A novel geometric error compensation method for improving machining accuracy of spiral bevel gear based on inverse kinematic model

The geometric errors (GEs) of the spiral bevel gear milling machine will seriously affect the machining accuracy of the tooth surface and need to be compensated. In this paper, an innovative method for compensating the geometric error of CNC gear milling machine is proposed. This method describes the explicit relationship between the motion axis of the machine tool and the geometric errors, realizes the dynamic compensation by tooth, and improves the machining accuracy and machining efficiency of the tooth surface. Firstly, the actual forward kinematics model (FKM) is constructed based on the geometric errors module, and the error tooth surface with GEs is established. Secondly, the corresponding relationship between the machine setting parameters of the spiral bevel gear universal generation machine (UGM) and the CNC machine tool motion axis is given, and then the functional expression between the motion axis with geometric errors and the machine setting parameters is established, which is the inverse kinematics model (IKM). Then, the tooth surface error correction model is established according to the relationship between the machine setting parameters and the tooth surface errors. The compensation amount of the machine setting parameters obtained by the model is introduced into the IKM to obtain the GEs compensation model. Finally, the effectiveness of the geometric error compensation technique is verified by numerical analysis and experiments. The results show that the tooth surface errors, contact stress, and loaded transmission error after geometric errors compensation are significantly reduced, and the contact pattern meets the design requirements, which verifies the feasibility and effectiveness of the geometric errors compensation technology.