Friction torque study on double-row tapered roller bearing

Aiming at analyzing the load characteristics and friction torque of triple-row hub bearings for new energy vehicles, this work established a comprehensive theoretical and experimental methodology for predicting the internal load distribution and friction torque. Firstly, considering the preload effect via an initial negative clearance, deformation coordination and force balance equations for the triple-row bearing under axial load were formulated, to analyze the external loads under various driving conditions. Based on contact deformation theory, a quasi-static model was developed to combine radial, axial, and moment loads. The Newton–Raphson iterative algorithm was employed to solve the ball load distribution equations, and the correctness was verified by using the finite element method. Furthermore, accounting for the elastic hysteresis, differential sliding, and spin sliding, the theoretical models for friction torque components were established, to investigate the influence of structural parameters and the total friction torque under different driving conditions. Finally, to confirm the effectiveness and the precision of the model, a finite element simulation and experimental measurements of friction torque were conducted, respectively, which showed good agreement with theoretical calculations. The main innovations include proposing a mechanical modeling method for triple-row hub bearings that accounts for preload effects, and establishing an integrated friction torque analysis model applicable to multiple driving conditions. This work provides theoretical support and a methodological foundation for the design of next-generation hub bearings for new energy vehicles.

In this paper it is presented a numerical simulation and an experimental study of total friction torque from radial ball bearings. For this purpose it is conceived a virtual CAD model of the experimental test bench for bearing friction torque measurement. The virtual model it is used for numerical simulation in Adams software, that allows dynamic study of multi-body systems and in particularly with facility Adams Machinery of dynamic behavior of machine parts. It is manufactured an experimental prototype of the test bench for radial ball bearings friction torque measurement. In order to measure the friction torque of the tested bearings it is used an equal resistance elastic beam element, with strain gauge transducer to measure bending deformations. The actuation electric motor of the bench has the shaft mounted on two bearings and the motor housing is fixed to the free side of the elastic beam, which is bended by a force proportional with the total friction torque. The beam elastic element with strain gauge transducer is calibrated in order to measure the force occurred. Experimental determination of the friction torque is made for several progressive radial loads. It is established the correlation from the friction torque and bearing radial load. The bench allows testing of several types and dimensions of radial bearings, in order to establish the bearing durability and of total friction torque.

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.

Under the pressure of stricter regulations on pollutant emissions and the desire of users for lower fuel consumption and more comfortable driving, engine control based on torque has been developed. To provide an accurate estimate of effective torque, friction losses must be modeled. The details of a model that predicts the total instantaneous friction torque for compression ignition engines are described. The model is based on a combination of the dynamic model of the crankshaft and the thermodynamic model. The total instantaneous friction torque is determined using the instantaneous measurements or numerical predictions of the gas pressure in the combustion chamber, the rotational speed of the crankshaft and the load torque. The experimental data and the numerical simulation results were compared. The comparison between the different variables shows a good agreement between the simulation and the experimental results.

Frictional torque of cylindrical roller thrust bearing in grease lubrication

With the increasing need for flexible operation (shorter startup time and higher load change rate etc.), clearance monitoring between the rotor and the stationary components in steam turbines is becoming more important. This is because as load change rate increases, minimum radial and axial clearances during operation tend to be smaller due to thermal deformation of steam turbines, and the risk of contact between the rotor and the stationary components becomes higher. This situation has accelerated development of clearance sensors. However, it is still difficult to monitor all possible points of contact only with physical sensors due to limited installation location and short lifetime in high temperature environment. From the above background, we have been developing a virtual clearance monitoring (VCM) technique based on a novel data fusion approach that utilizes both physical and data-driven models. Specifically, a reduced order model (ROM) is used as physical model in order to enable real-time prediction with an accuracy similar to that of finite element analysis (FEA). Then, the prediction error of the physical model is corrected by using a residual model built by machine learning from the past clearance sensor values and the corresponding physical model-based prediction results. As will be explained in this report, this technique has an advantage that the clearances can be predicted in real-time based only on operating data such as steam conditions at inlet and outlet, and some temperatures in the parts not modeled in the ROM. Therefore, the virtual sensor based on this technique can be used as a replacement for the physical sensor after it has failed. Furthermore, this technique can also be used to preliminarily study unsteady clearance behavior for inexperienced operating conditions. This paper describes how to build the ROM from a finite element model for thermal-structural analysis of an entire steam turbine by model order reduction (MOR), and the detail of the VCM technique, and a VCM system installed in a measurement room of a state-of-the-art GTCC power plant manufactured by Mitsubishi Power. In addition, the verification results of the VCM system are presented. In this research, the ROM and the residual model were built using the data obtained from four operations with different start-up modes each other. Then, VCM was performed for 12 operating cases. As a result, this survey revealed the followings: (1) This system is capable of real-time prediction with output intervals of roughly 2 seconds. (2) As for radial clearance prediction error during rotor rotating, the RMSEs and the absolute values of minimum value errors are less than or equal to 7.2 % and 7.0 % respectively relative to an initial radial clearance value during the steam turbine stopping. From the above results, we conclude that this VCM technique based on data fusion approach is effective in terms of computational speed and prediction accuracy. This means that if a physical clearance sensor fails, the radial clearance can be continuously monitored by a virtual clearance sensor with a residual model built using the data when the sensor was working normally. In the future, we plan to further improve the accuracy of this technique through improvement in physical modeling.

The effects of the uncertainty of angular misalignment on the wear of angular contact ball bearings in the spindle system are investigated. The wear model of bearing raceways is derived based on the Archard model. The angular misalignment caused by mounting error is assumed to comply with normal distribution, Monte Carlo method is used to extract the angular misalignment sample. Based on the spindle system model, the spinning speed, pitch angle, and contact force of ball elements in each angular contact ball bearing are calculated. The wear depth of bearing raceways is analyzed. The results show that the uncertainty of the initial angular misalignment leads to significant dispersion of wear depth of ball bearings, but the dispersion degree is related to spindle speed, angular misalignment cases, and bearing mounting position. Increasing the spindle speed increases the wear depth but decreases the wear depth dispersion.

The paper presents a detailed computational study of flow patterns and performance indices in a dimpled parallel thrust bearing. The bearing consists of eight pads; the stator surface of each pad is partially textured with rectangular dimples, aiming at maximizing the load carrying capacity. The bearing tribological performance is characterized by means of Computational Fluid Dynamics (CFD) simulations, based on the numerical solution of the Navier-Stokes and energy equations for incompressible flow. Realistic boundary conditions are implemented. The effects of operating conditions and texture design are studied for the case of isothermal flow. First, for a reference texture pattern, the effects of varying operating conditions, in particular minimum film thickness (thrust load), rotational speed and feeding oil pressure are investigated. Next, the effects of varying texture geometry characteristics, in particular texture zone circumferential/radial extent, dimple depth and texture density on the bearing performance indices (load carrying capacity, friction torque and friction coefficient) are studied, for a representative operating point. For the reference texture design, the effects of varying operating conditions are further investigated, by also taking into account thermal effects. In particular, adiabatic conditions and conjugate heat transfer at the bearing pad are considered. The results of the present study indicate that parallel thrust bearings textured by proper rectangular dimples are characterized by substantial load carrying capacity levels. Thermal effects may significantly reduce load capacity, especially in the range of high speeds and high loads. Based on the present results, favorable texture designs can be assessed.

The paper presents a detailed computational study of flow patterns and performance indices in a dimpled parallel thrust bearing. The bearing consists of eight pads; the stator surface of each pad is partially textured with rectangular dimples, aiming at maximizing the load carrying capacity. The bearing tribological performance is characterized by means of computational fluid dynamics (CFD) simulations, based on the numerical solution of the Navier–Stokes and energy equations for incompressible flow. Realistic boundary conditions are implemented. The effects of operating conditions and texture design are studied for the case of isothermal flow. First, for a reference texture pattern, the effects of varying operating conditions, in particular minimum film thickness (thrust load), rotational speed and feeding oil pressure are investigated. Next, the effects of varying texture geometry characteristics, in particular texture zone circumferential/radial extent, dimple depth, and texture density on the bearing performance indices (load carrying capacity, friction torque, and friction coefficient) are studied, for a representative operating point. For the reference texture design, the effects of varying operating conditions are further investigated, by also taking into account thermal effects. In particular, adiabatic conditions and conjugate heat transfer at the bearing pad are considered. The results of the present study indicate that parallel thrust bearings textured by proper rectangular dimples are characterized by substantial load carrying capacity levels. Thermal effects may significantly reduce load capacity, especially in the range of high speeds and high loads. Based on the present results, favorable texture designs can be assessed.

Parallel or/and angular misalignment between rotors connected by flexible coupling causes deformation of coupling elements and rotor shafts both. The forces and moments from flexible coupling act on driver and driven rotors simultaneously and depend upon dynamic response of coupled rotor system. The authors’ aim in the present work is to propose a methodology to incorporate the coupling stiffness matrix and coupling loads into the finite element model of flexibly coupled flexible rotors supported on deep groove ball bearings. The coefficients of coupling stiffness matrix and coupling loads are nonlinear and depend upon the amount of parallel and angular misalignments. To segregate the effect of nonlinear stiffness of coupling on the dynamic response of the system, the stiffness of ball bearing is initially considered to be linear. Thereafter, ball bearing nonlinearities arising from radial clearance, Hertzian deformation of balls and races, and varying compliance effect are included into the FE model of the system. Considering different types of misalignments in succession and combination, the dynamic response is characterized by the presence of 1N, 2N and other super or sub harmonics. The misalignment in one plane is found to affect the dynamic response in both the orthogonal planes. Comparing to the stiffness of flexible coupling, the stiffness of ball bearing is of higher order and therefore, nonlinear coupling forces and moments have dominant influence on the dynamic response of the system.

In addition to geometry and environmental factors, operating temperatures of bearings are directly affected by applied load, operating speed, friction torque, and lubricant type and viscosity. Without adequate heat dissipation, bearing temperatures will increase to the point that the lubricant is distressed, ultimately leading to bearing failure. Numerically investigating bearing operating temperatures for specific environment, geometry, and lubricant conditions provides the opportunity to design bearings for improved thermal performance. This is critical for high-speed bearings when using mist or vapor phase lubrication with reduced heat sink capability. For these conditions, heat generation can lead to temperatures too extreme for reliable operation. Interactions between the bearing cage and the bearing races are the primary component of the total heat generation in these bearings. As the loading during these interactions is a function of centrifugal forces, it has been predicted that a lower density cage material will provide thermal performance benefits due to reduced loading. If this lower density cage material also demonstrates acceptable strength and traction characteristics, it may be an excellent replacement for conventional cage materials. Carbon-carbon composites meet the desired cage properties and the effects of using C-C cages on bearing operating temperature have been investigated using the finite element method. Predicted heat generation and steady-state temperatures for a 30 mm ball bearing operating with mist lubricant delivered at 325°C for several shaft operating speeds are presented to demonstrate differences in thermal performance due to cage material. Presented at the 56th Annual Meeting in Orlando, Florida May 20–24, 2001

Skidding is a phenomenon that frequently occurs in ball–raceway contact areas of bearings and often leads to their early failure. This paper presents a skidding analysis of angular contact ball bearings (ACBBs) subjected to various boundary conditions. A five degrees-offreedom quasi-static model for ACBBs was employed to investigate skidding with ball and race contact forces and inertial loading by rotational speed. The model provided the internal load distribution of all rolling elements, which was subsequently used for the skidding prediction. Hirano’s criterion was used as a theoretical basis for the skidding analysis of ACBBs. Simulations were performed to investigate the influence of external loading, rotational speed, and angular misalignment on the bearing skidding. The effects of the preload method and initial contact angle on the skidding were also considered. As a result, this study provided an in-depth observation of skidding in ACBBs subjected to various operating conditions.

The purpose of a ball bearing is to reduce the rotational friction and support radial and axial loading. But it can’t avoid the heat generation by the friction, the wear and the power loss it was caused by the relative motion between the metal materials. Heat is generated by the friction in the bearings, which causes the temperature inside the bearing to increase. If the heat is not appropriately removed from the bearing, elevated temperatures may give rise to premature failure. It is, therefore, important to be able to calculate the temperature in the bearings due to friction. Here, we describe a method to estimate the equilibrium temperature on the angular contact ball bearing in a spindle system using a numerical approach. The frictional torque of the bearing in a spindle system was calculated by use of a bearing analysis tool and thermal analysis of the spindle system including the bearings was achieved using the finite element method (FEM). The actual spindle system with the same layout of the FEA was built and the frictional torque, the bearing temperature were measured in the experiment. The bearing temperature was compared with measured data to verify the validity of finite element analysis.

Friction torque and natural running temperature of ‘Light’ type and ‘Extra Light’ type bearings of bore 5 inches have been measured at speeds ranging from 5,000 to 11,000 r.p.m. Loads up to 2,400 lb. were applied at varying incidence of radial to thrust load. Lubrication was by liquid jet at the rate of 6 pints per min. It is concluded that a large proportion of the friction measured under the conditions of lubricant supply adopted in the experiments is attributable to viscous friction in the lubricant. An analysis of the friction torque based on the work of Poritsky, Hewlett, and Coleman (1947)‡ for varying angles of application of load shows no correlation with the experimental results obtained. Estimates of hysteresis loss based on the work of Tabor (1952, 1954) indicate that this factor represents a comparatively small proportion of the total frictional loss of bearings of this type.

Multi-objective optimization of surface textured journal bearing by Taguchi based Grey relational analysis