Rolling Resistance Model Research Articles

Comprehensive study of the effects of rolling resistance on the stress–strain and strain localization behavior of granular materials

This paper presents the results of a comprehensive study of the effects of rolling resistance on the stress–strain and strain localization behavior of granular materials using the discrete element method. The study used the Particle Flow Code (PFC) to simulate biaxial compression tests in granular materials. To study the effects of rolling resistance, a user-defined rolling resistance model was implemented in PFC. A series of parametric studies was performed to investigate the effects of different levels of rolling resistance on the stress–strain response and the emergence and development of shear bands in granular materials. The PFC models were also tested under a range of macro-mechanical parameters and boundary conditions. It is shown that rolling resistance affects the elastic, shear strength and dilation response of granular materials, and new relationships between rolling resistance and macroscopic elasticity, shear strength and dilation parameters are presented. It is also concluded that the rolling resistance has significant effects on the orientation, thickness and the timing of the occurrence of shear bands. The results reinforce prior conclusions by Oda et al. (Mech Mater 1:269–283, 1982) on the importance of rolling resistance in promoting shear band formation in granular materials. It is shown that increased rolling resistance results in the development of columns of particles in granular materials during strain hardening process. The buckling of these columns of particles in narrow zones then leads to the development of shear bands. High gradients of particle rotation and large voids are produced within the shear band as a result of the buckling of the columns.

Full Two-Dimensional Model for Rolling Resistance. II: Viscoelastic Cylinders on Rigid Ground

Following the previous paper, “Full two-dimensional model for rolling resistance: Hard cylinder on viscoelastic foundation of finite thickness,” addressing modeling of rigid cylinder rolling against viscoelastic foundation of finite thickness, this paper focuses on the development of a rigorous full two-dimensional semianalytical model for viscoelastic rollers with layered structure rolling against a rigid ground. In this model, the polar coordinate system is used, the solution is expanded into a set of Fourier series corresponding to the angular coordinate, the frequency domain master curves of G′ and G″ characterizing the general viscoelastic properties for a viscoelastic material are used to relate Fourier coefficients, and a special condensed structure model based on the Fourier series is developed to handle viscoelasticity and the rolling contact boundary condition. Examples are given to show the model capabilities to efficiently handle rolling resistance and contact stresses, and capture major characteristics of standing-wave phenomenon, such as sharp rise of rolling resistance, emergence of standing waves and material dynamic softening as the rolling speed approaches a critical value. The methodology may be of interest to industrial roller designers.

Rolling and Spinning Friction Characterization of Fine Particles Using Lateral Force Microscopy Based Contact Pushing

In this paper, we have utilized Lateral Force Microscopy (LFM) based mechanical pushing of micro/nano-objects to study adhesion and friction characterization at the micro/nanoscale. Continuum micro/nano-friction models for particle rolling, spinning and sliding cases are discussed for general particle–substrate interfaces. A rolling resistance model using the Double–Hertz model is devoloped for such general interfaces. Using the friction models, the effect of work of adhesion, effective Young's modulus, and contact radius at the particle–substrate interface are studied in detail. Combining friction models with experimental particle pushing vertical and lateral force data, the critical frictional interface parameters such as critical rolling distance and the interfacial shear strength are measured for a polystyrene particle and glass substrate interface. Results show that the critical rolling distance varies with the particle radius, and it is measured to be 42, 84 and 128 nm on average for 5, 10 and 15 μm radii particles, respectively. Next, using the particle spinning experimental data, the interfacial shear strength of the particle–substrate interface is measured as 9–15 MPa.

Full Two-Dimensional Model for Rolling Resistance: Hard Cylinder on Viscoelastic Foundation of Finite Thickness

A new full two-dimensional semianalytical method is developed to rigorously and efficiently solve the problem of a rigid cylinder rolling with any given constant speed over a viscoelastic foundation of finite thickness. In this new method, the solution is expanded into a set of Fourier series, the master curves of G′ and G″ characterizing the general viscoelastic properties for a viscoelastic material are used to relate Fourier coefficients, and a special boundary element based on the Fourier series is developed to handle viscoelasticity and the rolling contact boundary condition. A verification example is given to validate the methodology. Several numerical examples are given to study the influences of various factors on rolling resistance. The method as well as the conclusions drawn from the examples may be of interest to roller and belt-conveyor designers. This approach can be easily generalized to solve the general rolling contact problems of two viscoelastic bodies.

Study on tyre rolling resistance using experimental modal analysis

According to the method of modelling for tyre mechanical properties using experimental modal analysis proposed by the authors, the calculation model for tyre rolling resistance is established using the two-dimensional modal parameters extracted experimentally from the radial and tangential responses when the tyre is under excitation along these two directions. The modelling is based on the equilibrium and kinematics of a rolling tyre. The distributions of vertical reaction and horizontal tractional forces on the footprint of a rolling tyre can be calculated using this model. The rolling resistances of a 195/60R14 tyre at low speed under different vertical loads, inflation pressures and rolling speeds are calculated. The variation trend of rolling resistance with load, inflation pressure and rolling speed agrees with the test results in the literature and our experimental results. This demonstrates the rationality and feasibility of modelling a rolling tyre using experimental modal analysis.

Tread Depth Effects on Tire Rolling Resistance

Abstract This paper discusses the measurement and modeling of tire rolling resistance for a group of radial medium truck tires. The tires were subjected to tread depth modifications by “buffing” the tread surface. The experimental work used the equilibrium test method of SAE J-1269. The finite element analysis (FEA) tire model for tire rolling resistance has been previously presented. The results of the testing showed changes in rolling resistance as a function of tread depth that were inconsistent between tires. Several observations were also inconsistent with published information and common knowledge. Several mechanisms were proposed to explain the results. Additional experiments and models were used to evaluate the mechanisms. Mechanisms that were examined included tire age, surface texture, and tire shape. An explanation based on buffed tread radius, and the resulting changes in footprint stresses, is proposed that explains the observed experimental changes in rolling resistance with tread depth.

Dynamic contact stress and rolling resistance model for total knee arthroplasties.

Problems associated with premature failure of total knee replacements (TKR's) include: wear, creep, and oxidation of ultrahigh-molecular-weight polyethylene (UHMWPe) as well as adverse tissue reactions to polyethylene wear debris. These problems are associated in part with the mechanical behavior of UHMWPe. In TKR's, contact stress analyses have been performed on the UHMWPe tibial component; however, most have employed simplified material properties and not accounted for joint kinematics. A nonlinear viscoelastic rolling model was developed for TKR's to predict the contact stress and rolling friction for varying rolling speed, conformity, applied load, and tibial plateau thickness. Results indicated that the contact stress increased and rolling friction decreased with increasing rolling speed. Effects of conformity, applied load, and tibial plateau thickness were consistent with previous models. At large rolling speeds, predicted peak contact stresses were almost twice their static value, resulting in a compound fatigue problem in UHMWPe components due to normal cyclic loading, moving point of contact, and velocity-dependent stresses.

Comments on Rolling Resistance

Rolling resistance model, developed based on rigid body assumption, is further analyzed in this paper using a simplified analytical model and experimental results. The analysis leads to the conclusion that the effect of the reaction forces is equivalent to a resultant having the point of contact located outside the zone of contact.