High-Speed Friction Measurements Using a Modified Surface Forces Apparatus

Tribol Lett (2011) 42:117–127 DOI 10.1007/s11249-011-9746-1 TRIBOLOGY METHODS High-Speed Friction Measurements Using a Modified Surface Forces Apparatus D. D. Lowrey • K. Tasaka • J. H. Kindt • X. Banquy • N. Belman • Y. Min • N. S. Pesika G. Mordukhovich • J. N. Israelachvili • Received: 16 June 2010 / Accepted: 3 January 2011 / Published online: 18 January 2011 Ó Springer Science+Business Media, LLC 2011 Abstract Methods of measuring friction forces in the surface forces apparatus (SFA) are presented for sliding velocities from \1 nm/s to [10 m/s. A feed-forward control (FFC) system for the piezoelectric bimorph slider attachment is introduced to allow experiments at velocities up to *4 mm/s. For still higher speeds, a motor-driven rotating mini-disk setup using a pin-on-disk geometry is presented, with modifications to enable sliding velocities in the ranges 1 cm/s–5 m/s and 1–25 m/s. Example data sets demonstrate the applicability of the approach to modeling important tribological systems including hard-disk drives. We find that mechanical system parameters such as the resonant frequencies and mutual alignments of different moving parts become increasingly important in determining the tribological response at sliding velocities above *1 cm/s (for SFA or bench top devices). Smooth or stick-slip sliding—common features of low-speed sliding—become replaced by large-amplitude oscillatory responses that depend on the load and especially the driving speed or rotational/reciprocating frequencies. Detailed recordings and modeling of these complex effects are necessary for fully understanding and controlling frictional behavior at high speeds. D. D. Lowrey Materials Department, University of California, Santa Barbara, CA 93106, USA Present Address: Y. Min Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA K. Tasaka  X. Banquy  N. Belman  Y. Min  N. S. Pesika Department of Chemical Engineering, University of California, Santa Barbara, CA 93106, USA Present Address: K. Tasaka Hitachi Global Storage Technologies Japan, Ltd., Fujisawa, Japan Present Address: J. H. Kindt Nano Surfaces Business, Bruker, Dynamostr. 19, 68165 Mannheim, Germany Keywords Friction test methods  Boundary lubrication test methods 1 The Surface Forces Apparatus for Friction Studies The surface forces apparatus (SFA) is a powerful tool in the investigation of friction behavior. The traditional Present Address: N. S. Pesika Department of Chemical and Biomolecular Engineering, Tulane University, New Orleans, LA 70118, USA G. Mordukhovich General Motors Research & Development, 30500 Mound Road, Warren, MI 48090-905, USA J. N. Israelachvili (&) Department of Chemical Engineering and Materials Department, University of California, Santa Barbara, CA 93106, USA e-mail: [email protected] J. H. Kindt Department of Physics, University of California, Santa Barbara, CA 93106, USA 123 118 crossed-cylinders (or equivalently, sphere on flat) geometry gives a macroscopic area of contact while the instrumentation and imaging is sensitive to micro- and nano-level events [1–3]. Previous friction experiments using the SFA have used the motor-driven ‘‘friction device’’ attachment alone or together with the piezoelectric ‘‘bimorph slider’’ as shown in Fig. 1 [4]. The normal load, L, is applied through the normal load spring, which supports the lower surface and is in turn supported at the end of the bimorph slider. The bimorph slider is a two-segment, piezoelectric, double cantilever which gives a lateral displacement linearly proportional to the applied voltage. Normal shear experiments use a triangular wave voltage signal to provide a constant sliding speed during each half-cycle; for a sufficient sliding distance the time of direction change is negligible. Typical shear speeds, V, range from 1 nm/s to *0.4 mm/s, and shear distances (sliding amplitudes) from 40 to 150 lm, both limits being determined by the length and electro-mechanical properties of the piezo element. To achieve longer shearing distances one can increase the active bimorph length, but this has the adverse effect of lowering the stiffness and resonance frequency of the slider. The practical limits to the maximum achievable speed and, simultaneously, sliding distance or amplitude without nonlinearities are about 400 lm/s and 100 lm, respectively, using a 3-cm long sectored bimorph. Tribol Lett (2011) 42:117–127 2 Feed-Forward Control for Attaining Higher Speeds with a Bimorph Slider 2.1 Compensating Nonlinearities The bimorph slider of the SFA2000 consists of two parallel, coupled piezoelectric bimorphs (Fig. 1). Mechanically, this assembly approximates a weakly damped harmonic oscillator. When the bimorph is driven with a sine wave at frequencies well below its resonance frequency, f0, its position is proportional to the voltage applied. However, when the drive frequency approaches the actuator’s mechanical resonance frequency, it starts to oscillate freely, like a tuning fork. To drive the bimorph in a predictable way close to or above its resonance frequency, one has to observe the relationship between the driving signal and the actuator’s response. Increasing drive frequency, the actuator’s amplitude response is nearly constant until the resonance frequency is approached. Here, the actuator’s amplitude response rises to a peak. Above the resonance frequency, the amplitude rapidly approaches zero. In addition, the phase relation between drive and response is important. Drive voltage and response are in phase at low frequencies. At the resonance frequency, the drive is 90° ahead of the mechanical response, and continues toward 180° thereafter. For a non-sinusoidal drive signal, e.g., a triangle signal that gives a constant speed in either direction during each cycle, the situation is more complicated. The non-harmonic signal can be broken down into its sinusoidal (Fourier) components, fn, by Fourier analysis. The Fourier components of a triangle wave are: Aðfn Þ ¼ ð1Þn1 Fig. 1 Schematic of the SFA2000 with the ‘‘extended bimorph slider attachment’’ [4, 29] with laser positioning sensor and feed-forward system 123 8 sin½2pð2n  1Þft p2 ð2n  1Þ2 for n  1: Figure 2 shows the bimorph slider motion (response output) for triangular input waveforms/signals at 1, 8, 25, and 33 Hz. The resonant frequency of the slider, f0, was approximately 31 Hz. Since a triangular function generated by a function generator is a combination of many sinusoidal Fourier components, the triangular input signal contains high frequency components, above f0, that are damped out in the motion of the bimorph slider. The non-linear, i.e., non-triangular, motions of the slider, already evident at f = 8 Hz, and which become sinusoidal by 25 and 33 Hz, are caused by the first (lowest frequency) Fourier component being close to f0. At low frequencies, of 1 Hz and below, the system resonances are not excited and the slider motion faithfully reproduces the linear input signal. If the amplitude and phase response of the actuator for a given drive frequency are known, one can generate a drive signal which compensates this shift in the response (output signal, Ao) to give some desired amplitude and phase Tribol Lett (2011) 42:117–127 Fig. 2 Bimorph slider displacements (output signals Ao—solid lines) at different driving frequencies, f (input signals Ai—dashed lines) for a system of natural frequency f0 = 31 Hz. a f = 1 Hz: perfect triangular output motion providing constant velocity motion; b 8 Hz: some higher harmonics are suppressed, lower harmonics are amplified; c 25 Hz: only the fundamental (lowest) frequency remains significant, phase lag starts to become evident; and d 33 Hz: sinusoidal motion now fully 90° out-of-phase with the driving signal different from the drive (input, Ai) signal: the compensated drive signal’s amplitude is divided by the actuator’s amplitude response at the drive frequency, and its phase is shifted backward by the actuator’s phase response at this frequency. If the desired output signal is a triangle wave, every significant Fourier component must be compensated in amplitude and in phase according to the scheme above, and 119 the resulting waves added back together. Signal compensation works as long as the actuator approximates a linear system, which means that different frequencies do not influence each other, and hence can be treated separately. If the actuator is driven with this compensated signal, its mechanical response will be proportional to the original drive signal, i.e., before compensation. This method of compensation is known as feed-forward control (FFC) [5]. A schematic of the FFC circuit introduced to the SFA is shown in Fig. 3. To monitor the position of the bimorph slider, a laser position sensor (Keyence laser displacement meter LC-2420) was attached just outside a quartz window on the far wall of the SFA2000 chamber as shown in Fig. 1. The right side of the bimorph slider has a small Si wafer that reflects the laser beam back into the sensor. The LC-2420 sensor has a measuring range of 400 lm and a resolution of 0.01 lm (10 nm). Accurate detection of displacements requires that the reflecting surface be clean, with a mirror finish. In our implementation, the compensated drive signal is calculated by a LabVIEW Ver. 6 program (National Instruments), and fed to the actuator with a multifunction analog, digital, and timing I/O card, DAQCard-6062E (National Instruments). The program first drives the bimorph slider with a signal that contains all the relevant Fourier components, A(fn), each with an amplitude multiplier of one and a phase, u, of zero. It then observes the slider’s response via the position sensor, and correlates drive and position to derive the slider’s response values (amplitude and phase). These are then stored and used in the later experiment to generate a compensated drive signal (Fig. 3). Figure 4 shows the slider position when the FFC is in use. The LabVIEW program processes the drive signal to produce a complicated pattern (dashed line) that preserves the linear motion of the slider at frequencies approaching f0 (cf. Fig. 2). As a general trend, a decrease in the resultant displacement amplitude is observed as the frequency increases. For this setup, the maximum FFC speed obtained while preserving linear (triangular) motion was *4.5 mm/ s at 20 Hz. This compensation scheme addressed the primary contributions to the bimorph dynamics of the piezoelectric stack and the slider itself; compensating for the secondary influences of the frictional contact could be done with the additional complexity of using real-time adjustments to the signal compensation. In general, FFC allows for an increase of about one decade in linear speed for a bimorph slider. 2.2 Application to a Model Hard Disk System Figures 5 and 6 show examples of shear experiment data obtained with the FFC system. In this experiment, both the 123 120 Tribol Lett (2011) 42:117–127 Fig. 3 Generating high frequency non-sinusoidal waves becomes problematic when the period (dominant driving frequency) f1 is near or above the resonant frequency f0 of a device. Non-sinusoidal waves can be decomposed into a Fourier series of multiples of the dominant frequency—odd multiples in the case of triangular waves: f2 = 3f1, f3 = 5f1, etc. Resonance amplifies frequencies near the natural frequency of the bimorph f0 while higher frequency components are dampened and phase-lagged, until the triangular motion becomes a 90° out-of-phase sinusoidal motion. Feed-forward control sends a signal Ai to the bimorph which amplifies the higher harmonics of the signal from the function generator Ao and shifts their phases such that the resulting motion of the bimorph (triangular in this study) corresponds to the original signal from the function generator upper and lower mica surfaces had three layers deposited on them: first, a 1.5 nm layer of amorphous silicon, then a 5 nm layer of hydrogenated amorphous carbon, and finally a monolayer of Perfluoro-Polyether lubricant (Z-Dol2000)—a commercially available lubricant used to coat hard disks. The high friction forces relative to the low load indicate that the lubricant was present as a monolayer [6] or that the lubricant did not effectively coat the carbon layer [7], in either case the surfaces remained undamaged for the data presented. This system does experience wear, detected optically by the gradually reduced thickness of the amorphous carbon layer, but this wear is distinct from the damage caused by delamination of the carbon layer which drastically reduces friction and disrupts the optical integrity of the surfaces. The first general trend we observe, which we find in all our high-speed friction studies, is the replacement of smooth or stick-slip sliding with large-amplitude sinusoidal oscillations that cross the F = 0 baseline (indicative of oscillatory overshoots, as in the case of an under-damped swinging pendulum—see Fig. 12) at times other than direction change in the bimorph. The period of the oscillations correlate with some of the resonant (natural) frequencies of the device, determined by purely mechanical components of the apparatus (see Fig. 11), rather than with the stiffness and tribological or thin film rheological properties of the surfaces and lubricant layers that determine stick-slip frequencies [8–12]. The asymmetry of the friction trace is due to minor, unavoidable imperfections in the alignment between the crossed cylinder surfaces and the relative alignments of the other mechanical elements— a general phenomenon that is magnified at high speeds and large sliding amplitudes. Comparison of Figs. 5 and 6 also shows the effects of relative humidity (RH) on the frictional behavior of the system—previously also observed with other boundary lubricant layers [13–15]. Increasing the RH reduces the friction coefficient by a factor of about 4; but the replacement of smooth sliding by high frequency (30–300 Hz) oscillatory components, associated with 123 Tribol Lett (2011) 42:117–127 121 3 High Speed Motor-Driven Device for Attaining Speeds of m/s 3.1 Use of Rotating Disk in SFA Fig. 4 Displacement profiles of the SFA2000 bimorph slider (natural frequency: f0 = 31 Hz) at different driving frequencies, f with feedforward control. The solid lines are the nearly perfect triangular waveforms of the slider displacement as measured by the positioning sensor; the dashed lines are the highly complex driving signals sent to the bimorph various resonant frequencies of the apparatus, is still evident at sliding speeds above *1 mm/s as in Fig. 5. As already noted, a limitation of the FFC is that the actuation amplitude decreases as the reciprocating sliding speed (i.e., frequency) increases. One effect of reduced sliding amplitude is that a greater fraction of the data consists of sticking during the directional changes, with comparatively little data in the actual sliding regime. Previous work has shown that fluid-lubricated tribological systems reach steady-state sliding conditions only after sliding for a certain distance rather than, or in addition to, the sliding time [16]. Thus, the extended piezoelectric bimorph method falls well short of modeling many technologically important situations requiring large amplitudes or continuous steady-state sliding at speeds of 1 m/s and greater. Achieving speeds of 1–10 m/s requires a completely different approach, an implementation of which is shown in Fig. 7. The bimorph slider and lower disk holder are replaced by a small, powerful motor attached to a disk in an effective pin-on-disk geometry in the SFA. Pin-on-disk tribometers are prevalent in friction research [17, 18] due to the wide range of possible sliding velocities as well as long-sliding distances (compared to, e.g., 4-ball geometry). A challenge with pin-on-disk geometry is that there is an inherent load imbalance due to the edge loading on one side. As seen in Fig. 8, we have added a roller bearing to help stabilize the device. The disk is mounted with spring clips that hold the disk to the motor while several positioning screws tilt the disk in two axes, enabling rotation that is flat to within *10 lm per revolution [4]. With appropriate feedback and a sufficiently flat disk, height rotation could be reduced much more—down to nm levels. Using SFA interferometry with the pin-on-disk geometry would require this more stringent alignment, along with preparation of a smooth spherical surface as described elsewhere [19–22]. In addition, an optically appropriate annulus on the flat disk would be required along the sliding path, which could be opaque and reflecting for reflected beam interferometry [23]. The motor mount consists of stiff springs of known stiffness, kL, fitted with strain gages to allow continuous monitoring of the load. The friction forces are measured with stain gages attached to a double cantilever spring as in previous devices (see Fig. 1). Two types of motors were used in this device. A DC motor (A2520, Maxon Precision Motors, Inc., MA) was found to be effective for intermediate loads and speeds, up to 5 m/s (high loads increase the friction force which increases the torque on the motor which slows down the rotational speed). The voltage input determines the torque on the motor, so under tribological conditions the speed is not directly determined by the voltage. The rotational speed was monitored by fitting the lower disk with a collar of spaced reflective mirrors (Fig. 8). As the disk rotates, light from below is reflected to a voltage-biased photodiode and the cycling frequency (Hz) determined from the current spikes. Figure 9 shows friction and load traces obtained with the DC motor setup. The system is a silica sphere on a sapphire disk lubricated with the model lubricant squalane (Fig. 9a) or the alkane n-hexadecane (Fig. 9b). Tests with either lubricant resulted in a complex oscillatory, i.e., 123 122 Tribol Lett (2011) 42:117–127 Fig. 5 Friction force traces (solid lines) generated using feed-forward control of the extended bimorph slider displacement (dashed lines) and boundary lubricated surfaces. The tribological system mimics the surfaces of a hard-disk drive, with a fluorinated lubricant on carbon- on-silicon coated mica. Experiments done at 0% relative humidity, loads L of 3 or 9 mN, and speeds V varying from *60 to 2,400 lm/s (drive frequencies, f, of 0.1–8 Hz) sinusoidal rather than stick-slip, frictional behavior that appears to be a characteristic feature of high-speed sliding (see Figs. 5, 6, and 10, and accompanying paper, in preparation). Wear did not have a significant influence on this material system. With squalane (Fig. 9a) both the load and friction force exhibit oscillations (or vibrations) with a periodicity equal to the rotation frequency of the sapphire disk. These vibrations are due to unavoidable imperfections in the mechanical system (misalignment or tilt in the disk axis, imperfectly flat disk surface, etc.). For this welllubricated system, changing the load L has only a small effect on the average friction force, hFi, but the amplitude of the oscillations, DF, increases with the load. With hexadecane (Fig. 9b) the friction force oscillates at more than one frequency, giving rise to beats. These friction traces are in marked contrast to those obtained with these lubricants at low speeds (below mm/s) which are characterized by smooth or stick-slip sliding (the differences between these two modes of sliding are discussed in Fig. 12). Still higher speeds and loads require a more powerful motor. We found that the best performance for our SFA was given by an electrically commuted (EC) motor (EC 20 flat 3 W, Maxon Precision Motors, Inc., MA) which uses a motor controller to pulse voltage at different phases, so the control point is a rotational speed rather than a torque. Since the motor controller provides a rotational frequency output, the reflective collar can be omitted if necessary. The EC motor used allowed for speeds ranging from approximately 5 to 25 m/s. The lowest speed is determined by where the motor stalls or becomes unstable; the highest by the torque of the motor being opposed by the friction forces in the motor and at the interface. Data using this setup is shown in Fig. 10 for a sapphire disk, lubricated by hexadecane, sliding against a porous, resin-bonded cellulosic surface (friction material used in automotive wet clutch systems). The cellulosic surface, machined to a spherical shape (radius of curvature = 5 cm), showed some initial compaction or wear but was stable during data collection (see accompanying paper, in preparation). Highspeed data sampling ([2,500 samples per second) was found to be necessary in these experiments in order to see all the details of the friction traces without distortion (e.g., due to aliasing). 123 Tribol Lett (2011) 42:117–127 123 Fig. 6 Results for the same system as Fig. 5 at 75% relative humidity In all cases, the oscillations in the load L have a frequency determined primarily by the rotating disk, but the friction force F can exhibit additional harmonics which depend sensitively on the rotational or sliding speed. Thus, at 227 Hz (v0 = 23 m/s) both the load and friction force have oscillations at the same frequency, both equal to the rotational frequency (Hz) of the disk. At 82 Hz (v0 = 8 m/ s), there is a high-amplitude friction ‘‘bump’’ at the highest point on the disk during a rotation, i.e., due to imperfect surface flatness. At 145 Hz (v0 = 15 m/s), a large amplitude, high-frequency component at *345 Hz now dominates the friction response giving rise to a complex overall response exhibiting multiple frequencies (which can lead to beats through interference). The load response is dominated by the first sub-harmonic of f (0.5f * 73 Hz), but independent measurements confirm that the rotational frequency is 145 Hz. The large amplitude, high-frequency component, or resonance response, of the measured friction is system-specific—determined by the resonant frequency f0 of the friction force-measuring spring, and is here ‘‘activated’’ over a narrow rotational frequency band when the fifth harmonic of the load oscillations (2.5f) coincides with f0 = 345 Hz. Other large-amplitude resonance responses occur at other harmonics of f (not shown). 3.2 Temperature Effects As shown in Figs. 7 and 8, a type K thermocouple (A1316-K, Nanmac Corporation, MA) was embedded in the upper surface and two IR temperature sensors (OS36SMK-140F, Omega Engineering, Inc., CT) were trained on the sliding path. The resulting data showed that the measured temperature tracked with the overall temperature of the system, and that at high loads and friction forces the temperature in the contact tended to increase toward a stable value of a few degrees above ambient. Miniature thermocouples inserted into the top friction material within 0.5 mm (500 lm) of the surfaces recorded similarly low temperature changes. As reported by Reddyhoff et al. [24], the flash temperature is too localized to detect via such macroscopic methods, so that we could not successfully measure the actual temperature increase at the shearing junction which, from computer simulations [9, 25, 26], can transiently exceed 900 °C. 123 124 Tribol Lett (2011) 42:117–127 Fig. 7 SFA2000 modified for high-speed friction experiments, featuring a high-speed motor, normal (load) and lateral (friction) force-measuring springs. The friction device is oriented for sensitive lateral force detection, as well as to provide room for IR temperature sensors before and after the contact (top left). A piezoelectric tube connects the upper surface to the SFA box, allowing for the possibility of minute load changes or active vibration input. Adapted from [30] 4 Discussion and Conclusions: Frictional Behavior at High Speed Our experiments using two different attachments to the SFA for measuring friction at ‘‘high speed’’ (here defined as above 1 cm/s) or high amplitude coupled to high-rotational/reciprocating frequencies (f [ 1 Hz) reveal new features of lubricated friction that are not evident or important at lower speeds. Traditional tribological descriptions of low-speed sliding focus on effects due to the nature of the shearing surfaces and the thin film rheological properties of the lubricating layer or fluid [27], i.e., the properties of the interface Fint in Fig. 11. At low speeds Fint and the stiffness of the friction-measuring spring, kF, 123 are sufficient to explain the measured friction force, F, and the nature of the sliding, whether smooth or intermittent (regular or irregular stick-slip), including transients such as stiction spikes. At high speeds, inertial effects of the whole system and the resonant frequencies, f0, of the different mechanically interconnected parts in Fig. 11 become increasingly important and now dominate the friction response, giving rise to large-amplitude sinusoidal oscillations (also commonly described as vibrations, shudder, and chatter) that replace, and are quite different from, stick-slip friction (Fig. 12). These resonance responses are activated when one of the harmonics of the rotational/ reciprocating frequency (Hz) coincides with one of the resonant frequencies of the system, f0, which could be the Tribol Lett (2011) 42:117–127 125 Fig. 8 Photograph of the highspeed friction setup detail, showing the roller bearing which reduces the tilt effect of the applied load, and a collar of 12 reflective mirrors for measuring the speed of rotation (Hz) of the disk Fig. 9 Chart recorder traces of the load L and friction force F versus time for lubricated silica against a sapphire disk (effective sampling rate *300 samples per second). a Squalane lubricant at 12.5 Hz corresponding to v0 = 1.2 m/s. hFi is the average friction force and DF is the peak-to-peak amplitude of the friction force oscillations [31, 32]. b Hexadecane lubricant at 8.5 Hz corresponding to v0 = 0.8 m/s [33] natural frequency of the ‘‘friction-force sensing mechanism’’ or the ‘‘loading mechanism’’ (Fig. 11). Figure 12 illustrates how, even if there is stick-slip at the interface, the signal transmitted to the friction forcemeasuring spring can be dominated by the sinusoidal friction profile. Thus, even for a constant applied load and constant driving speed, the load spring deflection will vary during sliding which then registers as a varying load (and, in turn, friction force), giving rise to a complex friction versus load behavior containing multiple frequencies. These effects arise from mechanical alignment and surface imperfections (topology) which are unavoidable, and become magnified at high speeds. In the case of rotating disks (pin-on-disk tribometers) or reciprocating mechanisms these effects are repeated each revolution of the disk or back-and-forth cycle of the slider, and can include regimes where high bumps can even cause the surfaces to momentarily separate. In conclusion, as sliding velocities are increased frictional behavior becomes more complex and increasingly 123 126 Fig. 10 A high speed (v0 = 6–23 m/s) friction experiment using the setup shown in Fig. 7 for a cellulosic friction material sliding against sapphire, lubricated with hexadecane. Friction force F and load L were recorded at 5,000 samples per second, while average friction force hFi and average load hLi (dashed lines) are calculated from a 0.5 s moving average. In all cases, the oscillations in the load have a frequency of the rotating disk. a At a rotational frequency of 227 Hz (v0 = 23 m/s), oscillations in the friction force have the same Fig. 11 A simplified slider model of high-speed friction consists of a mass for each surface (m, M) connected to the normal load L through a spring of stiffness kL, and to the lateral forces through the interfacial friction force Fint and a spring of stiffness kF connected to the drive which moves at velocity Vdrive. Lateral forces F(x,t) are measured from the deflection of the friction spring, which at any instant may be different from the actual friction force at the interface, Fint, due to inertial effects [8]. Each corresponding element in the two friction devices is labeled in Figs. 1 and 7. With the bimorph slider (Fig. 1) the position, x, is reciprocating and under ideal conditions the lower surface M moves parallel to the upper surface m. With the pin-on-disk mechanism (Fig. 7) x moves unidirectionally which allows for constant velocity. In practice, even small surface irregularities, tilt and off-axis loading cause periodic changes in the load for either geometry and thus affect the resulting friction force governed by the physical (mechanical and inertial) constants of the system, particularly the resonant frequencies. Small height variations due to mechanical misalignments and surface topology become amplified and significantly affect how friction is both generated and measured [28]. 123 Tribol Lett (2011) 42:117–127 frequency as in the load, both equal to the rotational frequency (227 Hz) of the disk. b At 82 Hz (v0 = 8 m/s), there is a high amplitude friction bump at the highest (i.e., thickest) point on the disk during a rotation (which shows up as the lowest load in the cycle due to measurement location effects). c At 145 Hz (v0 = 15 m/s), additional high frequency system-specific resonance components give rise to multiple frequencies in the frictional response, primarily the natural frequency of the friction-measuring device f0 * 345 Hz Fig. 12 Theoretical schematic of friction forces resulting from sliding over rough or ‘‘structured’’ surfaces. a The potential energy diagram (upper curve) is the parabolic curve representing the deflection of the friction spring (due to sticking) added to the variable potential energy due to the surface structure (lower curve). b The characteristic curves of smooth, stick-slip, and oscillatory friction forces, with points A–E mapped to the instantaneous potential energies and deflections in (a). The period and magnitude of stick-slip or oscillatory motion is dependent on many factors including the load, adhesion energy, surface structure (topography), drive velocity, and energy-dissipation mechanism [34]. Adapted from [35] The results presented here highlight the need to separate load and friction vibrations and variations in friction-force experiments and tribometer tests. The results also give insights into how externally applied (e.g., oscillating and Tribol Lett (2011) 42:117–127 vibratory) loads affects and can be used to control friction. In a separate manuscript, we describe the high-speed frictional behavior of a model automotive wet clutch. 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