SMASIS WEAR REDUCTION THROUGH PIEZOELECTRICALLY-ASSISTED ULTRASONIC LUBRICATION

Transcription

1 Proceedings of the ASME 2013 Conference on Smart Materials, Adaptive Structures and Intelligent Systems SMASIS2013 September 16-18, 2013, Snowbird, Utah, USA SMASIS WEAR REDUCTION THROUGH PIEZOELECTRICALLY-ASSISTED ULTRASONIC LUBRICATION Sheng Dong Smart Materials and Structures Laboratory NSF I/UCRC on Smart Vehicle Concepts Dept. of Mechanical and Aerospace Engineering The Ohio State University Columbus, Ohio Marcelo J. Dapino Smart Materials and Structures Laboratory NSF I/UCRC on Smart Vehicle Concepts Dept. of Mechanical and Aerospace Engineering The Ohio State University Columbus, Ohio ABSTRACT Ultrasonic vibration has been proven effective in reducing dynamic friction when superimposed onto the macroscopic relative velocity between two surfaces. This phenomenon is often referred to as ultrasonic lubrication. Piezoelectric materials can be employed to generate ultrasonic vibration. Typically, solid or fluid lubricants are employed to mitigate wear. However, in applications such as aerospace systems, which operate in particularly harsh environments, traditional lubrication methods are not always applicable. This paper investigates the relationship between friction force reduction and wear reduction in ultrasonically lubricated surfaces. A pin-on-disc tribometer is modified through the addition of a piezoelectric transducer which vibrates the contact between pin and disc. A piezo-actuator is installed to generate 22 khz vibration in the direction perpendicular to the disc. Three different linear speeds are employed by changing rotation speeds of the disc and running time. Friction and wear metrics such as volume loss, surface roughness, friction forces and stick-slip effects are compared before and after application of ultrasonic vibration. Relationships between linear speed and friction reduction, stick-slip reduction, and wear reduction are analyzed. Address all correspondence to this author. INTRODUCTION Friction exists when two contacting surfaces slide relative to each other. When this occurs, materials on the surfaces suffer plastic deformation and are broken away from the body of the material, which is commonly referred to as wear [1]. It has been shown that by applying ultrasonic vibrations at the interface of two surfaces in sliding contact, the friction force can be reduced [2 9]. This phenomenon, often referred to as ultrasonic lubrication, is promising in applications in which traditional lubrication methods are unfeasible (e.g., vehicle seats, space mechanisms) or where friction modulation is desirable (e.g., steering components). Ultrasonic vibration is usually applied only to one of the two contacting surfaces and may be applied in one of three directions relative to the macroscopic sliding velocity: perpendicular, longitudinal or transverse. Several studies have been devoted to each of the three directions and combinations thereof. For example, Littman et al. [2, 3] used a piezoelectric actuator generating vibration at 60 khz, making it slide on a guide track longitudinally. Bharadwaj and Dapino [4, 5] also applied longitudinal ultrasonic vibration to investigate the dependence of friction reduction on macroscopic sliding velocity, normal load, contact stiffness, and global stiffness. Kumar [6] experimentally determined that longitudinal vibrations were more effective at reducing friction force than transverse vibrations and confirmed that the velocity ratio greatly influences the degree of friction re- 1 Copyright 2013 by ASME

2 duction. Popov et al. [7] studied the influence of ultrasonic vibration in different material combinations. It was shown that ultrasonic vibration creates less friction reduction on softer materials than harder ones. They argued that contact stiffness influences the amount of force reduction. Dong and Dapino [8,9] used the Poisson effect to generate vibrations in combined perpendicular and longitudinal directions and studied the relationship between friction reduction and various normal loads, contact materials, and global stiffness. They proposed an elastic-plastic cube model to explain ultrasonic friction reduction. There have been multiple attempts at utilizing ultrasonic lubrication in an effort to reduce wear between two contacting surfaces. For example, Chowdhury and Helali [10] developed a pin-on-disc test to examine the effects of micro vibration on wear reduction. The vibration was applied in a direction perpendicular to the disc surface, ranging from 0 to 500 Hz. They studied the correlation between wear reduction and vibration frequency, relative humidity, and sliding velocity. Their results proved that higher frequency leads to lower wear rate. Bryant and York [11, 12] did similar work using high amplitude, low frequency vibration to reduce wear. They created a slider, which generated vibration from 10 to 100 µm at frequencies ranging from 10 to 100 Hz. Utilizing this set-up, they achieved wear reduction of up to 50%. Goto and Ashida [13, 14] conducted tests at higher frequencies in the ultrasonic range. They also chose a vibration direction perpendicular to the disc plane and studied the relationship between wear rate and normal loads. Their findings proved that ultrasonic vibration can drastically reduce wear under various normal loads. In these tests, the amplitude of the ultrasonic vibration was 8 µm and the normal load was up to 88 N. They also studied contact time between two surfaces while ultrasonic vibration is applied. It has been shown that linear speed plays an important role in the performance of ultrasonic lubrication. However, few papers have addressed the influence of linear speed on wear reduction. Therefore, this paper focuses on the relationship between friction and wear reduction at various linear speeds. EXPERIMENT Set-up The experimental set-up used in this study is a modified pinon-disc tribometer, as shown in Fig. 1 (a). A tribometer creates a contact between a still pin and a rotating disc for the purpose of studying the characteristics of friction and wear on the disc surface. The pin has been modified with the addition of a piezoelectric actuator and an acorn nut with a rounded end (Fig. 1 (c)). The actuator imparts ultrasonic vibrations to the rotating disc along the direction perpendicular to the disc. The tribometer is held by a lever which is part of a gymbal assembly that has FIGURE 1. EXPERIMENTAL SET-UP: (A) OVERALL (B) GYM- BAL ASSEMBLY (C) PIEZO-ACTUATOR IN DETAIL been installed on the frame (Fig. 1 (b)). Weights connected to the gymbal assembly apply normal loads to the interface. The normal force is measured by a load sensor pad placed between the pin and the disc. The resistance of the sensor pad changes as a function of the applied force, resulting in a change of output voltage. The gymbal assembly is instrumented to measure friction forces using a load cell. The load cell is installed on one side of the assembly frame and pretensioned horizontally by a weight on the other side. The piezoelectric actuator generates vibration of 2.5 µm at a frequency of 22 khz. The temperature of the actuator can increase rapidly from the heat generated and accumulated during the test. To maintain even temperatures, air flow and a thermocouple are employed to cool down the actuator and monitor the 2 Copyright 2013 by ASME

3 TABLE 1. Parameter TEST PARAMETERS Value Group Linear speed (mm/s) Running time (h) Distance traveled by pin (m) Revolutions 1600 Pin material Stainless steel 316 Disc material Aluminum 2024 Nominal normal force (N) 3 Disc run out (mm) ± US frequency (khz) 22 US amplitude (µm) 2.5 Nominal Groove diameter (mm) 50 Nominal temperature ( C) 21±1 Nominal actuator temperature ( C) 31±1 Environment Laboratory air Sampling frequency (Hz) 400 temperature, respectively. The disc is 3 inches in diameter and held in place by a lathe chuck. The chuck, which is placed on a platform, is driven by a DC motor under it with adjustable rotating speeds. Parameters and Schematics Three groups of tests were conducted at different linear speeds, from 20.3 to 87 mm/s. In each group, tests were done with and without ultrasonic vibrations. Three different angular velocities were adopted, while the distance traveled by the pin and the number of revolutions were kept constant by changing the duration of the test. Other parameters were unchanged as listed in Table 1. Friction force was sampled at a frequency of 400 Hz and each sampling window was 2 seconds. Typical data from a single sampling window appears in Fig. 2, in which stick-slip is observed. The mean value and root mean square value (RMS) of the variation were calculated for each sampling window. A profilometer was then employed to measure the volume loss of the discs and the roughness parameters of the disc surfaces. FIGURE 2. EFFECT MEASURED FRICTION FORCE AND STICK-SLIP Procedures Each pin-on-disc test was conducted following the procedures suggested by ASTM G99 [15] with modifications: (a) Clean and dry the acorn nut and disc specimens immediately prior to testing. Ethanol and acetone were used to remove all foreign matter. (b) Insert the sample securely into the chuck so that the disc is perpendicular to the axis of revolution so that wobbling is minimized (c) Install the acorn nut and compress it tightly to the piezoactuator (d) Adjust the position of the pin, making sure that it is perpendicular to the disc surface (e) Add weight for application of normal loads (f) Start the motor and adjust the speed to the desired value while preventing the pin from making contact with the disc. Then stop the motor. (g) Record the temperature and ambient environment of the tests. Prepare the data acquisition system for testing. (h) Put the pin in contact with the disc. Start the motor and the piezoelectric actuator (when applicable). Stop the motor when the desired running time is reached. (i) Clean the specimens and measure the volume loss and roughness parameters using a profilometer. RESULTS AND DISCUSSION Friction Without Ultrasonic Vibration Mean friction values for three linear speeds are plotted against pin travel distance in Fig. 3. In each case, the friction force increases rapidly in the beginning, reaches a steady state after a given stabilizing distance, and remains at that level for the rest of the test. There is fluctuation of friction force after it reaches steady state. Unlike the fluctuation of friction observed in Fig. 2, which is due to stick-slip phenomenon, the fluctuation 3 Copyright 2013 by ASME

4 Friction force without US (N) v=20.3 mm/s v=40.6 mm/s v=87 mm/s Friction force with US (N) v=20.3 mm/s v=40.6 mm/s v=87 mm/s Distance (m) Distance (m) FIGURE 3. STEADY STATE FRICTION FORCES WITHOUT UL- TRASONIC VIBRATIONS FIGURE 4. MEASURED FRICTION FORCES WITH ULTRA- SONIC VIBRATIONS here is caused by the run out of the disc. The disc wobbles a small amount while rotating during the tests. The inertia from the up and down pin movement causes fluctuation of the normal force, and accordingly, a fluctuation of the friction force. The figure also shows that higher speed results in a higher steady state value for the force. Table 2 lists the steady state friction forces, their RMS values and the stabilizing distances. Results show that natural friction increases as the speeds increase which is in line with the conclusions from previous studies [16 18], that is, for metals, the friction-speed curve has a positive slope when speeds are low and a negative slope when speeds are high. The speeds adopted in this study are considered to be low. Friction Reduction The mean values of friction force versus sliding distance during the application of ultrasonic vibration are plotted in Fig. 4 for three linear speeds. Similar to natural friction, friction in each of these cases reaches steady state after a stabilizing distance. As in the previous case, the friction force fluctuates because of disc run out. However, the fluctuation amplitudes are smaller because of the application of the ultrasonic vibrations. One possible reason is because inertial acceleration, when ultrasonic vibration is present, is extensively reduced by the superposition of the acceleration that occurs from the vibration. Therefore, actual normal forces and friction forces are reduced. The friction reduction percentage is defined as P f = f 0 f 1 f 0 100, (1) where f 0 is the friction without ultrasonic vibration and f 1 is the friction with the application of ultrasonic vibration. The results are plotted in Fig. 5. It is shown that all three groups give con- Friction reduction percentage FIGURE 5. v=20.3 mm/s v=40.6 mm/s v=87 mm/s Distance (m) MEASURED FRICTION REDUCTION sistent friction reduction at steady state, and that a lower speed results in greater reduction. Table 2 lists the steady-state friction forces, their RMS values and stabilizing distances. As in the case without ultrasonics, the friction forces in the presence of ultrasonic vibrations increase as the speed increases. The trend is shown in Fig. 6, where the markers indicate the mean values and the error bars are the RMS of the steady state values. It is emphasized that it takes a shorter distance for the force to stabilize when ultrasonic vibrations are applied, regardless of the linear speed. We speculate that the ultrasonic vibrations make it easier for the pin and disc to break into each other, wear out the oxide-layers, and build up a steady contact at the beginning of the test while it takes a longer time to accomplish that without the assistance of ultrasonic vibrations. At the intermediate speed (40.6 mm/s) the force takes longer to stabilize both with and without ultrasonic vibration. 4 Copyright 2013 by ASME

5 Group TABLE 2. STEADY STATE FRICTION FORCES AND DISTANCES TO ACHIEVE STEADY STATE Linear speed US Steady state Distance to achieve RMS of steady Distance to achieve (mm/s) friction (N) steady state (m) state friction (N) steady state (m) No 1.024± ± Yes 0.379± ± No 1.201± ± Yes 0.748± ± No 1.472± ± Yes 1.041± ± RMS of friction force without US (N) v=20.3 mm/s v=40.6 mm/s v=87 mm/s Distance (m) FIGURE 6. RELATIONSHIP BETWEEN MEASURED FRICTION FORCE AND LINEAR SPEED RMS of Friction Force Variation As shown in Fig. 2, the instantaneous friction force fluctuates due to the stick-slip phenomenon. As the name suggests, stick-slip consists of two phases of motion. Stick is the stage when two objects stay relatively still and friction increases. Slip happens when the friction increases to such an extent that the two surfaces release to slide relative to each other again. A typical measurement of stick-slip is shown in Fig. 2 (inset). A commonly accepted explanation for stick-slip is that the static friction coefficient is usually larger than the dynamic coefficient so that friction varies within a range during sliding [18]. Another cause of stick-slip can be the waviness of the surface, which results in an inconsistency of the friction coefficient [16]. To quantify the stick-slip phenomenon in this study, an RMS value is derived for each 2-second window, which represents the average amplitude of the stick-slip fluctuation. The RMS friction force is plotted versus travel distance for each of the tests groups without ultrasonic vibrations (Fig. 7) and with ultrasonic vibrations (Fig. 8). In both cases, the RMS values reach steady state after a cer- FIGURE 7. RMS OF FRICTION FORCES WITHOUT ULTRA- SONIC VIBRATIONS RMS of friction force with US (N) FIGURE 8. TIONS Distance (m) v=20.3 mm/s v=40.6 mm/s v=87 mm/s RMS OF FRICTION WITH ULTRASONIC VIBRA- tain stabilizing distance is reached. Contrary to the mean values, however, it takes significantly longer for the stick-slip to stabilize when the ultrasonic vibrations are on than when they are off. The stick-slip amplitudes are nearly at the same level for three speeds when the ultrasonic vibrations are absent. When the vibrations 5 Copyright 2013 by ASME

6 FIGURE 9. RELATIONSHIP BETWEEN THE RMS OF FRICTION FORCES AND LINEAR SPEEDS the whole groove. In these images, it can be observed that the grooves from tests with ultrasonic vibrations (images A, C, E) appear more uneven and non-reflective than the ones without it (images B, D, F). For a closer view of the wear grooves, profilometer scans of the surfaces were conducted. The scanning provided 2D and 3D profiles, volume of the groove, and roughness parameters of the scanned surface. Eight spots along the path of each wear ring were selected for scanning in order to obtain average values of volume loss and roughness parameters. Each scan was conducted over an area of 1.8 mm by 2.0 mm with a scan stroke of±100 µm. The 3-D profiles of the grooves from all tests groups can be seen in Fig. 11. The grooves from the tests with ultrasonic vibrations on are narrower and curvier along the edges than those from the tests without ultrasonic vibrations. This explains why they appear more uneven to the naked eye. Furthermore, the wear groove becomes even curvier as the speed increases when the ultrasonic vibration is on. This effect is not observed in any of the cases without ultrasonic vibrations. The six pictures share one color code, with different scales presented in the legends. It shows the grooves on the left are deeper than the ones on the right. This observation is supported by the measurement of the roughness parameters, as listed in Table 4. It can be seen that the maximum height of the profile drops in each group while ultrasonic vibrations are present, which means that the grooves were created deeper. Not just the maximum height, but also all the other four indexes are smaller when ultrasonic vibrations are activated. The roughness parameters indicate evidence of significant wear reduction. Another quantifiable index is wear rate, which is defined as FIGURE 10. WEAR GROOVES: (A) GROUP 1 WITH US; (B) GROUP 1 WITHOUT US; (C) GROUP 2 WITHOUT US; (D) GROUP 2 WITH US; (E) GROUP 3 WITH US; (F) GROUP 3 WITHOUT US; are on, all three cases show amplitude reductions with different levels. The steady state values and the stabilizing distances can be found in Table 2 and the trends are shown in Fig. 9, where the markers indicate the mean values and the error bars are the RMS of the steady state values. Wear Reduction The materials in this study, stainless steel and aluminum, possess a hardness of kg/mm 2 and kg/mm 2, respectively. Due to the difference in hardness, the type of wear between them is abrasive: the harder material digs into the softer one, removing material and creating grooves [19]. Images of the wear grooves from all test groups are shown in Fig. 10. Each image shows approximately one quarter of w= V D, (2) where V is disc volume loss in mm 3 and D is the distance that the pin travelled in m. The disc volume loss is calculated from data of groove volume provided by the profilometer. The wear reduction percentage is defined as P w = w 0 w 1 w 0 100, (3) where w 0 is the wear rate without ultrasonic vibrations applied and w 1 is the wear rate with ultrasonic vibrations applied. The wear rates of all groups and the wear reduction percentages are listed in Table 3. The results show a weak dependence of wear rates on linear speeds, both with and without ultrasonic vibration. The wear reduction percentage slightly increases as the speed increases. Few previous studies were focused on the relationship between abrasive wear and sliding speed, but many have been done on the influence of sliding distance [20, 21]. It was found 6 Copyright 2013 by ASME

7 TABLE 4. COMPARISON OF SURFACE ROUGHNESS PARAM- ETERS: R a ARITHMETIC AVERAGE; R p MAXIMUM PEAK HEIGHT; R q ROOT MEAN SQUARED; R t MAXIMUM HEIGHT OF THE PROFILE; R v MAXIMUM VALLEY DEPTH Group US R a (µm) R p (µm) R q (µm) R t (µm) R v (µm) No wear N Y N Y N Y FIGURE 12. RELATIONSHIP BETWEEN REDUCTION RE- SULTS AND LINEAR SPEEDS that, when there is unlimited abrasive material (the harder material), the wear rate starts at a low level at the beginning of the test, increases and remains at a steady state value. However, if the abrasive material is limited, the wear rate will decrease as the test continues. In both cases, the wear rate is not dependent on the sliding velocity. Discussion These results indicate that ultrasonic vibration is effective in reducing friction, stick-slip, and wear at all three linear speeds (see Fig. 12). In terms of friction, as speed rises, friction reduction decreases from 62.2% for group 1 to 29.3% for group 3. This conclusion is in line with the studies conducted by Littmann et al. [2] which focused on the relationship between velocity ratio and friction ratio. In their study, the velocity ratio was defined as the macroscopic velocity divided by the velocity of ultrasonic vibration. The friction ratio was defined as the friction with ultrasonic vibrations over the one without ultrasonic vibrations. It was proposed that a higher velocity ratio results in a higher friction ratio, up to a limit of 1. In this study, the vibration velocity and the friction without ultrasonic vibrations remain constant. Therefore, higher velocities give higher velocity ratio, which results in a lower amount of friction reduction. Wear reduction remains confined within a range from 45.8% to 48.6%, while higher velocity results in slightly higher wear reduction. One possible reason could be that, as speed increases, the actual contact between the pin and the disc is reduced. Studies showed when the amplitude of ultrasonic vibration is large enough, contact time between two surfaces will be reduced as one surface moves away from the other [13, 14]. Assuming that the pin makes one contact with the disc and then moves away from it in one cycle of ultrasonic vibration, the number of contact times between the disc and the pin in three tests can therefore be estimated. These estimated numbers are presented in Table 3. With the presence of ultrasonic vibration, the contact between pin and disc is characterized by waviness along the grooves due to the stick-slip phenomenon. The pin moves up and down while travelling along the groove, making contacts with the disc during the stick phase and moving away from it during the slip phase. This assumption could help explain the curviness of the wear groove with ultrasonic vibration. As shown in Fig. 11, as the speed increases, the profile of the groove becomes curvier, especially seen in profile (F). It appears that the segment of the groove is formed by two separate pits, which are presumably created by the contacts between the pin and the disc during the stick phase. The distance between the two pits is mm based on the measurement. Theoretically, the distance can be estimated by d = t v, (4) where d is the distance between the centers, t is the time of one period of stick-slip, and v is the linear speed. The estimation results of the distance are respectively mm, mm, and mm for the speeds of 20.3 mm/s, 40.6 mm/s, and 87 mm/s. It can be seen that the measurement and the estimation match well for the speed of 87 mm/s. However, the pits separation is not as evident in the other two cases (profiles (B) and (D)) because the pits overlap with each other as the speed decreases. Furthermore, for the cases without ultrasonic vibration, the pin and disc make contact during both the stick and slip phases, creating little waviness along the grooves (see profiles (A), (C), and (E)). The reduction in stick-slip does not show a clear trend. For example, with a speed of 40.6 mm/s, group 2 experiences the 7 Copyright 2013 by ASME

8 (A) (B) (C) (D) (E) (F) FIGURE 11. 3D PROFILES OF WEAR GROOVES: (A) GROUP 1 WITHOUT US; (B) GROUP 1 WITH US; (C) GROUP 2 WITHOUT US; (D) GROUP 2 WITH US; (E) GROUP 3 WITHOUT US; (F) GROUP 3 WITH US; most reduction, while group 1, with a speed of 20.6 mm/s, experiences slightly less reduction. However, group 3, at a higher speed, does not exhibit such reduction. Studies have shown the amplitude of vibration caused by stick-slip is related to the stiffness and damping of the system and that increasing the stiffness can greatly reduce the amplitude of vibration [16]. The reason is that stick-slip can be deemed as an excitation to the system, and linear speeds in addition to the waviness of the surface can change the frequency of the excitation. Therefore, at certain speeds, the system is excited at its resonance frequency, which results in a magnification of the stick-slip vibration. The system resonance frequency can be increased if the system is stiffer. Therefore, the possibility of magnifying the vibration is reduced when the surfaces slide at the same range of speeds [22]. One possible explanation of the significant reduction in stick-slip for group 2 is because 20.3 mm/s falls in the range of speeds at which resonance takes place without the presence of ultrasonic vibration. In short, stick-slip peaks at that speed. However, when ultrasonic vibrations are applied, the friction force is reduced and the waviness is different from the one without vibrations. There- 8 Copyright 2013 by ASME

9 Group Linear (mm/s) speed TABLE 3. Wear without US (mm 3 /m) COMPARISON OF WEAR AND FRICTION REDUCTION Wear with US Wear reduction Wear reduction (%) Number (mm 3 /m) (mm 3 /m) contacts of Friction reduction (%) fore, the system does not vibrate at resonance at the speed of 20.3 mm/s, but at some higher speed (see Fig. 9). CONCLUDING REMARKS In this study, a modified pin-on-disc tribometer was built with the purpose of investigating the influence of ultrasonic vibration on the characteristics of friction and abrasive wear between stainless steel pins and aluminum discs under a low normal load of 3 N. Ultrasonic vibration was generated by a piezoelectric actuator with an amplitude of 2.5 µm and a vibration frequency of 22 khz. With the goal to quantify the relationship between friction, wear, and linear speed, three different speeds, 20.3 mm/s, 40.6 mm/s, and 87 mm/s were adopted while keeping other parameters unchanged through the tests. The results of friction forces show that ultrasonic vibration is effective in reducing dynamic friction, and that higher speeds result in higher friction both with and without the presence of ultrasonic vibrations. We also confirm a decrease in friction reduction as speeds increase. This result is in line with previous studies of the relationship between linear speeds and friction reduction. Future work will investigate the influence of other parameters such as initial surface roughness, normal load, and material combinations. The wear tests show a consistent reduction of up to 49%, which validates the effectiveness of ultrasonic vibration in wear reduction in addition to the difference between the mechanisms of friction and wear reduction. There exists a dependence of wear reduction on linear speeds, which could be explained by a reduction of contact time between two surfaces when ultrasonic vibrations are present. Additionally, stick-slip amplitudes are reduced to 50% under the application of ultrasonic vibration. However, no clear trend is found in the relationship between stick-slip reduction and linear speeds. Future work will focus on the relationship between system stiffness and stick-slip amplitudes. ACKNOWLEDGMENT The authors would like to acknowledge Dr. Tim Krantz from NASA Glenn and Duane Detwiler from Honda R&D for their technical support and in-kind contributions. Financial support for this research was provided by the member organizations of the Smart Vehicle Concepts Center ( a National Science Foundation Industry/University Cooperative Research Center (I/UCRC). S.D. is supported by a Smart Vehicle Concepts Graduate Fellowship. REFERENCES [1] Bhushan, B., Introduction to tribology. John Wiley & Sons, New York. [2] Littmann, W., Storck, H., and Wallaschek, J., Sliding friction in the presence of ultrasonic oscillations: superposition of longitudinal oscillations. Archive of Applied Mechanics, 71, pp [3] Littmann, W., Storck, H., and Wallaschek, J., Reduction in friction using piezoelectrically excited ultrasonic vibrations. In Proceedings of SPIE, Vol [4] Bharadwaj, S., and Dapino, M., Friction control in automotive seat belt systems by piezoelectrically generated ultrasonic vibrations. In Proceedings of SPIE, Vol. 7645, pp. 7645E [5] Bharadwaj, S., and Dapino, M., Effect of load on active friction control using ultrasonic vibrations. In Proceedings of SPIE, Vol. 7290, pp G [6] Kumar, V., and Hutchings, I., Reduction of the sliding friction of metals by the application of longitudinal or transverse ultrasonic vibration. Tribology International, 37, pp [7] Popov, V., Starcevic, J., and Filippov, A., Influence of ultrasonic in-plane oscillations on static and sliding friction and intrinsic length scale of dry friction processes. Tribology Letters, 39, pp [8] Dong, S., and Dapino, M., Piezoelectricallyinduced ultrasonic lubrication by way of poisson effect. In Proceedings of SPIE, Vol. 8343, pp. 8343L [9] Dong, S., and Dapino, M., Elastic-plastic cube model for ultrasonic friction reduction via poisson effect. Ultrasonics (accepted for publication). [10] Chowdhury, M., and Helali, M., The effect of frequency of vibration and humidity on the wear rate. Wear, 262, pp Copyright 2013 by ASME

10 [11] Bryant, M., Tewari, A., and York, D., Effect of micro (rocking) vibrations and surface waviness on wear and wear debris. Wear, 216, pp [12] Bryant, M., and York, D., Measurements and corelations of slider vibrations and wear. Journal of Tribology, 122, pp [13] Goto, H., Ashida, M., and Terauchi, Y., Effect of ultrasonic vibration on the wear characteristics of a carbon steel: analysis of the wear mechanism. Wear, 94, pp [14] Goto, H., Ashida, M., and Terauchi, Y., Wear behaviour of a carbon steel subjected to an ultrasonic vibration effect superimposed on a static contact load. Wear, 110, pp [15] ASTM G99-95, ed., Standard test method for wear testing with a pin on disc apparatus. [16] E. Robinowicz, ed., The friction and wear of materials. Wiley, New York. [17] Bowden, F., and Freitag, E., The friction of solids at very high speeds. Proceedings of Royal Society A, 248, pp [18] Burwell, J., and Rabinowicz, E., The nature of the coefficient of friction. Journal of Applied Physics, 24, pp [19] Cocks, M., Interaction of sliding metal surfaces. Journal of Applied Physics, 33, pp [20] Goddard, J., and Wilman, M., A theory of friction and wear during the abrasion of metals. Wear, 5, pp [21] Mulhearn, T., and Samuels, L., The abrasion of metals: A model of the process. Wear, 5, pp [22] Sampson, J., Morgan, F., Reed, D., and Muskat, M., Friction behavior during the slip portion of the stick-slip process. Journal of Applied Physics, 14, pp Copyright 2013 by ASME