Gear hobbing accounts for more than 90% of the gear forming process. In the cutting process of gear hobbing machine tool, there is inevitable vibration between tool and workpiece, which affects the geometric accuracy of gear, that is, there is tooth profile error. According to the nature of vibration, the vibration of machine tool can be divided into forced vibration, self-excited vibration, free vibration and random vibration. Among them, self-excited excitation and forced excitation have the greatest impact on the cutting stability of machine tool [40-45]. For gear hobbing machine working under normal working conditions, the vibration of machine tool mainly comes from self-excited vibration and forced vibration. In the process of gear hobbing cutting, the cutting edges take turns from cutting in to cutting out, and the cutting force gradually increases from small to large, and then gradually decreases. Periodic exciting force is generated between the workpiece and the tool, resulting in the relative displacement between the cutting edge and the machined surface of the workpiece. The relative displacement is analyzed theoretically, including establishing the vibration model and obtaining the vibration matrix; The vibration equation is decoupled and the transfer function is obtained by Laplace transform and expanding the vibration dimension; The response of tool and workpiece to excitation signal is obtained by inverse Laplace transform. Finally, the influence of vibration on the tooth surface morphology of the gear is obtained by using the relative displacement and the relative position relationship.
The influence of machine tool vibration on gear hobbing accuracy is studied. Firstly, the vibration theoretical modeling of the structure of gear hobbing machine is carried out. Through the analysis of the model, several factors affecting the machining accuracy of gear hobbing machine are obtained. Because the vibration of machine tool is inevitable and can not be eliminated, it can be limited in response, such as reducing the cutting feed of workpiece, avoiding the excitation frequency from reaching the resonance frequency of machine tool, and using high hardness alloy tools, Increase the number of cutting edges and so on to reduce the influence of machine tool vibration on gear hobbing accuracy; Then the influence of mechanical vibration on gear machining accuracy is deduced and verified by experiments; Finally, through the design of relevant monitoring facilities, the machine tool processing is monitored in real time, so as to keep the machine tool in normal working state at all times.