Kinematic calibration of the 3-degree-of-freedom redundantly actuated spatial parallel module of a five-axis hybrid machine

Abstract

As a new type of manufacturing equipment, redundant hybrid machines have the theoretical advantage over the traditional serial machines in efficiently processing large structural parts with high material removal ratio and complex parts with curved surfaces. In order to solve the accuracy problem of the redundantly actuated spatial parallel module of a five-axis hybrid machine, an improved kinematic calibration method is proposed in this article. First, different from error modeling for the corresponding non-redundant parallel module, the geometric error model of the redundantly actuated spatial parallel module considers the deformations at active joints caused by actuation redundancy as an error source. Then, the applicable error model is developed using projection technique to remove the need of active joints’ stiffness measurement or modeling. Later, the practical error model is derived from model reduction method to avoid using additional sensors or gratings. Finally, three forms of relative measurement and step identification are adopted for the calibration work, and the bilinear interpolation compensation function is introduced to ensure the calibration effect. On this basis, the kinematic calibration of the redundantly actuated spatial parallel module is conducted. The max position errors are reduced from original −0.192 to 0.075 mm after RM1 and SI1, and then further reduced to 0.014 mm after bilinear interpolation compensation, while the max orientation errors are reduced from −0.017° and 0.249° to −0.005° and −0.007° after RM2 and SI2, and RM3 and SI3, respectively. A contrasting experiment is also carried out with the previous method for the corresponding non-redundant parallel module. As a result, the proposed method shows better convergence value and speed in identifying error parameters, and therefore the effectiveness and efficiency of the proposed method for the redundantly actuated spatial parallel module are validated.

Vibration modelling analysis of defective parallel robots as machine tools for aerospace parts machining

“…vp T e and D = F T J e d. Substituting the initial conditions into equation (20), the solutions of this standing vibration equation can be solved. Finally, substituting the parameter values into the vibration equation, the vibration amplitudes of the fewer-DOFs and six-DOFs vibration systems can be solved via DP = Fu and are plotted in Figures 10 and 11, respectively.…”

“…18,19 As an initial trending research topic of vibration analysis, the vibration analysis of the Stewart platform was successful, and its studies have gradually transitioned from theoretical vibration analysis to a wide range of practical applications. 20,21 Since both the number of DOFs and the number of branches of the Stewart platform are equal to six, its Jacobian matrix, stiffness matrix and damping matrix are sixth-order matrices, and since the six branches are identical and only the axis stiffness is considered, the derivation of the vibration equation of the six-DOFs vibration system is feasible. However, when a parallel mechanism is used as a machine tool, the DPR is more popular due to the associated cost savings and simple control [22][23][24][25][26] ; however, relatively few vibration studies have been conducted on DPRs.…”