Slip Speeds Research Articles

Presence of Frozen Fringe Impacts Soft‐Bedded Slip Relationship

AbstractGlaciers and ice streams flowing over sediment beds commonly have a layer of ice‐rich debris adhered to their base, known as a “frozen fringe,” but its impact on basal friction is unknown. We simulated basal slip over granular beds with a cryogenic ring shear device while ice infiltrated the bed to grow a fringe, and measured the frictional response under different effective stresses and slip speeds. Frictional resistance increased with increasing slip speed until it plateaued at the frictional strength of the till, closely resembling the regularized Coulomb slip law associated with clean ice over deformable beds. We hypothesize that this arises from deformation in a previously unidentified zone of weakly frozen sediments at the fringe's base, which is highly sensitive to temperature and stress gradients. We show how a rheologic model for ice‐rich debris coupled with the thermomechanics of fringe growth can account for the regularized Coulomb behavior.

An Analysis of Power Friction Losses in Gear Engagement with Intermediate Rolling Elements and a Free Cage

Currently, mechanical gears with cycloid engagement are increasingly used in mechanisms along with involute ones. In modern drive mechanisms, using pin gears and gears with intermediate rolling elements (IRE) is widespread, which simultaneously use cycloid gears. To a greater extent, pin gears are now being investigated, but IRE gears have their undeniable advantages. Many works are devoted to the study of cycloid toothing for certain gears, but the efficiency, especially that of IRE gears, has practically not been investigated. Therefore, the analysis of power losses in the engagement of a gear with IRE and a free cage (IREFC) is relevant. In this analysis, the authors of the work have used laws of mechanics, methods of energy flows and a secant normal. Mathematical expressions have been obtained to estimate slip speeds and power friction losses in the engagement of a gear with IREFC, and a formula has been derived to determine the efficiency of a mentioned mechanical transmission. The calculation of slip speeds and power losses at the points of contact of a rolling element with cycloid profiles of wheels for selected initial parameters of a gear with IREFC has been presented. The friction power and the overall efficiency of the entire gear engagement have also been calculated. This work shows that power friction losses at the points of contact of a rolling element with cycloid profiles of tooth wheels of a gear with IREFC are not the same. The friction power in the contact of a rolling element with a cycloid profile of a cam is an order of magnitude higher than the friction power in the contact of a rolling element with a cycloid profile of a crown.

Friction Law for Rubber from Laboratory Abrasion Tester

ABSTRACT This paper aims to devise a method to obtain an empirical friction law for rubber using the Laboratory Abrasion Tester (LAT 100). The LAT 100 experiments, which aim to measure the side force at various slip angles, loads, and speeds, are carried out, followed by finite element simulation using ABAQUS. A friction law is implemented using a subroutine (UFRIC), which calculates the friction coefficient at each node on the contact patch based on contact pressure and slip velocity at the corresponding node. Coefficients of the frictional law, μ = a + b × e−1/(αp) + c × e−1/(βv), have been estimated by using a series of simulations along with minimizing the error between experiment and simulation side forces. The procedure followed in this paper can be used to fit friction models for rubber using LAT 100 side force experiments.

Effect of the grease thickener on tribological properties of Si3N4/GCr15 contact interface and the performance in hybrid ceramic ball bearing

Si3N4 hybrid bearings are considered the most promising motor bearings due to their characteristics of electrical insulation, high speed, low friction coefficient, and wear resistance, which can better meet the requirements of driving motors of electric vehicles. However, the tribological mechanism between the ceramic-grease-steel complex interface is unclear. Three kinds of greases, namely lithium, polyurea, and calcium sulfonate complex grease, were synthesized from poly alpha olefin 40 as base oil. The effects of grease thickener morphology on the tribological properties of Si3N4/GCr15 contact surfaces at different slip speeds were investigated, and the vibration and friction torque performances in 6204 hybrid ceramic balls were evaluated. The results showed that the thickener could form physical deposition film and friction film to protect the worn surface at low speed. The friction and wear conditions were significantly improved at high speed under lithium grease and polyurea grease lubrication, being a mixed lubrication state. In presence of lithium grease, the tribological performance of the Si3N4/GCr15 interface and the vibration performance, impacted condition, starting torque, and friction torque of the hybrid ceramic ball bearings were all the best. Because lithium grease is subjected to continuous shear of the ceramic ball, which releases the base oil stably, and forms a thick oil film with the broken thickener in the center of the raceway, the bearing is in a mild lubrication state. Therefore, for Si3N4 hybrid ceramic ball bearings, lithium grease is a lubricant with good application prospects.

Rapid Tremor Migration During Few Minute‐Long Slow Earthquakes in Cascadia

AbstractSlow earthquakes are now commonly found to display a wide range of durations, moments, and slip and propagation speeds. But not all types of slow earthquakes have been examined in detail. Here we probe tremor bursts with durations between 1 and 30 min, which are likely driven by few minute‐long bursts of aseismic slip. We use a coherence‐based technique to detect thousands of tremor bursts beneath Vancouver Island in Cascadia. Then we examine 17 of the ruptures by tracking their evolving tremor locations over an 8‐km region. We find that tremor migrates at rates of 3–25 m/s: faster than longer tremor bursts. Though some observational biases persist, the short events' speeds appear to fill a gap in the spectrum of observed slow earthquakes. They may provide further evidence that whatever fault zone process creates slow earthquakes, it must allow for faster slip and propagation in smaller ruptures.

The tire slip angle estimation algorithm based on intelligent tire technology

Tire slip angle is a very important parameter in tire/vehicle dynamics control. This paper proposes a tire slip angle estimation method that combines intelligent tire technology and machine learning. Firstly, a finite element model of a 205/55/R16 radial tire was established by ABAQUS software, and the tire finite element model is verified by the radial stiffness experiment and dynamics experiment. Secondly, the curves of lateral acceleration and the curves of the lateral displacement obtained by five virtual tri-axial accelerometers installed on the inner line of the finite element tire under different slip angles, tire pressures, loads, and speeds were analyzed. Finally, combined with linear correlation analysis method, the promising input eigenvalues were determined, and three slip angle prediction models were trained based on the same set of train sets to predict the same set of test sets. The prediction results showed that the slip angle prediction curve of BP model has the highest degree of coincidence with the actual curve, and the mean absolute percentage error is 3.55%, indicating that the slip angle estimation algorithm proposed in this paper is feasible, which is very important for the stability control of the vehicle.

ANALYSIS OF THE INFLUENCE OF THE DISPLACEMENT OF THE GEAR RACK PROFILE OF THE PAIR EVOLUTION GEARING ON THE QUALITY INDICATORS OF THE TRANSMISSION

The article is devoted to the study of the influence of the modification of the paired evolute gearing with convex-concave contact on the quality indicators of transmission, namely, the contact pressure and the speed of slippage in the engagement. Previous studies of evolute gears showed the presence of characteristic zones on the side surface of the tooth, which have worse values of quality indicators than in similar involute gear. One of the ways to remove these zones or to reduce their impact on the load capacity of the transmission is to modify the tooth profile, which will be implemented by shifting the profile of the processing gear rack. A displacement factor is added to the equation of the rail profile curve, which has the same value for the gear and wheel teeth, but the opposite sign. On the basis of the developed equation, the side profiles of the teeth of the gear and the wheel were constructed. Several values of the rack displacement coefficient with a positive and negative sign for the gear teeth are considered. The results of the research allow us to evaluate the influence of the amount and direction of the rail displacement on the curvature of the tooth profiles, the contact pressure in engagement along the height of the tooth, and the relative and absolute speed of sliding. The modifications of the profile of the processing toothed rack proposed in this work will expand the existence of paired evolute gears with a different set of quality indicators. This will make it possible to design gears with rational values of contact pressures and slip speeds when they are used in heavily loaded transmissions created for specific operating conditions. Gears with relatively high slip speeds can be used in road and construction equipment transmissions, which are characterized by low shaft rotation frequency, in which the speed of slip between the teeth does not have a significant effect on the life or efficiency of the transmission. Otherwise, gears with relatively low slip speeds are very relevant when they are implemented in the transmission of modern and promising vehicles with a hybrid or fully electric power unit, especially in the case of passenger cars with high-speed electric motors.

Brittle Faulting at Elevated Temperature and Vanishing Effective Stress

AbstractIf brittle fault strength depends only on friction, slip instability is discouraged at low effective normal stress, σ. Stress drop and the critical stiffness necessary for unstable sliding both vanish with σ; small earthquakes cannot occur. Very low σ is inferred in the source region of low‐frequency earthquakes (LFEs) on the San Andreas fault (SAF). Moreover, if pore pressure, p, is undrained at low σ, then instabilities are prevented at all scales. This is due to dilatant strengthening which arises due to a dependence of porosity on strain rate. Dilatant strengthening is σ‐independent and dominates at low σ. Undrained p is inferred over time scales of less than a few days for the SAF LFEs. Based on experiments that measure rapid contact overgrowth between 350 and 530°C at very low σ, fault failure controlled by time‐dependent cementation is invoked as an explanation for the SAF LFEs. Because this “cohesion” is σ‐independent, stress drops can occur at σ = 0. If in addition cohesion exceeds any dilatant strengthening during slip, cohesion dominates strength at low σ. Dilatancy measured in prior faulting and shear experiments indicate that at all stress levels steady‐state porosity depends on σ in addition to strain rate. Moreover, porosity at low σ depends elastically on the confining and differential stresses. A model with these additional pore pressure effects, friction, and time‐dependent cohesion, applied to the SAF LFEs produces stress drops, slip speeds, and durations that are consistent with the observations, when the shear‐induced dilatancy is not extreme.

Upper Plate Response to a Sequential Elastic Rebound and Slab Acceleration During Laboratory‐Scale Subduction Megathrust Earthquakes

AbstractAn earthquake‐induced stress drop on a megathrust instigates different responses on the upper plate and slab. We mimic homogenous and heterogeneous megathrust interfaces at the laboratory scale to monitor the strain relaxation on two elastically bi‐material plates by establishing analog velocity weakening and neutral materials. A sequential elastic rebound follows the coseismic shear‐stress drop in our elastoplastic‐frictional models: a fast rebound of the upper plate and the delayed and smaller rebound on the elastic belt (model slab). A combination of the rebound of the slab and the rapid relaxation (i.e., elastic restoration) of the upper plate after an elastic overshooting may accelerate the relocking of the megathrust. This acceleration triggers/antedates the failure of a nearby asperity and enhances the early slip reversal in the rupture area. Hence, the trench‐normal landward displacement in the upper plate may reach a significant amount of the entire interseismic slip reversal and speeds up the stress build‐up on the upper plate backthrust that emerges self‐consistently at the downdip end of the seismogenic zones. Moreover, the backthrust switches its kinematic mode from a normal to reverse mechanism during the coseismic and postseismic stages, reflecting the sense of shear on the interface.

Friction Characteristics of Open Graded Asphalt Friction Courses with BOF and EAF Steel Slag Aggregates

Friction properties of open graded asphalt friction course (OGAFC) mixtures play an essential role in ensuring traffic safety, especially under wet weather conditions. This study evaluated the friction characteristics of basic oxygen furnace (BOF) and electric-arc furnace (EAF) steel slag aggregate incorporated OGAFC mixes. Nine sets of OGAFC mixes were fabricated using five percentage replacements (0%, 25%, 50%, 75%, and 100%) of the coarse natural aggregate fraction by BOF and EAF steel slags. The effect of modified binder type (polymer and crumb-rubber modified) on the frictional characteristics of OGAFC mixes was also examined. The principal friction test devices used were the British pendulum tester and dynamic friction tester. Multiple friction performance aspects were studied: (1) effect of surface condition (dry, wet, and ponding) on the measured friction coefficient; (2) separate evaluation of adhesion and hysteresis friction components; (3) variation of friction coefficient with varying slip speeds, and (4) friction performance later in the OGAFC service life using artificially polished aggregates, and comparison of the performance with unpolished aggregates. Results revealed that the use of steel slags in OGAFC mixes considerably enhanced the frictional characteristics and that the skid resistance of OGAFC-BOF mixes was better than that of OGAFC-EAF mixes. Frictional resistance of the mixes was found to increase with an increase in steel slag content. OGAFC mixes comprising polished steel slag aggregates also showed promising results with the increment in steel slag content. The findings also indicated that OGAFC-CRMB mixes perform better than OGAFC-PMB mixes.

Characterizing Sediment Flux of Deforming Glacier Beds

AbstractDeformation of subglacial sediment during basal slip shapes the beds of many fast‐flowing glaciers and ice streams. The resultant sediment flux impacts glacier dynamics and rates of subglacial erosion over a range of timescales, but its fundamental dependencies are not well understood. Using a cryogenic ring shear device, we conducted experiments to investigate the effects of both effective stress and slip speed on rates of till transport. Sediment fluxes were computed using digital image correlation from a photographic time series of the till bed. We find a near‐linear relationship between sediment flux and slip speed, but a non‐monotonic, double‐valued dependency of sediment flux on effective stress. Deformation primarily occurred in a thin shear band near the ice sole, the thickness of which could vary with both parameters. Coupling between ice and till increased at higher slip speeds and effective stresses and scaled the magnitude of the flow profile.

Coulomb threshold rate-and-state model for fault reactivation: application to induced seismicity at Groningen

SUMMARY A number of recent modelling studies of induced seismicity have used the 1994 rate-and-state friction model of Dieterich 1994 to account for the fact that earthquake nucleation is not instantaneous. Notably, the model assumes a population of seismic sources accelerating towards instability with a distribution of initial slip speeds such that they would produce earthquakes steadily in the absence of any perturbation to the system. This assumption may not be valid in typical intraplate settings where most examples of induced seismicity occur, since these regions have low stressing rates and initially low seismic activity. The goal of this paper is twofold. First, to derive a revised Coulomb rate-and-state model, which takes into account that seismic sources can be initially far from instability. Second, to apply and test this new model, called the Threshold rate-and-state model, on the induced seismicity of the Groningen gas field in the Netherlands. Stress changes are calculated based on a model of reservoir compaction since the onset of gas production. We next compare the seismicity predicted by our threshold model and Dieterich’s model with the observations. The two models yields comparable spatial distributions of earthquakes in good agreement with the observations. We find however that the Threshold model provides a better fit to the observed time-varying seismicity rate than Dieterich’s model, and reproduces better the onset, peak and decline of the observed seismicity rate. We compute the maximum magnitude expected for each model given the Gutenberg–Richter distribution and compare to the observations. We find that the Threshold model both shows better agreement with the observed maximum magnitude and provides result consistent with lack of observed seismicity prior to 1993. We carry out analysis of the model fit using a Chi-squared reduced statistics and find that the model fit is dramatically improved by smoothing the seismicity rate. We interpret this finding as possibly suggesting an influence of source interactions, or clustering, on a long timescale of about 3–5 yr.

The Spatial Relationship Between Contemporaneous Tremor Detections in Relatively Low‐ and High‐Frequency Bands

AbstractAlthough tremor is believed to consist of myriad low‐frequency earthquakes (LFEs), it also contains longer‐period signals of unknown origin. We investigate the source of some of the longer‐period signals by locating tremor windows independently in relatively high‐frequency (“HF”, 1.25–6.5 Hz, containing typical LFEs) and low‐frequency (“LF”, 0.5–1.25 Hz) bands. We hypothesize that if tremor consists entirely of LFEs, such that the lower‐frequency signals come from the non‐uniform timing of higher‐frequency (∼2 Hz) LFEs, then contemporaneous LF and HF signals should be nearly co‐located. Here we search for a systematic offset between the locations of contemporaneous LF and HF detections during rapid tremor migrations (RTMs). This first requires correcting for apparent offsets in location that arise simply from filtering in different passbands. To guard against possible errors in our empirical filtering effect corrections, we focus on a region of the subduction interface beneath southern Vancouver Island that hosts migrations propagating in nearly opposing directions. We find that the LF energy appears to occur roughly 500 m farther behind the propagating fronts of RTMs than the HF energy, whether those fronts propagate to the ENE or to the WSW. This separation is small compared to the location error of individual LF detections, but the result seems robust owing to the large number of detections. If this result stands, it suggests that tremor consists of more than just a collection of LFEs, with longer‐period energy being generated farther behind the migrating fronts of RTMs, where slip speeds are presumably lower.

Variations in Hard‐Bedded Topography Beneath Glaciers

AbstractThe morphology of glacier beds is a first‐order control on their slip speeds and consequent rates of subglacial erosion. As such, constraining the range of bed shapes expected beneath glaciers will improve estimates of glacier slip speeds. To estimate the variability of subglacial bed morphology, we construct 10 high‐resolution (10 cm) digital elevation models of proglacial areas near current glacier margins from point clouds produced through a combination of terrestrial laser scanning and photogrammetry techniques. The proglacial areas are located in the Swiss Alps and the Canadian Rockies and consist of predominantly debris‐free bedrock of variable lithology (igneous, sedimentary, and metamorphic). We measure eight different spatial parameters intended to describe bed morphologies generated beneath glaciers. Using probability density functions, Bhattacharyya coefficients, principal component analysis, and Bayesian statistical models we investigate the significance of these spatial parameters. We find that the parameters span similar ranges, but the means and standard deviations of the parameter probability density functions are commonly distinct. These results indicate that glacier flow over bedrock may lead to a convergence toward a common bed morphology. However, distinct properties associated with each location prevent morphologies from being uniform.

Factors that contribute to the elongation of drumlins beneath the Green Bay Lobe, Laurentide Ice Sheet

AbstractDrumlin shape has been hypothesized to correlate with ice‐flow duration and slip speed, but modern‐day analogues and the Coulomb nature of till render the basis of these correlations in question. The evolution of flow‐parallel subglacial landforms is of importance for ice flow because the form drag they provide may be a dominant factor in regulating glacier slip speeds. Here we examine the relationship between drumlin shape and cumulative slip displacement (i.e. time‐integrated slip speed) as a dominant glaciological control on drumlin shape. First, a new method is developed that allows slip speed to be estimated for deformable bedded glaciers along a flow line from an ice surface profile. Then, reconstructed surface profiles for ice margin chronologies of the Green Bay Lobe (GBL) are used to construct and estimate the spatially varying cumulative slip displacement for use in comparison with drumlin elongation ratios. We focus on a sector of the GBL near the central flow line where the geology is simple and glaciological controls are likely to dominate bedform development. Using Bayesian statistical analysis, a positive and statistically robust relationship between cumulative slip displacement and drumlin elongation ratio is found. Our analysis indicates that drumlin shape could be used to infer palaeo glacier slip speeds if time under the ice can be well constrained and geologic influences are minimal. These findings also suggest that drumlin‐supplied drag could decrease with increased cumulative slip displacement in the absence of rigid geologic features that fix drumlin positions.

Is complex fault zone behaviour a reflection of rheological heterogeneity?

Fault slip speeds range from steady plate boundary creep through to earthquake slip. Geological descriptions of faults range from localized displacement on one or more discrete planes, through to distributed shearing flow in tabular zones of finite thickness, indicating a large range of possible strain rates in natural faults. We review geological observations and analyse numerical models of two-phase shear zones to discuss the degree and distribution of fault zone heterogeneity and effects on active fault slip style. There must be certain conditions that produce earthquakes, creep and slip at intermediate velocities. Because intermediate slip styles occur over large ranges in temperature, the controlling conditions must be effects of fault properties and/or other dynamic variables. We suggest that the ratio of bulk driving stress to frictional yield strength, and viscosity contrasts within the fault zone, are critical factors. While earthquake nucleation requires the frictional yield to be reached, steady viscous flow requires conditions far from the frictional yield. Intermediate slip speeds may arise when driving stress is sufficient to nucleate local frictional failure by stress amplification, or local frictional yield is lowered by fluid pressure, but such failure is spatially limited by surrounding shear zone stress heterogeneity.This article is part of a discussion meeting issue ‘Understanding earthquakes using the geological record’.

On the Effect of Clutch Dynamic Properties on Noise, Vibration and Harshness Phenomena

<div class="section abstract"><div class="htmlview paragraph">Noise, vibration and harshness (NVH) phenomena can manifest themselves during the engagement and disengagement of dry friction clutch systems. Such phenomena can have a negative impact on cabin occupants’ driving experience as well as on others in the immediate vicinity of the vehicle. Typically, unwanted NVH phenomena that pertain to the clutch system include Judder, Chatter, Squeal and Eek. These are recognized by the quality of the radiated noise, as well as the dynamics occurring during clutch actuation. The aim of the current study is to utilize a numerical clutch system model (fully coupling the main motions of the clutch components) to predict clutch dynamics during engagement manoeuvres. The model will be used to assess the effect of various clutch design parameters on mitigating system instability. The clutch model utilizes measured coefficient of friction data from a rotary tribometer at representative slip speeds and friction surface contact pressures. The paper highlights potential NVH issues and demonstrates the improvement of such unwanted behavior through varying clutch system dynamic properties. Improved understanding of the parameters that affect clutch dynamic stability can lead to NVH improvement.</div></div>

Torque Characteristics Analysis of Slotted-Type Eddy-Current Couplings Using a New Magnetic Equivalent Circuit Model

In this article, a new magnetic equivalent circuit (MEC) model was presented to predict torque characteristics and reaction flux in slotted-type eddy-current couplings (SECs). The magnetomotive force and reaction field caused by eddy current in the conductor were innovatively introduced into the model; particularly, the modulations of the magnetic field and eddy current by iron teeth in conductor disk were taken into account by dividing magnetic flux paths in air gap into several branches. The expressions of magnetic flux and torque were obtained by combining Kirchhoff’s law and Ampere’s loop law. The torque was calculated using the method proposed and was compared with those obtained by the 3-D finite element method (FEM) and experiment, respectively. The results indicated that the method proposed is accurate and effective under conditions of low slip speeds and short air gap lengths.

Noise, vibration and harshness during dry clutch engagement oscillations

Determining the root causes of various noise, vibration and harshness phenomena in modern automotive drivetrains is a critical task for industry, since noise, vibration and harshness issues often result in worsened driving experience. The aim of the current research is to investigate the dynamics during dry clutch engagement and the associated – often problematic – oscillations. This paper reports the development and partial validation of numerical models to study dry clutch behaviour. The models are used to investigate the influence of clutch and throttle actuation on the occurrence of unwanted clutch oscillations. The dynamic coefficient of friction between the clutch interacting surfaces was measured using a pin-on-disc rig under different slip speeds and contact pressure conditions, which are representative of a typical clutch engagement manoeuvre. The paper highlights the occurrence of instability issues in clutch dynamics (disc radial mode) as potential generators of aggressive noise, vibration and harshness, particularly during two different clutch pedal actuations. Such analysis has not hitherto been reported in the open literature.

Scale demarcation of self-affine surface of coarse aggregate and its relationship with rubber friction

The surface texture of aggregate is extremely related to the functional performance of asphalt pavement. The textures on different wavelength scales make varying contributions to tire-pavement interaction, especially the rubber friction on a rough road surface. This study develops a two-scaling-range approach based on self-affine to demarcate the wavelengths of texture. A piecewise-linear fitting model was established to determine the cut-off wavelengths employed to separate the window-textures by filtering methods. Afterwards, the window-roughness was introduced to characterise the roughness of texture in a specific scale range. The relationship between the window-roughness and the rubber frictions at different slip speeds was analysed using Pearson correlation. As a result, the self-affine approach is excellent to demarcate the scales without loss of similar characteristics of surface texture. The surface texture of aggregate significantly performs a two-scaling-range self-affine characteristic. The two critical wavelength values respectively vary within 0.10–0.25 mm and 1.0–4.0 mm due to the types of aggregates. Moreover, a strong correlation between the friction and the small-scale roughness will gradually decrease with the increasing slip speed. In contrast, the opposite change is obvious on the larger scales. The method provides guidance for determining the corresponding key wavelength ranges of road surface texture under a rubber slip speed.