This thesis studies in detail the dynamics of ball screw feed drives and expands understanding of the factors that impose limitations on their performance. This knowledge is then used for developing control strategies that provide adequate command following and disturbance rejection. High performance control strategies proposed in this thesis are designed for, and implemented on, a custom-made ball screw drive. A hybrid Finite Element (FE) model for the ball screw drive is developed and coded in Matlab programming language. This FE model is employed for prediction of natural frequencies, mode shapes, and Frequency Response Functions (FRFs) of the ball screw setup. The accuracy of FRFs predicted for the ball screw mechanism alone is validated against the experimental measurements obtained through impact hammer testing. Next, the FE model for the entire test setup is validated. The dynamic characteristics of the actuator current controller are also modeled. In addition, the modal parameters of the mechanical structure are extracted from measured FRFs, which include the effects of current loop dynamics. To ensure adequate command following and disturbance rejection, three motion controllers with active vibration damping capability are developed. The first is based on the sensor averaging concept which facilitates position control of the rigid body dynamics. Active damping is added to suppress vibrations. To achieve satisfactory steady state response, integral action over the tracking error is included. The stability analysis and tuning procedure for this controller is presented together with experimental results that prove the effectiveness of this method in high-speed tracking and cutting applications. The second design uses the pole placement technique to move the real component of two of the oscillatory poles further to the left along the real axis. This yields a faster rigid body response with less vibration. However, the time delay from the current loop dynamics imposes a limitation on how much the poles can be shifted to the left without jeopardizing the system???s stability. To overcome this issue, a lead filter is designed to recover the system phase at the crossover frequency. When designing the Pole Placement Controller (PPC) and the lead filter concurrently, the objective is to minimize the load side disturbance response against the disturbances. This controller is also tested in high-speed tracking and cutting experiments. The third control method is developed around the idea of using the pole placement technique for active damping of not only the first mode of vibration, but also the second and third modes as well. A Kalman filter is designed to estimate a state vector for the system, from the control input and the position measurements obtained from the rotary and linear encoders. The state estimates are then fed back to the PPC controller. Although for this control design, promising results in terms of disturbance rejection are obtained in simulations, the Nyquist stability analysis shows that the closed loop system has poor stability margins. To improve the stability margins, the McFarlane-Glover robustness optimization method is attempted, and as a result, the stability margins are improved, but at the cost of degraded performance. The practical implementation of the third controller, was, unfortunately, not successful. This thesis concludes by addressing the problem of harmonic disturbance rejection in ball screw drives. It is shown that for cases where a ball screw drive is subject to high-frequency disturbances, the dynamic positioning accuracy of the ball screw drive can be improved significantly by adopting an additional control scheme known as Adaptive Feedforward Cancellation (AFC). Details of parameter tuning and stability analysis for AFC are presented. At the end, successful implementation and effectiveness of AFC is demonstrated in applications involving time periodic or space periodic disturbances. The conclusions drawn about the effectiveness of the AFC are based on results obtained from the high-speed tracking and end-milling experiments.

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Thesis (D. Ed.)--Ball State University, 2009. / Title from PDF t.p. (viewed on Nov. 11, 2009). Includes bibliographical references (p. [115]-132).

At present the effects of friction are not included in three-dimensional mechanism simulation packages because of the difficulty of determining a friction model for joints such as the spherical joint where the frictional resistance to motion depends not only upon the coefficient of friction and the magnitude of the loading on the joint but also on the pressure distribution within the joint resulting from that loading. Thus the basis of this thesis has been the development of a mathematical model of the effects of friction in a spherical joint which could then be incorporated into a mechanisms simulation program. The model developed has shown that the main factors determining the magnitudes and directions of the frictional effects produced in a spherical joint, apart from the coefficient of friction and the magnitude of the loading, are the extent of the contact area between the ball and the socket and the magnitude of the angle between the axis of rotation of the joint and the direction of the applied load. Experimental results were obtained using apparatus that enabled the frictional moment produced on the socket of a joint to be measured while allowing the angle between the axis of rotation of the ball and the direction of the applied load to be varied between measurements. These results, obtained for a range of values of the coefficient of friction, confirm that this angle is a significant factor in the model and that the model usefully determines the frictional effects produced in a spherical joint.

This thesis is the first stage of a project to investigate the parameters effecting the performance of tube mills. The main topics that the project will cover are the motion of mill charge and the wear characteristics of the balls and the mill liners. A literature survey highlighted that no examination had been performed that investigated the motion of a particle with specific emphasis on the response to changes in the coefficient of friction between the particle and the liner. This thesis concentrates on the motion of a single particle moving on the inside of a smooth rotating cylinder. Three formulations are presented that model the motion of the particle. The first model assumes that the particle slides along the cylinder. To ensure that it slides, and does not roll, a block shaped particle is modelled. The second motion type assumes that a spherical shaped particle rolls along the cylinder. The assumption that is made, is that the point of contact between the ball and the cylinder does not slip or skid. This mode of rolling has been defined as Pure Rolling. A third model is proposed that is a combination of the sliding and rolling models. The formulation attempts to incorporate both actions, rolling and sliding. In this way the motion of the particle.is dependent on both the rolling and sliding interactions. The governing equations for the Sliding and Rolling models are solved numerically, using an Euler Forward Approximation. Both models are solved by a computer implementation of the resulting numerical equations. The Sliding program has been extended to animate the response of the block on the inside of the cylinder. The theoretical predictions from the two numerical solutions are presented and discussed.

Ball-and-plate balancing platforms have been utilized throughout academia to further understanding of nonlinearities that can occur when applying control algorithms to nonholonomic and underactuated systems. The objective of this thesis is to build upon an existing ball-and-plate balancing platform used in the Intro to Mechatronics class and create a robust platform system that can be utilized by future students to test various controller designs derived from MATLAB/Simulink®. The ball-and-plate platform design uses a myriad of sensors to track the system components in real time: a resistive touch panel is used to track the position of the ball on the plate, an inertial measurement unit is used to track the orientation of the top plate, and capacitive incremental encoders attached to the brushless-DC gimbal motors are used to both track the orientation of the motor actuation arms and commutate the motors. The gimbal motors are driven using the open-source ODrive motor driver, which receives torque commands from a separate STM32 microcontroller. The STM32 microcontroller aggregates and processes the data from the touch panel and IMU, and it acts as a “middle-man” for communication between the ODrive and MATLAB/Simulink® model running on a host PC. The platform successfully handles communications between the host PC, STM32, and ODrive at a rate of 200 Hz. The platform also incorporates a serial user interface that allows for fine position control of the motor arms for zeroing the top plate before each test.

<p dir="ltr">This thesis presents an investigation into the mechanism of friction generation and lubrication of cages used in modern Deep Groove Ball Bearings (DGBBs). Although cages provide a necessary function, e.g., ensuring proper spacing between rolling elements during assembly and operation, they also serve as an undesirable source of friction to the overall assembly. Cage friction originates primarily from two sources: i) localized cage pocket friction between the balls and the rollers and ii) churning losses from excess lubricant inside the bearing cavity. Localized cage pocket frictional losses were characterized through the development of a novel Bearing Cage Friction Test Rig (BCFTR). This rig was designed and developed to replicate the orientation and relative motion of a fully assembled bearing in steady state operation while measuring cage friction. The BCFTR uses a six-axis load cell to record forces and torques generated due to a rotating ball inside of a rigidly fastened cage segment. The test rig can be set up in two different configurations: i) a load control configuration where a friction coefficient is calculated due to a constant force applied between the ball and the cage segment and ii) a position control configuration where frictional torque is measured for specific positions of the ball relative to the cage. </p><p dir="ltr">In order to gain a deeper understanding of the relationship between cage position, lubrication, and friction, an acrylic cage segment with an exact cage pocket geometry was developed and tested on the BCFTR over a broad range of operating conditions. The clear acrylic cage allowed for the visualization of lubricant flow inside the cage pocket. Videos of oil flow revealed that the quantity of oil inside the pocket correlates closely with the measured frictional torque. Oil volume information from the videos was then used as an input to a cage pocket lubrication model. The model uses the finite difference method to solve the Reynolds and film thickness equations over a spherically defined cage pocket domain. The model was developed primarily to estimate cage pocket friction and corroborate with the results from the BCFTR; however, the model was also used to investigate the pressure distribution and lubricant shear stress in a variety of cage pocket shapes. The finite difference model uses oil volume fraction data to estimate frictional torque and corroborate experimental friction measurements. The results obtained from the model and experiments are in good agreement, proving that the key information required to estimate cage friction is the quantity of oil inside of the cage pocket.</p><p dir="ltr">The main contribution of overall cage friction in DGBBs can be attributed to local drag from inside the cage pocket; however, there remains an appreciable amount of friction and drag losses due to the interaction of the outside of the cage with oil in the bearing cavity. Because DGBB cages reside in the space between the rolling elements and have a significant effect on the churning behavior of the oil, it is paramount to understand how the size and shape of these cages affect the lubricant flow. To achieve this objective, a series of Computational Fluid Dynamics (CFD) models were developed. A full-scale simulation of the inner cavity of a DGBB was developed to observe fluid flow as a function of bearing geometry, operating conditions, and cage shape. Considerable effort was taken to perform optimization studies of the solution method. In addition, an efficient CFD model covering only three rolling elements was also used to investigate fluid flow in a bearing. This model utilized symmetry, periodic boundary conditions, and rotating reference frames to produce equivalent results to the full bearing simulation with a great reduction in computational effort. Results from the model were analyzed both qualitatively and quantitatively through the generation of contour maps of pressure and wall shear stress and the calculation of force and drag coefficient values for each cage.</p><p dir="ltr">The final development presented in this thesis is a high-fidelity Dynamic Bearing Model (DBM) capable of resolving local pocket and external cage lubrication effects of bearings in operation. In this dynamic simulation, the motion of the cage was determined using the finite difference method to solve for the pressure generation and resultant forces inside of each cage pocket at each time step. The computational domain of the finite difference model was designed to reflect the specific cage pocket geometry of four common cage designs. Additional testing on the bearing cage friction test rig was performed to characterize the lubrication state inside of each cage. An inverse distance weighting scheme was utilized to predict starvation parameters for a general ball position inside of the cage pocket. Additionally, the fluid drag losses associated with cage lubrication outside of the cage pocket were included in select dynamic simulations in the form of a drag torque applied to the cage. Results from the dynamic simulation reveal new knowledge on the effect of cage geometry and lubrication on dynamic behavior. Compared to simulations without cage lubrication, results from the new DBM demonstrate a reduction in median ball-cage contact force and improved stability in the trajectory of the center of mass of the cage.</p>