Multidisciplinary coupled dynamics modeling of electro-mechanical actuator considering nonlinear clearances in multiple stages
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摘要:
由于设计装配不确定性，电动舵机传动系统多环节存在间隙等非线性因素，严重影响工作品质，需建立非线性动力学模型。同时，其涵盖伺服控制、电机传动、减速机构、结构弹性等多学科，建模极具挑战。本研究以典型的滚珠丝杠式电动舵机为研究对象，考虑舵机传动元件的弹性刚度及齿轮副、支撑轴承和拨叉副处的间隙非线性，对电机动力学、伺服控制器进行精细化建模，建立了一种能考虑多环节间隙非线性的电动舵机系统高保真多学科动力学模型，并开展了电动舵机系统性能仿真分析。仿真结果与舵机-舵面系统地面振动试验结果进行了对比。结果表明：所建立的电动舵机多学科耦合动力学模型能够反映机构不同环节间隙非线性的影响和影响程度，仿真和试验结果吻合较好，最大误差小于10%。研究结果为航空航天复杂电动伺服系统的数字孪生研究奠定了基础。
Abstract:Due to uncertainties in the design and assembly process, nonlinear factors such as clearances often exist in multiple sectors of the aerospace electro-mechanical actuator transmission system, significantly affecting the working quality of the electro-mechanical actuator. Therefore, it is essential to accurately establish a nonlinear dynamic model for the electro-mechanical actuator accurately. Moreover, electro-mechanical actuators involve multiple disciplines such as servo control, motor transmission, reduction mechanism, structural elasticity, etc., making the modeling process highly challenging. The research object in this paper is a standard ball screw-type electro-mechanical actuator. Considering the elastic stiffness of actuator transmission components and the nonlinearity of clearances at gear pairs, supporting bearings, and fork pairs, the motor dynamics and servo controllers are finely modeled. The electro-mechanical actuator system is represented by a high-fidelity multidisciplinary dynamic model that can account for nonlinearities in different sector clearances. Furthermore, simulation analysis of the electro-mechanical actuator system performance is conducted. The simulation results are compared with ground vibration test results of the actuator-rudder system. The results indicate that the multidisciplinary coupled dynamic model of the electro-mechanical actuator established in this paper can reflect the influence and degree of influence of the clearances in different parts of the mechanism. The simulation and experimental results are in good agreement, with a maximum error of less than 10%. This research lays the foundation for the digital twin study of complex aerospace electric servo systems.
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图 3 电动舵机机械传动系统动力学模型
Figure 3. Dynamic model of electro-mechanical actuator transmission system
图 4 电动舵机机械传动系统框图模型
Figure 4. Block diagram model of electro-mechanical actuator transmission system
图 5 电动舵机整体机电耦合框图模型
Figure 5. Electromechanical coupling block diagram model of electro-mechanical actuator
图 6 1°阶跃激励下不同舵机仿真模型的结果对比
Figure 6. Comparison of the results of different actuator simulation models under a 1° step excitation
图 7 考虑多环节间隙的电动舵机舵偏角共振频率-共振幅值曲线
Figure 7. Resonance frequency-amplitude curve of rudder angle for electro-mechanical actuator considering various sectors clearances
图 8 考虑多环节间隙的电动舵机舵偏角激励力-共振频率曲线
Figure 8. Excitation force-resonance frequency curve of rudder angle for electro-mechanical actuator considering various sectors clearances
图 9 考虑单环节间隙的电动舵机舵偏角共振频率-共振幅值曲线
Figure 9. Resonance frequency-amplitude curve of rudder angle for electro-mechanical actuator considering single sector clearance
表 1 非线性电动舵机系统各环节间隙设置情况
Table 1. Clearance settings for various sectors in nonlinear electro-mechanical actuator system
工况 齿轮副间隙/rad 轴承间隙/mm 拨叉副间隙/rad 间隙最小组合 0.001 0.001 0.000 2 间隙最大组合 0.01 0.01 0.000 4 
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表 2 1°阶跃激励下电动舵机模型舵偏角阶跃响应仿真与试验结果
Table 2. Simulation and experimental results of step response of rudder angle in electro-mechanical actuator model under a 1° step excitation
工况 超调量/% 过渡过程时间/ms 指标 ≤25 ≤40 试验 15.06 16.00 简化模型 0.00 20.43 精细模型 4.40 16.83 间隙最小模型 4.20 16.83 间隙最大模型 6.70 16.45
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表 3 考虑多环节间隙的电动舵机舵偏角共振频率数据
Table 3. Resonance frequency data of rudder angle for electro-mechanical actuator considering various sectors clearances
激励力/N 试验共振频率/Hz 间隙最小组合共振频率/Hz 与试验结果误差/% 间隙最大组合共振频率/Hz 与试验结果误差/% 10 140.8 154.0 9.4 142.4 1.1 20 149.8 156.7 4.6 151.0 0.8 30 154.7 158.3 2.3 155.4 0.5 40 160.0 159.1 2.0 157.7 1.4 50 161.3 159.4 1.2 158.4 1.8
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表 4 不同激励工况下考虑单环节间隙的电动舵机舵偏角共振频率和共振幅值数据
Table 4. Resonance frequency and amplitude data of rudder angle for electro-mechanical actuator considering single sector clearance under various excitation conditions
工况 激励力/N 间隙最小共
振频率/Hz间隙最小共
振幅值/rad间隙最大共
振频率/Hz间隙最大共
振幅值/rad齿轮副
间隙10 160.3 $ 5.589\times {10}^{{-}5} $ 159.9 $ 3.494\times {10}^{{-}5} $ 20 160.3 $ 1.154\times {10}^{{-4}} $ 159.9 $ 9.493\times {10}^{{-}5} $ 30 160.3 $ 1.928\times {10}^{{-4}} $ 160.3 $ 1.525\times {10}^{{-4}} $ 40 160.3 $ 3.685\times {10}^{{-4}} $ 160.3 $ 3.069\times {10}^{{-4}} $ 50 160.3 $ 6.108\times {10}^{{-4}} $ 160.3 $ 5.518\times {10}^{{-4}} $ 轴承
间隙10 159.3 $ 6.438\times {10}^{{-}5} $ 152.1 $ 8.463\times {10}^{{-}5} $ 20 159.7 $ 1.227\times {10}^{{-4}} $ 156.0 $ 1.481\times {10}^{{-4}} $ 30 159.7 $ 2.040\times {10}^{{-4}} $ 158.0 $ 2.478\times {10}^{{-4}} $ 40 160.1 $ 3.856\times {10}^{{-4}} $ 158.9 $ 4.646\times {10}^{{-4}} $ 50 160.3 $ 6.321\times {10}^{{-4}} $ 159.3 $ 7.499\times {10}^{{-4}} $ 拨叉副
间隙10 154.9 $ 7.710\times {10}^{{-}5} $ 149.6 $ 9.128\times {10}^{{-}5} $ 20 157.3 $ 1.408\times {10}^{{-4}} $ 154.9 $ 1.542\times {10}^{{-4}} $ 30 158.4 $ 2.314\times {10}^{{-4}} $ 157.3 $ 2.647\times {10}^{{-4}} $ 40 159.3 $ 4.428\times {10}^{{-4}} $ 158.6 $ 4.937\times {10}^{{-4}} $ 50 159.6 $ 7.020\times {10}^{{-4}} $ 159.1 $ 7.772\times {10}^{{-4}} $
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