齿轮传动系统的振动频率成分复杂多变，许多频率成分难于进行力学解释。建立定轴齿轮系统啮合点处的单自由度动力学模型，并将模型激励划分为线性激励和非线性激励，分别推导正常状态和平稳型故障下的频率响应特性及诱导因素。正常状态下，齿轮振动响应频率成分为啮合频率及其倍频，由齿轮受载后产生的静弹性变形位移和啮合动刚度共同诱发，并由非线性反馈进一步形成更高阶啮合频率成分。平稳型故障下，响应频率成分除正常运行特有的频率成分外，还包括：故障齿轮转频及其倍频，由平稳型位移误差函数与系统参数作用产生的惯性激励力、阻尼激励力和弹性激励力共同诱发；啮合频率及其倍频两侧间隔为转频的调制边频带，是由位移误差函数与啮合动刚度产生的弹性激励力引起的，并经非线性反馈进一步形成更高阶啮合频率及调制边带。有限元仿真和试验均有效地验证了推导和分析的振动响应频率特征规律。
Vibration response of the gear system is complicated, and some frequency components are hard to analyze with mechanics. Kinetic models of the fixed-shaft gearbox under healthy state and steady-type fault are established, whose excitation forces are divided into linear and nonlinear parts, and the vibration response derivations are obtained, as well as the induction factors. Due to the interaction between the static elastic deformation and the dynamic mesh stiffness, a healthy gearbox generates vibration response of the mesh frequency and its higher harmonics. When a steady-type fault exists in the gear pair, in addition to the frequency components under healthy state, the gearbox's vibration response also contains two other parts. One part is the rotational frequency of the fault gear and its higher harmonics exited by the inertia force, the damping force and the elastic force, which are generated from the interactions between the displacement error function and the system parameters such as mass, damping and stiffness. The other part is the modulation sidebands, whose carriers are the mesh frequency harmonics and their modulation frequencies are the rotational frequency harmonics of the fault shaft or gear. This part is the result of convolution between the displacement error function and the dynamics mesh stiffness. Frequency characteristics of the fixed-shaft gearbox obtained from both the finite element simulations and experimental tests effectively demonstrate the correctness of the theory derivation and analysis of the vibration response.
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