为了节省360°全景视频的编码时间,对通用视频编码标准中的编码单元划分决策过程进行了研究,提出了一种面向360°全景视频的帧内预测编码的快速算法。通过优化编码树单元(Coding Tree Unit,CTU)的编码深度范围和编码单元的划分...为了节省360°全景视频的编码时间,对通用视频编码标准中的编码单元划分决策过程进行了研究,提出了一种面向360°全景视频的帧内预测编码的快速算法。通过优化编码树单元(Coding Tree Unit,CTU)的编码深度范围和编码单元的划分模式的选择过程,减少编码时间。实验结果表明,在全帧内模式下,所提算法比原始算法平均可以节省34.33%的时间复杂度,同时带来的BDBR平均增量仅为1.665%,BDPSNR的平均降低量仅为0.076 dB。展开更多
在拥有多个存储节点的云数据存储系统中,保持云存储系统的负载均衡水平为一个合理的值和最小化数据检索的时间是一个值得研究的问题。本文提出一种基于粒子群优化算法的云数据均衡放置策略(balanced placement strategy of cloud data b...在拥有多个存储节点的云数据存储系统中,保持云存储系统的负载均衡水平为一个合理的值和最小化数据检索的时间是一个值得研究的问题。本文提出一种基于粒子群优化算法的云数据均衡放置策略(balanced placement strategy of cloud data based on particle swarm optimization algorithm,BPCD),首先,给出一种云存储系统模型;其次,引入基尼系数作为衡量该系统负载均衡水平的指标,结合数据检索时间目标函数构建多目标约束优化模型;再次,采用粒子群优化算法对问题进行求解,主要包括数据节点编码与参数设置、种群初始化、粒子群空间搜索、算法迭代4个过程;最后,将本文算法与传统云数据放置算法进行对比分析。仿真实验表明,本文提出的云数据均衡放置策略在优化云存储系统的负载水平和数据检索时间方面具有良好的效果。展开更多
The current research of rail corrugation mainly focuses on the mechanisms of its formation and development. Compared with the root causes and development mechanisms, the wheel-rail impacts, the fatigue failure of vehi...The current research of rail corrugation mainly focuses on the mechanisms of its formation and development. Compared with the root causes and development mechanisms, the wheel-rail impacts, the fatigue failure of vehicle-track parts, and the loss of ride comfort due to rail corrugation should also be taken into account. However, the influences of rail corrugation on vehicle and track vibration, and failure of vehicle and track structural parts are barely discussed in the literature. This paper presents an experimental and numerical investigation of the structural vibration of metro bogies caused by rail corrugation. Extensive experiments are conducted to investigate the effects of short-pitch rail corrugation on the vibration accelerations of metro bogies. A dynamic model of a metro vehicle coupled with a concrete track is established to study the influence of rail corrugation on the structural vibration of metro bogies. The field test results indicate that the short-pitch rail corrugation generates strong vibrations on the axle-boxes and the bogie frames, therefore, accelerates the fatigue failure of the bogie components. The numerical results show that short-pitch rail corrugation may largely reduce the fatigue life of the coil spring, and improving the damping value of the primary vertical dampers is likely to reduce the strong vibration induced by short-pitch rail corrugation. This research systematically studies the effect of rail corrugation on the vibration of metro bogies and proposes some remedies for mitigating strong vibrations of metro bogies and reducing the incidence of failure in primary coil springs, which would be helpful in developing new metro bogies and track maintenance procedures.展开更多
While introducing foreign advanced technology and cooperating with Chinese famous research institutes,the high-speed vehicles are designed and take the major task of passenger transport in China.In high-speed vehicle,...While introducing foreign advanced technology and cooperating with Chinese famous research institutes,the high-speed vehicles are designed and take the major task of passenger transport in China.In high-speed vehicle,the characteristic of shock absorber is an important parameter which determines overall behavior of the vehicle.The most existing researches neglect the influence of the series stiffness of the shock absorber on the vehicle dynamic behavior and have one-sided views on the equivalent conicity of wheel tread.In this paper,a high speed passenger vehicle in China is modeled to investigate the effect of the parameters taking series hydraulic shock absorber stiffness into consideration on Ruzicka model.Using the vehicle dynamic model,the effect of main suspension parameters on critical speed is studied.In order to verify the reasonableness of shock absorber parameter settings,vibration isolation characteristics are calculated and the relationship between suspension parameters and the vehicle critical hunting speed is studied.To study the influence of equivalent conicity on vehicle dynamic behavior,a series of wheel treads with different conicities are set and the vehicle critical hunting speeds with different wheel treads are calculated.The discipline between the equivalent conicity of wheel tread and critical speed are obtained in vehicle nonlinear system.The research results show that the critical speed of vehicle much depends on wheelset positioning stiffness and anti-hunting motion damper,and the series stiffness produces notable effect on the vehicle dynamic behavior.The critical speed has a peak value with the equivalent conicity increasing,which is different from the traditional opinion in which the critical speed will decrease with the conicity increasing.The relationship between critical speed and conicity of wheel tread is effected by the suspension parameters of the vehicle.The study results obtained offer a method and useful data to designing the parameters of the high speed vehicle and simulation study.展开更多
The profile of wheel/rail has great concern with the vehicle running safety, the wheel/rail wear and the rolling contact fatigue between wheel and rail, due to its severer impact on the dynamic behavior of both the ra...The profile of wheel/rail has great concern with the vehicle running safety, the wheel/rail wear and the rolling contact fatigue between wheel and rail, due to its severer impact on the dynamic behavior of both the railway vehicle/track, and the wheel/rail rolling contact status. However, recent studies in this respect are mainly explored in reverse methods, where track parameters are predetermined and invariable during the optimizing process. This paper attempts to propose a wheel-rail profiles matching design method considering multi-parameter, through optimizing wheel/rail profile under different rail cants and track gauges, based on the existed optimization technology for the normal gap of wheel/rail. The method presented in this paper can also, compared with the prior reverse methods, be called "forward solution method" in which the riding comfort, wheel unloading rate and wheel/rail contact stress of the speed-up railway passenger car are calculated by means of a vehicle-track coupling dynamic model, with the range of the rail cant varying from 1/20 to 1/40 and the rail gauge from 1 433 mm to 1 441 mm. These results show that the distribution status of the pairs of contact points can be obviously improved and the contact stress can be reduced significantly; a great influence is exposed by the rail cant and track gauge on the dynamic behavior of the high speed passenger car, and an optimal vehicle dynamics behavior are obtained with the optimized wheel/rail profile when the rail cant is 1/30 and the track gauge is 1 435 mm. This research can provide important references for the investigation of the wheel-rail profiles matching design method considering multi-parameter.展开更多
The current researches of wheel vibration and sound radiation mainly focus on the low noise damped wheel. Compared with the traditional research, the relationship between the sound and wheel/rail contact is difficulty...The current researches of wheel vibration and sound radiation mainly focus on the low noise damped wheel. Compared with the traditional research, the relationship between the sound and wheel/rail contact is difficulty and worth studying. However, there are few studies on the effect of wheel load on wheel vibration and sound radiation. In this paper, laboratory test carried out in a semi-anechoic room investigates the effect of wheel load on wheel natural frequencies, damping ratios, wheel vibration and its sound radiation, The laboratory test results show that the vibration of the wheel and total sound radiation decrease significantly with the increase of the wheel load from 0 t to 1 t. The sound energy level of the wheel decreases by 3.7 dB. When the wheel load exceeds 1 t. the attenuation trend of the vibration and sound radiation of the wheel becomes slow. And the increase of the wheel load causes the growth of the wheel natural frequencies and the mode damping ratios. Based on the finite element method (FEM) and boundary element method (BEM), a rolling noise prediction model is developed to calculate the influence of wheel load on the wheel vibration and sound radiation. In the calculation, the used wheel/rail excitation is the measured wheel/rail roughness. The calculated results show that the sound power level of the wheel decreases by about 0.4 dB when the wheel load increases by 0.5 t. The sound radiation of the wheel decreases slowly with wheel load increase, and this conclusion is verified by the field test. This research systematically studies the cffcct of wheel load on wheel vibration and sound radiation, gives the relationship between the sound and wheel/rail contact and analyzes the reasons, therefore, it provides a reference for further research.展开更多
Thermal damage caused by frictional heat of rolling-sliding contact is one of the most important failure forms of wheel and rail. Many studies of wheel-rail frictional heating have been devoted to the temperature fiel...Thermal damage caused by frictional heat of rolling-sliding contact is one of the most important failure forms of wheel and rail. Many studies of wheel-rail frictional heating have been devoted to the temperature field, but few literatures focus on wheel-rail thermal stress caused by frictional heating. However, the wheel-rail creepage is one of important influencing factors of the thermal stress In this paper, a thermo-mechanical coupling model of wheel-rail rolling-sliding contact is developed using thermo-elasto-plastic finite element method. The effect of the wheel-rail elastic creepage on the distribution of heat flux is investigated using the numerical model in which the temperature-dependent material properties are taken into consideration. The moving wheel-rail contact force and the frictional heating are used to simulate the wheel rolling on the rail. The effect of the creepage on the temperature rise, thermal strain, residual stress and residual strain under wheel-rail sliding-rolling contact are investigated. The investigation results show that the thermally affected zone exists mainly in a very thin layer of material near the rail contact surface during the rolling-sliding contact. Both the temperature and thermal strain of rail increase with increasing creepage. The residual stresses induced by the frictional heat in the surface layer of rail appear to be tensile. When the creepage is large, the frictional heat has a significant influence on the residual stresses and residual strains of rail. This paper develops a thermo-meehanical coupling model of wheel-rail rolling-sliding contact, and the obtained results can help to understand the mechanism of wheel/rail frictional thermal fatigue.展开更多
The existing researches on the damping wheel mainly focus on investigating the influence of damping structure change on the vibro-acoustic control.The changes include the geometric size of the damping structure,the da...The existing researches on the damping wheel mainly focus on investigating the influence of damping structure change on the vibro-acoustic control.The changes include the geometric size of the damping structure,the damping material parameters,and the placement,and so on.In order to further understand the mechanism in reducing the acoustic radiation of railway wheel with layer damping treatment,in this paper,the wheel is simply modified by a full-sized circular plate.The circle plate side has stuck circumference constrained damping ridges and radial constrained damping ridges on it.Based on a hybrid finite element method-boundary element method(FEM-BEM),the paper develops a vibro-acoustic radiation model for such a distributed constrained damping structure.The vibration and acoustic radiation of the circular plate is analyzed.In the analysis,the dynamic response of the system is obtained by using the 3D finite model superposition method.The obtained vibration response is used as the initial boundary condition in solving Helmholtz boundary integral equation for the sound radiation analysis.In the procedure,firstly,the modal analysis of the circular plate is performed to get the distribution of the system modal strain energy.Secondly,the vibro-acoustic radiation characteristics of the plate with different kinds of circumference damping ridges and radial damping ridges are compared in order to try to find the best effective damping ridge structure.Thirdly,using the distribution of the plate modal strain energy investigates the effect of the ridge distribution locations on the circular plate on its vibro-acoustic radiation.The calculation and analysis research results show that,the sticking circumference and radial damping ridges on the plate can control the vibro-acoustic radiation of the plate effectively in different frequency range.The distribution of the constrained damping ridge has an effect on reduction in vibro-acoustic radiation of the circular plate.The present research is very useful in the design of railway wheel with low noise level.展开更多
The effects of structure elastic deformations of wheelset and track on creep forces of wheel and rail are investigated.Finite element method is used to calculate the influence coefficients expressing the relations bet...The effects of structure elastic deformations of wheelset and track on creep forces of wheel and rail are investigated.Finite element method is used to calculate the influence coefficients expressing the relations between structure elastic deformations of wheelset and track and the corresponding loads in the rolling direction and the lateral direction of wheelset,respectively.The influence coefficients of wheelset and track are used to revise some of the influence coefficients obtained with the formula of Bossinesq and Cerruti in Kalker's theory of three dimensional elastic bodies in rolling contact with non Hertzian form.The theory of Kalker and the modified theory of Kalker are respectively employed to analyze creep forces of wheelset and track.The numerical results obtained show a great influence of structure elastic deformations of wheelset and track on the creep forces.Therfore it is not reasonable that wheel and rail are treated as elastic half space in the analysis of wheel and rail in rolling contact,and the present theories of rolling contact based on the assumption of elastic half space need to be further improved展开更多
文摘为了节省360°全景视频的编码时间,对通用视频编码标准中的编码单元划分决策过程进行了研究,提出了一种面向360°全景视频的帧内预测编码的快速算法。通过优化编码树单元(Coding Tree Unit,CTU)的编码深度范围和编码单元的划分模式的选择过程,减少编码时间。实验结果表明,在全帧内模式下,所提算法比原始算法平均可以节省34.33%的时间复杂度,同时带来的BDBR平均增量仅为1.665%,BDPSNR的平均降低量仅为0.076 dB。
文摘在拥有多个存储节点的云数据存储系统中,保持云存储系统的负载均衡水平为一个合理的值和最小化数据检索的时间是一个值得研究的问题。本文提出一种基于粒子群优化算法的云数据均衡放置策略(balanced placement strategy of cloud data based on particle swarm optimization algorithm,BPCD),首先,给出一种云存储系统模型;其次,引入基尼系数作为衡量该系统负载均衡水平的指标,结合数据检索时间目标函数构建多目标约束优化模型;再次,采用粒子群优化算法对问题进行求解,主要包括数据节点编码与参数设置、种群初始化、粒子群空间搜索、算法迭代4个过程;最后,将本文算法与传统云数据放置算法进行对比分析。仿真实验表明,本文提出的云数据均衡放置策略在优化云存储系统的负载水平和数据检索时间方面具有良好的效果。
基金Supported by National Natural Science Foundation of China(Grant Nos.U1361117,51305360)PhD Programs Foundation of Ministry of Education of China(Grant No.20130184110005)+1 种基金Cultivation Program for the Excellent Doctoral Dissertation of Southwest Jiaotong UniversityGuangzhou Metro Corporation Program of China
文摘The current research of rail corrugation mainly focuses on the mechanisms of its formation and development. Compared with the root causes and development mechanisms, the wheel-rail impacts, the fatigue failure of vehicle-track parts, and the loss of ride comfort due to rail corrugation should also be taken into account. However, the influences of rail corrugation on vehicle and track vibration, and failure of vehicle and track structural parts are barely discussed in the literature. This paper presents an experimental and numerical investigation of the structural vibration of metro bogies caused by rail corrugation. Extensive experiments are conducted to investigate the effects of short-pitch rail corrugation on the vibration accelerations of metro bogies. A dynamic model of a metro vehicle coupled with a concrete track is established to study the influence of rail corrugation on the structural vibration of metro bogies. The field test results indicate that the short-pitch rail corrugation generates strong vibrations on the axle-boxes and the bogie frames, therefore, accelerates the fatigue failure of the bogie components. The numerical results show that short-pitch rail corrugation may largely reduce the fatigue life of the coil spring, and improving the damping value of the primary vertical dampers is likely to reduce the strong vibration induced by short-pitch rail corrugation. This research systematically studies the effect of rail corrugation on the vibration of metro bogies and proposes some remedies for mitigating strong vibrations of metro bogies and reducing the incidence of failure in primary coil springs, which would be helpful in developing new metro bogies and track maintenance procedures.
基金supported by Doctoral Discipline Foundation of Ministry of Education of China (Grant No. 20090184110023)Unite Project of Basic Research Program on High-speed Railway of Railway Ministry of China (Grant No. U1134202)Independent Research Project of Traction Power State Key Laboratory of Southwest Jiaotong University,China (Grant No. 2009TPL-T06)
文摘While introducing foreign advanced technology and cooperating with Chinese famous research institutes,the high-speed vehicles are designed and take the major task of passenger transport in China.In high-speed vehicle,the characteristic of shock absorber is an important parameter which determines overall behavior of the vehicle.The most existing researches neglect the influence of the series stiffness of the shock absorber on the vehicle dynamic behavior and have one-sided views on the equivalent conicity of wheel tread.In this paper,a high speed passenger vehicle in China is modeled to investigate the effect of the parameters taking series hydraulic shock absorber stiffness into consideration on Ruzicka model.Using the vehicle dynamic model,the effect of main suspension parameters on critical speed is studied.In order to verify the reasonableness of shock absorber parameter settings,vibration isolation characteristics are calculated and the relationship between suspension parameters and the vehicle critical hunting speed is studied.To study the influence of equivalent conicity on vehicle dynamic behavior,a series of wheel treads with different conicities are set and the vehicle critical hunting speeds with different wheel treads are calculated.The discipline between the equivalent conicity of wheel tread and critical speed are obtained in vehicle nonlinear system.The research results show that the critical speed of vehicle much depends on wheelset positioning stiffness and anti-hunting motion damper,and the series stiffness produces notable effect on the vehicle dynamic behavior.The critical speed has a peak value with the equivalent conicity increasing,which is different from the traditional opinion in which the critical speed will decrease with the conicity increasing.The relationship between critical speed and conicity of wheel tread is effected by the suspension parameters of the vehicle.The study results obtained offer a method and useful data to designing the parameters of the high speed vehicle and simulation study.
基金supported by National Natural Science Foundation of China (Grant No. 50821063, Grant No. 50875221)National Basic Research Program of China (973 Program, Grant No. 2007CB714702)+1 种基金Basic Research Program of Ministry of Railway, China (Grant No. 2008J001-A)Doctoral Discipline Foundation of China (Grant No. 20090184110023)
文摘The profile of wheel/rail has great concern with the vehicle running safety, the wheel/rail wear and the rolling contact fatigue between wheel and rail, due to its severer impact on the dynamic behavior of both the railway vehicle/track, and the wheel/rail rolling contact status. However, recent studies in this respect are mainly explored in reverse methods, where track parameters are predetermined and invariable during the optimizing process. This paper attempts to propose a wheel-rail profiles matching design method considering multi-parameter, through optimizing wheel/rail profile under different rail cants and track gauges, based on the existed optimization technology for the normal gap of wheel/rail. The method presented in this paper can also, compared with the prior reverse methods, be called "forward solution method" in which the riding comfort, wheel unloading rate and wheel/rail contact stress of the speed-up railway passenger car are calculated by means of a vehicle-track coupling dynamic model, with the range of the rail cant varying from 1/20 to 1/40 and the rail gauge from 1 433 mm to 1 441 mm. These results show that the distribution status of the pairs of contact points can be obviously improved and the contact stress can be reduced significantly; a great influence is exposed by the rail cant and track gauge on the dynamic behavior of the high speed passenger car, and an optimal vehicle dynamics behavior are obtained with the optimized wheel/rail profile when the rail cant is 1/30 and the track gauge is 1 435 mm. This research can provide important references for the investigation of the wheel-rail profiles matching design method considering multi-parameter.
基金Supported by National Science and Technology Support Program of China(Grant No.2009BAG12A01-B06)National Hi-tech Research and Development Program of China(863 Program,Grant No.2011AA11A103-2-2)+3 种基金Funds for Innovation Research Team of Ministry of Education of China(Grant Nos.IRT1178,SWJTU12ZT01)Fundamental Research Funds for the Central Universities and the Science of China(Grant No.SWJTU12ZT01)2015 Doctoral Innovation Funds of Southwest Jiaotong University of ChinaProject of State Key Laboratory of Traction Power of China(Grant No.2011TPL_T05)
文摘The current researches of wheel vibration and sound radiation mainly focus on the low noise damped wheel. Compared with the traditional research, the relationship between the sound and wheel/rail contact is difficulty and worth studying. However, there are few studies on the effect of wheel load on wheel vibration and sound radiation. In this paper, laboratory test carried out in a semi-anechoic room investigates the effect of wheel load on wheel natural frequencies, damping ratios, wheel vibration and its sound radiation, The laboratory test results show that the vibration of the wheel and total sound radiation decrease significantly with the increase of the wheel load from 0 t to 1 t. The sound energy level of the wheel decreases by 3.7 dB. When the wheel load exceeds 1 t. the attenuation trend of the vibration and sound radiation of the wheel becomes slow. And the increase of the wheel load causes the growth of the wheel natural frequencies and the mode damping ratios. Based on the finite element method (FEM) and boundary element method (BEM), a rolling noise prediction model is developed to calculate the influence of wheel load on the wheel vibration and sound radiation. In the calculation, the used wheel/rail excitation is the measured wheel/rail roughness. The calculated results show that the sound power level of the wheel decreases by about 0.4 dB when the wheel load increases by 0.5 t. The sound radiation of the wheel decreases slowly with wheel load increase, and this conclusion is verified by the field test. This research systematically studies the cffcct of wheel load on wheel vibration and sound radiation, gives the relationship between the sound and wheel/rail contact and analyzes the reasons, therefore, it provides a reference for further research.
基金supported by National Natural Science Foundation of China(Grant Nos.51175438,U1134202)National Science and Technology Support Program of China(Grant No.2009BAG12A01)Program for New Century Excellent Talents in University of China(Grant No.NCET-08-0824)
文摘Thermal damage caused by frictional heat of rolling-sliding contact is one of the most important failure forms of wheel and rail. Many studies of wheel-rail frictional heating have been devoted to the temperature field, but few literatures focus on wheel-rail thermal stress caused by frictional heating. However, the wheel-rail creepage is one of important influencing factors of the thermal stress In this paper, a thermo-mechanical coupling model of wheel-rail rolling-sliding contact is developed using thermo-elasto-plastic finite element method. The effect of the wheel-rail elastic creepage on the distribution of heat flux is investigated using the numerical model in which the temperature-dependent material properties are taken into consideration. The moving wheel-rail contact force and the frictional heating are used to simulate the wheel rolling on the rail. The effect of the creepage on the temperature rise, thermal strain, residual stress and residual strain under wheel-rail sliding-rolling contact are investigated. The investigation results show that the thermally affected zone exists mainly in a very thin layer of material near the rail contact surface during the rolling-sliding contact. Both the temperature and thermal strain of rail increase with increasing creepage. The residual stresses induced by the frictional heat in the surface layer of rail appear to be tensile. When the creepage is large, the frictional heat has a significant influence on the residual stresses and residual strains of rail. This paper develops a thermo-meehanical coupling model of wheel-rail rolling-sliding contact, and the obtained results can help to understand the mechanism of wheel/rail frictional thermal fatigue.
基金supported by National Natural Science Foundation of China (Grant No. 50821063)Technological Research and Development Programs of Railway Ministry of China (Grant No. 2008J001-A,Grant No. 2009J001)Natural Science Foundation of State Key Laboratory of Traction Power,China (Grant No. 2008TPL-Z07)
文摘The existing researches on the damping wheel mainly focus on investigating the influence of damping structure change on the vibro-acoustic control.The changes include the geometric size of the damping structure,the damping material parameters,and the placement,and so on.In order to further understand the mechanism in reducing the acoustic radiation of railway wheel with layer damping treatment,in this paper,the wheel is simply modified by a full-sized circular plate.The circle plate side has stuck circumference constrained damping ridges and radial constrained damping ridges on it.Based on a hybrid finite element method-boundary element method(FEM-BEM),the paper develops a vibro-acoustic radiation model for such a distributed constrained damping structure.The vibration and acoustic radiation of the circular plate is analyzed.In the analysis,the dynamic response of the system is obtained by using the 3D finite model superposition method.The obtained vibration response is used as the initial boundary condition in solving Helmholtz boundary integral equation for the sound radiation analysis.In the procedure,firstly,the modal analysis of the circular plate is performed to get the distribution of the system modal strain energy.Secondly,the vibro-acoustic radiation characteristics of the plate with different kinds of circumference damping ridges and radial damping ridges are compared in order to try to find the best effective damping ridge structure.Thirdly,using the distribution of the plate modal strain energy investigates the effect of the ridge distribution locations on the circular plate on its vibro-acoustic radiation.The calculation and analysis research results show that,the sticking circumference and radial damping ridges on the plate can control the vibro-acoustic radiation of the plate effectively in different frequency range.The distribution of the constrained damping ridge has an effect on reduction in vibro-acoustic radiation of the circular plate.The present research is very useful in the design of railway wheel with low noise level.
基金National Natural Science Foundation of China(No.59935100).
文摘The effects of structure elastic deformations of wheelset and track on creep forces of wheel and rail are investigated.Finite element method is used to calculate the influence coefficients expressing the relations between structure elastic deformations of wheelset and track and the corresponding loads in the rolling direction and the lateral direction of wheelset,respectively.The influence coefficients of wheelset and track are used to revise some of the influence coefficients obtained with the formula of Bossinesq and Cerruti in Kalker's theory of three dimensional elastic bodies in rolling contact with non Hertzian form.The theory of Kalker and the modified theory of Kalker are respectively employed to analyze creep forces of wheelset and track.The numerical results obtained show a great influence of structure elastic deformations of wheelset and track on the creep forces.Therfore it is not reasonable that wheel and rail are treated as elastic half space in the analysis of wheel and rail in rolling contact,and the present theories of rolling contact based on the assumption of elastic half space need to be further improved