A visco-elastoplastic model for the impact between a compact body and a composite target is presented. The model is a combination of a nonlinear contact law that includes energy loss due to plastic deformation and a viscous element that accounts for energy losses due to wave propagation and/or damping. The governing nonlinear equations are solved numerically to obtain the response. A piecewise linear version of the model is also presented, which facilitates analytical solution. The model predictions are compared to those of the well-known and commonly used HuntCrossley model. The effects of the various impact parameters, such as impactor mass, velocity, plasticity, and damping, on the impact response and coefficient of restitution are investigated. The model appears to be suitable for a wide range of impact situations, with parameters that are well defined and easily calculated or measured. Furthermore, the resulting coefficient of restitution is shown to be a function of impact velocity and damping, as confirmed by published experimental data.

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A crane is generally modeled as a simple pendulum with a point mass attached to the end of a massless rigid link. Numerous control systems have been developed to reduce payload oscillations in order to improve safety and positioning accuracy of crane operations. However, large-size payloads may transform the crane model from a simple-pendulum system to a double-pendulum system. Control systems that consider only one mode of oscillations of a double pendulum may excite large oscillations in the other mode. In multi-degree-of-freedom systems, command-shaping controllers designed for the first mode may eliminate oscillations of higher modes provided that their frequencies are odd integer multiples of the first mode frequency. In this work, a hybrid command-shaper is designed to generate acceleration commands to suppress travel and residual oscillations of a double-pendulum overhead crane. The shaper consists of a primary double-step command-shaper complemented by a virtual feedback system. The primary command-shaper is designed to eliminate oscillations in a slightly modified version of the crane model with frequencies satisfying the odd integer multiple criterion. The virtual feedback loop is then used to modify the commands of the primary shaper to accommodate the difference between the modified and the original models of the crane. It is shown that the suggested hybrid command-shaper is capable of minimizing oscillations of both modes of a scaled experimental double-pendulum model of an overhead crane. Results show that the hybrid command-shaper produces a reduction of 95% in residual oscillations in both modes of the double pendulum over the time-optimal rigid-body commands.

Changes in the thermal status of machine tools spindle-bearing system can have a noticeable effect on the performance of the machine itself, and therefore studying the thermal effect on the performance ball bearing during service is important. For this purpose, a study was carried out where a simple rotating shaft system supported by two angular contact ball bearings was taken into consideration. Heat was generated due to the contact between the balls and rings of the bearing. This thermal effect on the dynamics of the system was studied using a transient thermal model. The system was divided into nodes; each was assumed to be a uniform temperature. Thermal energy balance was used on each node to obtain a set of differential equations. ODE solver in MATLAB was used to solve the resulting system of differential equations. The thermal model considered an initial preload as well as the thermal preload that is caused by the uneven expansion of bearing components. In this research, a 5 DOF nonlinear dynamical system model is integrated with a spindle-bearing thermal model and then utilized to study the impact of preload variations on the spindle-bearing system of a grinding machine. The effect of different system parameters such as speed of rotation, type of bearing, ambient temperature, type of oil, initial preload on temperature output and thermal growth within the system was studied. The study shows that the heat generation rate is directly proportional to the rotational speed of the shaft and higher thermally induced preload is reached at higher speeds. It is also noticed that initial preload has a small effect on the heat generation, thermally induced preload, and temperature of the bearing. Also, the dominant frequency values of the spindle system generally increase with changing thermally induced preload values. This study is useful in predicting the thermal profile as well as preload value resulting in the bearing assembly, which in turn will be used to predict variation in the dynamics of the system.