New micro tribometer for rolling friction

Whereas for sliding friction the Amonton-Coulomb law clearly states the proportionality between the friction force and the normal force, the rolling friction torque and normal force dependency is assumed linear in some references and nonlinear in others. The coefficient of rolling friction can be obtained using various pendula, based on the assumption of linear dependence between the rolling friction torque and normal force. The theoretical models lead to a linear decrease of angular amplitude (confirmed experimentally for the dry sliding friction case) while the experimental damping of amplitude is nonlinear for any of the employed pendula. The basis for finding the rolling friction coefficient is the equality between the theoretical and experimental slopes of the decreasing angular amplitude of the pendulum. Due to this nonlinearity, the value of the coefficient of rolling friction depends on the launching amplitude of the pendulum. In the present paper the equation of motion of the evolvent pendulum is obtained based on the hypothesis that the dependency of resistant torque on normal force is a power law. Experimental tests performed with the new heavy pendulum have confirmed a nonlinear, exponential attenuation of angular amplitude. Thus, finding the coefficient of rolling friction for the least favourable situation was aimed. This happens when the launching amplitude of the pendulum has the highest possible value and occurs when the ratio between the tangential force and the normal force equals the coefficient of sliding friction. A technique is proposed for obtaining the critical value of the coefficient of rolling friction.

The paper proposes a device for finding the coefficient of rolling friction using a sphere in contact with the inner surface of a ring that rotates about a horizontal axis. The motion of the ball is characterized by the fact that for a stipulated rotation speed of the ring the centre of the ball executes a damped oscillatory motion and at equilibrium the centre of the ball is situated on different vertical than the one the centre of the ring is positioned. It is assumed that this feature is produced by the rolling friction torque that is proportional with the normal pressing force and the nonlinear differential equation of motion is obtained for the intended dynamic model. By the integration of the equation of motion there are confirmed the oscillatory motion of the ball and the eccentric equilibrium position and it is found a dependency of equilibrium position on the coefficient of rolling friction.

A 3D three-equation linear spring-dashpot model considering the normal contact force, the tangential contact force, and the rolling friction torque, and the corresponding programs for granular dynamics were developed. The flow and the segregation of the S-type binary granular mixtures in a thin rotating horizontal drum were simulated by using the new model. The influences of the rotation speed and the load of the drum on the pattern formation were discussed. The simulation results show that the pattern formation of the S-type binary granular mixtures in the rotating drum can be predicted accurately. As the rotation speed is high, the moon pattern appears,in which the small particles concentrate in a central core and the large particles distribute in the periphery. As the rotation speed is lowered, the petal pattern is found in thin drums, and the number of petals increases as the rotation speed decreases. The process of pattern formations was obtained by the simulation. As the petal pattern forms, the wavy flow of granules in the drum appears. Finally, the necessary condition and mechanisms of the pattern formation in the thin drums are discussed in the paper.

Analysis of the compound seismic system consisting of ERFPS system and dish spring

Solar-driven Joule cycle reciprocating Ericsson engines for small scale applications. From improper operation to high performance

Double-row tapered roller bearings (DTRBs) are key components of rotating machineries due to its great advantages in load-carrying and stiffness. Friction torque is one of the major indicators used to evaluate the performance of rolling bearing because it directly related to the power loss and heat generation. Nevertheless, the friction torque of DTRB is not deeply studied in the available literatures, especially those consider the influence of angular misalignment and radial clearance. Therefore, in current paper, the friction torque of DTRB is thoroughly investigated under combined radial and thrust load according to the extended mechanical model of DTRB. The total friction torque is considered as the summation of EHL rolling friction torque, elastic hysteresis loss, sliding friction at rib-roller end contact and viscous drag friction of lubricant. The current work mainly considers the influences of three parameters: axial pre-deformation, initial radial clearance and angular misalignment on the friction torque of the first and the second row of DTRB. The results indicate that the friction torque of these two rows of DTRB are greatly determined by the above parameters. Regardless the first or the second row, friction torques are both increase with the increase of axial pre-deformation and positive/negative angular misalignment, while decrease with the increase of initial radial clearance. The analysis of friction torque for DTRB will provide some useful guidance for the applications of DTRB.

The tire is a component of the vehicle in direct contact with the pavement surface. The friction coefficient of tire and road surface is inseparable from the driving safety, mobility and economy of the vehicle. This paper presents a method based on code and formula simulation to estimate the effect of friction between each tire and the road and the driving state of the whole vehicle. By classifying different road conditions, different tires and different speeds, using the Magic formula, rolling friction torque and substituting a series of vehicle basic data, the corresponding tire-road friction coefficient is obtained. All basic vehicle parameters and tire parameters are obtained from the manufacturer's official website, instructions and other channels. Then the linear images are processed by Kalman filter. These images show that different tire types, different road conditions and different driving habits will affect the friction coefficient. The feasibility of the conclusion is verified by simulation in Adams car 2020, to put forward suggestions and improved methods for the comprehensive performance of vehicle driving from many aspects.

In this paper, we investigate the motion of a homogeneous heavy ball rolling without slipping on the surface of a rotating cylinder in two settings: a setting without dissipation and a setting with rolling friction torque which is proportional to the angular velocity of the ball. In both cases we assume that there exists a non‐holonomic constraint that corresponds to the condition that there be no slipping at the point of contact. In the first case, the system of five differential equations on the level set of first integrals is reduced to quadratures. To define possible types of motion, we carry out a bifurcation analysis of the reduced system. In the case with friction we show that all trajectories shift on average downward and the ball falls.

This paper investigates the rolling without slipping of a homogeneous heavy ball on the surface of a rotating cone in two settings: without dissipation in a nonholonomic setting and with rolling friction torque which is proportional to the angular velocity of the ball. In the nonholonomic setting, the resulting system of five differential equations on the level set of first integrals is reduced to quadratures. A bifurcation analysis of the above system is carried out to determine the possible types of motion. In the second case, it is shown that there are not only trajectories emanating from the lower point of the cone (its vertex), but also trajectories to the vertex of the cone (fall). An analysis of the dependence of the type of terminal motion of the center of mass of the ball on initial conditions is carried out.

The efficiency analytical model of the inverted planetary roller screw mechanism is formulated based on the friction torque calculation. Firstly, the friction torque model considering the load distribution of thread teeth is established including the components such as curvature friction torque, friction torque due to spinning sliding, pure sliding friction torque between rollers and carriers, friction torque generated by the viscosity of lubricant, and preload torque. Secondly, the contribution of the friction torque components and torque distribution on the roller thread teeth are investigated. Finally, efficiency analysis is conducted by discussing the influences of structure parameters of the inverted planetary roller screw mechanism and operating conditions. Computational results reveal that the total friction torque and efficiency are influenced by axial load, number of roller thread teeth, nut speed, contact angle, and helix angle of nut with different extents. This study provides an understanding of the relationship between friction torque, transmission efficiency, and system design parameters, which can be employed to enhance the inverted planetary roller screw mechanism optimization design.

Discrete element method study of effects of the impeller configuration and operating conditions on particle mixing in a cylindrical mixer

Reliability of rotating machinery is determined to a considerable degree by the bearing units. For several applications the requirements in rotational speed, bearing load and maximal vibration level are so extreme that neither rolling-element bearings nor fluid-film bearings could provide necessary operating characteristics during all regimes of operation. Hybrid bearings, which are a combination of rolling-element and fluid-film bearings, can improve performance characteristics and reliability of the rotor-bearing systems. A hybrid bearing, where a rolling-element bearing and a fluid-film bearing are positioned parallel to the vector of external load (PLEX), has the following advantages compared to a single bearing, whether rolling-element or fluid-film one: increase of life expectancy, load capacity increase, friction reduction, thermal regime enhancement, increase of stiffness, and damping properties. The present paper presents the results of theoretical and numerical research of friction characteristics of PLEX in mixed sliding and rolling friction, i.e. combination of viscous and rolling contact friction, regime. The conditions of minimum friction effect occurrence have been substantiated, and rational relations between characteristics of hybrid rolling-element bearings and fluid-film bearings needed for provision of such effect have been experimentally proven. Finally, the paper presents recommendations regarding design of such hybrid bearings for heavily loaded bearing nodes of rolling mills.

In this study, the effects of three types of dimples with different internal structures on the fluid lubrication characteristics of seal-like thrust bearings were experimentally and numerically investigated. In the experiments, the load-carrying capacity and the frictional torque were measured. The measurements were performed with a fixed constant film thickness. The behaviors of cavitation bubbles occurred within the dimples were observed through the rotating glass plate. Three types of internal structures of dimples were tested: cylindrical, spherical and conical. The measurement results were simulated by using the Reynolds equation. In addition, applying the periodic condition, a single dimple was analyzed. As the results, in three types of dimples, the load-carrying capacity increased as the rotational speed increased. The cylindrical internal structure built up the largest pressure at the trailing edge of dimples, and consequently the largest load-carrying capacity. The frictional torque also increased with increasing the rotational speed in the dimpled bearings. However, the effect of the internal structure on the frictional torque was not significant. Analytical results showed that the pressure reached the maximum value at the trailing edge of the cylindrical internal structure. The conical and sphere internal structure had the maximum value slightly inside the trailing edge.

Experimental investigation of drivetrain resistance applied to small wind turbines

Magnetic fluid seals are among the most common applications of ferrofluids. In such seals, the torque friction results only from the internal friction in the fluid and there is no direct contact between seal elements. Despite this, the heat generated during operation can be significant due to the low volume of the ferrofluid in the seal and high rotational speeds. The difficulty in calculating the torque friction is because the ferrofluid is a non-Newtonian fluid and changes its viscosity under the influence of a magnetic field. In order to measure torque friction in magnetic fluid seals, a special test stand was built. Tests were performed at different rotation speeds, different temperatures, and two seal stage geometries (rectangle and trapezoid). Numerical simulations were performed to determine the magnetic field distribution in the seal. Dynamic viscosity under the influence of the magnetic field was measured on a rotary rheometer. Mathematical models were compared with laboratory results. The results obtained from the calculations in some cases gave overstated values almost twice in value. An additional correction in the case of ferrofluid viscosity is proposed.