Development of accurate contact force models for use with Discrete Element Method (DEM) modelling of bulk fruit handling processes

摘要

This thesis is primarily concerned with the development of accurate, simplified and validated contact force models for the discrete element modelling (DEM) of fruit bulk handling systems. The DEM is essentially a numerical technique to model a system of particles interacting with one another and with the system boundaries through collisions. The specific area of application envisaged is in postharvest agriculture, where DEM could be used in simulation of many unit operations with bulk fruit, such as harvesting, transportation, sorting, storage and processing. Such simulations would provide crucial information to aid equipment and process designs to optimise the systems or to limit physical damage to produce during machine handling, for instance. In a DEM model, the material behaviour at collision is captured by a contact force model relating the local deformation in the contact region to the contact force. Contact force models represent one of the crucial elements of a DEM model. They have a direct bearing on the accuracy with which the material behaviour can be captured by the model.In carrying out the main objective of this project, theoretical, experimental as well as numerical approaches were used in order to, among other things, identify, derive, validate and simplify the relevant contact models proposed. Using the elastic contact force models as bases, mathematical contact force models for viscoelastic spheres are derived, for normal contact, tangential contact as well as torsional contact. The derived model for torsional contact was experimentally validated using a rheometer setup. Still using the rheometer setup, parameters of the derived tangential contact force model were determined. These parameters are: the friction coefficient, the viscous constant and the static shear modulus.The finite element method was used to further investigate the normal and tangential contact force models for elastic spheres. Regarding normal contact, the validity of the Hertz contact model under conditions of frictional contact, non-Hertzian contact surfaces and finite strains was investigated. The effect of friction to the force-deformation behaviour of elastic spheres was found to be negligible. The same is the case for the effects from the non-flat contact surfaces that result when stiffer objects come into contact with the more compliant ones. On the other hand, the study of the effect of finite strains revealed a strong influence of the extent of deformation on the Hertz model. The error arising was found to increase quadratically with increase in the normal deflection.Regarding the tangential contact, because the relevant models currently available in literature are generally either too inaccurate or computationally too costly to be implemented in DEM simulations involving large numbers of particles, an alternative model was derived herein and proposed. The model, it is argued, is simple to implement and can have the same accuracy as the Mindlin-Deresiewicz model. Because the proposed model does not include many different conditions and loading scenarios, it is argued that it will be much more convenient and less costly, computationally.By numerically filtering out all the vibration modes in the transient dynamic analyses of normal collisions of elastic spheres using FEA, an estimation of the relative quantities of the kinetic energy involved in the propagation of elastic waves in the colliding bodies could be made. The proportions varied according to the impact velocity from very low (less 4 %) to substantial proportions of up to 40 %. The relationship with the impact velocity was estimated to be proportional to a power 1/3 of the impact velocity. While this observation does not prescribe the amount of energy dissipation that can occur, it is extremely important because it provides an indication of the quantities of energy that can be available as elastic waves energy during collisions, and which potentially can be lost under some conditions. A significant amount of translational energy loss was found to occur for purely elastic collisions through absorption of energy as elastic waves, depending on the material elastic properties. The restitution coefficients for the purely elastic collisions depend on the impact velocity.Eigenvalue analysis of apple fruit models (based on Jonagold apple properties) yielded frequency modes in the ranges from 87.3 Hz to 849.4 Hz. These results were in good agreement with the ranges of values found in literature. The transient analysis of the viscoelastic collisions of apples, using the time dependent properties obtained from literature revealed no viscous response by the fruits. This is explained by the fact that the time constants reported on, and obtained from stress relaxation experiments are much higher than the typical collision times of the fruits. Because pendulum experiments on apple fruits have revealed the existence of viscous response in apples for these kinds of impacts, it can be concluded that the stress relaxation or creep experiments are not suitable for obtaining viscoelastic data for instantaneous processes such as collisions. From further dynamic transient analysis of FE models of the collisions of viscoelastic objects, restitution coefficients due to viscous energy dissipation were found to be dependent in a nonlinear manner to the impact velocities. A method to determine the effective viscous coefficient in the case of two viscoelastic objects colliding was investigated and between the two investigated choices - sum of inverses of the individual coefficients and arithmetic sum of the individual coefficients, the former seemed to yield more accurate estimation of the effective coefficient.