Method and apparatus for controlling squeaking sounds of frictional interface

Abstract

A method is directed to controlling friction at a soft-rigid interface. The method includes providing a soft material of thickness H contacting a rigid material. The method also includes introducing a pattern of ridges on the soft material, the ridges acting as waveguides for opening slip pulses. The method also includes sliding the soft material relative to the rigid material at a velocity above a threshold velocity, thereby inducing the opening slip pulses propagating at a shear wave speed, cₛ, of the soft material. A frequency of the opening slip pulses is determined by the relationship f₀ ≈ cₛ / 2H. Activation of the opening slip pulses reduces a frictional force between the soft material and the rigid material.

Description

METHOD AND APPARATUS FOR CONTROLLING SQUEAKING SOUNDS OF FRICTIONAL INTERFACECROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims priority to and the benefit of U.S. Provisional Application No. 63 / 673,514, filed on July 19, 2024, which is incorporated herein by reference in its entirety.STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH

[0001] This invention was supported by the national Science Foundation (NSF) through the Harvard University Materials Research Science and Engineering Center grant number DMR-2011754.FIELD OF THE INVENTION

[0002] The present invention relates generally to control of frictional force and squeaking sounds at frictional interfaces. More particularly the present invention relates to a frictional interface between a pattern disposed on a soft material and a rigid material, wherein the amount of friction between the pattern and the rigid material and the frequency of the squeaking produced at the frictional interface is controllable by selection of the height of the soft material and the geometrical patern of the ridges.BACKGROUND OF THE INVENTION

[0003] Squeaking is a constant companion in various aspects of our daily lives, whether we are gliding rubber-soled shoes across hardwood floors, scraping chalk on a blackboard, engaging the brakes on a bicycle, or walking with a hip replacement. When two stiff bodies slide over each other, It is widely acknowledged that squeaking arises from self-excited stickslip oscillations, triggered by a decrease in friction coefficient with slip velocity. However, the sliding of a soft body on a rigid one presents a fundamentally different scenario, as the contacting interface never truly experiences slipping, but rather supports the propagation of opening pulses. Surprisingly, the propagation of these pulses has primarily been investigated in the realm of slow sliding, where squeaking is typically absent. A need exists for an understanding of the parameters that affect the relationship of squeaking produced by the sliding of the soft body over the rigid body. The present disclosure provides a solution to these and other needs.SUMMARY OF THE INVENTION

[0004] The term embodiment and like terms, e.g., implementation, configuration, aspect, example, and option, are intended to refer broadly to all of the subject matter of this disclosure and the claims below. Statements containing these terms should be understood not to limit the subject matter described herein or to limit the meaning or scope of the claims below. Embodiments of the present disclosure covered herein are defined by the claims below, not this summary. This summary is a high-level overview of various aspects of the disclosure and introduces some of the concepts that are further described in the Detailed Description section below. This summary is not intended to identify key or essential features of the claimed subject matter. This summary is also not intended to be used in isolation to determine the scope of the claimed subject matter. The subject matter should be understood by reference to appropriate portions of the entire specification of this disclosure, any or all drawings, and each claim.

[0005] According to certain aspects of the present disclosure, a method is directed to controlling friction at a soft-rigid interface. The method includes providing a soft material of thickness H contacting a rigid material. The method also includes introducing a pattern of ridges on the soft material, the ridges acting as waveguides for opening slip pulses. The method also includes sliding the soft material relative to the rigid material at a velocity above a threshold velocity, thereby inducing the opening slip pulses propagating at a shear wave speed, cs, of the soft material. A frequency of the opening slip pulses is determined by the relationship fo « Cs / 2H. Activation of the opening slip pulses reduces a frictional force between the soft material and the rigid material.

[0006] According to certain aspects of the present disclosure, a device is directed to controlling friction. The device includes a soft substrate of height H with integrated ridges configured to interface with a rigid material. The soft substrate is made of a material having a shear wave speed, cs. The ridges are structured to guide opening slip pulses. The height H and geometry of the ridges are selected to define a target pulse frequency fo ~ c5 / 2H. Sliding the soft substrate over the rigid material reduces friction therebetween through activation of the opening slip pulses.

[0007] According to certain aspects of the present disclosure, a system comprises a rigid material and a plurality of n soft blocks of differing heights Hi, H2, . . . Hn, each soft block respectively generating a distinct pulse frequency, foi, fo2, . . . fon, via a guided opening slip pulse when the soft block is translated across the rigid material. The system also includes a mechanism to translate each of the plurality of soft blocks at a prescribed velocity across therigid material to respectively activate the guided opening slip pulse and thereby generate the distinct pulse frequency foi, fo2, . . . fon, for friction control or sound generation.

[0008] According to certain aspects of the present disclosure, a method is directed to controlling squeaking at a frictional interface. The method includes providing a rigid material and providing a soft material. The soft material interfaces with the rigid material to cause a squeaking sound that has a squeaking pitch. A pattern material is inserted between the rigid material and the soft material to control the squeaking pitch.

[0009] According to some features of the above aspects, the method further includes adjusting a height of the soft material, the adjusting causing a change in frequency of the squeaking pitch.

[0010] According to some features of the above aspects, the pattern material includes a plurality of parallel ridges.

[0011] According to some features of the above aspects, the rigid material is a flat surface, the squeaking sound being caused by the plurality7of ridges making contact with the flat surface.

[0012] According to some features of the above aspects, each of the plurality of parallel ridges causes the squeaking sound if it has a width that is less than a threshold width.

[0013] According to some features of the above aspects, the fundamental frequency of squeaking remains approximately constant with an increasing of the width of each of the plurality of parallel ridges.

[0014] According to some features of the above aspects, each of the plurality of parallel ridges causes the squeaking sound if the soft material is moved relative to the rigid material at a sliding speed that is greater than a threshold sliding speed.

[0015] According to some features of the above aspects, the method further includes integrating the pattern material with the soft material.

[0016] According to some features of the above aspects, the soft material includes silicone, rubber, silicone rubber, thermoplastic polyurethane (TPU), or any combination thereof..

[0017] According to some features of the above aspects, the rigid material includes glass, metal, or hardwood.

[0018] According to some features of the above aspects, controlling the squeaking pitch via the pattern material also controls friction between soft material and the rigid material.

[0019] According to some features of the above aspects, controlling the friction between soft material and the rigid material include reducing the friction between soft material and the rigid material.

[0020] According to certain aspects of the present disclosure, a device is directed to controlling squeaking at a frictional interface. The device has a substrate including a first material configured to interface with a second material. The second material has a greater ri gi di ty property than the first material. The device further has a squeak-control pattern attached to the substrate. The squeak-control pattern has a plurality of ridges configured to make contact with the second material.

[0021] According to some features of the above aspects, the first material has a prescribed height, the height determining a respective squeaking pitch resulting from frictional contact between the plurality of ridges and the second material.

[0022] According to some features of the above aspects, the first material comprises silicone, rubber, silicone rubber, thermoplastic polyurethane (TPU), or any combination thereof .

[0023] According to some features of the above aspects, the plurality of ridges are integral to the substrate.

[0024] According to some features of the above aspects, the second material comprises glass, metal, or hardwood.

[0025] According to some features of the above aspects, the device further includes a driving mechanism to slide the substrate relative to the second material at a prescribed sliding velocity.

[0026] According to certain aspects of the present disclosure, a system is directed to producing squeaking sounds. The system has a rigid material, a plurality of substrates, and a rail-driven mechanism. Each of the plurality of substrates includes a second material configured to interface with the rigid material. The rigid material has a greater rigidity property than the second material. Each of the plurality of substrates has a prescribed height. A squeakcontrol pattern is attached to each of the plurality of substrates. The squeak-control pattern has a plurality of ridges configured to make contact with the rigid material. The rail-driven mechanism is configured to slide each of the plurality of substrates over the rigid material at a prescribed velocity and in a predetermined temporal pattern.

[0027] According to some features of the above aspects, the prescribed height of each of the plurality of substrates corresponds to a fundamental frequency of squeaking produced by sliding the substrate over the rigid material.

[0028] According to some features of the above aspects, the prescribed height of each of the plurality of substrates is selected to tune the fundamental frequency of the squeaking produced by sliding each of the plurality of substrates over the rigid material to a musical note.

[0029] According to some features of the above aspects, the predetermined temporal pattern and the prescribed height of each of the plurality of substrates produces a song when the plurality of substrates is slid over the rigid material by the rail-driven mechanism.

[0030] The above summary is not intended to represent each embodiment or every aspect of the present disclosure. Rather, the foregoing summary merely provides an example of some of the novel aspects and features set forth herein. The above features and advantages, and other features and advantages of the present disclosure, will be readily apparent from the following detailed description of representative embodiments and modes for carrying out the present invention, when taken in connection with the accompanying drawings and the appended claims. Additional aspects of the disclosure will be apparent to those of ordinary' skill in the art in view of the detailed description of various embodiments, which is made with reference to the drawings, a brief description of which is provided below.BRIEF DESCRIPTION OF THE DRAWINGS

[0031] The disclosure, and its advantages and drawings, will be better understood from the following description of representative embodiments together with reference to the accompanying drawings. These drawings depict only representative embodiments and are therefore not to be considered as limitations on the scope of the various embodiments or claims.

[0032] FIG. 1A shows an exemplary schematic diagram of the experimental setup used to explore the origin of squeaking between soft and rigid materials, according to certain aspects of the present disclosure.

[0033] FIG. IB shows an exemplary temporal evolution of a recorded sound signal produced by a basketball show slid across a glass plate, according to certain aspects of the present disclosure.

[0034] FIG. 1C shows a fast Fourier transform (FFT) of the recorded sound signal of FIG. IB, with dashed lines indicating a fundamental frequencyos= 4817 Hz and its harmonics, according to certain aspects of the present disclosure.

[0035] FIG. ID shows exemplary schematic snapshots of an exemplary frictional interface between the basketball shoe and the glass plate of FIG. IB at times t = 12.6 ms, 12.68 ms, and 12.76 ms, highlighting an opening pulse marked by7the dashed line moving from left to right, in the directing of sliding, where the light and dark areas indicate contact and no contact zones, respectively, according to certain aspects of the present disclosure.

[0036] FIG. IE shows in the top graph an exemplary contact spatio-temporal map showing the evolution as a function of time of the gray-scale values for pixels located along the line D-D of FIG. ID, and in the bottom graph an enlarged view of a portion of the contact spatiotemporal map of the top graph, according to certain aspects of the present disclosure.

[0037] FIG. IF shows an exemplary spectrum of the gray-scale intensity values along the line E-E of FIG. IE, with the dashed vertical lines indicating peaks in frequency, according to certain aspects of the present disclosure.

[0038] FIG. 2A shows exemplary schematic snapshots of a frictional interface at three different times for a sample with a sliding surface that is flat, according to certain aspects of the present disclosure.

[0039] FIG. 2B shows exemplary' schematic snapshots of a frictional interface at three different times for a sample with a sliding surface that features an array of parallel ridges, according to certain aspects of the present disclosure.

[0040] FIG. 2C shows an exemplary contact spatio-temporal map showing the evolution as a function of time of the gray-scale intensity values for the pixels located along the line A in FIG. 2A, according to certain aspects of the present disclosure.

[0041] FIG. 2D shows an exemplary contact spatio-temporal map showing the evolution as a function of time of the gray-scale intensity values for the pixels located along the line B in FIG. 2B, according to certain aspects of the present disclosure.

[0042] FIG. 2E shows an exemplary' spectrum of the recorded sound (shown by the darker trace) and the gray-scale intensity values (shown by the lighter trace) for the pixels located along the line C in FIG. 2C for a sample with a sliding surface that is flat, according to certain aspects of the present disclosure.

[0043] FIG. 2F show s an exemplary' spectrum of the recorded sound (shown by the darker trace) and the gray-scale intensity values (shown by the lighter trace) for the pixels located along the line D in FIG. 2D for a sample with a sliding surface that features an array of parallel ridges, according to certain aspects of the present disclosure.

[0044] FIG. 2G shows an exemplary contact spatio-temporal map showing the evolution as a function of time of the gray-scale intensity values for the pixels located along the vertical lines in FIG. 2A, according to certain aspects of the present disclosure, according to certain aspects of the present disclosure.

[0045] FIG. 2H shows an exemplary contact spatio-temporal map showing the evolution as a function of time of the gray-scale intensity values for the pixels located along the vertical lines in FIG. 2B, according to certain aspects of the present disclosure.

[0046] FIG. 21 shows an exemplary measured pulse length and angle for a sample with a flat sliding surface, according to certain aspects of the present disclosure.

[0047] FIG. 2J shows an exemplary measured pulse length and angle for a sample with a sliding surface featuring an array of ridges, according to certain aspects of the present disclosure.

[0048] FIG. 3A shows exemplary schematic snapshots of an exemplary frictional interface for samples with a single ridge of width w = 6 mm in the top image and w = 24 mm in the bottom image, according to certain aspects of the present disclosure.

[0049] FIG. 3B shows the spectra of the temporal evolution of the gray-scale values for the pixels located along a representative horizontal line along each ridge for four sample ridges featuring ridge widths as indicated, according to certain aspects of the present disclosure.

[0050] FIG. 3C shows pulse length (left) and angle (right) as a function of the ridge width, according to certain aspects of the present disclosure.

[0051] FIG. 4A shows an exemplary schematic drawing of cuboid samples of height H with the sliding surface featuring an array of parallel ridges being slid on a rigid plate by hand (on top) or via a rail-driven setup (bottom), according to certain aspects of the present disclosure.

[0052] FIG. 4B shows a graph of the fundamental frequency fo of a squeaking sound as a function of H, where the measured frequency follows the scaling prediction of fo = cs / 2H, so that by varying H, six blocks can be designed, each block producing a different musical note, according to certain aspects of the present disclosure.

[0053] FIG. 4C shows a partial transcription of the music score of “The Imperial March” composed by John Williams for the Star Wars saga on top with a corresponding spectrogram on the bottom played by moving blocks of the corresponding musical notes over rigid substrates, where the dashed lines represent the target frequency for each note, according to certain aspects of the present disclosure.DETAILED DESCRIPTION

[0054] Various embodiments are described with reference to the attached figures, where like reference numerals are used throughout the figures to designate similar or equivalent elements. The figures are not necessarily drawn to scale and are provided merely to illustrate aspects and features of the present disclosure. Numerous specific details, relationships, and methods are set forth to provide a full understanding of certain aspects and features of the present disclosure, although one having ordinary skill in the relevant art will recognize that these aspects and features can be practiced without one or more of the specific details, with other relationships, or with other methods. In some instances, well-known structures oroperations are not shown in detail for illustrative purposes. The various embodiments disclosed herein are not necessarily limited by the illustrated ordering of acts or events, as some acts may occur in different orders and / or concurrently with other acts or events. Furthermore, not all illustrated acts or events are necessarily required to implement certain aspects and features of the present disclosure.

[0055] For purposes of the present detailed description, unless specifically disclaimed, and where appropriate, the singular includes the plural and vice versa. The word "‘including’7means “including without limitation.” Moreover, words of approximation, such as “about,” “almost,” “substantially,” “approximately,” and the like, can be used herein to mean “at,” “near,” “nearly at,” “within 3-5% of,” “within acceptable manufacturing tolerances of,” or any logical combination thereof. Similarly, terms “vertical” or “horizontal” are intended to additionally include “within 3-5% of’ a vertical or horizontal orientation, respectively. Additionally, words of direction, such as “top,” “bottom,” “left,” “right,” “above,” and “below” are intended to relate to the equivalent direction as depicted in a reference illustration; as understood contextually from the object(s) or element(s) being referenced, such as from a commonly used position for the object(s) or element(s); or as otherwise described herein.

[0056] As disclosed herein, the origin of squeaking was determined when a soft material like a rubber comes under friction against a rigid smooth material in dry' conditions. It was determined that it is necessary to include a pattern on the surface to have a squeaking pitch (a sound with a fundamental frequency and its harmonics). It was further determined that once a squeaking pitch exists, it is possible to control its frequency by controlling the height of the soft material.

[0057] It was also determined that adding the pattern to the surface not only produced squeaking but also reduced friction between the soft material and the rigid smooth material. The reduction of friction resulting from the addition of the pattern can be important for applications directed to wear reduction, haptics, energy dissipation, and other areas. An experimental investigation of the processes occurring at soft rigid interfaces for sliding velocity large enough to trigger squeaking and reduce friction is disclosed.

[0058] The approach involves concurrent high-speed measurements of contact dynamics at the frictional interface and of the resulting sound. It was found that opening pulses propagate along the interface at the shear wave speed of the soft material - three orders of magnitude faster than previously observed. In the presence of thin ridges that act as waveguides, these pulses are periodically initiated, eventually leading to squeaking. Conversely, in the absence of ridges, initiation is aperiodic and does not result in squeaking but rather in broadband noise.

[0059] Furthermore, it was found that for a given soft material, the frequency of squeaking is solely dependent on the height of the sliding block and corresponds to the natural frequency associated with its lowest shear mode. A fundamental frequency of the squeaking is a function of the type of soft material and its height, H. The shear wave speed in the soft material, cs, is a material property of the soft material. For a soft material having a given height of H, the fundamental frequency of the squeaking is fo = cs / 2H. Notably, these findings carry significant implications, facilitating the development of surfaces with geometrical features that prevent squeaking during interaction with rigid surfaces, or alternatively, with geometrical features that allow intentional squeaking at desired frequencies, opening up a whole new design space for controlling friction and energy dissipation across scales. This is illustrated by the design of six blocks, each corresponding to a musical note, which when moved over rigid substrates, can be orchestrated to play songs.

[0060] At interfaces between soft and rigid materials, elastic instabilities within the soft solid give rise to wrinkles, which locally disrupt the interface and propagate as opening pulses, facilitating slip. When sliding velocities are slow (vsude < 10 mm / s), these pulses are commonly referred to as Schallamach waves. They propagate at a speed significantly slower than the shear wave speed of the soft material and they do not generate audible sound. However, theoretical models, integrating the elastodynamic equation with frictional contact boundary conditions, predict the existence of opening pulses traveling at sonic speed along soft-rigid frictional interfaces. Motivated by these theoretical insights, the experimental investigation demonstrates that at higher sliding velocities (vsnde ~ 1 m / s), opening pulses indeed travel at the shear wave speed of the soft material. Moreover , the results show a direct connection between their propagation and the generation of squeaking sound. Further, triggering the opening pulses traveling at the shear wave speed of the soft material not only creates squeaking but also reduces friction between the slow material and the rigid material over which the soft material is being slid.

[0061] Opening slip pulses can be geometrically guided through ridges of selected geometry. Intelligent selection of a particular soft material and its pattern of ridges can be used in both reducing friction of sliding and locking a desired frequency of squeaking. There is a direct physical link between a geometry of the soft material, including the height H, and the ridge pattern geometry, and the dynamics of opening slip pulses produced when the soft material is slid on a rigid surface. In turn, the dynamics of the opening slip pulses are directly linked to the frequency of sound produced and the level of friction of the sliding.

[0062] Referring to FIG. 1A, to explore the origin of squeaking, commercially available basketball shoes (for example. Nike CU3503-100) were slid across a glass plate at a velocity vsnde « 1 m / s while simultaneously capturing the sound and visualizing the contact. The rubber sole of the basketball shoe has a pattern of parallel ridges on the contact surface of the sole. When the parallel ridges of the sole's contact surface slide at a speed of about 1 m / s on a rigid material like a hardwood floor or a glass plate as exemplified here, the ridges cause periodic local opening slip pulses, and a squeaking sound is produced. The opening slip pulses propagate at the shear wave speed of the rubber material of the sole and repeat at a frequency set by the shoe sole’s thickness. As is described more fully below, this mechanism emits a squeaking sound at a fundamental frequency of the shear wave speed of the rubber. cs, divided by twice the height of the sole, 2H. the squeaking occurs t a predictable frequency and is accompanied by a reduced frictional force at the onset of the opening pulse.

[0063] As shown in FIG. IB , the recorded sound intensity peaks in the time interval t e [2, 18] ms. indicating the occurrence of squeaking during this time frame. Referring to FIG. 1C, upon examining the sound spectrum, its fundamental frequency is identified to be fo = 4817 Hz.

[0064] Referring to FIG. ID, simultaneously, total internal reflection was employed to visualize the interfacial contact between the sole and the glass plate, with the setup designed to generate images with bright pixels exclusively at the points of contact. The captured images reveal the presence of opening pulses propagating in the direction of sliding (areas delimited by the horizontal line in FIG. ID), which cause temporary' separation between the ridges of the shoe and the glass plate.

[0065] To quantify the repetition frequency and propagation speed of these pulses. FIG. IE shows the evolution as a function of time of the gray-scale values, Ig, for the pixels located along a representative horizontal line D-D on the plate as shown in FIG. ID. We find an array of nearly- horizontal bright lines . with each line representing a ridge on the sole that slides across the selected path D-D. Notably, for t e [2, 18] ms we observe a pattern of alternating bright and dark spots along these lines, indicating that the ridges periodically lose contact. Such pattern exhibits a period T ~ 0.207 ms, resulting in a repetition frequency foc= 1 / T ~ 4830 Hz that well aligns with the fundamental frequency of the recorded sound.

[0066] As shown in FIG. IF a nearly identical fundamental frequency,= 1 / T « 4830 Hz, is found from the spectrum of Igat a representative position X along the considered horizontal line E-E on the plate as shown in FIG. IE. As such, these results underscore thecausal relationship between opening pulses and the squeaking sound produced by the sole during sliding. Finally, the spatio-temporal diagrams of FIG. IE clearly indicate that these opening pulses propagate from one ridge to the other (trajectory highlighted by the dashed line in bottom the bottom graph of FIG. IE) at a speed of Cpuise = 64.5 ± 1.5 m / s, a speed much higher than the sliding speed. Squeaking is generated across various ridge geometries including ridges having various orientations and curvature other than just straight and parallel ridges.

[0067] The results of FIGs. 1A-1F reveal that squeaking is closely connected to opening pulses traveling along the frictional interface. In an effort to identify the conditions required to initiate these pulses, cuboid samples of size 40x40x20 mm, for example, made out of silicone rubber (Zhermack Elite Double) were tested. The material of the sliding element in these examples could be another soft material, for example without limitation, rubber, silicone, or thermoplastic polyurethane (TPU), or any combination thereof.

[0068] The physical relationships established herein between geometry and material choice of the soft material and frequency of squeaking and level of friction apply equally for soft materials that include biological materials. For example, it is understood that composite materials with a soft layer at the frictional interface fall under the same umbrella as illustrated by the hand which is a biological composite material.

[0069] Referring to FIGs. 2A-2J results of two of these samples are shown: one with a flat sliding surface and another with a sliding surface featuring an array of parallel ridges with height h = 1.5 mm. width w = 1.5 mm and center-to-center distance s = 3 mm. Each sample has a defined thickness or height of the sample, H. In the experiments, the position of the elastomeric samples is fixed so that a normal stress CTN = 22 kPa can be accurately prescribed, the glass plate is moved by suddenly applying a constant driving force of magnitude Fd = 160 N. The material of the rigid surface in these examples could be another rigid material, for example without limitation, polymethyl methacrylate (PMMA), metal, hardwood, or other suitable rigid material. It was found that in both samples opening pulses propagate along the frictional interface for sliding velocities Vsitde > 0.22 m / s. These pulses either initiate from perturbations at the contact interface, or are triggered by electric discharges that give rise to lightning.

[0070] Referring to FIG. 2A, in the case of the flat sample, the pulses exhibit vary ing widths and appear to lack order. In contrast, referring to FIG. 2B. in the sample featuring ridges, the pulses extend across the width of the ridges and systematically travel along them, causing localized bulging. To quantify these observations, the spatio-temporal evolution of contactalong representative horizontal and vertical lines on the samples (indicated by horizontal lines and vertical lines in FIGs. 2A and 2B) was examined.

[0071] Referring to FIGS. 2C and 2D, and focusing first on the evolution of contact along the horizontal lines, it was found that for both samples the opening pulses propagate in the direction of sliding at a speed Cpuise ~ 24 ± 1 m / s. Note that, in full agreement with analytical predictions, Cpuise closely matches the independently measured speed for shear waves propagating in the bulk of the considered rubber, cs= 21.8 ± 1 m / s. In the case of the flat sample, these pulses appear heterogeneously distributed in time and space. Conversely, for the sample with ridges, the pulse separations are consistent at At ~ 1.65 ms, resulting in a repetition frequency fo « 600 Hz. The ridges act as waveguides for the opening slip pulses during sliding.

[0072] Consequently, referring to FIGs. 2E and 2F, no distinct peak is evident in the spectrum of Igat a representative position X for the flat sample (FIG. 2E), whereas a clear fundamental frequency fo ® 600 Hz, accompanied by its harmonics, is observed for the sample with ridges (FIG. 2F). Importantly, the spectrum of Igat X aligns closely with the sound captured during the experiments for both samples, confirming the intrinsic connection between squeaking and the propagation of opening pulses.

[0073] While FIGs. 2C and 2D enable tracing of the trajectory of individual detachment pulses, examining the evolution of contact along the vertical lines using FIGs. 2G and 2H allows us quantification of their length, Zp, orientation, 0P. and thickness, tP. Referring to FIG. 21, it was found that for the flat sample the pulses vary' widely with lP= 7±5 mm, tP= 1.6 ±0.6 mm and 0P= 90± 10. In contrast, referring to FIG. 2J, for the sample with ridges, the traj ectones of the individual detachment pulses are predominantly perpendicular to the ridges and occupy their entire width (i.e. lP= 1.8±0.2 mm, tP= 2.3±0.7mm and 0P= 90±3).

[0074] Next, it was investigated whether the squeaking observed in the sample with ridges requires interactions among multiple ridges. Dependence of the squeaking on the width of the ridges was also investigated. Towards this end, additional experiments were conducted using cuboid samples featuring a single ridge. The height of the ridge in all samples is maintained at h = 1.5 mm, while its width is systematically varied within the range t e [3, 24] mm.

[0075] Referring to FIGs. 3A to 3C, the results show two key points. Firstly, a single thin ridge proves sufficient to induce squeaking. As shown in Fig. 3B, a single ridge produces a highly discernible fundamental frequency, close to that observed in the sample with multiple ridges considered in FIGs. 2A to 2J. Secondly, with increasing width w, the fundamental frequency remains approximately constant, but its magnitude tends to decrease relative to therest of the spectrum. Notably, for w = 24 mm, the spectrum of Igdisplays no clear peaks, indicating the absence of squeaking at this width. Additionally, as w becomes larger, the lateral extension length of the pulses 1Pprogressively decreases (so that the pulses do not span the full ridge width - i.e. lPw < 1), and their alignment becomes less pronounced (see the wider distribution of orientation angles ( in Fig. 3C). As such, these results suggest that thin enough ridges act as wave guides for the opening pulses, ultimately ensuring unidirectional propagation and resulting in the occurrence of squeaking with a highly discernible frequency.

[0076] The factors influencing the frequency of the squeaking sound were also explored. While the findings from FIGs. 3A-3C indicate that thin ridges are essential for triggering squeaking, they also reveal that their width does not impact the fundamental frequency of the sound produced, fo . Interestingly, it was found that fo can be adjusted by altering the height of the sample, H.

[0077] Referring to FIG. 4A, an embodiment of a method 100 for controlling squeaking at a frictional interface is shown. For example, cuboid samples of a soft material 110 of height H are interfaced with a rigid material 120. An exemplary cuboid of the soft material 100 is shown on the left featuring an array of parallel ridges 130. In an embodiment, the array of parallel ridges 130 making sliding contact with the flat surface of the rigid material 120 causes squeaking sounds. As noted above, it has been found that a speed of the sliding contact must exceed a threshold speed for the sliding to produce an audible squeaking.

[0078] As was also noted above with regard to FIG. 3B, increasing a width, w, of each of the array of parallel ridges 130 causes the fundamental frequency of the produced squeaking to remain approximately constant. However, increasing the width, w, of each of the array of parallel ridges 130 causes the magnitude of the fundamental frequency to decrease relative to the rest of the spectrum. Notably, for w = 24 mm. the spectrum of 4 displayed in FIG. 3B has no clear peaks, indicating the absence of squeaking at this width. It has therefore been found that each of the array of parallel ridges 130 needs to have a width less than a threshold width (in this example without limitation the threshold width is about 24 mm) for a squeaking sound to be produced.

[0079] Referring back to FIG. 4A, the cuboid samples of the soft material 110 are shown as being slid on the rigid plate 120 by a hand 140 (in the top drawing) or via an automated driving mechanism 150, for example without limitation, a rail-driven setup 150 (in the bottom drawing). The direction of the sliding of the soft material 110 relative to the rigid plate 120 can be in the direction shown or the reverse direction - back across the array of parallel ridges 130.It has been found that adjusting the height H of the soft material 110 adjusts the fundamental frequency of the produced squeaking. In an embodiment, the array of parallel ridges 130 is integral to the soft material 110. In another embodiment, the array of parallel ridges 130 is an additional layer that is adhered to or otherwise overlaid onto to the soft material 110. In an embodiment the soft material 110 includes, for example without limitation, silicone rubber. In an embodiment, the rigid material includes, for example without limitation, polymethyl methacrylate (PMMA), glass, hardwood, or other suitable rigid material.

[0080] Referring to FIG. 4B, results are presented for the experimentally measured fundamental frequency for patterned samples with H e [5, 20] mm. The results demonstrate an inverse relationship between the fundamental frequency and H. More specifically, we find that fo = cs / (2H). which corresponds to the natural frequency associated with the first shear mode for an elastic block with height H. infinite lateral dimensions and clamped top and bottom surfaces.

[0081] Referring again to FIG. 4 A, in an embodiment a device 200 for controlling squeaking at a frictional interface is shown. The device 200 includes a substrate including the first material 1 10 that is configured to interface with a second material 120, for example, the rigid surface 120. The second material 120 in this embodiment has greater rigidity than the first material 110. The first material 110 includes the array of parallel ridges 130 as a squeak-control pattern 130, where the squeak-control pattern 130 is configured to make contact with the second material 120.

[0082] In an embodiment of the device 200, the array of parallel ridges 130 is integral to the first material 110. In another embodiment, the array of parallel ridges 130 is an additional layer that is adhered to or otherwise overlaid onto to the first material 110. In an embodiment of the device 200. the first material 110 includes, for example without limitation, silicone rubber. In an embodiment of the device 200, the second material 120 includes, for example without limitation, polymethyl methacry late (PMMA), glass, hardwood, or other suitable rigid material.

[0083] In the device 200, the substrate including the first material 110 has a prescribed height, H, which determines a respective squeaking pitch resulting from frictional contact between the array of parallel ridges 130 and the second material 120. In an embodiment, the device 200 includes a driving mechanism 150 to forcibly slide the first material 110 relative to the second material 120 at a prescribed sliding velocity that is greater than the threshold velocity required to produce an audible sound. The device 200 can slide the first material 110relative to the second material 120 in a first direction, for example left to right as shown in FIG. 4A, or in the reverse direction - right to left back across the array of parallel ridges 130.

[0084] Therefore, these findings suggest that the frequency of squeaking is controlled by the frequency of the lowest shear mode for the sample . In the presence of sufficiently thin ridges, the opening pulses are all perpendicular to the ridges and exclusively stimulate this mode. Conversely, in the absence of thin ridges, the diverse orientation of the pulses trigger various vibration modes, effectively suppressing squeaking.

[0085] The results shown in FIG. 4B enable the design of surfaces that intentionally squeak at desired frequencies. For instance, by selecting the height of the samples, HDS = 20 mm, HF5 = 16.8 mm, HAAS , = 15.9 mm, HAS = 13.3 mm, HC = 10.6 mm, and / foe = 10 mm, frequencies corresponding to musical notes such as Ds (fbs = 600 Hz) , Fs (CFS = 713 Hz). F#s ( / F#S = 755Hz), As AS = 899 Hz), C#6 (fc#6 = 1132Hz), and De (fn>6 = 1200Hz) can be achieved. In an embodiment, the reference A4 is slightly shifted from 440 Hz \.ofA4 = 449 Hz.

[0086] Referring to FIGs. 4A to 4C, in an embodiment, a device 300 for producing squeaking sounds includes a plurality of the devices 200 as shown in FIG. 4 A. The device 300 includes at least one rigid first material 120. The device 300 further includes a plurality of substrates, each of the plurality of substrates including a soft second material 110 configured to interface with the rigid first material 120. Possible configurations for this interfacing includes all of the plurality of substrates interfacing with a single rigid first material 120, subgroups of the plurality of substrates each interfacing with a single rigid first material 120, or each of the plurality of substrates interfacing with a single rigid first material 120. The rigid first material 120 has a greater rigidity property7than the soft second material 110. In the device 300, each of the plurality of substrates of the soft material 110 has a prescribed height, H. Each of the plurality of substrates of the soft material 110 includes the array of parallel ridges 130 as a squeak-control pattern 130, where the squeak-control pattern 130 is configured to make contact with the rigid first material 120.

[0087] In an embodiment, the device 300 includes a driving mechanism 150 to forcibly slide each of the substrates that includes the soft second material 110 relative to the rigid first material 120 at a prescribed sliding velocity that is greater than the threshold velocity required to produce an audible sound, and in a predetermined temporal pattern. The device 300 can slide each of the substrates that includes the soft second material 110 relative to rigid first material 120 in a first direction, for example left to right as shown in FIG. 4A, or in the reverse direction - right to left back across the array of parallel ridges 130.

[0088] In an embodiment of the device 300, the array of parallel ridges 130 is integral to the soft second material 110. In another embodiment, the array of parallel ridges 130 is an additional layer that is adhered to or otherwise overlaid onto to the soft second material 110. In an embodiment of the device 300, the soft second material 110 includes, for example without limitation, silicone rubber. In an embodiment of the device 300, the rigid first material 120 includes, for example without limitation, polymethyl methacrylate (PMMA), glass, hardwood, or other suitable rigid material.

[0089] In the device 300, each of the plurality of substrates including the soft second material 110 has the prescribed height, H, which determines a fundamental frequency of squeaking produced by sliding the substrate of the soft second material 110 over the rigid first material 120. The prescribed height. H, of each of the plurality of substrates is selected to tune the fundamental frequency of the squeaking produced by sliding each of the plurality7of substrates over the rigid first material 120 to a particular musical note. For example, as shown in FIG. 4B, musical notes D, C, A, and F are shown for different values of the height, H. When the device 300 slides the plurality of substrates of the soft second material 110 each with a tuned height. H, over the rigid first material 120 in a predetermined temporal pattern, the device 300 produces music.

[0090] As a result, referring to FIG. 4C, a song can be played by sliding the plurality of substrates of the soft second material 110 over the rigid first material 120, either by using the device 300 and the driving mechanism 150 in a predetermined temporal pattern, or by hand. The device 300, by producing music demonstrates that an understanding of the existence and pitch of squeaking allows harnessing and engineering the squeaking sound.

[0091] An experimental investigation explored the behavior of soft-rigid frictional interfaces for high sliding velocities. The propagation of opening pulses traveling at sonic speed along the interface was observed. Additionally, it was demonstrated that in the presence of thin ridges acting as waveguides for these pulses, a consistent repetition frequency of pulse initiation occurs, resulting in the familiar squeaking sound. While the focus in this disclosure has been on arrays of parallel straight ridges slid longitudinally, further control of squeaking could be attained through exploration of more intricate surface ridge patterns and structured bulk materials. The findings herein are consistent across various materials and geometries. Additionally, although the investigation centered on the squeaking sound, the findings suggest that the opening pulses propagating along the soft-rigid frictional interface also induce a reduction in frictional force, thus presenting opportunities for friction coefficient modulation. Applications for the disclosed relationship between squeaking and the physical and materialproperties of a soft material slid across a rigid material include uses in shoes, elastomer components, diagnostics, material interfaces, and haptic devices.

[0092] Finally, this work has unveiled the presence of intricate wave phenomena awaiting deeper understanding and modeling. Specifically, the observed opening pulses seem to maintain their shape during propagation along ridges, suggesting they may have solitary nature. Furthermore, the role of opening waves propagating backward relative to Vsitde, at the longitudinal bulk wave velocity remains to be clarified.

[0093] Although the disclosed embodiments have been illustrated and described with respect to one or more implementations, equivalent alterations and modifications will occur or be known to others skilled in the art upon the reading and understanding of this specification and the annexed drawings. In addition, while a particular feature of the invention may have been disclosed with respect to only one of several implementations, such feature may be combined with one or more other features of the other implementations as may be desired and advantageous for any given or particular application.

[0094] While various embodiments of the present disclosure have been described above, it should be understood that they have been presented by way of example only, and not limitation. Numerous changes to the disclosed embodiments can be made in accordance with the disclosure herein, without departing from the spirit or scope of the disclosure. Thus, the breadth and scope of the present disclosure should not be limited by any of the above described embodiments. Rather, the scope of the disclosure should be defined in accordance with the following claims and their equivalents.

Claims

CLAIMSWhat is claimed is:

1. A method for controlling friction at a soft-rigid interface, the method comprising: providing a soft material of thickness H contacting a rigid material; introducing a pattern of ridges on the soft material, the ridges acting as waveguides for opening slip pulses; sliding the soft material relative to the rigid material at a velocity above a threshold velocity, thereby inducing the opening slip pulses propagating at a shear wave speed, cs, of the soft material; wherein a frequency of the opening slip pulses is determined by the relationship fo ~ cs / 2H; and wherein activation of the opening slip pulses reduces a frictional force between the soft material and the rigid material.

2. A device for controlling friction comprising: a soft substrate of height H with integrated ridges configured to interface with a rigid material, the soft substrate made of a material having a shear wave speed, cs, the ridges structured to guide opening slip pulses; and the height H and geometry of the ridges selected to define a target pulse frequency fo ~ cs / 2H; wherein sliding the soft substrate over the rigid material reduces friction therebetween through activation of the opening slip pulses.

3. A system comprising: a rigid material; a plurality of n soft blocks of differing heights Hi, H2, . . . Hn, each soft block respectively generating a distinct pulse frequency, foi, fo2, . . . fon, via a guided opening slip pulse when the soft block is translated across the rigid material; and a mechanism to translate each of the plurality of soft blocks at a prescribed velocity across the rigid material to respectively activate the guided opening slip pulse and thereby generate the distinct pulse frequency foi, fi>2, . . . fon, for friction control or sound generation.

4. A method for controlling squeaking at a frictional interface, the method comprising: providing a rigid material; providing a soft material that interfaces with the rigid material to cause a squeaking sound having a squeaking pitch; and inserting a pattern material between the rigid material and the soft material to control the squeaking pitch.

5. The method of claim 4, further comprising adjusting a height of the soft material, the adjusting causing a change in frequency of the squeaking pitch.

6. The method of claim 4, wherein the pattern material includes a plurality of parallel ridges.

7. The method of claim 6, wherein the rigid material is a flat surface, the squeaking sound being caused by the plurality of ridges making contact with the flat surface.

8. The method of claim 7, wherein each of the plurality of parallel ridges causes the squeaking sound if it has a width that is less than a threshold width.

9. The method of claim 8, wherein the fundamental frequency of squeaking remains approximately constant with an increasing of the width of each of the plurality of parallel ridges.

10. The method of clam 8, wherein each of the plurality of parallel ridges causes the squeaking sound if the soft material is moved relative to the rigid material at a sliding speed that is greater than a threshold sliding speed.

11. The method of claim 4, further comprising integrating the pattern material with the soft material.

12. The method of claim 4, wherein the soft material includes silicone, rubber, silicone rubber, thermoplastic polyurethane (TPU), or any combination thereof..

13. The method of claim 4, wherein the rigid material includes glass, metal, or hardwood.

14. The method of claim 4, wherein controlling the squeaking pitch via the pattern material also controls friction between soft material and the rigid material.

15. The method of claim 14, wherein controlling the friction between soft material and the rigid material include reducing the friction between soft material and the rigid material.

16. A device for controlling squeaking at a frictional interface, the device comprising: a substrate including a first material configured to interface with a second material, the second material having a greater rigidity properly than the first material; and a squeak-control pattern attached to the substrate, the squeak-control pattern having a plurality of ridges configured to make contact with the second material.

17. The device of claim 16, wherein the first material has a prescribed height, the height determining a respective squeaking pitch resulting from frictional contact between the plurality of ridges and the second material.

18. The device of claim 16, wherein the first material comprises silicone, rubber, silicone rubber, thermoplastic polyurethane (TPU), or any combination thereof.

19. The device of claim 18, wherein the plurality of ridges are integral to the substrate.

20. The device of claim 16, wherein the second material comprises glass, metal, or hardwood.

21. The device of claim 16, further comprising a driving mechanism to slide the substrate relative to the second material at a prescribed sliding velocity.

22. A system for producing squeaking sounds, the system comprising: a rigid material; a plurality of substrates, each of the plurality of substrates including a second material configured to interface with the rigid material, the rigid material having a greater rigidity property than the second material, each of the plurality' of substrates having a prescribed height; anda squeak-control pattern attached to each of the plurality of substrates, the squeakcontrol pattern having a plurality’ of ridges configured to make contact with the rigid material; and a rail-driven mechanism configured to slide each of the plurality of substrates over the rigid material at a prescribed velocity7and in a predetermined temporal pattern.

23. The system of claim 22, wherein the prescribed height of each of the plurality of substrates corresponds to a fundamental frequency of squeaking produced by sliding the substrate over the rigid material.

24. The system of claim 23, wherein the prescribed height of each of the plurality of substrates is selected to tune the fundamental frequency of the squeaking produced by sliding each of the plurality of substrates over the rigid material to a musical note.

25. The system of claim 24, wherein the predetermined temporal pattern and the prescribed height of each of the plurality of substrates produces a song when the plurality of substrates is slid over the rigid material by the rail-driven mechanism.

Images