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)

This thesis explores two aspects of modeling the behavior of joint friction in structures. The first aspect deals with the accurate and efficient simulation of a simple system that incorporates the LuGre friction law. Energy transfer and dissipation in a structural joint model is the second topic of this thesis. It is hypothesized that friction could serve to pump energy from one frequency to higher frequencies where it might be dissipated more quickly. Motivation for this study stems from the need to have accurate models of high-precision space structures. Because friction at connecting joints plays a major role in the damping capacity of the structure, a good understanding of this mechanism is necessary to predict the vibratory response and enhance the energy dissipation of the structure. Simulation results of a dynamic system with LuGre friction show that the system is relatively well-conditioned when the slip velocity is small, and ill-conditioned for large slip velocities. Furthermore, the most efficient numerical method to simulate this system is determined to be an implicit integration scheme. To study the energy transfer and dissipation, two models of a jointed structure with friction are considered. Results from the steady-state forced responses of the two structural systems indicate that friction converted low frequency, single harmonic excitation to multi-harmonic response through internal resonances. However, differences in energy dissipation results between the models show that the response of a frictional system is highly sensitive to system parameters and friction laws. Conclusions and suggestions for future research are also discussed.

<p>In sheet metal forming processes, friction has decisive effects on the strain distribution in the deformed sheets and the quality of the final product due to the large surface/thickness ratio of the blank sheets. It is well known that friction in sheet forming operations is dependent on local contact conditions such as surface roughness, contact pressure and sliding velocity. Adding complexity to this frictional behavior, some rolled sheets have oriented surface roughness and show considerable frictional anisotropy. A constant friction model without consideration of these relevant phenomena is regarded as the reason why sheet metal forming simulations often fail to produce satisfying results despite the well developed material models. </p> <p>To develop a friction model which considers both of the varying conditions of local contact and the frictional anisotropy was the aim of this thesis. For this purpose, the analysis method of the friction test (draw-bend test) had to be examined for the capability to evaluate these parameters independently. Through careful study using finite element simulations, it was found that the conventional method has shortcomings in addressing pressure dependent friction due to the pressure non-uniformity existing in the test. Therefore, a new analysis method, which can evaluate pressure dependency of a friction coefficient, was developed. In the new method, contact pressure maps obtained from simulations were included in the analysis of test data.</p> <p>The new analysis method was applied to friction measurement of aluminum sheets with known anisotropic mill finish, and friction coefficients were obtained as functions of contact pressure, sliding velocity and sliding direction. In the obtained friction model, a friction coefficient is a continuous surface over the domain of contact pressure and sliding velocity. Lastly, the new friction model was implemented into a finite element code and the model was validated through circular cup drawing experiments and simulations. The comparisons showed good agreements in the aspects of punch force, cup size and failure location. Thus, the newly developed model can accurately predict the effects of anisotropic friction in sheet metal forming processes. </p> / Thesis / Doctor of Philosophy (PhD)

Friction compensation is challenging but imperative for control engineers. For high-performance engineering systems, a friction-model-based controller is typically required to accommodate the nonlinearities arisen from the friction model employed. It is well known that the parameters of the friction model used in the friction compensation are nearly impossible to be accurately identified. Therefore, the objective of this research is to study the effect of these parametric uncertainties on the stability of a set-point position control system. With the above goal in mind, a variety of aspects are investigated in this work. Firstly, several common friction features and friction models are surveyed to provide background knowledge which helps select the friction model with the highest accuracy for our study. Secondly, an experimental setup is proposed and fabricated to validate the levels of accuracy given by the candidate friction models. The comparisons between the numerical and experimental results confirm that the LuGre friction model is the best approximation of the observed friction behaviours among all models selected. Moreover, a series of profound discussions addressing the relation between the candidate models’ structures and their numerical friction feature predictions are provided and followed by a summary table that recapitulates the properties of the candidate friction models. Last but not least, the state space models of the proposed setup formulated by the improved version of the LuGre model and the two controllers of interest, namely input-output linearization controller and nominal characteristic trajectory following (NCTF) controller, are derived for the stability analysis under the parametric uncertainties. Two parameters in the friction model used, σ_0 and σ_1, are perturbed for the stability analysis in which the results applying the concept of Lyapunov exponents (LEs) clearly illustrate the significant effect of the varying σ_0 and σ_1 values on the system stability. The effect of parametric uncertainties can depend quite significantly on the incorporated controller, and the stability results obtained here are applicable to the design and analysis of other systems that are inherently similar to our setup. The stability analysis conducted is this work is recommended for other control systems to avoid unwanted qualitative behaviours under parametric perturbations. / October 2016

Este trabalho dedica-se ao desenvolvimento de um modelo matemático de uma planta piloto de vazão tendo em conta as não linearidades mais significativas no sistema como perdas de carga nos instrumentos e o efeito de atrito nas válvulas de controle. Este efeito foi modelado com procedimentos que foram estudados previamente em outras pesquisas e que neste documento vão ser brevemente descritos. Para realizar a modelagem se usaram valores fornecidos pelos fabricantes dos instrumentos para o modelo ser o mais próximo da realidade. Foram realizados testes comparativos em estado transitório e estacionário para avaliar e validar o desempenho do modelo e propor futuras melhorias que podem ser realizadas no modelo e na planta. / This work will develop a mathematic model of a flow pilot plant taking into account the most significant non-linearities in the system as load loses in the instruments and the effect of friction in the control valves. This effect was modeled with procedures that were studied in other researches and they will be briefly described. The modeling work was done using the values supplied by the manufacturers for the model to be as close to reality. Comparative tests were performed, on transient and steady-state in order to evaluate and validate the performance of the model and propose future improvements that can be made in the model and the plant.

<p>All mechanical systems with moving parts are affected by friction, including industrial robots. Being able to design an accurate friction model would further increase the performance of todays robots. Friction is a complex dynamic phenomena that is constantly changing depending on the state and environment of the robot. It is therefore beneficial to update the parameters of the friction model online. An estimate of the friction will be made using the feedback control signal with the help of a feedforward control scheme in a two axis simulation setup. The friction estimate is then used for an offline identification of three friction model parameters in a static Lugre friction model. Improvements on the identification will be done by introducing some shut-off rules that will improve the estimate. The normalized least mean square method (NLMS) will then be used to update the parameters online. A simulation of friction compensation with a fixed friction model, and with an adaptive friction model will be studied. The method will also be simulated using experimental data taken from a real industrial robot.</p>

All mechanical systems with moving parts are affected by friction, including industrial robots. Being able to design an accurate friction model would further increase the performance of todays robots. Friction is a complex dynamic phenomena that is constantly changing depending on the state and environment of the robot. It is therefore beneficial to update the parameters of the friction model online. An estimate of the friction will be made using the feedback control signal with the help of a feedforward control scheme in a two axis simulation setup. The friction estimate is then used for an offline identification of three friction model parameters in a static Lugre friction model. Improvements on the identification will be done by introducing some shut-off rules that will improve the estimate. The normalized least mean square method (NLMS) will then be used to update the parameters online. A simulation of friction compensation with a fixed friction model, and with an adaptive friction model will be studied. The method will also be simulated using experimental data taken from a real industrial robot.

Sheet metal forming is one of the most common forming processes used in the industry, especially in the automotive industry. It becomes a common sense, that by increasing the accurate simulation of sheet metal forming, the industry can save dramatic cost in trial-and-error process when designing the sheet metal forming tools. In past decades, considerable studies have been done in the field of numerical analysis of metal forming processes, particularly in springback prediction. Significant progresses have been made, but the accuracy of simulation results still needs to improve. One reason is that, in the typical sheet metal forming analysis the tools are considered as absolute un-deformable rigid bodies. The deformation of the tools, which happens in the real production, is not taken into account. Another reason may be that the classic simulation considers the friction coefficient between the tools and blank as constant. However, the actual friction condition depends on a number of parameters. The objective of this thesis work is trying to investigate how it will affect the springback prediction results when either the tool deformation or more complex friction conditions are considered. The purpose is nothing related with the precise simulation about the true problem or how accuracy the simulation results show compared to the experiment results. The work is only to give an emphasis hint that how the FE-model and friction mode chosen affects the springback results when doing a numerical analysis. A simple model called flex rail is used for sheet metal forming simulations with three different friction models. A comparison between the results clearly shows a difference when advanced friction models are applied. A 3D elastic solid model is created to compare the result with rigid model. The results show the difference when deformation of the tools is taken into account. Finally, an actual case with tools from the industry is investigated. The tools are from SAAB Cars Body Components. This case is to investigate the possibility and necessity of applying the advanced friction model and elastic tools when a complex real industry problem is faced. Further study is needed to do with comparison experimental data to verify the accuracy when these models are used.

Friction is one of the important parameters in metal forming processes since it affects metal flow in the die, forming load, strain distribution, tool and die life, surface quality of the product etc. The range of coefficient of friction in different metal forming applications is not well known and the factors affecting variation are ambiguous. Commercially available FEA packages input the coefficient of friction as constant among the whole process which is not a realistic approach. In this study, utility of user-subroutines is integrated into MSC SuperForm v.2004 and MSC Marc v.2003 FEA packages, to apply a variable coefficient of friction depending on the contact interface conditions. Instead of using comparatively simple friction models such as Coulomb, Shear (constant) models, friction models proposed by Wanheim-Bay and Levanov were used to simulate some cold forging operations. The FEA results are compared with the experimental results available in literature for cylinder upsetting. Results show that, large variation on the coefficient of friction is possible depending on the friction model used, the part geometry and the ratio of contact normal pressure to equivalent yield stress. For the ratio of contact normal pressure to equivalent yield stress values above 4, coefficient of friction values are approximately same for both friction models.

Este trabalho dedica-se ao desenvolvimento de um modelo matemático de uma planta piloto de vazão tendo em conta as não linearidades mais significativas no sistema como perdas de carga nos instrumentos e o efeito de atrito nas válvulas de controle. Este efeito foi modelado com procedimentos que foram estudados previamente em outras pesquisas e que neste documento vão ser brevemente descritos. Para realizar a modelagem se usaram valores fornecidos pelos fabricantes dos instrumentos para o modelo ser o mais próximo da realidade. Foram realizados testes comparativos em estado transitório e estacionário para avaliar e validar o desempenho do modelo e propor futuras melhorias que podem ser realizadas no modelo e na planta. / This work will develop a mathematic model of a flow pilot plant taking into account the most significant non-linearities in the system as load loses in the instruments and the effect of friction in the control valves. This effect was modeled with procedures that were studied in other researches and they will be briefly described. The modeling work was done using the values supplied by the manufacturers for the model to be as close to reality. Comparative tests were performed, on transient and steady-state in order to evaluate and validate the performance of the model and propose future improvements that can be made in the model and the plant.