Research On Nonlinear Elastic Dynamics Of High-Speed Space Parallel Coordinate Measuring Machine

During high speed operation, parallel coordinate measuring machine exhibits obvious elastic deformation and elastic vibration. This leads to reducing running precision and shortening service life of the machine. Therefore, the research on the high-speed space parallel coordinate measuring machine is of great theoretical significance and practical value.In this thesis, high-speed space PCMM is taken as object of study. Theoretical research on the kinematics, nonlinear elastic dynamics modeling and numerical analysis is performed.Firstly, the composition and characteristic of the PCMM is introduced. The degree of freedom of the mechanism is calculated using formula of the degree of freedom. The kinematics analyses of the driving limbs are taken in. The inverse kinematics solution of the driving limbs is given. Velocity Jacobian matrix of the PCMM is educed.Secondly, the nonlinear elastic dynamic modeling of the PCMM is studied. The spatial beam element is used to discretize the flexible driving limbs by using finite element method. The kinetic energy equation containing the coupling effect between rigid body and elastic motion of flexible limbs and the strain energy equation considered on the geometrical nonlinearity are given. Then the dynamic equation of element is derived according to Lagrange equation. From constraint among elements, the dynamic equations of branches are derived. Using the kinematic and dynamic constraint equations of the system, the overall system nonlinear elastic dynamic equation of the PCMM is obtained by assembling the dynamic equations of branches.Finally, the newmark method is introduced to solve the nonlinear elastic dynamic equation. The displacement error, velocity, acceleration of the PCMM are analyzed. The calculated numerical results show that the effectiveness and correctness of the nonlinear elastic dynamic models proposed in this thesis.