Strain energy equivalence-based gravity-induced deformation prediction and accuracy partitioning enhancement of a parallel machining module

Abstract

Structural errors, gravity-induced deformation and other non-geometrical errors simultaneously affect the accuracy of machining equipment. On the one hand, separating gravity-induced deformation from the total pose error is very difficult, which makes the identification of structural errors lacks reliable pose error data. On the other hand, the pose error caused by the other non-geometrical errors is often overlooked in calibration, and it will generate a random disturbance to the pose error caused by structural errors, which makes the error compensation effect worsen as the calibration region expands. In this article, a gravity-induced deformation prediction model based on strain energy equivalence criterion is proposed, which reduces the maximum and mean gravity-induced deformation prediction errors by 55.00 % and 65.32 % in simulation. On this basis, the error model of a five-axis parallel machining module considering gravity-induced deformation is established. Then, an accuracy partitioning enhancement method is proposed, in which the workspace is divided into eight sub-regions and 19 transition regions. A continuous transition function without poles is designed, which guarantees the continuity of structural errors among sub-regions without large fluctuations in transition regions. The pose error caused by structural errors is obtained by removing the predicted gravity-induced deformation from the measured total pose error. The structural errors in sub-regions and transition regions are obtained through the identification process and transition function, respectively, and are compensated into the inverse kinematic model separately. Then, the predicted gravity-induced deformation is compensated into command poses. After accuracy partitioning enhancement with the proposed method to consider gravity-induced deformation, the maximum/mean position error was reduced from 0.1266 mm/0.0238 mm to 0.0548 mm/0.0148 mm, and the maximum/mean posture error was reduced from 0.0897°/0.0280° to 0.0537°/0.0215° compared to the kinematic calibration method that does not apply the accuracy partitioning enhancement method. An S-shaped test piece was machined, and the maximum/mean error of the measuring points was reduced from 0.0817 mm/0.0253 mm to 0.0581 mm/0.0158 mm. The experimental results verify the effectiveness of the gravity-induced deformation prediction model and accuracy partitioning enhancement method. The proposed method can also be applied to other equipment with parallel kinematics.