电梯系统垂直振动的频率敏感度分析与鲁棒设计

考虑曳引绳刚度在电梯运行过程中具有变刚度的特性,利用Lagrange方程对电梯系统建立了7自由度的振动微分方程,通过试验设计方法得出随机变量与系统频率响应的数值关系,利用人工神经网络技术获得随机变量与频率响应之间的显性函数关系式。根据激振频率与固有频率之比不超过规定值的关系准则,定义了电梯系统纵向振动的可靠性模式,运用频率可靠性分析方法,提出多频激励情况下的系统的频率可靠性及其敏感度的分析方法。在此基础上,结合可靠性敏感度理论与稳健设计方法,将可靠性敏感度融入到目标优化设计中,建立系统频率可靠性鲁棒设计模型。通过工程算例,将可靠性敏感度理论和稳健设计方法应用到电梯系统设计当中,得到满足鲁棒设计要求的随机参数值。结果表明,该方法具有较高的计算效率和求解精度,可以作为电梯系统稳健设计的理论依据。

Study on Frequency Reliability Sensitivity Analysis and Robust Design for Vertical Vibration of the Elevator System

In order to study the vertical vibration characteristics of the elevator system, a seven-degrees-of-freedom dynamical equation was established considering its time-varying traction rope stiffness based on the Lagrange equation. The design of experimental(DOE) method was applied to obtain the quantitative relationship between random variables and system frequency responses. Then, artificial neural network (ANN) technology was used to fit the explicit functional relationship between the random variables and system responses. According to the criterion that the ratio of the excitation frequency and the natural frequency of the system structure cannot exceed a certain value, the frequency reliability mode of the elevator system in the vertical direction was defined to calculate the frequency reliability and related frequency reliability sensitivity with respect to random variables and variances based on the frequency reliability theory. Finally, the reliability-based robust design of structures was studied using the reliability based optimization model, and the numerical method of frequency reliability-based robust design was proposed. The frequency reliability sensitivity and reliability robust design was discussed for elevator systems with vibration in the longitudinal direction using the above theory. The result shows that this method has high computational efficiency and accuracy, and can serve as a theoretical method for the robust design of an elevator system and its components.