Time-varying Friction Coefficient Research Articles

Reinforcement of articular cartilage with a tissue-interpenetrating polymer network reduces friction and modulates interstitial fluid load support.

Osteoarthritis (OA) is associated with increased articular cartilage hydraulic permeability and decreased maintenance of high interstitial fluid load support (IFLS) during articulation, resulting in increased friction on the cartilage solid matrix. This study assesses frictional response following in situ synthesis of an interpenetrating polymer network (IPN) designed to mimic glycosaminoglycans (GAGs) depleted during OA. Cylindrical osteochondral explants containing various interpenetrating polymer concentrations were subjected to a torsional friction test under unconfined creep compression. Time-varying coefficient of friction, compressive engineering strain, and normalized strain values (ε/εeq) were calculated and analyzed. The polymer network reduced friction coefficient over the duration of the friction test, with statistically significantly reduced friction coefficients (95% confidence interval 14-34% reduced) at equilibrium compressive strain upon completion of the test (P=0.015). A positive trend was observed relating polymer network concentration with magnitude of friction reduction compared to non-treated tissue. The cartilage-interpenetrating polymer treatment improves lubrication by augmenting the biphasic tissue's interstitial fluid phase, and additionally improves the friction dissipation of the tissue's solid matrix. This technique demonstrates potential as a therapy to augment tribological function of articular cartilage.

Research on the dynamic response of high-contact-ratio spur gears influenced by surface roughness under EHL condition

Employing high-contact-ratio (HCR) gear is an effective method of decreasing the load on a single tooth, as well as reducing vibration and noise. While the spindlier tooth leads to greater relative sliding, having more teeth participate in contact at the same time makes the HCR gear more sensitive to the surface quality. Available literature regarding HCR gear primarily investigates the geometrical optimization, load distribution, or efficiency calculation. Limited work has been conducted on the effect of rough surfaces on the dynamic performance of HCR gear. For this reason, a multi-degree-of-freedom (MDOF) model is presented mathematically to characterize the static transmission error based on fractal theory, investigate the relative sliding friction using an EHL-based friction coefficient formula, and detail the time-varying friction coefficient suitable for HCR gear. Based on numerical results, the surface roughness has little influence on system response in terms of the dynamic transmission error but has a large effect on the motion in off-line-of-action (OLOA) direction and friction force. The impact of shaft-bearing stiffness and damping ratio is also explored with results revealing that a greater shaft-bearing stiffness is beneficial in obtaining a more stable motion in OLOA direction, and a larger damping ratio results in a smaller effective friction force. The theory presented in this report outlines a new method of analyzing the dynamics of HCR gear in respect of introducing surface roughness into MDOF model directly, as well as establishing an indirect relationship between dynamic responses and surface roughness. This method is expected to guide surface roughness design and manufacturing in the future.

Time varying mesh stiffness calculation of spur gear pair considering sliding friction and spalling defects

Abstract Spalling is one of the common tooth surface failures of gear teeth and is defined as the formation of deeper cavities that are mainly developed from subsurface defects. The time varying mesh stiffness (TVMS) of gear pairs, gives significant information about the health of the system. The change indirection of time varying friction on both sides of the pitch line causes the change of gear mesh stiffness. This article proposes a computer simulation based approach to study the effect of time varying friction coefficient on the total effective mesh stiffness for the spur gear pair. An analytical method to calculate the TVMS of the spur gear for different spall shapes, size and location considering sliding friction is also proposed in this study. The results show that spall shape, size and location are very important parameters that need to be considered for calculation of TVMS and subsequently to know the dynamic response of the gear pair in the presence of a spall.

The influence of mesh misalignment on the dynamic characteristics of helical gears including sliding friction

Due to either elastic deformations or errors in the manufacturing or assembling of gears, shafts, bearings and their housings, it is an inevitable consequence that mesh misalignment between teeth occurs. The change in length of the contact line or the change in load distribution along the length of the contact line induced by mesh misalignment causes changes in the dynamic characteristics of helical gears. There is currently no satisfactory solution for the modeling and calculation of the internal excitation in helical gears with mesh misalignment and sliding friction that would reveal the changes in the dynamic characteristics. In this study, an improved calculation method of friction excitation is proposed based on the time-varying length of the contact line and the time-varying friction coefficient model in helical gears. By considering the change in the mesh position and the change in the length of the contact line or the change of the displacement error along the contact line induced by mesh misalignment, the time-varying sliding friction force and the dynamic mesh force may be obtained. An eight degree-of-freedom analytical helical gear pair model is developed by incorporating the time-varying sliding friction force and dynamic mesh force and considering the mesh misalignment. By assuming a constant mesh stiffness density along the contact line, the rules governing the variation of the dynamic response are obtained using simulations of helical gear pair examples with different friction coefficient models and mesh misalignment. The developed analytical model provides a new method for the study of excitation characteristics in helical gears with mesh misalignment.

Adaptive Friction Compensation: A Globally Stable Approach

In this paper, an adaptive friction compensation scheme is proposed. The friction force is computed as a time-varying friction coefficient multiplied by the sign of the velocity and an online update law is designed to estimate this coefficient based on the actual position and velocity errors. Furthermore, a modified signum function definition is proposed to better capture the behavior of friction over varying velocity profiles than the signum function commonly used in friction models. The properties of the closed-loop behavior of the proposed scheme are analyzed and stability of the closed-loop system is proven. Simulations and real-world experimental results are provided to confirm the theoretical findings: the compensator is able to eliminate steady-state errors, significantly decrease the stick-slip effect and compensate even rapidly varying friction forces.

Coupling dynamics of a geared multibody system supported by ElastoHydroDynamic lubricated cylindrical joints

A comprehensive computational methodology to study the coupling dynamics of a geared multibody system supported by ElastoHydroDynamic (EHD) lubricated cylindrical joints is proposed throughout this work. The geared multibody system is described by using the Absolute-Coordinate-Based (ACB) method that combines the Natural Coordinate Formulation (NCF) describing rigid bodies and the Absolute Nodal Coordinate Formulation (ANCF) characterizing the flexible bodies. Based on the finite-short bearing approach, the EHD lubrication condition for the cylindrical joints supporting the geared system is considered here. The lubrication forces developed at the cylindrical joints are obtained by solving the Reynolds’ equation via the finite difference method. For the evaluation of the normal contact forces of gear pair along the Line Of Action (LOA), the time-varying mesh stiffness, mesh damping and Static Transmission Error (STE) are utilized. The time-varying mesh stiffness is calculated by using the Chaari’s methodology. The forces of sliding friction along the Off-Line-Of-Action (OLOA) are computed by using the Coulomb friction models with a time-varying coefficient of friction under the EHD lubrication condition of gear teeth. Finally, two numerical examples of application are presented to demonstrate and validate the proposed methodology.

Nonlinear tire-road friction control based on tire model parameter identification

A hierarchical control structure is a more suitable structural scheme for integrated chassis control. Generally, this type of structure has two main functions. The upper layer manages global control and force allocation, while the bottom layer allocates realized forces with 4 independent local tire controllers. The way to properly allocate these target forces poses a difficult task for the bottom layer. There are two key problems that require attention: obtaining the nonlinear time-varying coefficient of friction between the tire and different road surfaces and accurately tracking the desired forces from the upper layer. This paper mainly focuses on longitudinal tire-road friction allocation and control strategies that are based on the antilock braking system (ABS). Although it is difficult to precisely measure longitudinal tire-road friction forces for frequently changing road surface conditions, they can be estimated with a real-time measurement of brake force and angular acceleration at the wheels. The Magic Formula model is proposed as the reference model, and its key parameters are identified online using a constrained hybrid genetic algorithm to describe the evolution of tire-road friction with respect to the wheel slip. The desired wheel slip, with respect to the reference tire-road friction force from the top layer, is estimated with the inverse quadratic interpolation method. The tire-road friction controller of the extended anti-lock braking system (Ext-ABS) is designed through use of the nonlinear sliding mode control method. Simulation results indicate that acceptable modifications to changes in road surface conditions and adequate stability can be expected from the proposed control strategy.

Coupled Dynamic and Vibration Analysis of Beveloid Geared System

Dynamic modeling of beveloid gears is less developed than that of spur gears, helical gears and hypoid gears because of their complicated meshing mechanism and 3-dimsional dynamic coupling. In this study, a nonlinear systematic coupled vibration model is created considering the time-varying mesh stiffness, time-varying transmission error, time-varying rotational radius and time-varying friction coefficient. Numerical integration applying the explicite Runge-Kutta formula and the implicit direct integration is used to solve the nonlinear dynamic model. Also, the dynamic characteristics of the marine gear system are investigated.

A Statistical Analysis of Forces at a Sliding Interface

A statistical analysis has been made of the normal and tangential forces involved in friction and wear tests of two long range ordered (LRO) alloys. The analysis used descriptive statistics and a regression technique which provided a time varying friction coefficient M(t) in addition to M(a), a coefficient based on average force values. The normal and tangential forces responded differently. Part of the differences was due to the specimen mounting arrangement which damped and filtered the tangential more than the normal force. Another part was due to the film formation on the LRO alloy. One alloy did not form a stable and durable film; this alloy has a fairly constant M(a) and a zero M(t) value. The other alloy did form a stable film; this alloy had a M(a) which increased to a constant value during testing while M(t) was not zero. Thus the sensitivity and information content of a straightforward friction and wear test was considerably improved by a statistical analysis of the forces involved. Presented as...