Abstract: Inertial cone crushers had the problems of large amplitude and high energy consumption, which restricted the further development in the industrial field. The multi-body dynamics solution may provide a theoretical calculation method for clarifying the relationship of the main dynamics parameters and the amplitude and energy consumption of the whole crushers. When absolute coordinate method was used for model, the constraints of pure rolling of moving cones were equivalent to holonomic and linear nonholonomic constraints.The differential-algebraic equations(DAEs) with first-order liner nonholonomic constraints were obtained. A LU state space method with variable step size was proposed based on implicit Runge-Kutta integration. To verify the validity of the model and numerical algorithm, under the stable conditions, the simulation results of dynamic response of each measuring point of fixed cone were compared and analyzed
 with the industrial field test results. Results show that driving speed, mass of fixed cone, damping coefficient and mass of moving cone have great influences on the amplitude, but the stiffness coefficient has little effects on the amplitude. Increase of the mass of fixed cone may effectively reduce the specific energy consumption, and increase of the damping coefficient in a certain range may increase the damping dissipation and the specific energy consumption.

Key words: inertia cone crusher; , multi-body dynamics, nonholonomic constraint, state space method, specific energy consumption

摘要： 惯性圆锥破碎机存在整机振幅大且能耗高等问题，制约了其在工业领域的进一步发展，其多体动力学求解可以为明确各主要动力学参数与整机振幅和能耗的关系提供理论计算方法。采用绝对坐标法建模，将动锥的纯滚动约束等效为完整和线性非完整约束，得到了含一阶线性非完整约束的微分代数方程组,提出了基于隐式Runge-Kutta积分变步长的LU状态空间法。在稳定工况下，对定锥各测量点动态响应的仿真结果和工业现场试验结果进行对比分析，验证了模型和数值算法的有效性。计算结果表明：驱动转速、定锥质量、阻尼系数和动锥质量对振幅的影响较大，刚度系数对振幅几乎没有影响；增加定锥的质量可以有效降低单位能耗；在一定范围内，增加阻尼系数会造成阻尼耗散增大，使单位能耗升高。

关键词: 惯性圆锥破碎机, 多体动力学, 非完整约束, 状态空间法, 单位能耗