变体飞行器伸缩机构的滑动导轨间隙大且刚度低,导致其动力学特性复杂。该文针对伸缩机构中滑动导轨动力学建模方法和动力学特性开展研究,考虑导轨变形,采用有限元梁单元建立导轨模型;考虑导轨与滑块之间的间隙,提出一种判断导轨和滑块接触状态的检测方法。为避免导轨与滑块线接触和面接触的接触力模型计算的接触力差距较大问题,该文修正了变刚度接触力模型的阻尼系数;综合考虑导轨变形和导轨与滑块之间间隙,基于Lagrange乘子法和Baumgarte违约修正建立了滑动导轨动力学模型,并提出动力学模型的稳定数值求解方法,揭示了导轨弹性、间隙尺寸和导轨形式对滑动导轨动力学特性的影响规律。结果表明：考虑导轨弹性时,滑块侧向位移增大,接触力峰值降低;间隙尺寸增大会引起更剧烈的碰撞,使导轨变形增大;相较于单导轨,双级双导轨形式下滑块侧向位移显著增大,且发生卡滞现象的可能性更大。该文研究结果可为伸缩机构滑动导轨的设计和控制提供参考。
Abstract
[Objective] The sliding guide used in the telescopic mechanisms of morphing aircraft typically exhibits large clearance and low stiffness, resulting in complex dynamic behavior that significantly affects mechanism performance. Most existing studies on sliding guide dynamics focus on machine tool guides, which differ substantially in structural and operating conditions. Therefore, a specialized dynamic model that accounts for guide flexibility and clearance effects is needed to accurately characterize the dynamic performance of telescopic sliding guides. [Methods] A dynamic model of a sliding guide with clearance was developed. The guide rail was represented by finite element beam elements based on the Euler–Bernoulli beam theory to capture its elastic deformation. A multipoint contact detection method was introduced to avoid missed detections of contact states between the slider and the deformed guide. Contact may occur in either line or area contact modes. To compute the contact force in area contact mode, a variable stiffness contact force model was proposed; its damping coefficient was chosen manually. Because different contact mode calculations could produce large discrepancies in contact force and cause numerical instability, a modified variable stiffness contact force model was introduced for area contact, in which the damping coefficient was corrected using the material restitution coefficient. For line contact, the Flores contact force model was adopted. Friction forces were calculated using the Ambrósio modified Coulomb friction model. The dynamic equations of the slider and the guide were formulated using the Lagrange multiplier method with Baumgarte stabilization. A unified numerical solution strategy based on MATLAB’s ode15s solver was implemented to simulate the dynamic response. [Results] Numerical simulations revealed the influence of key parameters on dynamic behavior. When guide elasticity was included, peak contact forces decreased, but the lateral displacement of the slider increased, accompanied by sustained oscillation owing to cantilevered guide vibration. Larger clearance sizes yielded higher peak contact forces and larger amplitude oscillations in guide tip deflection, while the time-averaged friction force decreased. In a dual-stage, dual-guide configuration, the system exhibited more frequent collisions and chaotic lateral motion, with notable jamming caused by asynchronous deformation of the two guides. Reducing the interguide spacing mitigated this jamming effect. Experimental validation using a prototype with adjustable clearance showed that the equivalent friction coefficient decreased with increasing clearance under different actuation speeds and modes, consistent with simulation trends. This effect was more pronounced during deployment than during retraction and at lower speeds. The effect diminished at larger clearances, exhibiting nonlinear saturation. The deviation between simulated and experimental friction coefficients was within 30.00%, confirming the validity of the proposed dynamic model. [Conclusions] This paper presents a comprehensive dynamic modeling framework for sliding guides in telescopic mechanisms that incorporates guide elasticity and clearance effects. The proposed contact detection method and modified contact force model increase modeling accuracy and numerical stability. The simulation and experimental results demonstrate that guide elasticity, clearance size, and guide configuration considerably affect dynamic behavior. These findings provide a theoretical foundation for the design and control of sliding guides in deployable aerospace mechanisms.
关键词
滑动导轨 /
间隙 /
接触力模型 /
动力学模型 /
动力学特性
Key words
sliding guide /
clearance /
contact force model /
dynamic model /
dynamic characteristics
{{custom_sec.title}}
{{custom_sec.title}}
{{custom_sec.content}}
参考文献
[1] 朱玮, 吴玉国, 时礼平, 等. T型槽织构化机床滑动导轨的摩擦学特性[J]. 安徽工业大学学报(自然科学版), 2020, 37(4): 356-363. ZHU W, WU Y G, SHI L P, et al. Tribological properties of sliding guide rail of T-groove textured machine tool[J]. Journal of Anhui University of Technology (Natural Science), 2020, 37(4): 356-363. (in Chinese)
[2] 孙光明, 杨景景, 张大卫, 等. 精密机床导轨装配误差一致性工艺控制方法研究[J]. 天津理工大学学报, 2024, 40(4): 29-34. SUN G M, YANG J J, ZHANG D W, et al. Research on control technology of consistency of guide rail assembly error of precision machine tool[J]. Journal of Tianjin University of Technology, 2024, 40(4): 29-34. (in Chinese)
[3] MABLEKOS-ALEXIOU A, DA CRUZ L, BERGELES C. Friction-inclusive modeling of sliding contact transmission systems in robotics[J]. IEEE Transactions on Robotics, 2021, 37(4): 1252-1267.
[4] ZHANG X Y, WANG H L, ZHAO Q J, et al. Structural modeling and dynamic analysis of the two-segment deployable beam system[J]. International Journal of Mechanical Sciences, 2022, 233: 107633.
[5] HAN Y W, DONG Y Y, ZHANG Z J. Bistable click mechanism for dipteran flight robot[J]. International Journal of Mechanical Sciences, 2024, 281: 109555.
[6] QIAN M B, QIN Z, YAN S Z, et al. A comprehensive method for the contact detection of a translational clearance joint and dynamic response after its application in a crank-slider mechanism[J]. Mechanism and Machine Theory, 2020, 145: 103717.
[7] 金国光, 王志敏, 畅博彦, 等. 含间隙变胞机构动力学建模与平稳性分析[J]. 机械工程学报, 2024, 60(21): 144-155. JIN G G, WANG Z M, CHANG B Y, et al. Dynamic modeling and stationarity analysis of metamorphic mechanism with clearance joint[J]. Journal of Mechanical Engineering, 2024, 60(21): 144-155. (in Chinese)
[8] ZHENG X D, LI J, WANG Q, et al. A methodology for modeling and simulating frictional translational clearance joint in multibody systems including a flexible slider part[J]. Mechanism and Machine Theory, 2019, 142: 103603.
[9] 王成志, 王云超. 运动副间隙及受力状态对空间转向机构转向误差的影响[J]. 机械工程学报, 2022, 58(4): 240-249. WANG C Z, WANG Y C. Influence of clearances and force state of joints on steering error of spatial steering mechanism[J]. Journal of Mechanical Engineering, 2022, 58(4): 240-249. (in Chinese)
[10] 俞武勇, 季林红, 阎绍泽, 等. 含间隙机构运动副的动力学模型[J]. 机械科学与技术, 2001, 20(5): 665-669. YU W Y, JI L H, YAN S Z, et al. A survey of dynamics model of pairs with clearances in mechanism[J]. Mechanical Science and Technology, 2001, 20(5): 665-669. (in Chinese)
[11] ZHANG Y F, DING Y, XU G S. A continuous contact-force model for the impact analysis of viscoelastic materials with elastic aftereffect[J]. Multibody System Dynamics, 2024, 61(3): 435-451.
[12] WANG G X, JIA W X, NIU Z P, et al. Optimal damping factors explored for eliminating nonphysical attraction forces from viscous contact models used in cohesionless granular system[J]. Communications in Nonlinear Science and Numerical Simulation, 2025, 150: 109074.
[13] TONG J C, MENG D J, LIAN Y B, et al. Comparison of different contact force and friction combined models in dynamic analysis of roller guide joint with clearance for a vehicle sliding door mechanism[J]. Journal of Computational and Nonlinear Dynamics, 2025, 20(9): 091004.
[14] 黄剑锋, 余涛, 陈江义. 刚体碰撞的Hertz接触力模型比较分析[J]. 机械设计与制造, 2017(8): 28-30. HUANG J F, YU T, CHEN J Y. Comparison and analysis of Hertz contact force models for collision of rigid bodies[J]. Machinery Design & Manufacture, 2017(8): 28-30. (in Chinese)
[15] WU X Z, SUN Y, WANG Y, et al. Dynamic analysis of the double crank mechanism with a 3D translational clearance joint employing a variable stiffness contact force model[J]. Nonlinear Dynamics, 2020, 99(3): 1937-1958.
[16] AMBRÓSIO J A C. Impact of rigid and flexible multibody systems: Deformation description and contact models[M]// SCHIEHLEN W, VALÁŠEK M. Virtual Nonlinear Multibody Systems. Dordrecht: Springer, 2003: 57-81.
基金
空间物理重点实验室开放基金课题项目(SPL2024009)
PDF(6566 KB)
