Grey Relation between Nonlinear Characteristic and Dynamic Uncertainty of Rolling Bearing Friction Torque

The rolling bearing friction torque which is characterized by its uncertainty and nonlinearity affects heavily the dynamic performance of a system such as missiles, spacecrafts and radars, etc. It is difficult to use the classical statistical theory to evaluate the dynamic evaluation of the rolling bearing friction torque for the lack of prior information about both probability distribution and trends. For this reason, based on the information poor system theory and combined with the correlation dimension in chaos theory, the concepts about the mean of the dynamic fluctuant range （MDFR） and the grey relation are proposed to resolve the problem about evaluating the nonlinear characteristic and the dynamic uncertainty of the rolling bearing friction torque. Friction torque experiments are done for three types of the rolling bearings marked with HKTA, HKTB and HKTC separately; meantime, the correlation dimension and MDFR are calculated to describe the nonlinear characteristic and the dynamic uncertainty of the friction torque, respectively. And the experiments reveal that there is a certain grey relation between the nonlinear characteristic and the dynamic uncertainty of the rolling bearing friction torque, viz. MDFR will become the nonlinear increasing trend with the correlation dimension increasing. Under the condition of fewer characteristic data and the lack of prior information about both probability distribution and trends, the unitive evaluation for the nonlinear characteristic and the dynamic uncertainty of the rolling bearing friction torque is realized with the grey confidence level of 87.7%-96.3%.

Methodology for the assessment of the friction torque of ball slewing bearings considering preload scatter

This manuscript presents an innovative methodology for the assessment of the friction torque of ball slewing bearings.The methodology aims to overcome the limitations of state-of-the-art approaches,especially when the friction torque is conditioned by the preload of the balls.To this end,the authors propose to simulate the preload scatter when solving the load distribution problem,prior to the friction torque calculation.This preload scatter allows to simulate a progressive transition of the balls from a four-point contact state to a two-point contact one.By implementing this capability into an analytical model,the authors achieve a successful correlation with experimental results.Nonetheless,depending on the stiffness of the structures to which the bearing is assembled,it is demonstrated that the rigid ring assumption can lead to inaccurate friction torque results when a tilting moment is applied.The methodology described in this research work is meant to have a practical application.Therefore,the manuscript provides guidelines about how to use and tune the analytical model to get a reliable friction torque prediction tool.

Investigations for vibration and friction torque behaviors of thrust ball bearing with self-driven textured guiding surface

In order to improve the starved lubrication condition of rolling bearings,three kinds of textures,namely dimple,groove texture,and gradient groove texture,were developed on the guiding surface of thrust ball bearings in this study.The results show that gradient groove texture has the one-way self-driving function of liquid droplets.The root mean square(RMS)value of vibration acceleration of gradient groove textured bearing(GGB)decreased by 49.1% and the kurtosis decreased by 24.6% compared with non-textured bearing(NB)due to the directional spreading effect of gradient groove textures on oil.The frequency domain analysis showed that the textures mainly suppressed the medium and high-frequency energy of bearing vibration,and the GGB was reduced the most with 65.3% and 48%,respectively.In addition,whether the grease is sufficiently sheared has a large impact on the oil guiding effect,and the friction torque of GGB could decrease by 10.5% compared with NB in the sufficiently sheared condition.Therefore,the gradient groove texture with oil self-driven effect on the guiding surface of rolling bearing can effectively improve the lubrication condition of the bearing and thus reduce the bearing vibration and friction torque,which has a promising application prospect.

Study on Friction Torque Loading with an Electro-hydraulic Load Simulator

This article, in order to precisely impose friction on aircraft and weapon actuation systems, presents a new friction loading method characteristic of ＂torque-zero velocity＂ switching control with an electro-hydraulic load simulator. As the general Stribeck friction model has little related to static friction, it proposes a ＂torque-zero velocity＂ switcher, in which a zero-velocity controller is developed to load the static friction and a torque controller the kinetic friction. With the help of mathematical modeling, this article designs a ＂torque-zero velocity＂ switching controller and, correspondingly, provides a ＂dual-threshold judgment＂ algorithm. Simulation results indicate that the proposed method can be successfully used to carry out the static and kinetic friction simulation with an electro-hydraulic load simulator.

Model analysis and experimental investigation of the friction torque during the CMP process

A model for calculating friction torque during the chemical mechanical polishing（CMP） process is presented,and the friction force and torque detection experiments during the CMP process are carried out to verify the model.The results show that the model can well describe the feature of friction torque during CMP processing. The research results provide a theoretical foundation for the CMP endpoint detection method based on the change of the torque of the polishing head rotational spindle.

METHOD TO ELIMINATE THE INFLUENCE OF SERVO－MOTOR FRICTION TORQUEON ULTRA－LOW SPEED PERFORMANCE OFELEC

A nonlinear observer of friction torque is formulated for valve controlled servomotor system. The effect of the observer is studied with simulating method and its applied condition is analyzed. When the above observer is not suitable foe use, a simple PID controlling method with variable parameters is presented. The method has been proved to be effective by the experimental results.

Study on Mt control method of friction welding

A new type control method in friction welding is suggested in this pa- per,that is compositive control method of friction torque and friction time,it called Mt control method for short.The principle of Mt control method and its feature are concisely explained.

Research and experimental analysis of precision degradation method based on the ball screw mechanism

As a key transmission component in computer numerical control(CNC) machine tools,the ball screw mechanism(BSM) is usually investigated under working load conditions. Its accuracy degradation process is relatively long,which is not conducive to the design and development of new products. In this paper,the normal wear depth of the BSM nut raceway is calculated under the variable speed operation condition using the fractal wear analysis method and the BSM’s accelerated degradation proportional wear model. Parameters of the acceleration degradation model of the double-nut preloaded ball screw pair are calculated based on the physical simulation results. The accelerated degradation test platform of the BSM is designed and manufactured to calculate the raceway wear model when the lubrication condition is broken under the variable-speed inertial load and the boundary lubrication condition under the uniform speed state. Three load forces and two samples are selected for the accelerated degradation test of the BSM. The measured friction torque of the BSM is employed as the evaluation index of the accuracy degradation test. In addition,the life cycle of the accuracy retention is accurately calculated by employing the parameters of the physical simulation model of the BSM. The calculations mentioned above can be used to estimate BSM’s accuracy performance degradation law under normal operating conditions. The application of the proposed model provides a new research method for researching the precision retention of the BSM.

Dynamic engagement characteristics of wet clutch based on hydro-mechanical continuously variable transmission

The effect of the design parameter on the clutch engagement process of the hydro-mechanical continuously variable transmission(CVT)was investigated.First,the model of the power train was developed with the software of SimulationX,and the clutch shift experiment was used to validate the correctness of the model.Then,the friction coefficient function was fitted with the test data to get the friction coefficient model suitable for this paper.Finally,based on the evaluating index of the friction torque and the friction power,two groups of design parameters(oil pressure and friction coefficient)were simulated and explained the changing regulation theoretically.According to the simulation results,the high oil pressure and friction coefficient can reduce the slipping time.The large oil pressure can increase the peak torque but the effect of friction coefficient on the peak torque is not so significant.The friction power reaches the maximum value at 3.2 s,the peak value increases as the oil pressure and friction coefficient increase.The effect of the oil pressure on the clutch engagement and thermal performance is greater than the friction coefficient.

A combined experimental and analytical method to determine the EHL friction force distribution between rollers and outer raceway in a cylindrical roller bearing

Friction force is a crucial factor causing power loss and fatigue spalling of rolling element bearings.A combined experimental and analytical method is proposed to quantitatively determine the elastohydrodynamic lubrication(EHL)friction force distribution between rollers and outer raceway in a cylindrical roller bearing(CRB).An experimental system with the instrumented bearing and housing was developed for measuring radial load distribution and friction torque of bearings.A simplified model of friction force expressed by dimensionless speed,load,and material parameters was given.An inequality constrained optimization problem was established and solved by using an experimental data-driven learning algorithm for determining the uncertain parameters in the model.The effect of speed,load,and lubricant property on friction force and friction coefficient was discussed.

Atmospheric Angular Momentum Transport and Balance in the AGCM-SAMIL

NCEP/NCAR reanalysis data and the spectral atmospheric general circulation Model （AGCM） of IAP/LASG （SAMIL） are employed to investigate the transport and balance of atmospheric angular mo-mentum （AAM）. It is demonstrated that SAMIL depicts the general features of the AAM transport and balance reasonably well. The AAM sources are in the tropics and sinks are in the mid-latitudes. The strongest meridional transport occurs in the upper troposphere. The atmosphere gains westerly momen- tum and transports it upward in the areas of surface easterlies, and downward into the areas of surface westerlies. Consequently, AAM balance is maintained. Systematic biases of the model compared to the reanalysis and observations are revealed. Possible mechanisms for these biases are investigated. In SAMIL, the friction torque in the tropics is stronger compared to the observations, which is probably due to the excessive precipitation along the Inter-tropical convergence zone （ITCZ） in the model, since the simulated Hadley circulation is much stronger than observed. In the winter half of the year, the transport center is in the lower troposphere in the SAMIL model, but it is in the upper troposphere in the reanalysis and observations. These discrepancies also suggest that simulations of convection and tropical precipitation need to be improved and that higher resolution is necessary for a quantitative simulation of AAM transport and balance. Results also demonstrate that the analysis of the transport and balance of atmospheric angular momentum is a powerful tool in diagnosing climate models for potential improvement.

电磁轴承系统动力学行为与辅助轴承性能的关系研究

Auxiliary bearings(ABs)are important backup and safety components in active magnetic bearing(AMB)systems.The performance of ABs significantly affects the reliability,safety,and serviceability of theAMB system and the rotating equipment.Research on the dynamic behavior during the touchdown process is crucial for analyzing the severity of the touchdown and the behavior is closely related to the performance of theAB.In this paper,a friction torque coefficient is introduced to evaluate the performance ofAB and the touchdown process is simulated and evaluated with various values of this coefficient with a detailed rotor-AB model of a verticalAMB system.The results show that large friction torque coefficient will result in undesired backward whirl of the rotor and catastrophic large load on the AB.Based on these results,this paper suggests that large friction torque coefficient ofABshould be avoided in practice.

Modeling the frictional torque of a dry-lubricated tapered roller bearing considering the roller skewing

In this paper, an equation for the calculation of the frictional torque of a dry-lubricated tapered roller bearing(TRB) is provided in which the effect of the roller skewing is emphasized. Calculations were performed to investigate the effect of the roller skewing on the torque of dry-lubricated TRB for two representative preload methods, that is, axial force preload and axial displacement preload. The results show that a proper roller skewing angle under axial force preload benefits the reduction of the TRB torque. However, the roller skewing angle should not exceed a certain critical value;otherwise, it will cause a steep rise in the TRB torque. Finally, the critical value of the roller skewing angle as a function of the friction coefficient and cage pocket clearance is presented. The developed torque model provides a tool for the internal design and torque optimization of dry-lubricated TRBs.

Spatial and Temporal Variations of Global Frictional Torque during the Period 1948–2011

Frictional torque is an important mean for momentum exchange between the atmosphere and earth, and significantly influences the variation in atmospheric angular momentum. Using NCEP-NCAR reanalysis data for the period 1948-2011, we examined the spatial and temporal patterns of frictional torque. It was found that the globally integrated frictional torque turned from positive to negative in 1972, suggesting that angular momentum was transferred from the earth to the atmosphere before 1972, but from the atmosphere to the earth thereafter. The global frictional torque steadily declined from 1948 to 1994, but has been increasing since 1995. It was also found that the global frictional torque is mainly determined by the wind systems in the mid and low latitudes of the Southern Hemisphere （SH）, where large changes in frictional torque occurred during the study period. Westerly wind increased continuously in the midlatitudes after 1948, while easterly wind decreased in the tropics of the SH after the 1980s.

An exploration of frictional and vibrational behaviors of textured deep groove ball bearing in the vicinity of requisite minimum load

In case of lightly loaded radial ball bearings,failure mechanisms other than fatigue such as smearing of raceways due to increased frictional torque and vibrations often prevail.Hence,attempts have been made herein for reducing the frictional torque and minimizing the vibrations of a radial deep groove ball bearing employing surface textures at the inner race.Nanosecond pulsed laser was used to create texture(involving micro-dimples having different dimple area density)on the inner race of test bearings.Using an in-house developed test rig,frictional torque and vibrational parameters were measured at different speeds and light loads(i.e.in vicinity of 0.01C,where C is dynamic load capacity of radial ball bearing).Significant reduction in frictional torque and overall vibrations were found in the presence of micro-dimples on inner race at light loads irrespective of operating speeds.Even without satisfying the minimum load needed criteria for the satisfactory operation,substantial reduction in smearing marks was found on the races of textured ball bearings in comparison to conventional cases.

Effects of the radial force on the static contact properties and sealing performance of a radial lip seal

The radial force is a critical factor to determine the sealing performance of radial lip seals.The effects of radial force produced by garter spring and interference on the static contact properties and sealing performance of a radial lip seal are investigated by numerical simulations and experiments.Finite-element analysis and mixed elastohydrodynamic lubrication simulation are used.Radial force,contact width,temperature in the sealing zone,the reverse pumping rate and friction torque are measured.A critical value of interference for a cost-effectively designed radial lip seal is found.Spring force is required to compensate the decrease of the radial force because of the interference and used as a possible way to obtain intelligent control of sealing performance.The quantitative results gotten in this study could provide guide for the seal design and improvement.

The effect of texture on the shaft surface on the sealing performance of radial lip seals

On the basis of elastohydrodynamic model,the present study numerically analyzes the effect of various microdimple texture shapes,namely,circular,square,oriented isosceles triangular,on the pumping rate and the friction torque of radial lip seals,and determines the microdimple texture shape that can produce positive pumping rate.The area ratio,depth and shape dimension of a single texture are the most important geometric parameters which influence the tribological performance.According to the selected texture shape,parameter analysis is conducted to determine the optimal combination for the above three parameters.Simultaneously,the simulated performances of radial lip seal with texture on the shaft surface are compared with those of the conventional lip seal without any texture on the shaft surface.

Improvement of Deep Groove Ball Bearing’s Performance Using a Bionic Textured Inner Race

Micro-textured surfaces have improved the tribological performance of contact surfaces under lubricated conditions;however,not practiced due to manufacturing challenges.In addition to simpler micro-pits or straight-trench type textures,sophisticated bioinspired textures on commercial radial ball bearings have been scarcely studied.In this work,Dendroaspis polylepis(Mamba snake)skin-type textures were fabricated on the inner race of FAG radial ball bearings using a nanosecond fiber laser machine.Though the snake textures were primarily meant to enhance friction,the dimensions of the texture have been carefully chosen to improve the tribological performance under lubricated condition.The textured bearings were assembled and experimented at various rotational speeds and lightly loaded conditions to measure vibrational amplitude,frictional torque,and temperature rise.Compared to untextured(conventional)bearing,the snake-skin type textured bearings resulted in improved tribo-dynamic performance.

Study of the influences of rotary table speed on stick-slip vibration of the drilling system

Stick-slip vibration presents one of the major causes of drilling problems,such as premature tool failures,low drilling efficiency and poor wellbore quality.The objective of this work is to investigate the influences of rotary table speed(RTS)on stick-slip phenomenon of the drilling system.In this study,the drilling system is treated as a lumped torsional pendulum model of which the bit/rock interaction is regarded as Coulomb friction.By analyzing cases with different RTS,two types of vibrations on the bit are found:stick-slip vibration and uniform motion.With an increase in the RTS,the stick-slip vibration on the drill bit disappears once the RTS arrives at its critical value.For the cases that stick-slip vibrations occur,the phase trajectories converge toward a limit cycle.For the cases that stick-slip vibration does not appear,the drill bit tends to stabilize at a uniform motion and the phase trajectories correspond to contracting spirals observed in the phase plane.