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 work treats dual-plane automatic ball balancing of elastically-mounted cylindrical rotors. The application is primarily to systems with a vertically-oriented single-bearing support, but extension is also made to horizontally-oriented single-bearing support as typically found in a vehicle wheel. The rotor elastic mounting includes three translational degrees of freedom for the body geometric center and three rotational degrees of freedom. Damping is included for each of these six degrees of freedom. The model for the automatic ball balancer consists of up to two arbitrarily-located hollow circumferential races, each of which contains up to two sliding particles. The friction model for the particles includes both viscous and Coulomb friction forces. Of considerable complexity is the logic path for the individual particles being either in motion or stationary relative to the rotor. The exact equations of motion for the overall system are derived via a Newtonian approach. Numerical-integration results show that the balancer performance depends strongly on the friction levels as well as the operating speed of the body. Simulations conducted with a pure static imbalance show that ideal automatic balancing is possible only for vertical-axis rotors that have zero Coulomb friction levels between the balancing particles and the races. Simulations with a horizontal-axis statically-imbalanced rotor show that an automatic balancer can improve performance for certain operating speeds and non-zero Coulomb friction levels in the presence of gravitational forces. Simulations conducted with a pure dynamic imbalance show that there is no inherent mechanism to counteract rotational displacements of the rotor about its geometric center. As a result, the balancing particles exhibit several phenomena described in previous works such as synchronous motion and oscillatory behaviors within their respective races. Simulations for an arbitrarily located imbalance show that rotor performance can be improved using dual-plane balancing techniques for certain operating speeds and Coulomb friction levels. Due to the inherent complexity in eliminating an arbitrarily located mass imbalance, the system is generally unable to reach a perfectly balanced configuration, but performance can be improved for carefully-selected initial conditions. / Ph. D.

Sensitivity analysis is one of the most prominent gradient based optimization techniques for mechanical systems. Model sensitivities are the derivatives of the generalized coordinates defining the motion of the system in time with respect to the system design parameters. These sensitivities can be calculated using finite differences, but the accuracy and computational inefficiency of this method limits its use. Hence, the methodologies of direct and adjoint sensitivity analysis have gained prominence. Recent research has presented computationally efficient methodologies for both direct and adjoint sensitivity analysis of complex multibody dynamic systems. Multibody formulations with joint friction were developed in the recent years and these systems have to be modeled by highly non-linear differential algebraic equations (DAEs) that are difficult to solve using numerical methods. The sensitivity analysis of such systems and the subsequent design optimization is a novel area of research that has been explored in this work. The contribution of this work is in the development of the analytical methods for computation of sensitivities for the most commonly used multibody formulations incorporated with joint friction. Two different friction models have been studied, capable of emulating behaviors of stiction (static friction), sliding friction and viscous drag. A case study has been conducted on a spatial slider-crank mechanism to illustrate the application of this methodology to real-world systems. The Brown and McPhee friction model has been implemented using an index-1 formulation for computation of the dynamics and sensitivities in this case study. The effect of friction on the dynamics and model sensitivities has been analyzed by comparing the sensitivities of slider velocity with respect to the design parameters of crank length, rod length, and the parameters defining the friction model. Due to the highly non-linear nature of friction, it can be concluded that the model dynamics are more sensitive during the transition phases, where the friction coefficient changes from static to dynamic and vice versa. / Master of Science / Mechanisms have been in existence since the earliest days of technology and are more relevant than ever in this age of robotics, artificial intelligence and space exploration. Innovations like myoelectric and neural prosthetics, legged robotics, robotic surgeries, advanced manufacturing, extra-terrestrial vehicles and so on are the modern day manifestations of the traditional mechanisms that formed the backbone of the industrial revolution. All of these innovations implement precision controlled multibody dynamic systems as part of their function. This thesis explores the modelling of such dynamic systems using different mathematical formulations. The contribution of this work is the incorporation of friction in the formulation of such systems. The performance of any dynamical system depends on certain parameters, which can be optimized to meet a certain objective criteria. This is achieved by performing a sensitivity analysis with respect to those parameters on the mathematical formulation of the mechanism. The derivation of this approach has been explored in this thesis. For the benefit of the reader, the application of this method has been discussed using a case study of a simple 3-dimensional slider crank mechanism.

A small shear sensor utilizing an array of carbon nanotubes to support a sensor head was developed for use in steady, high speed, 2D flow. The sensor is a non-intrusive, direct measurement device with a 2 x 2 mm square sensor head surrounded by a small gap on each side (~0.004 inches). The translation of the sensing element is due to the nanotubes bending when a shear force is applied to the sensor head. Displacements are measured by an interferometric technique using fiber-optics to measure the distance the sensor head travels by viewing a polished side of the head. The fiber-optical displacement sensor is bonded to a stationary substrate so that all measurements are relative to a fixed position. Arrays of carbon nanotubes were grown on bare 2 x 2 mm square silicon chips. The nanotubes were grown to heights of 75 microns with a thin layer of amorphous carbon on top. The silicon chips were then flipped, and the amorphous layer of carbon was bonded to bare 1 x 1 cm silicon substrates, making the bottom of 2 x 2 mm silicon chip the sensor head. The sensors were calibrated at Luna Innovations using a point-load technique. Four of the six sensors could not be successfully calibrated because they were fatally damaged during the last step of the calibration process. Wind tunnel tests were conducted on the one sensor that survived the calibration. An arrangement was designed and built from aluminum to test the performance of the sensor in the Virginia Tech Supersonic Wind Tunnel. Seven test runs were conducted in this cold-flow facility at a nominal Mach number of 2.4 and stagnation pressures ranging from 50 - 90 psia. Two test runs gave skin friction values 3 - 20% lower than those values predicted by indirect measurement techniques before the sensor was damaged. While these first results are encouraging, further studies are clearly needed. Due to distinct anomalies in the displacement data during test run 3, it was concluded that the sensor was damaged during this run. Possible explanations of the failure of this sensor are offered along with suggestions for future work. / Master of Science

A non-intrusive direct-measuring skin friction device with a rubber RTV sheet over the surface of the floating head, gap and housing was developed for application in 3D, unsteady, transonic flight conditions. Design conditions required optimum gage performance at altitudes ranging from 15,000 to 45,000 feet, Mach numbers ranging from 0.6 to 0.99 resulting in shear values of 0.3 to 1.5 psf. under vibration conditions up to 8.0 grms over a 15 - 2,000 Hz frequency range. The gage consisted of a rubber RTV sheet-coated floating element attached to an aluminum cantilevered beam. A dual-axis, full bridge strain gage configuration was used with the application of semi-conductor strain gages to increase instrument sensitivity. The gage was studied with and without a viscous liquid (glycerin) fill in the housing. Vibration verification testing was performed at 1.0 grms in the Virginia Tech modal analysis lab to ensure adequate damping performance over a 0−3200 Hz frequency range. Tests revealed that the rubber RTV compound sheet provided adequate viscoelastic damping, with or without viscous liquid fill. Gage performance verification testing was performed on in the Virginia Tech supersonic wind tunnel at shear levels of tw = 3.9 to 5.3 psf in a Mach 2.4 flow. Skin friction values in good agreement with previous testing and analytical predictions were obtained from the tests with adequate damping in the low vibration environment of the Virginia Tech supersonic wind tunnel. The gage proved robust as it survived repeated runs including the violent start and unstart processes typical of a supersonic, blowdown wind tunnel. Flight tests were performed at NASA Dryden Flight Research Center, with the gage mounted in a plate suspended below an F-15 aircraft. This provided a mildly 3D, turbulent boundary layer on a vibrating surface. The gage was tested without liquid fill in the gage cavity, and it performed satisfactorily in this high vibration environment. The gage demonstrated adequate damping and good robustness, surviving the complete flight test intact and remained fully operational. The sensor measured skin friction values 30%-50% higher than those predicted by indirect methods and analogies generally valid for 2D, steady flows. The gage indicated trends in skin friction values for different flight conditions in good agreement with the other methods. Possible reasons for the differences in numerical values are discussed in detail, including potential uncertainties in the gage output and limitations and uncertainties in the methods used for comparison. Finally, suggestions for further development of such gages are provided for flight test applications. / Master of Science

These studies developed from Scanning Electron Microscope (SEM) observations of abrasive wear of a polymer disk sliding against metal asperity models. The investigator was unable to observe actual particle formation but did identify elastic and plastic deformation of the polymer, and a debris buildup and extrusion process occurring at the leading edge of the asperity. On the assumption that this process could lead to a surface fatigue condition, pin-on-disk wear trials were completed using a spherical steel ball sliding on polycarbonate, rigid PVC, and ultra-high molecular weight polyethylene specimens in dry and lubricated conditions. A delay in debris formation was observed in the rigid PVC and polycarbonate dry sliding trials. In each case a higher rate of friction force increase coincided with debris formation. No debris was produced in the ultra-high molecular weight polyethylene dry sliding trials, and the friction force trace was flat. An SEM analysis of the polycarbonate and rigid PVC wear tracks revealed pitting consistent with the Delamination Theory of wear. The effect of the lubricants was to significantly alter the form of the friction force traces, but not to eliminate wear in rigid PVC and polycarbonate. The results of the investigation, particularly the delay in wear debris generation, indicated that a fatigue wear mechanism appeared to exist in dry metal pin-on-polymer disk sliding systems. A qualitative wear model was developed to relate the in-situ SEM observations and the results of the pin-on-disk trials. / M.S.

This paper will present an online approach for friction approximation to be utilized in con- cert with whole body control on humanoid robots. This approach allows humanoid robots with ankle mounted force-torque sensors to extrapolate information about the friction constraints at the hands during multi-contact poses without the addition of hardware to the platform. This is achieved by utilizing disturbance detection as a method of monitoring active forces at a single external point and deriving available friction force at said contact point in accordance with Coulomb's Law of Friction. First, the rigid body dynamics and required compliant humanoid model optimization are established which allow incorporation of friction constraints. These friction constraints are then informed by monitoring of external forces, which can be used as an indicator of slip based on tangential force. In practice, the robot with operational multi-contact whole body control is navigated to the desired contact surface and normal force only contact is initiated. Using an iterative coefficient estimation based on the achieved system forces, the robot tests the boundaries of its operable force range by inducing slip. Slip detection is utilized as the basis for coefficient estimation, which allows the robot to further understand its environment and apply appropriate forces to its contact points. This approach was implemented on a simple 3 link model to verify expected performance, and then on both the simulated model of Virginia Tech's ESCHER robot and in practice on the actual ESCHER platform. The proposed approach was able to achieve estimation of slip parameters, based largely on time spent measuring, actual friction coefficient, and the available contact force. Though the performance of the proposed approach is dependent on a number of variables, it was able to provide an operational parameter for the robot's whole body controller, allowing expansion of the support region without risking multi-contact slip. / Master of Science / This paper presents an approach for humanoid robots to use their hands to approximate the friction parameters of contact surfaces without prior knowledge of those parameters. This is accomplished as part of the robot’s control system and integrated into its balancing and movement operating system so that it may determine these parameters without ceasing operation. The proposed approach relies on the force sensors typically embedded in the ankles of bipedal robots as its sole force input, so no additional hardware need be added to the robot in order to employ this functionality. Once placed in contact, the robot is able to approximate the forces at its hand with these sensors, and use those approximate values as the basis for estimating the static friction coefficient of the system, in accordance with Coulomb’s Law of Friction. The robot’s onboard controller is able to utilize this information to ensure that it does not overestimate the available force that may be applied at the contact point, using prior knowledge of the robot model’s range of motion. In practice, the robot with this functionality is navigated to the desired contact surface and a hand contact that does not risk slip is initiated. Using an iterative coefficient estimation based on the achieved system forces, the robot tests the boundaries of its operable force range by inducing slip. Slip detection is utilized as the basis for coefficient estimation, which allows the robot to further understand its environment and apply appropriate forces to its contact points. This approach was implemented on a simple 3 link robot model to verify expected performance, and then on both the simulated model of Virginia Tech’s ESCHER robot and in practice on the actual ESCHER platform. The proposed approach was able to achieve estimation of slip parameters, based largely on time spent measuring, actual friction coefficient, and the available contact force. Though the performance of the proposed approach is dependent on a number of variables, it was able to provide an operational parameter for the robot’s whole body controller, allowing expansion of the support region without risking multi-contact slip.

Clay consolidation has generally been considered from a macro-scale perspective by measuring the macro-scale compression of a clay soil over time. Clay particles in consolidation tests experience shear and normal forces at the inter-particle level due to force applied to the soil at the macro-scale. These shear and normal forces cause the particles to slide at the micro-scale and produce macro-scale changes in soil volume and shape. By considering the inter-particle interactions at the micro-scale, the shear force - normal force - velocity relationship can be described by the Rate Process Theory (RPT). This research investigated the use of the RPT for analyzing sliding at individual clay particle contacts during secondary compression to describe macro-scale clay behavior. The novel micro-scale friction experiments conducted in this research demonstrated that an Atomic Force Microscope (AFM) can be used to obtain coefficient of friction (μ) measurements for montmorillonite. This method allows for the measurements to be performed over spatial scales of a few microns, can be done under dry conditions or a wide range of aqueous solutions, and requires no calibration beyond making a few microscopic measurements of the probe. Control tests of silica on mica (μ = 0.29 ± 0.02) agree with literature values where limits indicate one standard deviation.μ values for wet and dry sodium montmorillonite were determined to be 0.20 ± 0.03 and 0.72 ± 0.03, respectively. The micro-scale AFM and macro-scale triaxial shear, ring shear, and direct shear experimental data ofμ as a function of sliding velocity were found to match well with those calculated using common RPT parameter values. The activation energy for the macro-scale triaxial shear and corresponding micro-scale friction regime experiments fall within the expected range for pure montmorillonite of 84–109 kJ/mol. Additionally, the micro-scale and macro-scale experimental results fall within the expected range for the number of bonds per unit of normal force of 10^7–10^9 bonds/N. A discrete element method (DEM) model was developed to calculate thin, disk-shaped clay particle movement in three dimensions during compression using the RPT as a contact model. The DEM compression results were compared to macro-scale consolidation experiments conducted on the same reference clay as the micro-scale AFM experiments. The influences on the compression of the number of bonds at each clay contact per unit of normal contact force and the activation energy were quantified. Increasing the activation energy decreased the compression, as expected. Similarly, increasing the number of bonds per unit of normal force at the contacts decreased the compression, as expected. Realistic clay fabrics with varying particle sizes, particle size distributions, and aspect ratios led to a compression model with behavior similar to the macro-scale laboratory compression tests. This research provides evidence of the close correspondence between macro-scale and micro-scaleμ measurements and contributes to multi-disciplinary understanding of factors that control friction between clay particles and deformation of clay masses. The results from this work can be applied to a wide range of time-dependent phenomena such as clay secondary compression, shear deformation, and fault dynamics behavior. / Ph. D.

Yes / Results and analysis from investigations into the behaviour of the interfacial layer (Tribolayer) at the friction interface of a brake friction pair (resin bonded composite friction material and cast iron rotor) are presented in which the disc/pad interface temperature has been measured using thermocouple methods. Using a designed experiment approach, the interface temperature is shown to be affected by factors including the number of braking applications, the friction coefficient, sliding speed, braking load and friction material. The time-dependent nature of the Tribo-Iayer formation and the real contact area distribution are shown to be causes of variation in interface temperatures in friction braking. The work extends the scientific understanding of interface contact and temperature during friction braking.

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