Under low gravity,the Lagrange equations in the form of volume integration of pressure of nonlinear liquid sloshing were built by variational principle. Based on this,the analytical solution of nonlinear liquid sloshi...Under low gravity,the Lagrange equations in the form of volume integration of pressure of nonlinear liquid sloshing were built by variational principle. Based on this,the analytical solution of nonlinear liquid sloshing in pitching tank could be investigated. Then the velocity potential function was expanded in series by wave height function at the free surface so that the nonlinear equations with kinematics and dynamics free surface boundary conditions were derived. Finally,these nonlinear equations were investigated analytically by the multiple scales method. The result indicates that the system's amplitude-frequency response changes from ‘soft-spring’ to ‘hard-spring’ in the planar motion with the decreasing of the Bond number,while it changes from ‘hard-spring’ to ‘soft-spring’ in the rotary motion.展开更多
通过理论分析和试验验证,着重研究了非线性弹簧力和非线性摩擦力对数控工作台动态特性的作用。数控工作台受滚珠丝杠轴向力、横向力、扭矩、摩擦力和切削力等多种载荷的作用,滚珠丝杠各类刚度的大小与滚珠丝杠的支承方式密切相关;各类...通过理论分析和试验验证,着重研究了非线性弹簧力和非线性摩擦力对数控工作台动态特性的作用。数控工作台受滚珠丝杠轴向力、横向力、扭矩、摩擦力和切削力等多种载荷的作用,滚珠丝杠各类刚度的大小与滚珠丝杠的支承方式密切相关;各类刚度随着工作台位移和运动方向的变化而变化,呈现出软弹簧特性或硬弹簧特性等非线性规律;摩擦力变化规律服从Streibeck曲线。指出非线性弹簧力作用可以用有阻尼的Duffing方程描述,非线性摩擦力作用可以用van der Pol方程描述,非线性弹簧力和非线性摩擦力的耦合作用可以用Lienard方程描述。软硬弹簧特性引起的跳跃现象和非线性摩擦力自激振动引起的爬行现象使系统响应的稳定区域复杂化;跳跃现象主要发生在激励频率与固有频率接近的情况下,而爬行现象主要发生在低速润滑条件不良的情况下。极限环的存在表明非线性因素是限制失稳状态无限发展的稳定因素。展开更多
基金the National Defense Foundation of China(Grant No.41320020301).
文摘Under low gravity,the Lagrange equations in the form of volume integration of pressure of nonlinear liquid sloshing were built by variational principle. Based on this,the analytical solution of nonlinear liquid sloshing in pitching tank could be investigated. Then the velocity potential function was expanded in series by wave height function at the free surface so that the nonlinear equations with kinematics and dynamics free surface boundary conditions were derived. Finally,these nonlinear equations were investigated analytically by the multiple scales method. The result indicates that the system's amplitude-frequency response changes from ‘soft-spring’ to ‘hard-spring’ in the planar motion with the decreasing of the Bond number,while it changes from ‘hard-spring’ to ‘soft-spring’ in the rotary motion.
文摘通过理论分析和试验验证,着重研究了非线性弹簧力和非线性摩擦力对数控工作台动态特性的作用。数控工作台受滚珠丝杠轴向力、横向力、扭矩、摩擦力和切削力等多种载荷的作用,滚珠丝杠各类刚度的大小与滚珠丝杠的支承方式密切相关;各类刚度随着工作台位移和运动方向的变化而变化,呈现出软弹簧特性或硬弹簧特性等非线性规律;摩擦力变化规律服从Streibeck曲线。指出非线性弹簧力作用可以用有阻尼的Duffing方程描述,非线性摩擦力作用可以用van der Pol方程描述,非线性弹簧力和非线性摩擦力的耦合作用可以用Lienard方程描述。软硬弹簧特性引起的跳跃现象和非线性摩擦力自激振动引起的爬行现象使系统响应的稳定区域复杂化;跳跃现象主要发生在激励频率与固有频率接近的情况下,而爬行现象主要发生在低速润滑条件不良的情况下。极限环的存在表明非线性因素是限制失稳状态无限发展的稳定因素。
