Geometric error identification of five-axis machine tools using dual quaternion

• A universal kinematic model of five-axis machine tools based on the UDQ is proposed. • The PIGEs of translational/rotary axes are redefined based on the UDQ. • The synchronous motion trajectory of dual rotary axes is proposed using a DBB. • A DBB trajectory equalization algorithm is established. • The identification method is extended to other five-axis machine tools. A universal identification method for position independent geometric errors (PIGEs) of dual rotary axes of five-axis machine tools with arbitrary rotary axis position structures is proposed based on the unit dual quaternion (UDQ). The PIGEs of translational/rotary axes are redefined based on UDQ transformation, which effectively reduces the transformation parameters and avoids the unitization process of UDQ compared with the existing UDQ kinematics model. Based on the redefined PIGEs, a kinematic error model of a five-axis machine tool is established for error identification. Taking the cradle-type five-axis machine too with non-intersecting rotary axes as the research objective, a novel method for identifying PIGEs through the synchronous motion of dual rotary axes using a double ball bar (DBB) is proposed. Compared with BK1 and BK2 in ISO10791-6 and other existing methods, the advantage of the proposed method is that it can greatly reduce the complexity of the experiment and the operation steps by directly constructing the relative kinematic relationship between the tool and the workpiece based on the error model. Only one installation and one measurement trajectory are needed to simultaneously identify the eight PIGEs of the dual rotary axes. In addition, a trajectory equalization algorithm is proposed to effectively solve the asynchronous problem of motion and data sampling in DBB trajectory operation. By combining the simplified error model with the sampling data of DBB, the pseudo-inverse matrix is used for decoupling. The effectiveness of the proposed method is verified by DBB compensation comparison experiment. The proposed error identification method can be applied to other types of five-axis machine tools with a few changes in the configural parameters, which is ideal for periodic checks and calibration to ensure the machining accuracy.