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Minimizing self-oscillation in belt drives: Surface texturing
Tribology International 145 (2020) 106157
Contents lists available at ScienceDirect
Tribology International journal homepage: http://www.elsevier.com/locate/triboint
Minimizing self-oscillation in belt drives: Surface texturing Yingdan Wu, Michael J. Leamy, Michael Varenberg * George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA, 30332, USA
A R T I C L E I N F O
A B S T R A C T
Keywords: Contact mechanics Elastomers Rolling Stick-slip Detachment waves
Detachment waves have recently been identified as one of the main sources for self-oscillation and accompanying energy losses in belt drive systems under low-speed and otherwise steady operation. In light of this, herein we explore mitigation of detachment wave-induced instabilities via regular and irregular texturing of the belt contact surface. The results document that surface texturing reduces the magnitude of belt drive oscillations, with the reduction being significantly more pronounced in the driver case than in the driven case. While both regular and irregular surface topographies are useful in minimizing the vibrations, regular patterns result in a stronger effect. The aspect ratio of surface projections is found to be the most important parameter, while excessive texturing of the belt surface is shown to result in belts losing their tractive capabilities.
1. Introduction Frictional interactions in both sliding and rolling elastomeric con tacts are significantly affected by adhesion [1–3]. When unable to slide due to stiction, the tangentially-loaded elastomeric surface repeatedly buckles under compression [4–6], forming narrow lines of lost contact, termed Schallamach detachment waves, that propagate across the interface to allow for relative displacement between the contacting bodies [7]. This unstable surface behavior [6] is observed in contacts incorporating rubber-like materials if the contact area is large [8], and though it is obviously undesirable in mechanical systems, even the presence of lubricant between the elastomer and its counterpart cannot always prevent the associated vibrations [9,10]. Though known already for several decades [7,11], waves of detachment had only recently been observed in a belt drive system for the first time [12]. Interestingly, analysis of dynamic behavior of a model belt drive reveals that local detachment events at the belt-pulley interface are responsible for global self-oscillations of the system [13]. Moreover, it is also found that the detachment wave-induced in stabilities significantly lower the energy efficiency of a belt drive [14]. Given that belt drives are employed for transmitting mechanical power in numerous engineering applications, this calls for research on tech niques that can be used for the disruption of detachment waves at the rolling belt-pulley interface. Modifying the surface chemistry or topography can affect adhesion [15] and, hence, the formation and propagation of detachment waves, which may help in stabilizing the elastomer friction. In chemical
modification, different functional groups are introduced at the elasto meric surface by treatment with strong acids or chlorinating agents [16]. Atmospheric plasma treatments [17] are also used to introduce adhesion-oriented functional groups [18,19] on elastomeric surfaces as well as to deposit a plasma polymerized coating on top of them [20,21]. Laser cladding was also recently employed to produce a polymer-based coating on elastomer substrates [21]. However, these methods are time-consuming and often based on substances that are not environ mentally friendly. Moreover, large elasticity of elastomers makes coating them challenging as it necessitates a strong adhesion over a wide range of strains. Modification of surface topography, on the other hand, does not produce any of the above-mentioned issues and can be achieved by polymer curing against a template surface. It is clear that modifying surface topography is preferable over chemical modification. In light of the above, here we explore the possibility to minimize detachment wave-induced instabilities via texturing of the belt contact surface, with the extensible belt working in a low-speed regime. In so doing, we answer the question of whether regular surface patterns known to reduce detachment waves in sliding [22,23] can be also employed in rolling, and we compare their performance to that of irregular surface textures. 2. Experimental details 2.1. Preparation of textured belts All belt specimens were made of a transparent polydimethylsiloxane
* Corresponding author. E-mail address: [email protected] (M. Varenberg). https://doi.org/10.1016/j.triboint.2020.106157 Received 23 October 2019; Received in revised form 1 January 2020; Accepted 2 January 2020 Available online 7 January 2020 0301-679X/© 2020 Elsevier Ltd. All rights reserved.
Y. Wu et al.
Tribology International 145 (2020) 106157
Fig. 1. Schematic of transferring texture from an original surface onto a PDMS belt.
Fig. 2. Schematic and optical microscopy images of replicated surfaces with regular and irregular topography. (a)–(d) 3D-printed hexagonal and square patterns. Arrows in the direction of rolling. (e) 3D-printed and polished surface. (f)–(h) 1200, 150 and 80 grit abrasive paper sheets, respectively.
(PDMS, Sylgard 184, Dow Corning, Midland, MI) elastomer at a 10:1 mixture ratio of Sylgard 184 pre-polymer and its cross-linker. The mixture was cured in light vacuum (to ensure no air bubbles trapped inside the belt) for 14 h at 65 οC in negative molding templates prepared using a four-step molding technique (Fig. 1) [24] to replicate the topography of either regularly or irregularly textured surfaces (Fig. 2). Use of three additional materials (PU, PVS and Epoxy, see Fig. 1) was required to ensure clean demolding since none of these materials can be easily separated from both the replicated surfaces and PDMS. PU (polyurethane, F-160 A/B, BJB Enterprises, Tustin, CA) was cured for 3 h at 25οC and then for 16 h at 71οC in light vacuum oven against replicated surfaces (see below for details). PVS (Affinis light body, €tten, Switzerland) was poured onto the PU Coltene Holding, Altsta template and cured for 10 min at 25οC. Epoxy (Spurr low viscosity embedding kit, Sigma Aldrich, St. Louis, MO) was cured for 8 h at 70οC in light vacuum oven against the PVS template. The textured belts were 400 mm in length, 2 mm in thickness, and 10 mm in width, while the reference smooth belt was 7 mm wide to ensure similar apparent contact areas. The replicated surfaces with regular topography (Fig. 2a–d) were 3Dprinted out of Formlabs Clear Resin (Formlabs, Somerville, MA) to have hexagonal and square projections with height h, size D, and lattice
constant a. These projections were polished with SiC 2000 grit abrasive paper (Struers, Cleveland, OH) to different heights and a surface roughness Ra of less than 150 nm. Our previous studies on the size effects of regular topography on sliding friction [23,25] reveal that the lattice constant, a, and the aspect ratio, AR ¼ h/D, are important parameters, while the area density, AD ¼ (D/a)2, is insignificant. To this end, all patterned surfaces shared the same area density, AD � 70% (chosen to have good grip, while still being able to fabricate gaps between smallest texture elements), while the examined parameters were the lattice constant, a ¼ 0.6, 1, 3 mm, the aspect ratio, AR ¼ 0.1, 0.2, 0.3, 0.4, 0.5, and the pattern shape and orientation (Fig. 2a–d). The template for casting the smooth reference belt was prepared using the same tech nology of 3D printing and polishing to a surface roughness Ra of less than 150 nm (Fig. 2e). The replicated surfaces with irregular topography (Fig. 2f–h) were SiC abrasive paper sheets of 2000, 1200, 800, 400, 200, 150, and 80 grit (Struers, Cleveland, OH; Lot Fancy Inc, San Francisco, CA). The surface profiles of abrasive papers were characterized using a Hommel Etamic W5 profiler (Jenoptik AG, Jena, Germany).
Fig. 3. Experimental apparatus: (a) schematic representation and (b) system as built. 2
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Tribology International 145 (2020) 106157
Fig. 4. Tension difference and angular velocity measured on (a) reference smooth belt and (b) hexagonally patterned (a ¼ 1 mm, AR ¼ 0.2) belt, and characteristic sequences of optical images representing evolution of the contact area (shown in black) in the driver case.
2.2. Set-up and operating conditions A custom-built test rig [12] used in this study is shown in Fig. 3. The belt wraps around a pulley and is drawn at a prescribed constant speed by a driving weight and a releasing motor that control the driving stage motion. The belt loading is controlled via the tension and torque weights connected to the backend of the belt and to the pulley, respectively. Both the driver and driven case scenarios can be implemented by reversing the direction at which the torque is applied to the pulley (solid and dashed configuration, respectively, as shown in Fig. 1a). Two load cells attached at the two ends of the belt measure the belt tension and a rotary encoder connected to the pulley tracks its angular displacement. A digital camera is used for the observation of the belt/pulley interface. Similar to our previous studies, the driving speed was set to 3 mm s 1 and the tension at the tight and slack sides of the belt was adjusted to 6 N and 2 N, respectively. The travel distance of the driving stage was 300 mm. The temperature and relative humidity in the laboratory during the tests were 23 � C and 35%, respectively. All statistical tests were per formed using one-way ANOVA (all pairwise multiple comparison pro cedures (Holm–Sidak method), overall significance level 0.05) in the ORIGIN software package (OriginLab Corporation, Northampton, MA).
Fig. 5. The effect of the pattern shape and orientation on frequency. f, and amplitude, A, of the fluctuations in the tension difference, T, (a), (b), respec tively, and in the angular pulley velocity, α, (c), (d), respectively, in both the driver and driven cases. The fluctuations in the tension difference presented here correspond to detachment events only. All patterns share the same lattice constant and aspect ratio (a ¼ 1 mm, AR ¼ 0.2). The error bars show stan dard deviations.
3. Results and discussion The raw measurements of the difference in the belt tension and the pulley angular velocity obtained for the smooth (reference) and hex agonally patterned belts in the driver case are plotted in Fig. 4 along with the characteristic images of the contact area. The effect of regular surface texture is obvious. With the reference smooth belt, the selfoscillation of the pulley, which is generated due to contact instabilities [13] and induces large-scale fluctuations in the belt tension difference (Fig. 4a), is so powerful that the pulley periodically halts, as follows from inspection of the angular velocity signal. When the patterned belt is used, the pulley rotates much steadier, and only subtle fluctuations are observed around the prescribed angular velocity (~0.3 rad s 1), which reflects also on the fluctuations in the belt tension (Fig. 4b). Looking at the evolution of the contact area, which visualizes the source of system instabilities, we can also clearly see the difference in the behavior of the
flat and patterned belts. First, the size of the detachment zone is greatly reduced (from ~7 mm to ~0.5 mm) when regular surface pattern is introduced. Second, the characteristic surface folds representing waves of detachment (isolated air-pockets within the contact area, such as the one seen on image 3 in Fig. 4a) are barely distinguishable for the patterned belt. Detachment waves in the driver pulley case appear due to a shearinduced moment generated at the belt exit region [12,14]. When the belt surface is split into multiple disconnected and independent sub-contacts via patterning, its stiffness is reduced such that a much smaller moment is needed to start detachment. To this end, since the shear-induced moment grows until it is relaxed by detachment, the detachment waves also have a smaller scale and are formed more often, 3
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Tribology International 145 (2020) 106157
Fig. 6. The effect of lattice constant on frequency. f, and amplitude, A, of the fluctuations in the tension difference, T, (a), (b), respectively, and in the angular pulley velocity, α, (c), (d), respectively, in both the driver and driven cases. The fluctuations in the tension difference presented here correspond to detachment events only. All patterns share the same aspect ratio (AR ¼ 0.2). The error bars show standard deviations.
Fig. 7. The effect of aspect ratio on frequency. f, and amplitude, A, of the fluctuations in the tension difference, T, (a), (b), respectively, and in the angular pulley velocity, α, (c), (d), respectively, in both the driver and driven cases. The fluctuations in the tension difference presented here correspond to detachment events only. All patterns share the same lattice constant (a ¼ 1 mm). The error bars show standard deviations.
leading to less violent excitation of the system. In light of this ration alization, we may expect to be able to minimize the self-oscillation of the belt drive system by modifying the geometrical characteristics of the independent contact elements.
case when the belt surface is textured. 3.2. Effect of lattice constant Decreasing the lattice constant (i.e., increasing the number of indi vidual sub-contacts per unit area) does show a small measurable effect, though no statistically significant difference is observed between different lattice constants in both the driver and driven cases (Fig. 6). This agrees with observations made in other studies where the most significant effect is achieved during initial contact splitting, while further minimization of vibrations requires increasing the number of individual sub-contacts by several orders of magnitude [23], which may be considered impractical. Given that we were limited by the resolution of 3D printing in preparing the molding templates, our finest pattern was based on the lattice constant of 0.6 mm, which results in just 25 times more individual sub-contacts than in the case of our coarsest pattern with the lattice constant of 3 mm. Evidently, this change is not strong enough.
3.1. Effect of the pattern shape and orientation Hexagon- and square-shaped patterns oriented differently with respect to the rolling direction (H1, H2, S1 and S2, as shown in Fig. 2) were tested and compared with the reference smooth belt in terms of the frequency and amplitude of the belt and pulley oscillations (Fig. 5). The oscillations in the belt tension difference (as shown in Fig. 4) were decomposed into large-scale and small-scale components associated with pulley motion and detachment events, respectively [13]. Given that the characteristics of the pulley motion-related oscillations in the belt tension difference resemble those of the oscillations in the pulley angular velocity shown also in Fig. 5, only the detachment event-related oscillations in the belt tension difference are presented. The second order oscillations in the pulley angular velocity that correspond to detachment events are also not shown as they are similar to those in the tension difference signal. Fig. 5 demonstrates similar oscillation characteristics for all patterned belts regardless of the pattern shape and orientation in both the driver and driven cases, and no statistically significant difference between these patterns is observed either. This observation supports our hypothesis regarding the core mechanism of the disruption of detach ment waves — the reduction of surface stiffness is independent of the pattern type (to a first approximation), so the belt can detach easier from the pulley as long as its surface is split, while the shape and orientation of the contact patches are not important. This finding allows us to use just one representative shape, and the pattern H1 is chosen for the following study. The effect of patterning, however, is different for the driver and driven cases. For the driver pulley, the amplitude of both types of oscillation is reduced by a factor of approximately 3, and the frequency is increased by a factor of approximately 1.5, while for the driven pulley, the observed effect is much weaker. This is explained by the difference in the mechanism of detachment [12]. In the former case, the detachment is shear-driven, and surface conditions are vital, while in the latter case, it is stretch-driven, and the surface conditions are less decisive as volume effects dominate. Another important observation is that the oscillations in the driver case become even less pronounced than those in the driven
3.3. Effect of aspect ratio The aspect ratio of the hexagonally shaped projections is next varied from 0.1 to 0.5. Increasing the aspect ratio from 0.1 to 0.4 leads to an increase in frequency and to a decrease in amplitude of the oscillations in both the belt tension difference and the pulley angular velocity, as shown in Fig. 7. However, a statistically significant effect of aspect ratio is observed only in the driver pulley case, which results from the dif ference in the mechanisms of detachment in the driver and driven cases as discussed above. Interestingly, the belt patterned to have an aspect ratio of 0.5 was incapable of carrying the prescribed torque in either the driver or the driven pulley. These observations are explained in the following way. As the aspect ratio increases, the bending stiffness of the hexagonal projections is reduced. As a result, these projections bend easier under shear traction. Correspondingly, since the threshold for the formation of detachment waves is easier to reach, the detachment events initiated by the shear-induced moment in the driver case occur more frequently and have smaller range. However, with large enough aspect ratio, the pro jections bend to such a degree that their flat ends lose contact with the pulley [25] regardless of the shear direction. This leads to a great reduction in the real contact area and in the ability to resist shear. The so-called “slip” zone then grows until it consumes the entire belt-pulley interface in both the driver (Fig. 8) and the driven cases. At this moment, 4
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Tribology International 145 (2020) 106157
Fig. 8. Optical images representing evolution of the patterned contact area (shown in black) obtained in the driver case with a camera installed at different angular orientations. (a) AR ¼ 0.4, torque is transmitted. (b) AR ¼ 0.5, torque is not transmitted. Hatched areas represent the regions out of view.
Fig. 9. Comparison of the effects of surface roughness (irregular topography) and aspect ratio (regular topography) on frequency, f, and amplitude, A, of the fluctuations in the tension difference, T, (a), (b), respectively, and in the angular pulley velocity, α, (c), (d), respectively, in both the driver and driven cases. The fluctuations in the tension difference presented here correspond to detachment events only. The error bars show standard deviations.
a global displacement between the pulley and the belt is established, and no further power can be transmitted. The resolution of our imaging system does not enable us to say whether bent hexagonal projections truly slide, or small-scale detachment waves allow for relative motion in the slip zone, but in any event they can move independently and the scale of global frictional instabilities is reduced due to scattering of local “slip” events over time and space [23].
surface topography on oscillation characteristics of textured belts can be plotted in one figure. Notably, similar to the regularly textured belts, the belts with irregular surface topography could not transmit the pre scribed torque when the roughness ratio was too high (Ra/Sm � 0.041, for the belt cast against the roughest abrasive sheet of 80 grit). This allowed us to scale the horizontal axes of Aspect Ratio and Ra/Sm such that the data could be conveniently compared as shown in Fig. 9 – i.e., the far right-end of the Ra/Sm (bottom horizontal axis; irregular textures) and Aspect Ratio (top horizontal axis; regular textures) domains both correspond to gross slip. Studying the self-oscillation behavior of the irregularly textured belts, we see that it resembles that of the belts with regular topography, while the observed effects are generally weaker (Fig. 9). Most likely, this is due to surface irregularities on rough belts having smaller contact area and less bending compliance as compared to surface projections on regularly patterned belts, making the effect of texturing less
3.4. Effect of roughness Given that the aspect ratio of regular topography was found to be the dominant parameter affecting the belt drive oscillations, to study the effect of irregular surface topography, we have constructed a similar ratio of vertical and horizontal profile characteristics, Ra/Sm, where Ra and Sm are standard roughness average and mean spacing of profile ir regularities, respectively. In this way, the effects of regular and irregular 5
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Tribology International 145 (2020) 106157
pronounced. Further, while maintaining statistically indistinguishable values in the driven case, in the driver case the frequencies and ampli tudes of the oscillations related to both the detachment events and angular velocity signal change significantly as Ra/Sm increases up to 0.02 and then remain constant for larger values of Ra/Sm. This can possibly be related to the irregularly patterned belt surfaces having random shapes, sizes and distribution of asperities, so other character istics can change simultaneously with the aspect ratio of surface asper ities and lead to deviation from the expected effect of the aspect ratio alone. In general, the similarity between the effects of regular and irregular surface texturing validates our hypothesis that splitting the contact area into disconnected sub-contacts helps minimizing detachment waveinduced instabilities in rolling. The regular surface texturing, however, has an advantage over the irregular surface texturing since the system’s self-oscillations can be minimized to a greater extent, and both the driver and the driven rolling can be improved.
the work reported in this paper. Acknowledgement This material is based upon work supported by the National Science Foundation under Grant No. 1562129. References [1] Rabinowicz E. The intrinsic variables affecting the stick-slip process. Proc Phys Soc Lond 1958;71:668–75. [2] Barquins M. Adherence, friction and wear of rubber-like materials. Wear and Friction of Elastomers. ASTM International; 1992. [3] Persson BNJ. On the theory of rubber friction. Surf Sci 1998;401:445–54. [4] Best B, Meijers P, Savkoor AR. The formation of Schallamach waves. Wear 1981; 65:385–96. [5] Barquins M, Roberts AD. Rubber-friction variation with rate and temperature – some new observations. J Phys D Appl Phys 1986;19:547–63. [6] Rand CJ, Crosby AJ. Insight into the periodicity of Schallamach waves in soft material friction. Appl Phys Lett 2006;89. Artn 261907. [7] Schallamach A. How does rubber slide? Wear 1971;17:301–12. [8] Barquins M. Sliding friction of rubber and Schallamach waves - a review. Mater Sci Eng 1985;73:45–63. [9] Lindner M, Kr€ oger M, Popp K. Stick-slip vibrations of pneumatic seals. Mach Dyn Probl 2001;25:121–30. [10] Sheng G, Lee JH, Narravula V, Song D. Experimental characterization and analysis of wet belt friction and the vibro-acoustic behavior. Tribol Int 2011;44:258–65. [11] Barquins M, Maugis D, Blouet J, Courtel R. Contact area of a ball rolling on an adhesive viscoelastic material. Wear 1978;51:375–84. [12] Wu Y, Leamy MJ, Varenberg M. Schallamach waves in rolling: belt drives. Tribol Int 2018;119:354–8. [13] Wu Y, Varenberg M, Leamy MJ. Schallamach wave-induced instabilities in a beltdrive system. J Appl Mech 2019;86:031002. [14] Wu Y, Leamy MJ, Varenberg M. Belt-drive mechanics: friction in the absence of sliding. J Appl Mech 2019;86. 101001. [15] Czichos H. Tribology: a systems approach to the science and technology of friction, lubrication, and wear. Elsevier; 2009. [16] Romero-S� anchez MaD, Pastor-Blas MM, Martı ́n-Martứnez JM. Adhesion improvement of SBR rubber by treatment with trichloroisocyanuric acid solutions in different esters. Int J Adhesion Adhes 2001;21:325–37. [17] Mittal KL. Polymer surface modification: relevance to adhesion, vol. 3. CRC Press; 2004. [18] Liu C, Cui N, Brown NM, Meenan BJ. Effects of DBD plasma operating parameters on the polymer surface modification. Surf Coat Technol 2004;185:311–20. [19] Noeske M, Degenhardt J, Strudthoff S, Lommatzsch U. Plasma jet treatment of five polymers at atmospheric pressure: surface modifications and the relevance for adhesion. Int J Adhesion Adhes 2004;24:171–7. [20] Paulussen S, Rego R, Goossens O, Vangeneugden D, Rose K. Plasma polymerization of hybrid organic–inorganic monomers in an atmospheric pressure dielectric barrier discharge. Surf Coat Technol 2005;200:672–5. [21] Verheyde B, Rombouts M, Vanhulsel A, Havermans D, Meneve J, Wangenheim M. Influence of surface treatment of elastomers on their frictional behaviour in sliding contact. Wear 2009;266:468–75. [22] Varenberg M, Gorb SN. Hexagonal surface micropattern for dry and wet friction. Adv Mater 2009;21:483–6. [23] Kligerman Y, Varenberg M. Elimination of stick-slip motion in sliding of split or rough surface. Tribol Lett 2014;53:395–9. [24] Gorb SN. Visualisation of native surfaces by two-step molding. Microsc Today 2007;15:44–6. [25] Murarash B, Itovich Y, Varenberg M. Tuning elastomer friction by hexagonal surface patterning. Soft Matter 2011;7:5553–7.
4. Conclusion The results obtained in this work allow us to draw the following conclusions: 1. Surface texturing can be successfully employed for minimizing local and global self-oscillations in belt drive systems, and the effect is much more pronounced in the driver case than in the driven case due to different mechanisms for formation of detachment waves. 2. Both regular and irregular surface topographies are useful in mini mizing the belt drive vibrations, but regular surface textures provide a stronger effect. 3. The aspect ratio of surface projections is found to be the most important parameter, and the lattice constant is found to be marginally effective, while the pattern shape and orientation show no effect at all on the belt drive performance. 4. Too excessive texturing of the belt surface can lead to the belt losing its tractive capabilities. Author Contributions Yingdan Wu: Methodology, Formal analysis, Investigation, Writing Original Draft Michael J. Leamy: Conceptualization, Methodology, Writing - Re view & Editing, Supervision, Funding acquisition Michael Varenberg: Conceptualization, Methodology, Writing - Re view & Editing, Supervision, Funding acquisition Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence
6
Contents lists available at ScienceDirect
Tribology International journal homepage: http://www.elsevier.com/locate/triboint
Minimizing self-oscillation in belt drives: Surface texturing Yingdan Wu, Michael J. Leamy, Michael Varenberg * George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA, 30332, USA
A R T I C L E I N F O
A B S T R A C T
Keywords: Contact mechanics Elastomers Rolling Stick-slip Detachment waves
Detachment waves have recently been identified as one of the main sources for self-oscillation and accompanying energy losses in belt drive systems under low-speed and otherwise steady operation. In light of this, herein we explore mitigation of detachment wave-induced instabilities via regular and irregular texturing of the belt contact surface. The results document that surface texturing reduces the magnitude of belt drive oscillations, with the reduction being significantly more pronounced in the driver case than in the driven case. While both regular and irregular surface topographies are useful in minimizing the vibrations, regular patterns result in a stronger effect. The aspect ratio of surface projections is found to be the most important parameter, while excessive texturing of the belt surface is shown to result in belts losing their tractive capabilities.
1. Introduction Frictional interactions in both sliding and rolling elastomeric con tacts are significantly affected by adhesion [1–3]. When unable to slide due to stiction, the tangentially-loaded elastomeric surface repeatedly buckles under compression [4–6], forming narrow lines of lost contact, termed Schallamach detachment waves, that propagate across the interface to allow for relative displacement between the contacting bodies [7]. This unstable surface behavior [6] is observed in contacts incorporating rubber-like materials if the contact area is large [8], and though it is obviously undesirable in mechanical systems, even the presence of lubricant between the elastomer and its counterpart cannot always prevent the associated vibrations [9,10]. Though known already for several decades [7,11], waves of detachment had only recently been observed in a belt drive system for the first time [12]. Interestingly, analysis of dynamic behavior of a model belt drive reveals that local detachment events at the belt-pulley interface are responsible for global self-oscillations of the system [13]. Moreover, it is also found that the detachment wave-induced in stabilities significantly lower the energy efficiency of a belt drive [14]. Given that belt drives are employed for transmitting mechanical power in numerous engineering applications, this calls for research on tech niques that can be used for the disruption of detachment waves at the rolling belt-pulley interface. Modifying the surface chemistry or topography can affect adhesion [15] and, hence, the formation and propagation of detachment waves, which may help in stabilizing the elastomer friction. In chemical
modification, different functional groups are introduced at the elasto meric surface by treatment with strong acids or chlorinating agents [16]. Atmospheric plasma treatments [17] are also used to introduce adhesion-oriented functional groups [18,19] on elastomeric surfaces as well as to deposit a plasma polymerized coating on top of them [20,21]. Laser cladding was also recently employed to produce a polymer-based coating on elastomer substrates [21]. However, these methods are time-consuming and often based on substances that are not environ mentally friendly. Moreover, large elasticity of elastomers makes coating them challenging as it necessitates a strong adhesion over a wide range of strains. Modification of surface topography, on the other hand, does not produce any of the above-mentioned issues and can be achieved by polymer curing against a template surface. It is clear that modifying surface topography is preferable over chemical modification. In light of the above, here we explore the possibility to minimize detachment wave-induced instabilities via texturing of the belt contact surface, with the extensible belt working in a low-speed regime. In so doing, we answer the question of whether regular surface patterns known to reduce detachment waves in sliding [22,23] can be also employed in rolling, and we compare their performance to that of irregular surface textures. 2. Experimental details 2.1. Preparation of textured belts All belt specimens were made of a transparent polydimethylsiloxane
* Corresponding author. E-mail address: [email protected] (M. Varenberg). https://doi.org/10.1016/j.triboint.2020.106157 Received 23 October 2019; Received in revised form 1 January 2020; Accepted 2 January 2020 Available online 7 January 2020 0301-679X/© 2020 Elsevier Ltd. All rights reserved.
Y. Wu et al.
Tribology International 145 (2020) 106157
Fig. 1. Schematic of transferring texture from an original surface onto a PDMS belt.
Fig. 2. Schematic and optical microscopy images of replicated surfaces with regular and irregular topography. (a)–(d) 3D-printed hexagonal and square patterns. Arrows in the direction of rolling. (e) 3D-printed and polished surface. (f)–(h) 1200, 150 and 80 grit abrasive paper sheets, respectively.
(PDMS, Sylgard 184, Dow Corning, Midland, MI) elastomer at a 10:1 mixture ratio of Sylgard 184 pre-polymer and its cross-linker. The mixture was cured in light vacuum (to ensure no air bubbles trapped inside the belt) for 14 h at 65 οC in negative molding templates prepared using a four-step molding technique (Fig. 1) [24] to replicate the topography of either regularly or irregularly textured surfaces (Fig. 2). Use of three additional materials (PU, PVS and Epoxy, see Fig. 1) was required to ensure clean demolding since none of these materials can be easily separated from both the replicated surfaces and PDMS. PU (polyurethane, F-160 A/B, BJB Enterprises, Tustin, CA) was cured for 3 h at 25οC and then for 16 h at 71οC in light vacuum oven against replicated surfaces (see below for details). PVS (Affinis light body, €tten, Switzerland) was poured onto the PU Coltene Holding, Altsta template and cured for 10 min at 25οC. Epoxy (Spurr low viscosity embedding kit, Sigma Aldrich, St. Louis, MO) was cured for 8 h at 70οC in light vacuum oven against the PVS template. The textured belts were 400 mm in length, 2 mm in thickness, and 10 mm in width, while the reference smooth belt was 7 mm wide to ensure similar apparent contact areas. The replicated surfaces with regular topography (Fig. 2a–d) were 3Dprinted out of Formlabs Clear Resin (Formlabs, Somerville, MA) to have hexagonal and square projections with height h, size D, and lattice
constant a. These projections were polished with SiC 2000 grit abrasive paper (Struers, Cleveland, OH) to different heights and a surface roughness Ra of less than 150 nm. Our previous studies on the size effects of regular topography on sliding friction [23,25] reveal that the lattice constant, a, and the aspect ratio, AR ¼ h/D, are important parameters, while the area density, AD ¼ (D/a)2, is insignificant. To this end, all patterned surfaces shared the same area density, AD � 70% (chosen to have good grip, while still being able to fabricate gaps between smallest texture elements), while the examined parameters were the lattice constant, a ¼ 0.6, 1, 3 mm, the aspect ratio, AR ¼ 0.1, 0.2, 0.3, 0.4, 0.5, and the pattern shape and orientation (Fig. 2a–d). The template for casting the smooth reference belt was prepared using the same tech nology of 3D printing and polishing to a surface roughness Ra of less than 150 nm (Fig. 2e). The replicated surfaces with irregular topography (Fig. 2f–h) were SiC abrasive paper sheets of 2000, 1200, 800, 400, 200, 150, and 80 grit (Struers, Cleveland, OH; Lot Fancy Inc, San Francisco, CA). The surface profiles of abrasive papers were characterized using a Hommel Etamic W5 profiler (Jenoptik AG, Jena, Germany).
Fig. 3. Experimental apparatus: (a) schematic representation and (b) system as built. 2
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Fig. 4. Tension difference and angular velocity measured on (a) reference smooth belt and (b) hexagonally patterned (a ¼ 1 mm, AR ¼ 0.2) belt, and characteristic sequences of optical images representing evolution of the contact area (shown in black) in the driver case.
2.2. Set-up and operating conditions A custom-built test rig [12] used in this study is shown in Fig. 3. The belt wraps around a pulley and is drawn at a prescribed constant speed by a driving weight and a releasing motor that control the driving stage motion. The belt loading is controlled via the tension and torque weights connected to the backend of the belt and to the pulley, respectively. Both the driver and driven case scenarios can be implemented by reversing the direction at which the torque is applied to the pulley (solid and dashed configuration, respectively, as shown in Fig. 1a). Two load cells attached at the two ends of the belt measure the belt tension and a rotary encoder connected to the pulley tracks its angular displacement. A digital camera is used for the observation of the belt/pulley interface. Similar to our previous studies, the driving speed was set to 3 mm s 1 and the tension at the tight and slack sides of the belt was adjusted to 6 N and 2 N, respectively. The travel distance of the driving stage was 300 mm. The temperature and relative humidity in the laboratory during the tests were 23 � C and 35%, respectively. All statistical tests were per formed using one-way ANOVA (all pairwise multiple comparison pro cedures (Holm–Sidak method), overall significance level 0.05) in the ORIGIN software package (OriginLab Corporation, Northampton, MA).
Fig. 5. The effect of the pattern shape and orientation on frequency. f, and amplitude, A, of the fluctuations in the tension difference, T, (a), (b), respec tively, and in the angular pulley velocity, α, (c), (d), respectively, in both the driver and driven cases. The fluctuations in the tension difference presented here correspond to detachment events only. All patterns share the same lattice constant and aspect ratio (a ¼ 1 mm, AR ¼ 0.2). The error bars show stan dard deviations.
3. Results and discussion The raw measurements of the difference in the belt tension and the pulley angular velocity obtained for the smooth (reference) and hex agonally patterned belts in the driver case are plotted in Fig. 4 along with the characteristic images of the contact area. The effect of regular surface texture is obvious. With the reference smooth belt, the selfoscillation of the pulley, which is generated due to contact instabilities [13] and induces large-scale fluctuations in the belt tension difference (Fig. 4a), is so powerful that the pulley periodically halts, as follows from inspection of the angular velocity signal. When the patterned belt is used, the pulley rotates much steadier, and only subtle fluctuations are observed around the prescribed angular velocity (~0.3 rad s 1), which reflects also on the fluctuations in the belt tension (Fig. 4b). Looking at the evolution of the contact area, which visualizes the source of system instabilities, we can also clearly see the difference in the behavior of the
flat and patterned belts. First, the size of the detachment zone is greatly reduced (from ~7 mm to ~0.5 mm) when regular surface pattern is introduced. Second, the characteristic surface folds representing waves of detachment (isolated air-pockets within the contact area, such as the one seen on image 3 in Fig. 4a) are barely distinguishable for the patterned belt. Detachment waves in the driver pulley case appear due to a shearinduced moment generated at the belt exit region [12,14]. When the belt surface is split into multiple disconnected and independent sub-contacts via patterning, its stiffness is reduced such that a much smaller moment is needed to start detachment. To this end, since the shear-induced moment grows until it is relaxed by detachment, the detachment waves also have a smaller scale and are formed more often, 3
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Fig. 6. The effect of lattice constant on frequency. f, and amplitude, A, of the fluctuations in the tension difference, T, (a), (b), respectively, and in the angular pulley velocity, α, (c), (d), respectively, in both the driver and driven cases. The fluctuations in the tension difference presented here correspond to detachment events only. All patterns share the same aspect ratio (AR ¼ 0.2). The error bars show standard deviations.
Fig. 7. The effect of aspect ratio on frequency. f, and amplitude, A, of the fluctuations in the tension difference, T, (a), (b), respectively, and in the angular pulley velocity, α, (c), (d), respectively, in both the driver and driven cases. The fluctuations in the tension difference presented here correspond to detachment events only. All patterns share the same lattice constant (a ¼ 1 mm). The error bars show standard deviations.
leading to less violent excitation of the system. In light of this ration alization, we may expect to be able to minimize the self-oscillation of the belt drive system by modifying the geometrical characteristics of the independent contact elements.
case when the belt surface is textured. 3.2. Effect of lattice constant Decreasing the lattice constant (i.e., increasing the number of indi vidual sub-contacts per unit area) does show a small measurable effect, though no statistically significant difference is observed between different lattice constants in both the driver and driven cases (Fig. 6). This agrees with observations made in other studies where the most significant effect is achieved during initial contact splitting, while further minimization of vibrations requires increasing the number of individual sub-contacts by several orders of magnitude [23], which may be considered impractical. Given that we were limited by the resolution of 3D printing in preparing the molding templates, our finest pattern was based on the lattice constant of 0.6 mm, which results in just 25 times more individual sub-contacts than in the case of our coarsest pattern with the lattice constant of 3 mm. Evidently, this change is not strong enough.
3.1. Effect of the pattern shape and orientation Hexagon- and square-shaped patterns oriented differently with respect to the rolling direction (H1, H2, S1 and S2, as shown in Fig. 2) were tested and compared with the reference smooth belt in terms of the frequency and amplitude of the belt and pulley oscillations (Fig. 5). The oscillations in the belt tension difference (as shown in Fig. 4) were decomposed into large-scale and small-scale components associated with pulley motion and detachment events, respectively [13]. Given that the characteristics of the pulley motion-related oscillations in the belt tension difference resemble those of the oscillations in the pulley angular velocity shown also in Fig. 5, only the detachment event-related oscillations in the belt tension difference are presented. The second order oscillations in the pulley angular velocity that correspond to detachment events are also not shown as they are similar to those in the tension difference signal. Fig. 5 demonstrates similar oscillation characteristics for all patterned belts regardless of the pattern shape and orientation in both the driver and driven cases, and no statistically significant difference between these patterns is observed either. This observation supports our hypothesis regarding the core mechanism of the disruption of detach ment waves — the reduction of surface stiffness is independent of the pattern type (to a first approximation), so the belt can detach easier from the pulley as long as its surface is split, while the shape and orientation of the contact patches are not important. This finding allows us to use just one representative shape, and the pattern H1 is chosen for the following study. The effect of patterning, however, is different for the driver and driven cases. For the driver pulley, the amplitude of both types of oscillation is reduced by a factor of approximately 3, and the frequency is increased by a factor of approximately 1.5, while for the driven pulley, the observed effect is much weaker. This is explained by the difference in the mechanism of detachment [12]. In the former case, the detachment is shear-driven, and surface conditions are vital, while in the latter case, it is stretch-driven, and the surface conditions are less decisive as volume effects dominate. Another important observation is that the oscillations in the driver case become even less pronounced than those in the driven
3.3. Effect of aspect ratio The aspect ratio of the hexagonally shaped projections is next varied from 0.1 to 0.5. Increasing the aspect ratio from 0.1 to 0.4 leads to an increase in frequency and to a decrease in amplitude of the oscillations in both the belt tension difference and the pulley angular velocity, as shown in Fig. 7. However, a statistically significant effect of aspect ratio is observed only in the driver pulley case, which results from the dif ference in the mechanisms of detachment in the driver and driven cases as discussed above. Interestingly, the belt patterned to have an aspect ratio of 0.5 was incapable of carrying the prescribed torque in either the driver or the driven pulley. These observations are explained in the following way. As the aspect ratio increases, the bending stiffness of the hexagonal projections is reduced. As a result, these projections bend easier under shear traction. Correspondingly, since the threshold for the formation of detachment waves is easier to reach, the detachment events initiated by the shear-induced moment in the driver case occur more frequently and have smaller range. However, with large enough aspect ratio, the pro jections bend to such a degree that their flat ends lose contact with the pulley [25] regardless of the shear direction. This leads to a great reduction in the real contact area and in the ability to resist shear. The so-called “slip” zone then grows until it consumes the entire belt-pulley interface in both the driver (Fig. 8) and the driven cases. At this moment, 4
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Fig. 8. Optical images representing evolution of the patterned contact area (shown in black) obtained in the driver case with a camera installed at different angular orientations. (a) AR ¼ 0.4, torque is transmitted. (b) AR ¼ 0.5, torque is not transmitted. Hatched areas represent the regions out of view.
Fig. 9. Comparison of the effects of surface roughness (irregular topography) and aspect ratio (regular topography) on frequency, f, and amplitude, A, of the fluctuations in the tension difference, T, (a), (b), respectively, and in the angular pulley velocity, α, (c), (d), respectively, in both the driver and driven cases. The fluctuations in the tension difference presented here correspond to detachment events only. The error bars show standard deviations.
a global displacement between the pulley and the belt is established, and no further power can be transmitted. The resolution of our imaging system does not enable us to say whether bent hexagonal projections truly slide, or small-scale detachment waves allow for relative motion in the slip zone, but in any event they can move independently and the scale of global frictional instabilities is reduced due to scattering of local “slip” events over time and space [23].
surface topography on oscillation characteristics of textured belts can be plotted in one figure. Notably, similar to the regularly textured belts, the belts with irregular surface topography could not transmit the pre scribed torque when the roughness ratio was too high (Ra/Sm � 0.041, for the belt cast against the roughest abrasive sheet of 80 grit). This allowed us to scale the horizontal axes of Aspect Ratio and Ra/Sm such that the data could be conveniently compared as shown in Fig. 9 – i.e., the far right-end of the Ra/Sm (bottom horizontal axis; irregular textures) and Aspect Ratio (top horizontal axis; regular textures) domains both correspond to gross slip. Studying the self-oscillation behavior of the irregularly textured belts, we see that it resembles that of the belts with regular topography, while the observed effects are generally weaker (Fig. 9). Most likely, this is due to surface irregularities on rough belts having smaller contact area and less bending compliance as compared to surface projections on regularly patterned belts, making the effect of texturing less
3.4. Effect of roughness Given that the aspect ratio of regular topography was found to be the dominant parameter affecting the belt drive oscillations, to study the effect of irregular surface topography, we have constructed a similar ratio of vertical and horizontal profile characteristics, Ra/Sm, where Ra and Sm are standard roughness average and mean spacing of profile ir regularities, respectively. In this way, the effects of regular and irregular 5
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pronounced. Further, while maintaining statistically indistinguishable values in the driven case, in the driver case the frequencies and ampli tudes of the oscillations related to both the detachment events and angular velocity signal change significantly as Ra/Sm increases up to 0.02 and then remain constant for larger values of Ra/Sm. This can possibly be related to the irregularly patterned belt surfaces having random shapes, sizes and distribution of asperities, so other character istics can change simultaneously with the aspect ratio of surface asper ities and lead to deviation from the expected effect of the aspect ratio alone. In general, the similarity between the effects of regular and irregular surface texturing validates our hypothesis that splitting the contact area into disconnected sub-contacts helps minimizing detachment waveinduced instabilities in rolling. The regular surface texturing, however, has an advantage over the irregular surface texturing since the system’s self-oscillations can be minimized to a greater extent, and both the driver and the driven rolling can be improved.
the work reported in this paper. Acknowledgement This material is based upon work supported by the National Science Foundation under Grant No. 1562129. References [1] Rabinowicz E. The intrinsic variables affecting the stick-slip process. Proc Phys Soc Lond 1958;71:668–75. [2] Barquins M. Adherence, friction and wear of rubber-like materials. Wear and Friction of Elastomers. ASTM International; 1992. [3] Persson BNJ. On the theory of rubber friction. Surf Sci 1998;401:445–54. [4] Best B, Meijers P, Savkoor AR. The formation of Schallamach waves. Wear 1981; 65:385–96. [5] Barquins M, Roberts AD. Rubber-friction variation with rate and temperature – some new observations. J Phys D Appl Phys 1986;19:547–63. [6] Rand CJ, Crosby AJ. Insight into the periodicity of Schallamach waves in soft material friction. Appl Phys Lett 2006;89. Artn 261907. [7] Schallamach A. How does rubber slide? Wear 1971;17:301–12. [8] Barquins M. Sliding friction of rubber and Schallamach waves - a review. Mater Sci Eng 1985;73:45–63. [9] Lindner M, Kr€ oger M, Popp K. Stick-slip vibrations of pneumatic seals. Mach Dyn Probl 2001;25:121–30. [10] Sheng G, Lee JH, Narravula V, Song D. Experimental characterization and analysis of wet belt friction and the vibro-acoustic behavior. Tribol Int 2011;44:258–65. [11] Barquins M, Maugis D, Blouet J, Courtel R. Contact area of a ball rolling on an adhesive viscoelastic material. Wear 1978;51:375–84. [12] Wu Y, Leamy MJ, Varenberg M. Schallamach waves in rolling: belt drives. Tribol Int 2018;119:354–8. [13] Wu Y, Varenberg M, Leamy MJ. Schallamach wave-induced instabilities in a beltdrive system. J Appl Mech 2019;86:031002. [14] Wu Y, Leamy MJ, Varenberg M. Belt-drive mechanics: friction in the absence of sliding. J Appl Mech 2019;86. 101001. [15] Czichos H. Tribology: a systems approach to the science and technology of friction, lubrication, and wear. Elsevier; 2009. [16] Romero-S� anchez MaD, Pastor-Blas MM, Martı ́n-Martứnez JM. Adhesion improvement of SBR rubber by treatment with trichloroisocyanuric acid solutions in different esters. Int J Adhesion Adhes 2001;21:325–37. [17] Mittal KL. Polymer surface modification: relevance to adhesion, vol. 3. CRC Press; 2004. [18] Liu C, Cui N, Brown NM, Meenan BJ. Effects of DBD plasma operating parameters on the polymer surface modification. Surf Coat Technol 2004;185:311–20. [19] Noeske M, Degenhardt J, Strudthoff S, Lommatzsch U. Plasma jet treatment of five polymers at atmospheric pressure: surface modifications and the relevance for adhesion. Int J Adhesion Adhes 2004;24:171–7. [20] Paulussen S, Rego R, Goossens O, Vangeneugden D, Rose K. Plasma polymerization of hybrid organic–inorganic monomers in an atmospheric pressure dielectric barrier discharge. Surf Coat Technol 2005;200:672–5. [21] Verheyde B, Rombouts M, Vanhulsel A, Havermans D, Meneve J, Wangenheim M. Influence of surface treatment of elastomers on their frictional behaviour in sliding contact. Wear 2009;266:468–75. [22] Varenberg M, Gorb SN. Hexagonal surface micropattern for dry and wet friction. Adv Mater 2009;21:483–6. [23] Kligerman Y, Varenberg M. Elimination of stick-slip motion in sliding of split or rough surface. Tribol Lett 2014;53:395–9. [24] Gorb SN. Visualisation of native surfaces by two-step molding. Microsc Today 2007;15:44–6. [25] Murarash B, Itovich Y, Varenberg M. Tuning elastomer friction by hexagonal surface patterning. Soft Matter 2011;7:5553–7.
4. Conclusion The results obtained in this work allow us to draw the following conclusions: 1. Surface texturing can be successfully employed for minimizing local and global self-oscillations in belt drive systems, and the effect is much more pronounced in the driver case than in the driven case due to different mechanisms for formation of detachment waves. 2. Both regular and irregular surface topographies are useful in mini mizing the belt drive vibrations, but regular surface textures provide a stronger effect. 3. The aspect ratio of surface projections is found to be the most important parameter, and the lattice constant is found to be marginally effective, while the pattern shape and orientation show no effect at all on the belt drive performance. 4. Too excessive texturing of the belt surface can lead to the belt losing its tractive capabilities. Author Contributions Yingdan Wu: Methodology, Formal analysis, Investigation, Writing Original Draft Michael J. Leamy: Conceptualization, Methodology, Writing - Re view & Editing, Supervision, Funding acquisition Michael Varenberg: Conceptualization, Methodology, Writing - Re view & Editing, Supervision, Funding acquisition Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence
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