Study On Acceleration Characteristics Of Kinematic Geometry And Application

As concentrated expression and evaluation index of the comprehensive performance of machine tools,the accuracy of machine tools determines the overall level of manufacturing in a country.The ideal worktable translation motion is strictly limited to five degrees of freedom(DOF).But actually,when static errors such as geometric errors and elastic deformation of components,or dynamic errors like interpolation errors,servo following errors,and vibration errors of the drive system are taken into consideration,the real motion of the kinematic pair has 6 DOFs in three-dimensional space.At present,there is no uniform standard for the dynamic accuracy measurement of machine tool,and the quasi-static precision can't fully represent the overall error of machine tools in the running process.Therefore,it is necessary to find a method that can test the dynamic accuracy of kinematic pair quickly and easily.In Kinematic geometry,the moving frame and its differential formula studies the trajectory of points or lines by differential motion,which can link kinematics with geometry.Therefore,if the acceleration feature of kinematic geometry can be found,the geometric trajectory and spatial attitude of the error motion can be solved by the acceleration measurement.Aiming at the above problems,by applying the theory of kinematic geometry,this paper derive the relationship between the acceleration characteristics of the geometric elements on the rigid body and the spatial pose,angular velocity and angular acceleration of the rigid body.Then based on the rigid body assumption,it is applied to the attitude measurement and precision detection An acceleration-based method to dynamic error measurement of the prismatic pair in machine tools is discussed.It not only enriches the application of kinematic geometry in guiding pose solving,but also provides an idea for dynamic measurement.The research contents of this paper are as follows:Firstly,using the moving frame and the accompanying movement method,the trajectory,velocity and acceleration of a point on a space or plane moving rigid body can be described under the moving or fixed axode Frenet frame or centrode Frenet frame.The relationship between the kinematic parameters of rigid body(angular velocity,angular acceleration)and the geometric parameters of the trajectory surface or trajectory curve(induced structural parameters,spherical image curve arc length of unit vector of straight bus,induced curvature,instantaneous centerline arc length)also can be obtained.Then,combined with the homogeneous coordinate transformation method,the relationship between the instantaneous angular velocity of a rigid body and the rotation angle around each axis at any time under the fixed coordinate system is obtained.According to the acceleration expression of a point on rigid body,the nonlinear differential equations about the line acceleration of three non-collinear points of the rigid body and the three attitude angles of the rigid body can also gained.Then,RCCC mechanism is used to verify the correctness of the positive and negative solutions of the model.Finally,the differential equations are applied in the measurement of the error motion for prismatic pair in the CNC machine tools.The accuracy test model based on the full accelerometer measurement for the CNC machine tools is proposed.The triaxial CCLD accelerometer is used to test the acceleration value of the three non-collinear points on the worktable.The three-direction angle pendulum error of the worktable can be calculated by solving the differential equations.The three-direction translation error of worktable can be solved by the second integral of the acceleration data.