Modal flexibility is the degree to which a modal frequency of the system is easily excited by the transmission error of a specified meshing gear. It is defined as:

Where_represents the eigenvector under excitation and corresponds to the modal mode, [K] is the corresponding modal stiffness matrix.The higher the value of modal flexibility indicates that at this frequency, the more easily the modal modes are excited by the transmission error of the gear analyzed.When the modal flexibility is low, the dynamic response generally does not generate strong vibration or noise, as it requires more energy to excite.

Figure 1 shows the modal flexibility of each mode frequency excited by the transmission error of second gear during second gear engagement.The frequency range takes into account the input speed range from 0 to 6000 rpm, and the transmission error amplitude is 1um.As can be seen from the diagram, the system has several modal frequencies that are easily excited by the transmission errors of the second gear: 288 Hz, 655 Hz, 782 Hz, 1844 Hz, 2059 Hz.These frequencies are prone to vibration and noise problems.

Figure 2 shows the modal compliance of the system when the transmission error of a constant-rod gear corresponds to second gear engagement.As can be seen in the figure, at 668Hz, 655Hz and 756Hz, the modal modes have high modal flexibility. These modes are easily excited by the constant rodent gears and cause vibration and noise problems.