Derivation and application of refined gear time varying meshing stiffness model

“Innovation, coordination, green, open and sharing” are the five core supporting development concepts to promote the green transformation of traditional manufacturing industry, promote the establishment of green low-carbon circular development industry system, and encourage the renovation of enterprise technology and equipment, so as to improve product quality and maximize the benefits of product design and Application. With the development demand of national industrial equipment and the urgent need to improve industrial products, strict requirements are put forward for the bearing capacity, stability, vibration and noise of gear transmission. Vibration and noise, as one of the important indexes to measure the dynamic response of gear transmission device, is particularly important for the early prediction and discovery of the uneven response caused by the fatigue pitting or spalling of tooth surface and the misalignment of shaft staggering under the premise of meeting the design of geometric parts. It is urgent to study the dynamic response of the gear transmission system. It is of great significance to study the dynamic response characteristics of the gear transmission system caused by gears, transmission shafts and bearings, and the dynamic response characteristics of the transmission system caused by parts failure (gear tooth surface pitting, etc.). By studying the dynamic response characteristics of non-destructive and fault gear system, it has great guiding significance for improving the gear lightweight design and bearing capacity, reducing the system vibration and noise, early monitoring and fault type identification of transmission device fault characteristics and other performance indicators and fault diagnosis and identification.

According to the structure composition and energy reserve characteristics of gear, the composition of gear meshing stiffness is defined. According to the meshing kinematics of gear pair, the analytical equations of meshing in and meshing out limit position of gear along the meshing line and the process of single double meshing alternate motion of gear are derived in detail. Based on the conversion process of load work and energy reserve, the mathematical analytical equations of each component of gear meshing stiffness (tooth stiffness, contact stiffness and matrix stiffness) are derived in detail. In the tooth stiffness module, the refined geometric parameters of tooth profile composed of fillet transition curve and involute curve are considered in detail to analyze the tooth stiffness, and finally the tooth stiffness is constructed The refined mathematical model of the time-varying meshing stiffness of the wheel.

The effects of different gear basic parameters (modulus, pressure angle, tooth width, aperture, etc.) on the component stiffness and the comprehensive meshing stiffness are studied in detail. The simulation results show that different basic parameters have different response characteristics to the stiffness, and the main characteristics are the change of meshing stiffness value and the change of single double meshing stiffness region . At the same time, the calculation methods and application scenarios of two kinds of contact stiffness models are discussed in detail. The finite element model of elastic three-dimensional gear pair is basically consistent with the meshing stiffness calculation results of the proposed energy analysis method, and they have been verified each other, which further shows that the established refined mathematical model of meshing stiffness of gear pair has certain feasibility and reliability, improves the calculation efficiency and timeliness, and makes the preliminary research foundation for the rapid stiffness excitation simulation analysis of system dynamics .