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.

This Master‘s thesis deals with the construction design of the ball screw shaft supports. Designed supports will serve to increase stability of rotating ball screws. In the introduction detailed description of the ball screws is presented including description of the individual parameters of the ball screw. Next part includes parameters of different ball screw properties and design of individual supports with description and design calculations of individual parts of the supports. Concepts of the supports will be designed in compliance with the ball screw product series of the KSK Precise Motion a.s. company.

The linear actuator is widely used in the industrial and aerospace arenas. The application of the linear actuator varies. The ball screw type linear actuator or ball screw system is one design. The ball screw is a mechanical system that converts rotation motion into a linear motion. The ball screw linear actuator, compared with other linear actuators, has better efficiency, higher speed, less noise, and higher load capacity. Ball screw linear actuators are used in a number of areas, such as coordinated measuring machines, 3D printers, and aerospace actuators. In this research, the industrial sponsor provided a ball screw linear actuator, and they required its accuracy to be improved. The linear actuator suffers from an accuracy problem due to various reasons. One of the major problems is nonlinear friction, which makes it difficult to estimate using the simple friction model. In this thesis, a LuGre friction model is introduced and applied to the ball screw system. The sponsor’s ball screw system includes the ball screw sliding table, AC servo drive, AC servo motor, and a linear encoder sensor. The hardware control system for the ball screw system needs to be built. Therefore, this thesis describes how a custom ball screw control system was built. The control hardware ball screw system includes a microcontroller and a custom-made digital-to-analog converter. The linear encoder position sensor’s reading methods were tested and implemented in the microcontroller. A custom digital-to-analog converter was made and tested. The control algorithms based on the LuGre friction compensator are discussed and were simulated in the Matlab Simulink environment. Then, the physical implementation of the control algorithms on ball screw system hardware were made. Finally, a new proposed control method based on the LuGre friction model performed best in terms of accuracy consistence and tracking compare to the other mentioned controllers. / Thesis / Master of Applied Science (MASc)

The aim of this thesis is ball screw service life measurement. Text is divided on two major parts, theoretical one and practical one. Theoretical part describes three basic methods of ball screws manufacturing – rolling, whirling and grinding. Subsequently, methods of heat treatment (inductive and laser hardening) are mentioned. Practical part is devoted to ball screw service life testing and evaluation of results. Tests were carried out on two sets of two ball screws. First set was manufactured by whirling and grinding followed by inductive hardening. Second set was manufactured by grinding followed by inductive hardening in one case and laser hardening in the second one. Test results were evaluated according to international standards.

This thesis deals with construction of rotary-nut ball screw. In the first chapter technical research at the current state of linear positioning systems and matters associated with them is listed. The next chapter treats of basic concepts and designs referring to ball screws. Further on the boundary between rotary ball screw and rotary- nut ball screw is described. On basis of restrictions and selected criterions solution of one size of rotary – nut ball screw with all the calculations.

Diploma thesis deals with a topic of lubrication and cooling of the ball screw rotary nuts. The first part is focused on a research behind the theory of ball screws and ball screw rotary-nuts. The three types of construction were developed in the second half of the thesis. Each construction is designed as an external attachable cooling and lubrication unit, which can be installed on an existing, slightly modified ball screw rotary-nut. For cooling and lubrication, only one type of medium is used and that is a cooled oil. External unit provides medium flow to ball screws working space. On top of diploma thesis tasks a design concept of ball screw rotary-nut with an integrated cooling and lubrication is introduced itself. Both described designs could become interesting for an industrial market.

Master´s thesis is directed for long ball screws of nut. It is here wrote their principle, essential type, parameters and current status of single used components. For this thesis is created at program Microsoft Excel methodical calculating of required parameters ball screws of nut. Another they are investigated status of affect length shaft ball screws, as mode storage, type actuator and possible damping. In last part is solved the design of supports long shaft ball screws and is here proposed conceptual process used supports.

Industrial demands for higher productivity rates and more stringent part tolerances require faster production machines that can produce, assemble, or manipulate parts at higher speeds and with better accuracy than ever before. In a majority of production machines, such as machine tools, ball screw drives are used as the primary motion delivery mechanism due to their reasonably high accuracy, high mechanical stiffness, and low cost. This brings the motivation for the research in this thesis, which has been to develop new control techniques that can achieve high bandwidths near the structural frequencies of ball screw drives, and also compensate for various imperfections in their motion delivery, so that better tool positioning accuracy can be achieved at high speeds. A precision ball screw drive has been designed and built for this study. Detailed dynamic modeling and identification has been performed, considering rigid body dynamics, nonlinear friction, torque ripples, axial and torsional vibrations, lead errors, and elastic deformations. Adaptive Sliding Mode Controller (ASMC) is designed based on the rigid body dynamics and notch filters are used to attenuate the effect of structural resonances. Feedforward friction compensation is also added to improve the tracking accuracy at velocity reversals. A bandwidth of 223 Hz was achieved while controlling the rotational motion of the ball screw, leading to a servo error equivalent to 1.6 um of translational motion. The motor and mechanical torque ripples were also modeled and compensated in the control law. This improved the motion smoothness and accuracy, especially at low speeds and low control bandwidths. The performance improvement was also noticeable when higher speeds and control bandwidths were used. By adding on the torque ripple compensation, the rotational tracking accuracy was improved to 0.95 um while executing feed motions with 1 m/sec velocity and 1 g acceleration. As one of the main contributions in this thesis, the dynamics of the 1st axial mode (at 132 Hz) were actively compensated using ASMC, which resulted in a command tracking bandwidth of 208 Hz. The mode compensating ASMC (MC-ASMC) was also shown to improve the dynamic stiffness of the drive system, around the axial resonance, by injecting additional damping at this mode. After compensating for the lead errors as well, a translational tracking accuracy of 2.6 um was realized while executing 1 m/sec feed motions with 0.5 g acceleration transients. In terms of bandwidth, speed, and accuracy, these results surpass the performance of most ball screw driven machine tools by 4-5 times. As the second main contribution in this thesis, the elastic deformations (ED) of the ball screw drive were modeled and compensated using a robust strategy. The robustness originates from using the real-time feedback control signal to monitor the effect of any potential perturbations on the load side, such as mass variations or cutting forces, which can lead to additional elastic deformations. In experimental results, it is shown that this compensation scheme can accurately estimate and correct for the elastic deformation, even when there is 130% variation in the translating table mass. The ED compensation strategy has resulted in 4.1 um of translational accuracy while executing at 1 m/sec feed motion with 0.5 g acceleration transients, without using a linear encoder. This result is especially significant for low-cost CNC (Computer Numerically Controlled) machine tools that have only rotary encoders on their motors. Such machines can benefit from the significant accuracy improvement provided by this compensation scheme, without the need for an additional linear encoder.

Industrial demands for higher productivity rates and more stringent part tolerances require faster production machines that can produce, assemble, or manipulate parts at higher speeds and with better accuracy than ever before. In a majority of production machines, such as machine tools, ball screw drives are used as the primary motion delivery mechanism due to their reasonably high accuracy, high mechanical stiffness, and low cost. This brings the motivation for the research in this thesis, which has been to develop new control techniques that can achieve high bandwidths near the structural frequencies of ball screw drives, and also compensate for various imperfections in their motion delivery, so that better tool positioning accuracy can be achieved at high speeds. A precision ball screw drive has been designed and built for this study. Detailed dynamic modeling and identification has been performed, considering rigid body dynamics, nonlinear friction, torque ripples, axial and torsional vibrations, lead errors, and elastic deformations. Adaptive Sliding Mode Controller (ASMC) is designed based on the rigid body dynamics and notch filters are used to attenuate the effect of structural resonances. Feedforward friction compensation is also added to improve the tracking accuracy at velocity reversals. A bandwidth of 223 Hz was achieved while controlling the rotational motion of the ball screw, leading to a servo error equivalent to 1.6 um of translational motion. The motor and mechanical torque ripples were also modeled and compensated in the control law. This improved the motion smoothness and accuracy, especially at low speeds and low control bandwidths. The performance improvement was also noticeable when higher speeds and control bandwidths were used. By adding on the torque ripple compensation, the rotational tracking accuracy was improved to 0.95 um while executing feed motions with 1 m/sec velocity and 1 g acceleration. As one of the main contributions in this thesis, the dynamics of the 1st axial mode (at 132 Hz) were actively compensated using ASMC, which resulted in a command tracking bandwidth of 208 Hz. The mode compensating ASMC (MC-ASMC) was also shown to improve the dynamic stiffness of the drive system, around the axial resonance, by injecting additional damping at this mode. After compensating for the lead errors as well, a translational tracking accuracy of 2.6 um was realized while executing 1 m/sec feed motions with 0.5 g acceleration transients. In terms of bandwidth, speed, and accuracy, these results surpass the performance of most ball screw driven machine tools by 4-5 times. As the second main contribution in this thesis, the elastic deformations (ED) of the ball screw drive were modeled and compensated using a robust strategy. The robustness originates from using the real-time feedback control signal to monitor the effect of any potential perturbations on the load side, such as mass variations or cutting forces, which can lead to additional elastic deformations. In experimental results, it is shown that this compensation scheme can accurately estimate and correct for the elastic deformation, even when there is 130% variation in the translating table mass. The ED compensation strategy has resulted in 4.1 um of translational accuracy while executing at 1 m/sec feed motion with 0.5 g acceleration transients, without using a linear encoder. This result is especially significant for low-cost CNC (Computer Numerically Controlled) machine tools that have only rotary encoders on their motors. Such machines can benefit from the significant accuracy improvement provided by this compensation scheme, without the need for an additional linear encoder.

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