圆柱刚体滚动的动力学分析  

DYNAMIC ANALYSIS FOR THE ROLLING OF CYLINDRICAL RIGID BODY

作　　者：董焱章[1] 李鑫[1] 曾红燕[1] 

机构地区：[1]汽车动力传动与电子控制湖北省重点实验室,湖北汽车工业学院汽车工程系,湖北十堰442002

出　　处：《物理与工程》2016年第6期34-38,共5页Physics and Engineering

基　　金：国家自然科学基金青年科学基金(11502075);湖北省自然科学基金(2014CFB629);湖北汽车工业学院博士科研启动基金(BK201501)资助项目

摘　　要：刚体滚动是理论力学中常见的问题,其摩擦力的分析一直受到研究者关注.笔者对圆柱刚体滚子受到任意集中力作用下的运动情况进行了分析,事实上只要圆柱刚体未离开支撑面,起实质作用的只有平行于支撑面的集中力分量,进而得到了相应情形下滚子的角加速度和质心加速度表达式,并研究了滚子角加速度和质心加速度的极值问题,从而提出了摩擦类型判别函数式;并对无摩擦条件下圆柱刚体的滚动状态进行了探讨;最后对滚子静止不动、原地打滑、纯滑动等特殊运动情况作了讨论.Rolling of rigid body is a common problem in theoretical mechanics,and the analysis of friction has attracted researchers.In this paper,a cylindrical rigid roller under an arbitrary concentrated load is analyzed according to different cases.In fact,as long as the cylindrical rigid roller is not away from its support,only the parallel component of the concentrated load plays an essential role.Then the angular acceleration and the acceleration of mass center of the roller are derived,and their extreme value results are obtained.Sequentially the general form of friction discrimination function is proposed.Rolling state of cylindrical rigid body under the frictionless case is also explored.Finally,statics,in-situ slipping,pure sliding and other special movement cases are discussed.

关 键 词：圆柱 刚体滚动 摩擦力 角加速度 质心加速度 

分 类 号：O313.3[理学—一般力学与力学基础]