Friction drive of an SAW Motor. Part I: measurements

The surface acoustic wave motor in this study utilized transparent lithium niobate for a stator. We then measured the normal and tangential displacements of the frictional surface of the slider via the transparent stator by means of 2 laser Doppler vibrometers. We thoroughly inspected the measurement conditions and indicated that the measured data were reliable and usable for subsequent precise analyses of the friction drive. The driving conditions for the measurements were a driving frequency of 9.61 MHz and a wave vibration amplitude of 20 nm. The start-up transients of the motor for a duration of 10.4 micros were measured. The measurements showed that the frictional surface of the slider displaced in both the normal and tangential directions followed each wave vibration. The displacements increased with the wave's vibration amplitude: they increased to 10 nm in both directions, in response to the transient increase of the wave's vibration amplitude to 20 nm, under the 15 N preload condition. Moreover, the slider surface rotated in the same direction as the wave surface and its trajectories were a tilted elliptical orbit. Since the surface of the wave rotated in an upright elliptical orbit, the result indicated that the tangential displacement of the slider surface was delayed in relation to that of the wave. The delay was in the range from 30 degrees to 60 degrees under the 15 N preload condition.     

Friction drive of an SAW motor. Part III: modeling

A 2-layer modeling method of friction drive of a surface acoustic wave motor is proposed. The surface layer accounts for the previously proposed point-contact friction drive model, which was generalized to correspond spatially to the underlying layer that is comprised of a 3-D elasticity field. A method to determine stiffness through the use of analytical solutions of 3-D contact problems bridges the 2 layers. Because the determined stiffness expresses the accuracy of the results regarding either layer, the validity of the results concerning the stiffness and the resulting stress field was evaluated by comparison with the results of finite element analysis. Furthermore, we executed numerical simulations by using the friction drive model, which were compared with the measured displacements of the frictional surface of the slider. The simulation accurately represented the normal displacement of the frictional surface; the modeling procedure in the normal direction was found to be reliable. However, because the friction coefficient drastically changes the tangential displacement, we could not discuss the reliability of the modeling procedure in the tangential direction. A thorough discussion of the friction drive would thus require further investigation of the friction phenomena.     

Friction drive of an SAW motor. Part IV: physics of contact

A procedure for modeling the frictional heating and electricity of a surface acoustic wave (SAW) motor is proposed. The frictional heat is developed during friction drive when sliding occurs at the frictional interface; the heat is conducted into the solids, resulting in an increase in temperature. The spatial distribution of the heat source was associated with the contact pressure distribution, and the heat conduction from the heat source was formulated. Owing to the piezoelectricity and pyroelectricity of the stator used in the present study, the elastic deformation and temperature increase produce the electric fields. The electric fields in the stator were determined with respect to each cause. Electric discontinuity at the boundary between the stator and the slider, moreover, produces electrostatic force, which was calculated using a Maxwell stress tensor. All the analyses revealed the underlying physical fields in addition to the mechanical fields of the SAW motor. By the use of those analytical methods, the frictional properties of the SAW motor were discussed. We pointed out that another physical phenomenoniquestcontact electrificationiquestcould arise at the contact interface. The electrostatic force due to contact electrification had sufficient strength to change the friction property, which corresponded to the variation of the friction coefficient from 0.1 to 1.     

Elastic contact conditions to optimize friction drive of surface acoustic wave motor

The optimum pressing force, namely the preload, for a slider to obtain superior operation conditions in a surface acoustic wave motor have been examined. We used steel balls as sliders. The preload was controlled using a permanent magnet. The steel balls were 0.5, 1, and 2 mm diameter, with the differences in diameter making it possible to change contact conditions, such as the contact pressure, contact area, and deformation of the stator and the slider. The stator transducer was lithium niobate, 128 degrees rotated, y-cut x-propagation substrate. The driving frequency of the Rayleigh wave was about 10 MHz. Hence, the particle vibration amplitude at the surface is as small as 10 nm. For superior friction drive conditions, a high contact pressure was required. For example, in the case of the 1 mm diameter steel ball at the sinusoidal driving voltage of 180 V(peak), the slider speed was 43 cm/sec, the thrust output force was 1 mN, and the acceleration was 23 times as large as the gravitational acceleration at a contact pressure of 390 MPa. From the Hertz theory of contact stress, the contact area radius was only 3 mum. The estimation of the friction drive performance was carried out from the transient traveling distance of the slider in a 3 msec burst drive. As a result, the deformation of the stator and the slider by the preload should be half of the vibration amplitude. This condition was independent of the ball diameter and the vibration amplitude. The output thrust per square millimeter was 50 N, and the maximum speed was 0.7 m/sec. From these results, we conclude that it is possible for the surface acoustic wave motor to have a large output force, high speed, quick response, long traveling distance, and a thin micro linear actuator.     

Simulation of surface acoustic wave motor with spherical slider

The operation of a surface acoustic wave (SAW) motor using spherical-shaped sliders was demonstrated by Kurosawa et al. (1994). It was necessary to modify the previous simulation models for usual ultrasonic motors because of this slider shape and the high frequency vibration. A conventional ultrasonic motor has a flat contact surface slider and a hundredth driving frequency; so, the tangential motion caused by the elasticity of the slider and stator with regard to the spherical slider of the SAW motor requires further investigation. In this paper, a dynamic simulation model for the SAW motor is proposed. From the simulation result, the mechanism of the SAW motor was clarified (i.e., levitation and contact conditions were repeated during the operation). The transient response of the motor speed was simulated. The relationships between frictional factor and time constant and vibration velocity of the stator and the slider speed were understood. The detailed research regarding the elastic deformation caused by preload would be helpful to construct an exact simulation model for the next work.     

Estimation of the squeeze film effect in a surface acoustic wave motor

This paper describes the air film characteristic in the interface between the slider and stator substrate of a surface acoustic wave (SAW) motor, and the difference of the squeeze film effect by the form of the slider. Because the vibration amplitude of the SAW motor is several 10 nm order, analysis of pressure was performed by using the molecular gas-film lubrication (MGL) equation. In the analysis, the MGL equation was split into advection phase and nonadvection phase, and calculation of advection and nonadvection phases was performed by using the cubic interpolated propagation (CIP) method and the finite difference method, respectively. From analysis results it was found that the time to steady pressure of air film depends on the radius of projection arranged on the contact surface of the slider. Also found was that the steady pressure in the interface does not depend on the radius and height of the projection, but it depends on the minimum spacing between the slider and the stator substrate.     

Friction drive of an SAW motor. Part V: design criteria

Design criteria for the stable and durable operation of a surface acoustic wave (SAW) motor are discussed. The low electric conductivity and pyroelectricity of the lithium niobate (LN) stator used in the motor hindered the motor's stability. We demonstrated that the use of LN whose conductivity had been enhanced by chemical reduction counteracted the instability caused by contact electrification and meniscus adhesion. The severe failure of the stator surface limits the durability of the SAW motor. Owing to the chemical inertness of LN, the surface failure of the stator was caused by mechanical stresses resulting from the indentation and sliding of the projections placed at the slider surface. The as-fabricated sharp edges of the projections are the obvious cause of failure. Thus, if the projections are necessary, a procedure in which the edges are worn off before operation is the only feasible method to correct this problem. Nevertheless, the optimum geometry to prevent surface failure was deduced as flat plane. The flat plane geometry was useful if the contact pressure is sufficiently large to diminish the effect of the layer of squeezed air between the surfaces.     

The validity and reliability of a portable slip meter for determining floor slipperiness during simulated heel strike

A previously developed test rig was used as starting point for designing a portable slip meter with two new features. First, an inflatable pneumatic test wheel, consisting of six slider units, was introduced as the impacting contact element relative to floor surface. Second, an inductive trigger was built into the system to facilitate a precise timing of the slider-floor contact during the test. This new test rig was designed to measure transitional friction properties of contaminated floor surfaces during simulated heel strike, which is considered the most critical phase of gait from the slip and fall point of view. Another objective was to quantify the validity and reliability of this test method in the laboratory, but not yet in the field. The measurement process was evaluated on eight wet and oily floor surfaces (vinyl and ceramic tile floorings) using two slider materials (plain, profiled), two normal loads (100, 200 N), and two sliding velocities (0.15, 0.30 m/s) as independent variables. The outputs of the portable slip meter, in terms of transitional friction coefficients, were compared to force platform-based friction values and to slip resistance values obtained with a slip simulator apparatus for laboratory testing of shoes and floor surfaces. The outputs were also evaluated against slipperiness ratings made by three male subjects in paired comparison trials, in which the subjects walked over eight wet floor surfaces wearing shoes with the plain soling material. The results showed that test option 200 N and 0.15m/s led to optimum validity despite its tendency to promote frictional vibrations (stick-slip) in the contact surface. Compared to the lower sliding speed, the higher speed reduced both stick-slip and measurement bias. Test option 200 N and 0.30 m/s was the most reliable one in this experiment. It yielded lower friction coefficients than any other test option and reduced the likelihood of underestimating slip and fall hazards. The results implied that the minimum friction coefficient was 0.25 for preventing a fall on wet floor surfaces, whereas the limit for preventing a slip was in the range 0.30-0.35. Transitional friction measurement was found to be a valid and reliable indicator for slip resistance. A more accurate control of the normal force during testing is needed for actual field use of the test method.     

Nanometer stepping drives of surface acoustic wave motor

High resolution (from nanometer to subnanometer) stepping drives of a surface acoustic wave motor are presented. It was shown that step displacement was easily controlled by adjusting a number of driving waves, using a steel ball slider equipped with permanent magnet for preload. By means of this open loop control, the step displacement was controlled from centimeter-order to submicrometer-order. In this paper, using a silicon slider equipped with a ball bearing linear guide, the stepping motions of a surface acoustic wave motor were investigated. A laser interferometer equipped with a 2-picometer resolution displacement demodulator was introduced. Motions of the slider ranging from several hundreds of nanometers to several nanometers in each step displacement were observed. Reduction of the driving waves down to 25 cycles, under a 100 V/sub peak/ driving voltage and a 30 N preload condition, generated about 2 nm stepping motion using our experimental setup under an open loop condition. We also demonstrated subnanometer step movements. These experimental results indicated that the surface acoustic wave motor has an ability of subnanometer positioning with a centimeter-level stroke.     

A standing wave-type noncontact linear ultrasonic motor

In this study, a novel standing wave-type noncontact linear ultrasonic motor is proposed and analyzed. This linear ultrasonic motor uses a properly controlled ultrasonic standing wave to levitate and drive a slider. A prototype of the motor was constructed by using a wedge-shaped aluminum stator, which was placed horizontally and driven by a multilayer PZT vibrator. The levitation and motion of the slider were observed. Assuming that the driving force was generated by the turbulent acoustic streaming in the boundary air layer next to the bottom surface of the slider, a theoretical model was developed. The calculated characteristics of this motor were found to agree quite well with the experimental results. Based on the experimental and theoretical results, guidelines for increasing the displacement and speed of the slider were obtained. It was found that increasing the stator vibration displacement, or decreasing the gradient of the stator vibration velocity and the weight per unit area of the slider, led to an increase of the slider displacement. It was also found that increasing the amplitude and gradient of the stator vibration velocity, or decreasing the weight per unit area of the slider and the driving frequency, gave rise to an increase of the slider speed. There exists an optimum roughness of the bottom surface of the slider at which the slider speed has a maximum     

Friction and frictional tracks on thick silica films prepared by vacuum deposition

Friction and frictional tracks on 2 µm thick SiO₂ films evaporated on polymethylmethacrylate (PMMA) substrate were investigated. Diamond spherical sliders of radius 30 and 100 µm, respectively, were slid on these coatings under a load of 50 to 200g at a sliding speed of 15 cm min^–1. The static and dynamic friction coefficients for SiO₂ films were found to be 0.1 and 0.06, respectively, depending on the load and radius of the slider. For lower load and small slider radius the tracks on SiO₂ film were groove-like, and whisker-like cracks regularly grew from the edges of the tracks. For higher loads and larger slider radius, semicircular cracks in the film were regularly found behind the slider, but in thicker film (6 µm thick), circular cracks occurred. The origin of these cracks is discussed in terms of a tension zone produced around the contact area between the slider and the substrate under frictional force.     

Adhesion and friction properties of micro/nano-engineered superhydrophobic/hydrophobic surfaces

Hydrophobic micro/nano-engineered surfaces (MNESs) with good adhesion and frictional performances were fabricated by the combination of aluminum-induced crystallization (AIC) of amorphous silicon (a-Si) and octadecyltrichlorosilane (OTS) coating. The AIC of a-Si technique was used to produce silicon micro/nano-textured surfaces, while an OTS self-assembled monolayer was used to lower the surface energies of the textured surfaces. The wetting properties of the MNESs were studied using a video-based contact angle measurement system. The adhesion and friction properties of the MNESs were investigated using a TriboIndenter. This study shows that the adhesion and frictional performances of all MNESs are significantly improved compared to untreated silicon substrate surfaces, and the adhesion and frictional performances of the OTS-modified textured surfaces strongly correlate to their surface wetting property, i.e., the larger the water contact angle, the better the adhesion and frictional performances of the OTS-modified textured surfaces.     

Dry Coupling Ultrasonic High Frequency (10–100 MHz) Sensors for Detection of Surface and Tribological Properties at a Submicrometric Scale

Acoustic plane sensors adequately pressed against materials are suitable to measure elastic constants from flight-time measurement, without any coupling fluid for high temperature, with longitudinal and transverse acoustic waves in the megacycle range. Soft delay lines are generally used to match the sample roughness and to make mechanical play correction easier. At the opposite, our sensors use a hard delay line with a mirror-polished end surface. An experimental set-up is presented to perform acoustic reflection measurement in various contact conditions by increasing the applied mechanical load. The frequency dependence of this parameter is also measured in the 10- to 100-MHz range. Reproducibility tests are presented to validate this experimental set-up, but the main results concern the surprising ability of this technique to detect surface property modifications limited to thickness less than 1 m. Indeed, surface modification induced by different solvents on glass substrates has been detected by this means. This technique has also been used to detect surface property modifications of lixiviated glasses. In this case, atomic force microscopy and inductively coupled plasma analyses have demonstrated that the earlier stage of the surface damage had been detected whereas the thickness altered by ionic diffusion was less than 100 nm with almost no roughness variation. Similarly, tests on mechanically scratched glasses have shown that samples with an average roughness, respectively, of 4 and 120 nm were easily identified from their reflection coefficient versus load curves. Moreover, the pressure dependence of the acoustic reflection is used to estimate the contact stiffness and the contact area between the sensor and the material as a function of the applied compressive stress for contact, adhesion, and friction investigations.     

超环面行星蜗杆传动摩擦理论研究

文章通过相对运动关系分析，给出了超环面行星蜗杆传动中共轭运动零件行星轮与定子、行星轮与蜗杆之间相对滑动率的计算方法，得出了凸峰接触时行星轮与定子及蜗杆之间摩擦系数的计算公式；以弹流润滑理论为基础，给出了液体润滑时行星轮与定子及蜗杆之间齿面摩擦系数的计算公式；进而给出了混合摩擦状态下行星轮与定子及蜗杆之间摩擦系数的计算公式。然后，运用上述公式讨论了液体润滑时行星轮与定子及蜗杆之间齿面摩擦系数的相对大小及其随传动参数的变化规律；给出了行星轮与定子全部为凸峰接触时摩擦系数随传动参数的变化规律；讨论了混合摩擦状态下，行星轮与定子之间摩擦系数随膜厚比的变化规律。     

摆线针轮传动接触热弹流润滑特性

针对摆线针轮行星传动啮合过程中啮合齿面摩擦行为影响系统动态特性、传动效率及接触疲劳特性等问题,基于牛顿流体及指数率、Ree-Eyring模型建立摆线针轮线接触时变热弹流润滑数值分析模型,获得理想安装的摆线针轮副完整啮合周期内摩擦力、摩擦系数及摩擦损失功率变动。结果表明,基于牛顿流体及指数率流体模型所得摩擦系数与工程实际不符;基于Ree-Eyring模型纯滚动啮合产生的热效应在重载下对啮合过程中膜厚、摩擦损失功率影响较大,对压力、摩擦系数影响较小。研究非牛顿流体特征参数与摆线针轮传动设计参数对啮合中摩擦系数、摩擦损失功率影响规律表明,流体特征应力增加摩擦系数及损失功率均减小;短幅系数取较大值时大部分啮合区间摩擦系数增加、摩擦损失功率减小。     

Reciprocating sliding friction and contact stress of some thermoplastics against steel

This study considers the sliding friction in reciprocating motion, plane on plane and dry contact between very smooth surface of a steel slider and three engineering thermoplastics: ultrahigh-molecular weight polyethylene, polyoxymethylene and PA 66. Dynamic coefficients of friction were accurately measured at ranges of apparent contact pressure varying between 25 and 800 kPa and sliding speed between 0.01 and 0.1 m s^-1, using plastic samples whose surface roughness was fully characterized. The frictional behaviours in reciprocating motion were found to be equivalent to those reported by previous workers who have tested similar materials in continuous motion. These results were used in the evaluation of non-Hertzian elastic contact stresses considering a simplified model of cylindrical tips of asperities of plastic materials making contact with a polished and hard semi-infinite plane. Fatigue failure analysis was conducted and the combination of the Marin equation and the Soderberg fatigue failure criterion used to evaluate the factor of safety. The results of this analysis were summarized graphically in the form of load–frequency capabilities that represent the onset of excessive fatigue wear for each plastic material. Scanning electron microscopy observations of worn plastic samples enabled the illustration of the mechanism of formation of wear particles in the case of the present tribological system. The results of the qualitative evaluation of the amount of wear showed the importance of the decrease in normal load in order to increase the factor of safety, despite the increase in the coefficient of friction so induced for most thermoplastics. This revised version was published online in November 2006 with corrections to the Cover Date.     

On the possibility of using acoustic spectra to study deformation processes in surface layers during friction

Elastic waves generated during friction are considered to be a source of information on the processes of deformation, fracture, and adhesive interactions in the friction contact zone. Results of computer simulations show that, in view of the dynamic nature of friction, the analysis of acoustic signals detected even in a steady-state regime requires applying frequency-temporal techniques in addition to the Fourier transform. It is concluded that the laws of frictional wear can be studied by analyzing the corresponding acoustic spectra.     

Porous slider bearing with couple stress fluid

Summary Theoretical study of porous slider bearing with couple stress fluid as lubricant is made and the lubrication qualities of couple stress fluid are examined. The lower surface is covered by a thin porous material and the upper one, having arbitrary shape, moves in its own plane with constant velocity. Analytical expressions for load capacity, frictional force and the centre of pressure are derived. It yields increase in, load capacity and ensures the decrease in coefficient of friction. The problem is also discussed in the context of various geometries viz, (1) Rayleigh step bearings and (2) inclined slider bearings. Bounds on flow rate, frictional coefficient, centre of pressure and time-height relation are obtained and compared with classical case, Gross [1]. Suitable design parameters are predicted for the efficient lubrication of slider bearings.     

Finger pad friction and its role in grip and touch

Many aspects of both grip function and tactile perception depend on complex frictional interactions occurring in the contact zone of the finger pad, which is the subject of the current review. While it is well established that friction plays a crucial role in grip function, its exact contribution for discriminatory touch involving the sliding of a finger pad is more elusive. For texture discrimination, it is clear that vibrotaction plays an important role in the discriminatory mechanisms. Among other factors, friction impacts the nature of the vibrations generated by the relative movement of the fingertip skin against a probed object. Friction also has a major influence on the perceived tactile pleasantness of a surface. The contact mechanics of a finger pad is governed by the fingerprint ridges and the sweat that is exuded from pores located on these ridges. Counterintuitively, the coefficient of friction can increase by an order of magnitude in a period of tens of seconds when in contact with an impermeably smooth surface, such as glass. In contrast, the value will decrease for a porous surface, such as paper. The increase in friction is attributed to an occlusion mechanism and can be described by first-order kinetics. Surprisingly, the sensitivity of the coefficient of friction to the normal load and sliding velocity is comparatively of second order, yet these dependencies provide the main basis of theoretical models which, to-date, largely ignore the time evolution of the frictional dynamics. One well-known effect on taction is the possibility of inducing stick–slip if the friction decreases with increasing sliding velocity. Moreover, the initial slip of a finger pad occurs by the propagation of an annulus of failure from the perimeter of the contact zone and this phenomenon could be important in tactile perception and grip function.     

Three‐dimensional finite element computations for frictional contact problems with non‐associated sliding rule

This paper presents an algorithm for solving anisotropic frictional contact problems where the sliding rule is non‐associated.The algorithm is based on a variational formulation of the complex interface model that combine the classical unilateral contact law and an anisotropic friction model with a non‐associated slip rule. Both the friction condition and the sliding potential are elliptical and have the same principal axes but with different semi‐axes ratio. The frictional contact law and its inverse are derived from a single non‐differentiable scalar‐valued function, called a bi‐potential. The convexity properties of the bi‐potential permit to associate stationary principles with initial/boundary value problems. With the present formulation, the time‐integration of the frictional contact law takes the form of a projection onto a convex set and only one predictor–corrector step addresses all cases (sticking, sliding, no‐contact). A solution algorithm is presented and tested on a simple example that shows the strong influence of the slip rule on the frictional behaviour. Copyright 2004 John Wiley & Sons, Ltd.