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Dynamic inversion and optimal tracking control on the ball-plate system based on a linearized nonholonomic multibody model 基于线性化非整体多体模型的球-板系统动态反转和优化跟踪控制
IF 4.5 1区 工程技术 Q1 ENGINEERING, MECHANICAL Pub Date : 2024-09-21 DOI: 10.1016/j.mechmachtheory.2024.105795
A.G. Agúndez , A. Saccon , D. García-Vallejo , E. Freire
This paper addresses the optimal control of the ball-plate system, a well-known nonholonomic system in the context of nonprehensile manipulation, using a multibody dynamics approach. The trajectory tracking control of a steady-state circular motion of the ball on the plate, for any radius and potentially off-centric with respect to the plate’s pivoting point, is achieved by designing a Linear-Quadratic Regulator. A spatial multibody model of the ball-plate system is considered. A key contribution is the analytical computation of the circular steady motion of the ball by dynamic inversion, including the control actions to achieve this reference solution. This enables the analytical computation of the linearized equations along this reference motion, resulting in a periodic linear time-varying (LTV) system, and the application of linear controllability criteria for LTV systems. A controllable linear system, involving the Cartesian coordinates of the contact point and the yaw angle of the sphere, is obtained using a convenient coordinate partition in the linearization. Compared to existing results on the same problem, closed-loop stability about the desired trajectory is achieved for any radius of the circular trajectory.
球-板系统是一种著名的非全局系统,本文采用多体动力学方法对其进行优化控制。通过设计一个线性-二次调节器,可实现对球在板上的稳态圆周运动的轨迹跟踪控制,该运动的半径不限,且可能相对于板的支点偏离中心。考虑了球-板系统的空间多体模型。其主要贡献在于通过动态反演分析计算了球的圆周稳定运动,包括实现该参考解的控制行动。这样就能分析计算出沿着该参考运动的线性化方程,从而形成周期性线性时变(LTV)系统,并应用 LTV 系统的线性可控性标准。在线性化过程中,利用方便的坐标分割,得到了一个涉及接触点笛卡尔坐标和球体偏航角的可控线性系统。与关于同一问题的现有结果相比,在圆轨迹的任何半径上都能实现对所需轨迹的闭环稳定性。
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引用次数: 0
Analytical determination of the optimal effective regular workspace of a 6-6 Stewart platform manipulator for a specified orientation workspace 分析确定指定方向工作空间的 6-6 斯图尔特平台机械手的最佳有效规则工作空间
IF 4.5 1区 工程技术 Q1 ENGINEERING, MECHANICAL Pub Date : 2024-09-20 DOI: 10.1016/j.mechmachtheory.2024.105791
Bibekananda Patra , Anirban Nag , Sandipan Bandyopadhyay
This article presents an analytical method to identify the largest effective regular workspaces (ERWs) of a class of 6-6 Stewart platform manipulators for a given orientation workspace. The ERWs are modelled as spheres. The orientation workspace is specified in terms of ranges of Euler angles, as is the standard practice in the parallel robot industry. The radius of the said sphere is maximised through an optimisation problem, which is solved analytically. Consequently, the results obtained are exact in nature. The analytical formulation of the problem and its exact solutions constitute the novel theoretical contributions of this article. Moreover, since the results hold good over a given subset of SO(3), the proposed method obviates the need for numerical scanning of the orientation workspaces in design-related computations, thus improving the accuracy, robustness, as well as computational efficiency. Finally, the significance of the neutral height in harnessing the desired extents of position and orientation workspaces has been established through parametric studies. The formulations are illustrated via applications to Stewart platform manipulators of three distinct platform dimensions.
本文提出了一种分析方法,用于确定一类 6-6 斯图尔特平台机械手在给定方向工作空间内的最大有效规则工作空间(ERW)。ERW 以球体为模型。按照并联机器人行业的标准做法,以欧拉角的范围来指定方向工作空间。所述球体的半径通过一个优化问题达到最大化,该问题通过解析法求解。因此,得到的结果是精确的。问题的分析表述及其精确解构成了本文新颖的理论贡献。此外,由于结果适用于 SO(3) 的给定子集,因此在与设计相关的计算中,所提出的方法无需对方位工作区进行数值扫描,从而提高了准确性、稳健性和计算效率。最后,通过参数研究确定了中性高度在利用位置和方向工作空间的理想范围方面的重要性。这些公式应用于三种不同平台尺寸的斯图尔特平台机械手。
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引用次数: 0
A new iterative identification algorithm for estimating the LuGre friction model parameters 用于估计鲁格莱摩擦模型参数的新迭代识别算法
IF 4.5 1区 工程技术 Q1 ENGINEERING, MECHANICAL Pub Date : 2024-09-19 DOI: 10.1016/j.mechmachtheory.2024.105797
Saeed Mahmoudkhani , Johnathan Gorenstein , Keivan Ahmadi
The parameters of dynamic friction models like the LuGre model are commonly identified by computationally intensive nonlinear optimization methods. In this paper, an alternative least-square-based iterative algorithm is proposed to simultaneously identify the LuGre model parameters and the inertial properties from a limited set of measurements. The LuGre model, expressed in two forms allowed independent identification of the static and dynamic parameters. Moreover, since the method uses response-input time–history instead of numerous constant velocity experiments (CVEs), both the inertial and friction parameters can be identified in much fewer experiments (theoretically one). A variant of the Sparse Identification of Nonlinear Dynamics method called SR3 is embedded in the algorithm to capture the nonlinear viscous friction and Stribeck effects in the friction model. Application of the algorithm to an industrial robot joint shows that the convergence of the algorithm is fast and the identified model is accurate in predicting the joint’s dynamics in a wide range of velocities. The friction-velocity curves resulting from the identified model are compared to those obtained by traditional CVEs to confirm the accuracy of the identified model.
像 LuGre 模型这样的动态摩擦模型的参数通常是通过计算密集型非线性优化方法确定的。本文提出了另一种基于最小二乘法的迭代算法,可同时从有限的测量集合中识别 LuGre 模型参数和惯性特性。以两种形式表示的 LuGre 模型允许独立识别静态和动态参数。此外,由于该方法使用的是响应-输入时间-历史,而不是大量的恒速实验(CVE),因此惯性参数和摩擦参数都可以通过更少的实验(理论上只需一次)来识别。算法中嵌入了一种名为 SR3 的非线性动力学稀疏识别方法的变体,以捕捉摩擦模型中的非线性粘性摩擦和 Stribeck 效应。将该算法应用于工业机器人关节的结果表明,算法收敛速度很快,识别出的模型能准确预测关节在各种速度下的动态。将识别模式得出的摩擦-速度曲线与传统 CVE 得出的摩擦-速度曲线进行比较,以确认识别模式的准确性。
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引用次数: 0
Transient analysis of non-uniform tilting-pad journal bearing for wind turbine main shaft under dynamical loading 风力涡轮机主轴非均匀斜垫式轴颈轴承在动态载荷下的瞬态分析
IF 4.5 1区 工程技术 Q1 ENGINEERING, MECHANICAL Pub Date : 2024-09-19 DOI: 10.1016/j.mechmachtheory.2024.105792
Chaosheng Song, Ronghua Zhang, Ye Zhou, Jianjun Tan, Caichao Zhu
The non-uniform distributed tilting-pad journal bearing (NDTPJB), designed for large megawatt wind turbine main shafts, has not been assessed for transient stability under typical random wind conditions. Particularly, the dynamic interaction between low-speed, heavy-load operations with varying magnitude and direction, and the bearing's asymmetric structure, has not been fully explored. A new transient tribo-dynamic model is developed to analyze 6MW wind turbine's NDTPJB transient friction behavior, accounting for variable wind loads, pad distribution asymmetry, mixed lubrication (ML), and elastic pivot effects. Key parameters affecting tribo-dynamic friction performance—pad wrap angle, pad distribution count, and pivot stiffness—were comprehensively investigated. Findings show that dynamic loading cause asymmetrical behaviors in main and secondary pads, with performance significantly affected by the number of bottom distributed pads and improved stability with setting the number of above distributed pads to three. The stiffness of pivots significantly and complexly affects bearing dynamics, optimization of stiffness should be conducted after pad distribution determination. These discoveries guide further research and enhancements of NDTPJB in large rotating machinery under low-speed and heavy-load conditions.
为大型兆瓦级风力涡轮机主轴设计的非均匀分布斜垫式轴颈轴承(NDTPJB)尚未对典型随机风力条件下的瞬态稳定性进行评估。特别是,低速、重载、不同幅度和方向的运行与轴承的非对称结构之间的动态相互作用尚未得到充分探讨。本文建立了一个新的瞬态摩擦动力学模型,用于分析 6MW 风力涡轮机 NDTPJB 的瞬态摩擦行为,其中考虑到了可变风载荷、衬垫分布不对称、混合润滑 (ML) 和弹性枢轴效应。全面研究了影响三动态摩擦性能的关键参数--衬垫包角、衬垫分布数量和枢轴刚度。研究结果表明,动态载荷会导致主垫和副垫的非对称行为,底部分布垫的数量对性能有显著影响,而将上面分布垫的数量设为三个时,稳定性会得到改善。枢轴的刚度会对轴承的动力学产生重要而复杂的影响,因此应在确定衬垫分布后对刚度进行优化。这些发现为进一步研究和改进低速重载条件下大型旋转机械中的 NDTPJB 提供了指导。
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引用次数: 0
Design and optimization of a novel multi-layer conical Kresling origami mechanism (MCKOM) for linear actuation 设计和优化用于线性驱动的新型多层锥形克瑞斯林折纸机构 (MCKOM)
IF 4.5 1区 工程技术 Q1 ENGINEERING, MECHANICAL Pub Date : 2024-09-19 DOI: 10.1016/j.mechmachtheory.2024.105796
Cuiying Jiang , Decheng Wang , Peng Cheng , Lifang Qiu , Chongxiang Li

To address the inevitable twisting issue of modular configurations with different morphological parameters, this paper takes conical Kresling units as the research object, and a novel multi-layer conical Kresling origami mechanism (MCKOM) for linear actuation is designed. The main body consists of m serially connected flat-foldable bistable units with the same chirality but different morphological parameters. The design objective of achieving pure linear actuation under torque drive is realized by introducing external systems. Kinematic coupling and inner product models are established and multi-objective optimization algorithms are employed to optimize the structure. Based on optimized values, simulation and experimental validation of the motion behavior are conducted using ABAQUS and prototypes. The results show that the total twist angle decreased by 10.076° and the inner product increased by 60,291.98 mm3. Furthermore, the crease vertices cutting eliminates the influence of internal pressure on the guiding plate's outward deviation and increases the folding ratio from 41.49 % to 48.88 % under experimental conditions. The proposed novel pure linear actuation mechanism can be applied in actuation scenarios that require the conversion of rotational motion into linear displacement.

为了解决形态参数不同的模块结构不可避免的扭曲问题,本文以锥形克瑞斯林单元为研究对象,设计了一种新型的线性致动多层锥形克瑞斯林折纸机构(MCKOM)。其主体由多个串联的平面可折叠双稳态单元组成,这些单元具有相同的手性,但形态参数不同。通过引入外部系统,实现了在扭矩驱动下实现纯线性致动的设计目标。建立了运动耦合和内积模型,并采用多目标优化算法对结构进行优化。在优化值的基础上,使用 ABAQUS 和原型对运动行为进行了仿真和实验验证。结果表明,总扭转角减少了 10.076°,内积增加了 60,291.98 mm3。此外,折痕顶点切割消除了内部压力对导向板向外偏差的影响,并将实验条件下的折叠率从 41.49 % 提高到 48.88 %。所提出的新型纯线性致动机构可应用于需要将旋转运动转换为线性位移的致动方案。
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引用次数: 0
A novel method of modelling contact dynamics for spur gear transmission 正齿轮传动接触动力学建模新方法
IF 4.5 1区 工程技术 Q1 ENGINEERING, MECHANICAL Pub Date : 2024-09-18 DOI: 10.1016/j.mechmachtheory.2024.105793
Lixin Xu , Yuankui Luo , Ruhao Hu

Taking a pair of spur gears as the research object, a contact dynamic model of the spur gear system was established based on the theories of contact mechanics and multi-body dynamics. The characteristics of the model are such that it can describe the dynamic contact behavior of a gear pairs, the meshing action of gear pairs no longer depends on the stiffness model of single and double teeth undergoing alternating meshing, and the model can be visualized in real time. In the process of modelling, firstly, the mathematical model of spur gear is established. The spur gear dynamic model is then built. Finally, the vibration responses obtained by the three methods (the propose method, the lumped parameter method and the experimental method) are compared. It is found that the proposed method is more consistent with the experimental method than the traditional lumped parameter method, which verifies the validity of the contact dynamic model of spur gear transmission. The proposed model and research results lay the foundation for research fields such as performance analysis, design optimization and fault diagnosis of gear systems.

以一对正齿轮为研究对象,基于接触力学和多体动力学理论,建立了正齿轮系统的接触动力学模型。该模型的特点是可以描述齿轮对的动态接触行为,齿轮对的啮合动作不再依赖于交替啮合的单齿和双齿的刚度模型,并且模型可以实时可视化。在建模过程中,首先要建立正齿轮的数学模型。然后建立正齿轮动态模型。最后,比较了三种方法(建议方法、叠加参数方法和实验方法)得到的振动响应。结果发现,与传统的叠加参数法相比,提议法与实验法的一致性更高,这验证了直齿轮传动接触动态模型的有效性。提出的模型和研究成果为齿轮系统的性能分析、优化设计和故障诊断等研究领域奠定了基础。
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引用次数: 0
Numerical study on the effectiveness of the optimization of the load distribution in ball screw actuators 滚珠丝杠推杆载荷分布优化效果的数值研究
IF 4.5 1区 工程技术 Q1 ENGINEERING, MECHANICAL Pub Date : 2024-09-16 DOI: 10.1016/j.mechmachtheory.2024.105781
L. Sangalli, A. Oyanguren, M. Izquierdo, J. Larrañaga, I. Ulacia

Load distribution in ball screws is characterized by non-uniformity, leading to imbalances in the contact load of the balls along the nut. This non-uniformity negatively impacts the stiffness, accuracy and service life of the ball screw. This work proposes a solution to reduce the ball screw load distribution non-uniformity through an optimization model and two implementation methods: the variable pitch method and the ball offset method. Both methods involve applying an initial preload in certain areas of the nut to compensate for load imbalance. A case study tests both methods and evaluates the implications of implementing the optimization model.

Results confirm the model’s ability to reduce the load distribution non-uniformity, with a ratio improvements up to 61%. Additionally, this optimization enhances stiffness by up to 78% and extends service life by up to 17 times. The study also identifies the model’s limits and possible adverse effects, concluding that the specific case conditions must be considered in the optimization process.

滚珠丝杠的载荷分布不均匀,导致滚珠沿螺母的接触载荷不平衡。这种不均匀性会对滚珠丝杠的刚度、精度和使用寿命产生负面影响。本研究提出了一种解决方案,通过优化模型和两种实施方法来减少滚珠丝杠载荷分布的不均匀性:变螺距方法和滚珠偏移方法。这两种方法都涉及在螺母的某些区域施加初始预紧力,以补偿载荷不平衡。一项案例研究对这两种方法进行了测试,并对实施优化模型的影响进行了评估。结果证实,该模型能够减少载荷分布的不均匀性,比率改善高达 61%。此外,这种优化还能将刚度提高 78%,将使用寿命延长 17 倍。研究还确定了模型的局限性和可能产生的不利影响,并得出结论:在优化过程中必须考虑具体情况。
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引用次数: 0
Optimization design and key-term separation identification of parallel six-dimensional pose sensor with high sensitivity and high precision 高灵敏度和高精度并行六维姿态传感器的优化设计和关键项分离识别
IF 4.5 1区 工程技术 Q1 ENGINEERING, MECHANICAL Pub Date : 2024-09-13 DOI: 10.1016/j.mechmachtheory.2024.105716
Jianfeng Lin , Chenkun Qi , Yan Hu , Feng Gao

The integrated bearing-positioning parallel manipulator is an important mean for ground testing of space optical telescope before being launched into space. To ensure positioning accuracy, the manipulator requires a pose sensor for the end-effector measurement with six degrees of freedom (DOF), real-time, high-precision, and operation in a vacuum environment. However, it is challenging for the current pose sensor to simultaneously meet all these requirements. In this paper, a novel concept of six-dimensional pose sensor based on parallel mechanism is proposed. A new mechanism design approach is presented to achieve the large measurement range, real-time measurement performance, and high accuracy measurement based on performance atlas. First, the GF sets synthesis is developed to optimize the configuration of pose sensor. Next, two new design indicators are proposed to evaluate the real-time and high accuracy performance. Mechanism parameters are optimized by combining with mechanism singularity analysis. To guarantee high measurement accuracy, a key-term separation identification method with double neural networks is presented. Experiments on 6-UPS pose sensor demonstrate the effectiveness of the proposed mechanism design and key-term identification approach.

集成轴承定位平行机械手是太空光学望远镜发射到太空前进行地面测试的重要手段。为确保定位精度,该机械手需要一个具有六个自由度(DOF)、实时、高精度且可在真空环境中工作的姿态传感器来测量末端执行器。然而,目前的姿态传感器要同时满足所有这些要求具有挑战性。本文提出了一种基于并联机构的六维姿态传感器的新概念。本文提出了一种新的机构设计方法,以实现大测量范围、实时测量性能和基于性能图集的高精度测量。首先,开发了 GF 组合成来优化姿态传感器的配置。其次,提出了两个新的设计指标来评估实时性和高精度性能。结合机构奇异性分析优化机构参数。为保证高测量精度,提出了一种采用双神经网络的关键项分离识别方法。在 6-UPS 姿态传感器上进行的实验证明了所提出的机构设计和关键项识别方法的有效性。
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引用次数: 0
Fast mobility analysis for generative design applications through a real vector space representation of mobilities 通过移动性的真实向量空间表示,为生成式设计应用提供快速移动性分析
IF 4.5 1区 工程技术 Q1 ENGINEERING, MECHANICAL Pub Date : 2024-09-11 DOI: 10.1016/j.mechmachtheory.2024.105790
Guilain Lang , Julien Rouvinet

During the early stages of design, mechanisms are commonly modeled as perfect joints assembled with infinitely rigid bodies. This representation enables the prediction of the system’s mobilities through a mobility analysis. However, traditional mobility analysis tools can be computationally expensive or lack critical information, such as the type or direction of mobilities. It hinders the generation of topology and configuration through generative design schemes.

In this paper, we propose an alternative approach to mobility analysis based on a real vector space representation of mobilities. Our method provides relevant information for early design steps while being computationally effective through a novel formulation of series and parallel assembly topological operations. A benchmark on four selected use cases highlights an acceleration of 3 to 4 orders of magnitude compared to traditional approaches. Additionally, design rules on the joints’ positions can be automatically generated with our approach. It enables the automation of the complete design process, including topology and configuration. As such, we provide guidelines to develop a generative design scheme dedicated to the synthesis of guiding mechanisms.

在设计的早期阶段,机械装置通常被建模为由无限刚性体组装而成的完美关节。通过这种表示方法,可以通过流动性分析预测系统的流动性。然而,传统的流动性分析工具计算成本高昂,或缺乏关键信息,如流动性的类型或方向。在本文中,我们提出了另一种基于真实移动性向量空间表示的移动性分析方法。我们的方法为早期设计步骤提供了相关信息,同时通过新颖的串联和并联装配拓扑操作,提高了计算效率。四个选定使用案例的基准测试表明,与传统方法相比,我们的计算速度提高了 3 到 4 个数量级。此外,我们的方法还能自动生成关节位置的设计规则。这使得包括拓扑和配置在内的整个设计过程实现了自动化。因此,我们为开发专门用于合成导向机构的生成式设计方案提供了指导。
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引用次数: 0
Computerized generation, deviation correction and rapid tooth contact analysis of helical face gear 螺旋齿面齿轮的计算机生成、偏差修正和快速齿面接触分析
IF 4.5 1区 工程技术 Q1 ENGINEERING, MECHANICAL Pub Date : 2024-09-10 DOI: 10.1016/j.mechmachtheory.2024.105789
Yaolong Yan , Hui Guo , Jun Gu , Ning Zhao , Li Liu

This paper delves into the generation of helical face gears using a grinding worm. It investigates the computerized generation process and explores the inherent geometric constraints associated with the application of a grinding worm for helical face gears. An approximate grinding method, tailored for helical face gears featuring large helix angles, is proposed, with an evaluation of the resulting theoretical deviations. Furthermore, a novel rapid computational approach for determining the bearing contact of helical face gear pairs is introduced and validated through Finite Element Analysis (FEA). The subsequent analysis comprehensively examines the effects of the machine tool positioning errors on tooth flank deviations, bearing contact, and transmission errors. A sensitivity matrix is developed to elucidate the relationship between machine tool positioning errors and the tooth flank deviations, leading to the proposition of a correction method for theoretical generating deviations. Finally, the paper introduces a tooth flank modification method for helical face gears and the meshing performance is highly improved.

本文深入探讨了使用磨削蜗杆生成斜面齿轮的问题。它研究了计算机生成过程,并探讨了与螺旋面齿轮磨削蜗杆应用相关的固有几何限制。针对螺旋角较大的斜面齿轮提出了一种近似磨削方法,并对由此产生的理论偏差进行了评估。此外,还介绍了一种新的快速计算方法,用于确定斜面齿轮对的轴承接触情况,并通过有限元分析(FEA)进行了验证。随后的分析全面考察了机床定位误差对齿面偏差、轴承接触和传动误差的影响。通过灵敏度矩阵阐明了机床定位误差与齿面偏差之间的关系,从而提出了理论偏差的修正方法。最后,论文介绍了斜面齿轮的齿面修正方法,啮合性能得到极大改善。
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引用次数: 0
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Mechanism and Machine Theory
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