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摘要:
颤振是一种危险的气动弹性失稳形式，舵机动刚度对舵系统的颤振特性具有不可忽视的影响，因此舵机的精确建模与仿真分析十分有必要。针对此问题，提出了一种电动舵机模块化建模方法及动刚度计算机模拟方法。以“直流电机-减速齿轮-滚珠丝杠-拨叉副”典型结构的电动伺服舵机为对象，将其分解为具备核心功能的子模块，充分考虑了实际结构中可能出现的主要非线性因素，再根据子模块之间的连接关系来搭建整体的舵机模型。基于该舵机模型，提出了利用步进正弦扫频信号激励、最小二乘法数据处理得到动刚度的计算方法，并以某舵机为算例，开展了舵机主要线性参数及非线性因素对舵机动刚度影响的研究。电动舵机模块化建模方法通用性好，便于不同舵机的拓展。电机转子阻尼、减速器的传动比以及输出轴处的阻尼对舵机的动刚度影响很大，间隙、接触刚度和摩擦这3类非线性因素对舵机的动刚度特性也具有重要的影响。
Abstract:Flutter is a dangerous aeroelastic instability form. The influence of actuator dynamic stiffness on the fin-actuator system flutter characteristics cannot be ignored. Therefore, accurate actuator modeling and simulation are necessary. A modular modeling method and dynamic stiffness computer simulation method for electromechanical actuator are proposed. The object is the actuator composed of DC motor, reduction gear and ball screw-fork. It is divided into submodules with core functions. The main nonlinear factors that may appear are fully considered. Then the whole actuator model is built according to the connection between the submodules. Based on the above, a calculation method using step sine sweep signal as excitation and processing the data by least square method is proposed. Taking a certain actuator as an example, the influence of the actuator main linear and nonlinear parameters on the dynamic stiffness is studied. The modular modeling method has good generality, which is convenient for the modeling of different actuators. The damping of the motor rotor, the transmission ratio of the reducer and the damping at the output shaft have a great influence on the dynamic stiffness, and three nonlinear factors, clearance, contact stiffness and friction, also have important influence.
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Key words:
- electromechanical actuator /
- modeling /
- dynamic stiffness /
- aeroservoelasticity /
- nonlinearity
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图 14 减速器与传动机构子模块简图
Figure 14. Simplified diagram of reducer and transmissionmechanism submodule
图 22 舵机模型指令信号与响应对比
Figure 22. Comparison of command signal and response of actuator model
图 24 线性航机输出轴的响应(43~44.5 Hz)
Figure 24. Response of linear actuator output shaft (43~44.5 Hz)
图 26 线性航机输出轴的响应(98~99.5 Hz)
Figure 26. Response of linear actuator output shaft (98~99.5 Hz)
图 28 非线性舵机输出轴的响应(43~44.5 Hz)
Figure 28. Response of nonlinear actuator outputshaft (43~44.5 Hz)
图 29 非线性舵机输出轴的响应(98~99.5 Hz)
Figure 29. Response of nonlinear actuator outputshaft (98~99.5 Hz)
图 38 舵机仅包含间隙时激励幅值对动刚度的影响
Figure 38. Influence of excitation amplitude on dynamic stiffness of outuator with freeplay only
图 45 舵机仅包含摩擦时激励幅值对动刚度的影响
Figure 45. Influence of excitation amplitude on dynamic stiffness of outuator with friction only
参数 数值 电感L/mH 6.53×10-4 电阻R/Ω 1.1 力矩系数Km/(N·m·A-1) 0.024 反电动势系数Ce/(V·s·rad-1) 0.034 电机转子转动惯量Jm/(kg·m2) 1.09×10-6 电机转子黏性阻尼系数bm 0.003 电机与减速器连接刚度km/(N·m·rad-1) 1 000 小齿轮转动惯量J1/(kg·m2) 2.4×10-8 大齿轮转动惯量J2/(kg·m2) 4×10-6 小齿轮半径r1/m 0.005 大齿轮半径r2/m 0.022 5 齿轮啮合刚度kg/(kg·s2·rad-1) 108 齿轮与传动机构连接刚度kz/(N·m·rad-1) 1 000 滚珠丝杠转动惯量Jsg/(kg·m2) 1.12×10-5 滚珠丝杠螺旋角λ/(°) 6.06 滚珠丝杠半径rsg/m 0.006 滚珠丝杠效率η 0.85 拨叉长度Lbc/m 0.028 5 输出轴转动惯量Jshaft/(kg·m2) 4.1×10-5 接触刚度Kjc 6×10-6 间隙半宽度dfp/rad 0.000 5 库伦摩擦参数Fc/N 1 静摩擦系数Fs/N 1.5 动态摩擦参数σ0/(N·s·m-1) 105 切换速度Vs/(m·s-1) 0.001 动态摩擦参数σ1/(N·s·m-1) 316.23 黏性阻尼参数σ2/(N·s·m-1) 0.4 
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表 2 舵机参数对动刚度的影响
Table 2. Influence of actuator parameters on dynamic stiffness
参数 影响程度 幅值关系 相位关系 线圈电感 小 ↓ — 电阻 小 ↑ — 力矩系数 大 — — 反电动势系数 很小 — — 电机转子转动惯量 大 ↓ ↓ 电机转子黏性阻尼系数 大 ↓ ↑ 小齿轮转动惯量 很小 — — 大齿轮转动惯量 很小 — — 小齿轮半径 大 ↑ ↑ 大齿轮半径 大 ↓ ↓ 齿轮啮合刚度 很小 — — 齿轮与传动机构连接刚度 很小 ↑ — 滚珠丝杠转动惯量 小 ↓ ↓ 滚珠丝杠半径 大 ↑ ↑ 滚珠丝杠效率 大 ↓ ↓ 拨叉长度 很大 ↑ ↓ 输出轴滚珠惯量 小 ↓ ↑ 输出轴阻尼 很大 ↑ ↑
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