic curves. The assembled system is then used to generate d a m a g e results for various road, vehicle and load p a r a m e t e r values. The effects of b u m p height, vehicle velocity, location on the truck tray and vertical position in the load are investigated. The p a p e r concludes with an assessment of the validity and usefulness of the transport d a m a g e model.

2. The road-vehicle-load (RVL) system The input to the R V L system is the road surface. A vehicle laden with fruit or vegetables travelling along a smooth road at constant speed may be considered to be in 259 0021-8634/91/120259 + 14 $03.00/0

© 1991 Silsoe Research Institute

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P R E D I C T I N G D A M A G E TO P R O D U C E D U R I N G T R A N S P O R T

Notation

F k, k2 F~ F~nv F~_~ e ~i

tSi_~

force deflection spring or damping constant force at time i enveloping loading curves force at time step i - 1 exponential deflection at time i deflection at time i - 1

fl F(t) to Pe D t~ a, b, c t At

suspension parameter external force on chassis vertical deflection mass per unit plate area flexural rigidity rate of change of deflection constants time time step

vertical static equilibrium. The forces between the various system elements are constant and there is no transformation of energy. However when the vehicle encounters a discontinuity in the road surface, a bump for example, some of the kinetic energy of the vehicle is dissipated in deforming the road and, of interest in this paper, in deforming tyres, suspension chassis, package, cushioning and produce. Damage to the produce is the direct result of the dissipation of energy in the produce. 4 The energy storage and energy dissipative characteristics of the constituent elements of the vehicle-load system, and the way the elements are linked, determine the overall system response and thus the amount of damage to the load. Fig. I shows the physical elements and couplings for the RVL system. The disturbance provoked by the vehicle encountering a bump is transmitted by compression forces to the tyre, then through mechanical links in the tyre-suspension-chassis sub-system which provide both tension and compression forces. This sub-system then excites the load through a partially constrained connection, commonly provided by strapping or tying down. The produce itself is loosely contained in a multilayered package, with cushioning between layers, the top cover of the package restricting upward movement of the top layer. Again in this part of the system the forces are compressive. In the figure the double-ended arrows signify tension and compression and the single arrows compression, but directed either up or down. Vehicle suspensions are typically modelled by the Kelvin formulation of a spring and damper in parallel. An alternative method of representing the energy dissipative characteristics of suspensions is to use a force-characteristic description. The forcecharacteristic approach is also applicable to tyres. Experimental investigations have provided compression curves for a variety of horticultural produce, s and packaging material too is best described by force-deformation curves. The force-characteristic approach has therefore been adopted in the modelling of the vehicle-load system elements. 3. Detailed models of RVL system elements

3.1. Road Bhatti and Garg e identified seven profile shapes which characterize isolated geometry variations on railway tracks viz. cusp, bump, jog, plateau, trough, sinusoid and damped sinusoid. Each shape was described by a mathematical expression for use in direct simulation of ride qualities of railway vehicles. For rubber-tyred vehicles, however, it seems that the enveloping properties of the tyre mask subtle changes in profile. These properties are described by Hooker and Gambling. 7 Three shapes can be used to

C. S. JONES ET AL.

261 Produce

~ . Limited upward movemenl

Cushioning

Package

~

~

Partial constraint

Chassis i Mechanically linked

Suspension I

Tyre

Mechanically linked

~ I~

Road Fig. 1. Elements and couplings for the road-vehicle-load system (~ ~, compression only, $ tension and compression) represent road discontinuities, the cusp, jog and trough, with a simpler construction. These are shown in Fig. 2a, using common road transport terminology, i.e. bump, kerb and pothole respectively. In this paper only the bump case is used. 3.2. Tyre Cebon 8 assumed a near linear spring for the force-deformation curve for a tyre and added a linear damper to provide for energy dissipation. O ' C o n n o r et aL e showed that the energy dissipation was independent of strain rate and suggested a bi-linear forcedeformation curve as shown i n Fig. 2b. They found that a vertical transition between the loading and unloading curves was sufficiently accurate. The loading and unloading curves are, respectively, F = k16 and F = k26 where F is the tyre force, 6 is the tyre deflection and kl, k2 are spring constants; k2 was found to be approximately 0.9kl.9 3.3. Suspension O ' C o n n o r et al. s obtained experimental load-deflection curves for the spring of a rear suspension unit of an International A C C O 1810A truck, as well as for the tyres. From these results they proposed a force-characteristic curve for leaf springs as shown in Fig. 2c, where the curves ab and cd are the loading and unloading paths respectively. The characteristic is thus markedly history dependent. Fancher et al. lo tested five different leaf spring units and found the same curved form and hysteretic behaviour for the loading and

262

P R E D I C T I N G D A M A G E TO P R O D U C E D U R I N G T R A N S P O R T

"lllll~l~lllll

Bump

/lllllil. IIIIIIlllp

Kerb

IIIIIVlllli,

Pothole

/

(a) Road profiles

(b) Tyre

h

80 (c) Suspension

8m,~

(d) Produce

Fig. 2. Element descriptions for road-vehicle-load interactions

unloading curves. O'Connor et al. s fitted parabolic curves to the experimental transition paths da and bc. Fancher et al. lo described the transitions by exponentials and devised the following equation to represent the characteristics of leaf springs; g = F .v, + ( E - , - & . 0 e

-

I~i-

6i-11

where F~= suspension force at time i, F~_~= force at previous time step, 6i = suspension deflection at time i and 6i-1 = deflection at previous time step. F~nv are the enveloping loading and unloading curves (ab and cd), which one is operative depending on whether the suspension is compressing or expanding, fl is a parameter which describes the steepness of the transition paths, again depending on whether the suspension is being loaded or unloaded. It is also dependent on 6 itself, the suspension deflection. We have adopted this description for suspension behaviour. 3.4. Chassis Typically a truck chassis is constructed from two main longitudinal beams, smaller lateral beams at intervals along their main members and a structurally flexible deck or tray. To simplify the modelling task some investigators have assumed the chassis to be a

C. S. J O N E S

ET AL.

263

rigid member, a'~l i.e. possessing a mass and m o m e n t of inertia but no flexibility. In reality, as Cebon a notes, such frames have flexural models of vibration which are not modelled by such a formulation. For the sort of loads we are considering, flexing of the tray may be quite important, inducing different dynamic responses in individual packages at different locations on the tray. That being the case, a flexible plate subjected to forced vibrations is a better approximation to the chassis. The standard equation for such a structure is

O.(a to

F(t) = V409 + D \ Ol2 ,] where F(t) = external force on the chassis, to = vertical deflection of the plate, pp = mass per unit plate area and D = flexural rigidity. The chassis is thus treated as one long plate to which the suspension units are attached. 3.5. Package Fruit and vegetables are normally packaged in bulk bins, fibre board cartons or plastic returnable crates. Bins are made of solid timber and, if properly braced on a pallet base, may be considered as rigid structures. Plastic crates are also fairly stiff individually and in multiple package stacks. Fibreboard carton standards in the USA require individual packages to withstand compression test loads TM of between 2000-5000 N. Since in normal practice the imposed loads are usually less than 1000 N, deflections are limited and the assumption of a stiff structure is reasonable. However, Kawano and Iwamoto ~3 found that stacks of cartons have a fundamental resonant frequency of between 3-7 Hz and a secondary one between 10-18 Hz. Some investigators TM have reported natural frequencies of this order for fruits, so that the stiff assumption may not be wholly satisfactory for cartons. With this qualification, packages in our simulation have been modelled as rigid bodies, absorbing no energy, and interacting with the chassis as shown in Fig. 1. 3.6. Cushioning Cushioning between layers of produce, or between the produce and the package, on the other hand, is specifically added to absorb energy. It seems reasonable to model cushioning in terms of a linear, viscous damper with a force-characteristic of the form

F=b3 where F = damping, force, 6 = rate of deflection and b = damping constant. This equation applies only when 6 < 0 and 6 < 0, otherwise F = 0. 3.7. Produce It has been shown that mechanical damage in fruit and vegetables may be classified as cleavage, slip or bruising. TM For example, strawberries, apples and ripe pears fail under compression by bruising (cell bursting), green pears and potatoes by slip (shearing) while cabbages fail by cracking. TM Potatoes can also fail by cracking as well, depending on the induced stress state. The general form of the force-deflection curve for all three modes of failure is the same and may be approximated to that shown in Fig. 2d. Initial compression, ab, is approximately linear, the recovery path, bc, parabolic and the recompression, dashed line cb, again linear. If subsequent deflection exceeds 6~ax the force-deflection curve extends along the direction ab. If secondary compressions along the dotted line cb do not reach b the recovery curve drops vertically to meet the full line bc

264

PREDICTING

DAMAGE

TO PRODUCE

DURING

TRANSPORT

and then follows that path to c. Compression of horticultural produce can thus be modelled by F=k16 F = k26 F = a62 + b6 + c

and

F=O

when when when when

6 > 6 .... 6o < 6 < 6m~x and 6 > O, 6o < 6 < 6 m a x and 6 < O, 6 < 60.

given that 6max is initially zero. For any compression cycle, the area bounded by the loading and unloading curves is the energy dissipated in the produce. The damage suffered by the produce is thus directly proportional 4 to the shaded area in Fig. 2a which is given by area abc (along solid lines) = area abd - area bdc

4. Solution process The maximum deflection, 6max at point d in Fig. 2d, experienced by individual items of produce as a result of a loaded truck traversing a discontinuity in the road profile can now be calculated using the model described in Fig. 1. Given the force-characteristics of the elements, and the nature of the connections between the elements, to do so it is necessary to solve for the state (velocity and position) of the R V L system as the event unfolds over time. The accelerations of the element masses can be derived from the forcecharacteristics. These can then be integrated twice with respect to time to give first velocity and then position to define a new state. The deflection of the produce can then be calculated from the relative positions of individual produce masses. The area under the force-deformation curve gives the energy absorbed by the produce. The amount of damage is dependent on this energy absorbed. The adoption of a force-characteristic formulation for the system requires a numerical solution technique. The R V L system may be classified as mathematically stiff, that is, while some elements have high spring rates, others do not. For example tyres have a much higher spring rate than horticultural produce. The truck chassis is typically much stiffer structurally than the suspension. These differences in spring rates govern the choice of integration technique. Fuhrer 17 recommends the Adams-Basforth type formulation for such conditions. Adams-Basforth is a predictor-corrector method by which an estimate of a new state at time t + At is made from an extrapolation of previous states. The estimate is compared with a value derived from the integration of the characteristic curves. If the error exceeds preset limits (either relative or absolute) the time step, At, is reduced, a new estimate made and the process repeated. The iterative procedure continues until the estimated and calculated states converge satisfactorily. Obviously the method is suited for implementation on a computer. A program to simulate the R V L system model was written in " C + + " language and implemented on an IBM compatible 386 PC. The program is suitable for either DOS or UNIX operating systems. With the 20 MHz PC run times are of the order of 90 min for the complete damage data (total bruising, distribution, location) for each load, velocity and bump height combination.

5. Parametric study The computer simulation was used to predict damage in multilayered loads of apples under various transport conditions on a hypothetical truck loaded as shown in Fig. 3.

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ET AL.

Position

©

.,"

®

@

.':'": ................ r.~"'":............... .i ...'

."

®

......... .~;"'"

1.25 m

.."

1.25 m - - - ~ 3.75 m

Fig. 3. Loading positions on an hypothetical truck

Apples were chosen for a number of reasons. Apples exhibit only one mode of mechanical failure, bruising, which can generally be measured reasonably easily. TM The fruit stores well for long periods and is thus readily available for experimental work. As well, results of experiments on the compression behaviour of single apples and of apples in various multilayered packs under dynamic conditions have been described elsewhere, s'19"2° Table 1 shows the parameter values selected for this study. The loading on the hypothetical truck tray requires some elaboration. The fruit was assumed to be packaged in eight bulk bins in eight layers. This gives an internal base dimension of about 1 m x 1 m for the bins when the total load is 4 t. Each bin load is considered to be concentrated at the centre of the bin base, giving a tray loaded at eight points 1.25 m apart to allow for bin wall thickness and clearance. For the 2, 1 and 0.1 t Table 1 System parameters A. Input Profile type Profile height, m Vehicle velocity, ms- 1

Bump (45 ° slopes) acting on both wheels at an axle 0.05, 0.075, 0.1,0.125 5, 10, 15, 20 B. Vehicle, load

Suspension type

Load mass, t Package Cushioning

Multi-leaf front and rear springs, no separate dampers (numerical values extracted from Fancher et al 1°) 0.1,1,2,4 Bulk bin (with lid) 25 N sm-t (acting at all interfaces to allow for wall friction)

PREDICTING DAMAGE TO PRODUCE DURING TRANSPORT

266

loads, the bins were effectively assumed to shrink in plan area to maintain eight layers of produce, acting on the tray at the same nodes. This artifice was adopted to enable the effects of changing load to be separated out from those of changing position. Of course, in reality fewer packages would be needed. In each package the apples were assumed to be stacked in vertical columns thus giving two potential bruise sites on each apple. The bruise volume at damaged sites was calculated from the energy under the forcedeformation curve assuming a constant bruise resistance of 6-4 ml J - ' . This is an average value for common apple varieties. 21 5.1. Average bruise volume Fig. 4 shows contour plots of bruise volume, averaged over the eight loading positions, against bump height and truck velocity. The contour patterns are similar for all four loads. Above a certain velocity the contours are, in general, parallel to the velocity axis implying that damage is largely influenced by bump height. Below this velocity threshold however, the damage is dependent on velocity and independent of bump height. This effect is clear for the 0.1, 1 and 2t cases. For the heaviest load, 4t, there is some interaction between bump height and velocity as bump height increases perhaps due to increased energy dissipation in the springs at larger deflections. This effect can be

20 15

O"'"i@.(~)(2(~

,,2 1 /

10

E 0

>

(I.3 / 0-35 /

O

~

20 2t

4t

15

0.

,

.

10 (15

0

2'5

?o

7'5

160

125 0 2'5 Bump height, mm

5})

Fig. 4. Total average bruise volume, ml

7;

1(~)

125

C,

S,

ET AL.

JONES

267

anticipated from the non-linear curves in Fig. 2c. Another feature is that for the 1 and 2 t cases damage decreases as bumps are traversed at higher velocities. While the contour pattern remains basically the same, the magnitude of bruising decreases as the truck load increases. The maximum average bruise volume is 1-3 ml for the 0.1 t load, an order of magnitude larger than bruising in the 4 t case, and three times larger than the 1 and 2 t cases.

5.2. The effect of position on the truck tray on average bruise volume Figs 5 and 6 show the effect of position on average bruising for the 0.1 and 2 tonne cases. The contour pattern remains the same as that shown in Fig. 4 for the global average. The quantitative effect of position however, is quite marked. The maximum average bruise volume at position 4, behind the rear axle, for the 0.1 t lightly loaded case is 3-5 ml compared with 0.8, 0.4 and 0.55 ml for positions 1, 2 and 3 respectively. For the 2 t medium load case the maximum is again at position 4, 1 ml, compared with 0.175, 0-175 and 0-25 for positions 1, 2 and 3. Consistently the maximum average damage occurs behind the rear axle.

20 Pos 2 ~ ~ / ~ ~ ~ ~ ~ (

Pos 1 15 10 5 I !

--~ 20 >ca

!

Pos 4

Pos 3

15 10 .

0

0

2'5

?0

7'5

160

125

5~0

Bump height, mm Fig. 5. Average bruise volume, ml, for 0.I t case

?~5

100

125

268

PREDICTING

D A M A G E TO P R O D U C E D U R I N G T R A N S P O R T

/

20

Pos 1

Pos 2

)

0'725

) o o~

15

/

i

/

I

~ IIIII

_...-~)11(I

OOTS.' , ~ . ,~i

1 1i

Ii I

10

r

0 o >

i

I

I

20 Pos 3

15

10

\ \-o~--.....__ o

0 o

50

7;

100

125

0

25

50

75

100

125

B u m p height, m m

Fig. 6. Average bruise volume, ml, for 2 t case 5.3. Maximum bruise volume

Fig. 7 shows the bruise volume at each damage site within a column of eight apples for loads positioned in front of and behind the rear axle (positions 2 and 4 respectively). The plots have been prepared for a bump height of 75 mm and a velocity of 10 m s -1, with the truck loaded at 0-1t and 2t. T h e r e are nine interfaces where damage may occur, including the contact of the bottom apple with the container floor and the contact of the top apple with the container lid. In between these sites it is assumed that the bruise volumes on the pair of apples involved at an interface are equal. The maximum bruise volume for the 0-1 t load occurs on the bottom apple at position 4 and is 2.5 ml. The maximum bruise volume for the 2 t load, 0-5 ml, on the other hand, occurs on the top apple. For the 0-1 t load there is a large difference between maximum bruising at positions 2 and 4, as is expected from Fig. 4, while for the 2 t load there is not much difference for the two positions. The distribution of bruising up the column shows that apples in the middle layers suffer less damage than those at either the top or the bottom. 6. Discussion The results predicted by this model of the r o a d - v e h i c l e - l o a d system seem to make sense. The effects of parameters such as load and location on the truck tray are in accord

C. S. J O N E S

269

ET AL.

3 0.1t

2.51

2

1.5

|

O.

E

-~=

o

3 2t 2.5

1.5

0 Bottom

Top Interface

Fig. 7. Bruise volume at damage sites in a vertical column at two loads as indicated (75mm, lOms-l). ~ , Position 4; m, Position 2

270

PREDICTING DAMAGE TO PRODUCE DURING TRANSPORT

with operating experience. The authors have often observed during the unloading of produce vehicles at wholesale markets that lightly loaded trucks appear to cause more damage than heavily loaded ones and that the worst damage occurs over or behind the rear axle and is also exacerbated by a stiff suspension. The effect of this motion is demonstrated in Figs 5 and 6 where average bruise volumes reach 3.5 ml for a package located behind the rear axle on a 0-1 t loaded truck. The effects of bump height and velocity are also consistent with experience. Above a "threshold" value of velocity, about 5 m s -l, increasing bump height produces increased average bruise volume. For example, in Fig. 4 for the 0-1 t case bruise volume goes from 0.1 ml at a bump height of 50 mm to 1.3 ml at 125 mm. It appears that, at low velocities, it is possible for the vehicle suspension to follow the road profile and bumps do not matter much. However as the velocity increases the suspension begins to react, energizing the system and promoting damage. At higher velocities still, at least for the bump profile used in this study, the height of the bump virtually controls the energy transfer, independent of the approach velocity. This sort of behaviour occurs in practice. The distribution of damage within a column predicted by the model (Fig. 7) corresponds to that found in experiments. ~ Table 2 shows experimental bruise volumes at the interfaces in a column of five apples dropped on an experimental rig to simulate a bump during transport. These results were obtained with apples constrained in a light paper tube with no lid. The top apple was prevented from jumping out during impact by a loose loop of tape over the tube top. This condition differs from that of the simulation results in Fig. 7 where the top layer was constrained by a lid. This lid accounts for the increase in damage at the uppermost interfaces for the simulation. Apart from this the simulated and experimental distributions are similar with the largest bruises occurring at the bottom interface and a steady reduction in bruising further up the column. The soft and hard suspensions in Table 2 correspond to the heavily and lightly loaded truck. Again the total bruise figures follow the same pattern. Commercially too, the bottom layer of produce in a package is typically more heavily damaged than subsequent layers. The provision of a lid for the package, or the presence of another container on top, also produces damage to the top layer. 1 It may also be noted that the predicted bruise volumes are, in some cases, quite significant in terms of visual damage. A bruise volume of 0-5 ml corresponds to a bruise diameter on the surface of an apple of about 12 mm which would be obvious in a shop Table 2 Experimental bruise volumes in dropped apple column ~

Suspension type

Interface number

Bruise volume, ml

Soft

5 4 3 2 1 (bottom)

2-2 2.0 3.2 4.5 5.2 Total 17-0

Hard

5 4 3 2

3"4 4"1 7-4 7"9 7"0 Total 29.7

1

c. s JONES e r

271

at.

display. For a lightly loaded truck (0-1 t), with the load positioned aft of the rear axle (position 4) the average bruise volume is 3-5 ml, corresponding to a bruise diameter of 25 mm. Such a bruise would have a significant effect on perceived quality and thus on market price. On the other hand, at all positions on a heavily loaded truck (4t) the average bruise size does not exceed 0.1 ml, corresponding to a diameter of about 5 mm, which may not be particularly noticeable. The model seems to be predicting realistic levels of bruising as well as predicting the trend effects of the various parameters.

7. Conclusions It may be concluded that this approach to predicting damage to horticultural produce during transport offers considerable promise for both the design and management of distribution systems. Although we have investigated only selected values of the system parameters in this paper, conceptually there is no difficulty with studying the effects of a more comprehensive range including various road profiles, vehicle types and suspensions and different load configurations. Such a study could provide important insights into the transport of horticultural produce.

Acknowledgement The authors wish to thank the Commonwealth Department of Primary Industry and Energy for providing funds through the Australian Special Rural Research Council to support the project " T R A N S I M : computer transport simulation of produce damage".

References 10'Brien, M.; Pearl, R. C.; Vilas, E. P.; Dreisbach, L. The magnitude and effect of in-transit vibration damage of fruit and vegetables on processing quality and yield. Transactions of the American Society of Agricultural Engineers 1969, 124:452-455 z Maindonald, J. H.; Finch, G. R. Apple damage from transport in wooden bins. New Zealand Journal of Technology 1986, 2:171-177 3 Schoorl, D.; Holt, I. E. Road-vehicle-load interactions for transport of fruit and vegetables. Agricultural Systems 1982, 8:143-155 4 Holt, J. E.; Schoorl, D. Bruising and energy dissipation in apples. Journal of Texture Studies 1977, 7:421-432 s Holt, J. E.; Schoorl, D. Fracture in potatoes and apples. Journal of Material Science 1983, 18: 2017-2028 e Bhatti~ M. H.; Garg, V. K. A review of railway vehicle performance and design criteria. International Journal of Vehicle Design 1984, 5:232-254 7 Hooker, R. J.; Gambling, K. W. The radial dynamic properties of pneumatic tyres. Noise, Shock and Vibration Conference, Monash University, Melbourne 1974, 272-279 e Cebon, D. Theoretical road damage due to dynamic tyre forces of heavy vehicles. Part 1: dynamic analysis of vehicles and road surfaces. Proceedings of the Institution of Mechanical Engineers 1988, 202:103-108 s O'Connor, C.; Kunjamboo, K. K. F.; Nilsson, R. D. Dynamic simulation of a single axle truck suspension unit. Proceedings of the Australian Road Research Board 1980, 10: Part 3, 176-184 1. Faneher, P. S.; Ervin, R. D.; MacAdam, C. C.; Winider, C. B. Measurement and representation of the mechanical properties of truck leaf springs. Society of Automotive Engineers, West Coast International Meeting, Los Angeles, August 11-14, 1980 800905, 1-13 11 Miller, C. W.; Swamaell, P. Bridge-vehicle interaction with particular reference to Six Mile creek bridge. Metal Structures Conference, Brisbane, May 18-20, 1983, 197-202 la Godshall, W. D. Effects of vertical dynamic loading on corrugated fiberboard containers. US Department of Agriculture, Forest Service, Research Paper FPL94, 1968, 1-20

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PREDICTING DAMAGE TO PRODUCE DURING TRANSPORT

is Kawtmo, S.; l w m o t o , M. Analysis of vibrating characteristics for highly stacked corrugated fiberboard boxes. Joint ASAE and CSAE Summer Meeting, Winnipeg, Canada, June 24-27, 1979, 79-6016, 1-20 14 O'Brien, K.; Claypool, L. L.; Leonard, S. J.; York, G. K.; MacGillivray, J. H. Causes of fruit bruising on transport trucks. Hilgardia 1963, 35:113-124 15 Holt, J. E. Schood, D. Mechanics of failure in fruit and vegetables. Journal of Texture Studies 1982, 11:83-96 16 Holt, J. E.; Schoorl, D. Cracking and energy dissipation in cabbages. Journal of Texture Studies 1983, 14:99-111 17 Fuhrer, C. Numerical integration methods in vehicle dynamics simulations. Proceedings of 3rd International Conference on Transport Systems, Course and Seminar on Advanced Vehicle System Dynamics, Amalfi 1988, 329-345 18 Schood, D.; Holt, J. E. Bruise resistance measurements in apples. Journal of Texture Studies 1982, 11:389-394 is Holt, J. E.; Schoorl, D.; Lucas, C. Prediction of bruising in impacted multilayered apple packs. Transactions of the American Society of Agricultural Engineers 1981, 24:242-247 20 Schood, D.; Holt, J. E. Impact bruising in 3 apple pack arrangements. Journal of Agricultural Engineering Research 1982, 27:507-512 zl Schoorl, D.; Holt, J. E. The effects of storage time and temperature on the bruising of Jonathan, Delicious and Granny Smith apples. Journal of Texture Studies 1977, 8:409-416 " Holt, J. E.; Schoorl, D. A theoretical and experimental analysis of the effects of suspension and road profile on bruising in multilayered apple packs. Journal of Agricultural Engineering Research 1985, 31:297-308