Stiffness Modeling Method Research Articles

Equivalent Stiffness Modeling Method of a Battery System for Evaluating Vehicle Rear-End Collision Performance

Equivalent Stiffness Modeling Method of a Battery System for Evaluating Vehicle Rear-End Collision Performance

Research on High Precision Stiffness Modeling Method of Redundant Over-Constrained Parallel Mechanism.

Traditional stiffness modeling methods do not consider all factors comprehensively, and the modeling methods are not unified, lacking a global stiffness model. Based on screw theory, strain energy and the virtual work principle, a static stiffness modeling method for redundant over-constrained parallel mechanisms (PMs) with clearance was proposed that considers the driving stiffness, branch deformation, redundant driving, joint clearance and joint contact deformation. First, the driving stiffness and branch deformation were considered. According to the strain energy and Castiliano's second theorem, the global stiffness matrix of the ideal joint mechanism was obtained. The offset of the branch was analyzed according to the restraint force of each branch. The mathematical relationship between the joint clearance and joint contact deformation and the end deformation was established. Based on the probability statistical model, the uncertainty of the offset value of the clearance joint and the contact area of the joint caused by the coupling of the branch constraint force was solved. Finally, taking a 2UPR-RR-2RPU redundant PM as an example, a stiffness simulation of the mechanism was carried out using the finite element method. The research results show that the high-precision stiffness modeling method proposed in this paper is correct, and provides an effective method for evaluating the stiffness performance of the PM.

Stiffness characteristics analysis of a Biglide industrial parallel robot considering the gravity of mobile platform and links

For the machining process of industrial parallel robots, the gravity generated by the weight of mobile platform and links will lead to the deviation of the expected machining trajectory of the tool head. In order to evaluate this deviation and then circumvent it, it is necessary to perform the robotic stiffness model. However, the influence of gravity is seldom considered in the previous stiffness analysis. This paper presents an effective stiffness modeling method for industrial parallel robots considering the link/joint compliance, the mobile platform/link gravity, and the mass center position of each link. First, the external gravity corresponding to each component is determined by the static model under the influence of gravity and mass center position. Then, the corresponding Jacobian matrix of each component is obtained by the kinematic model. Subsequently, the compliance of each component is obtained by cantilever beam theory and FEA-based virtual experiments. In turn, the stiffness model of the whole parallel robot is determined and the Cartesian stiffness matrix of the parallel robot is calculated at several positions. Moreover, the principal stiffness distribution of the tool head in each direction over the main workspace is predicted. Finally, the validity of the stiffness model with gravity is experimentally proved by the comparison of the calculated stiffness and measured stiffness in identical conditions.

Stiffness Modeling and Dynamics Co-Modeling for Space Cable-Driven Linkage Continuous Manipulators

The space cable-driven continuous manipulator (SCCM) has a slender structure, ultra-high degrees of freedom, and a low mass, which make it suitable for equipment inspection and maintenance operations in an unstructured and limited space environment. In this paper, the SCCM including the cable network and plenty of joint links was deeply modeled. Firstly, the mapping relationship between the cable-driving space, joint space, and task space of the SCCM was studied, and the complete kinematic relationship of the SCCM was established. Secondly, the stiffness components of the SCCM are discussed, and the stiffness modeling method of each part is given. Finally, the Cartesian space equivalent stiffness model of the end was established. Then, a dynamic co-modeling method of Matlab + Adams is proposed, which greatly improved the modeling efficiency while ensuring the modeling accuracy. Finally, based on the stiffness model, the end stiffness characteristics of a specific configuration were analyzed, and the influence of the cable tension on the stiffness and frequency of the manipulator was analyzed. Based on the dynamic co-modeling, the task trajectory dynamics’ simulation analysis and space slit crossing experiment were carried out, which verified that the designed SCCM can meet the needs of slit crossing.

FESM-based approach for stiffness modeling, identification and updating of collaborative robots

PurposeThe purpose of this paper is to introduce a method for stiffness modeling, identification and updating of collaborative robots (cobots). This method operates in real-time and with high precision and can eliminate the modeling error between the actual stiffness model and the theoretical stiffness model.Design/methodology/approachTo simultaneously ensure the computational efficiency and modeling accuracy of the stiffness model, this method introduces the finite element substructure method (FESM) into the virtual joint method (VJM). The stiffness model of the cobots is built by integrating several 6-degree of freedom virtual joints that represent the elastic deformation of the cobot modules, and the stiffness matrices of these modules can be identified and obtained by the FESM. A model-updating method is proposed to identify stiffness influence coefficients, which can eliminate the modeling error between the actual prototype model and the theoretical finite element model.FindingsThe average relative error and the cycle time of the proposed method are approximately 6.14% and 1.31 ms, respectively. Compared with other stiffness modeling methods, this method not only has high modeling accuracy in high dexterity poses but also in low dexterity poses.Originality/valueA hybrid stiffness modeling method is introduced to integrate the modeling accuracy of the FESM into the VJM. Stiffness influence coefficients are proposed to eliminate the modeling error between the theoretical and actual stiffness models.

A virtual joint method of analytical form for parallel manipulators

Oriented towards the stiffness optimization of parallel manipulators, a stiffness modeling method based on subspace analysis was proposed. The paper revealed the “shielding effect” of passive joints, i.e. shielding the partial local stiffness of a mechanism on Cartesian space, and accordingly brought forward the concept of Effective Stiffness Tensor (EST), which was then obtained by introducing the orthogonal projector. The method allows a stiffness model of analytical form as well as high computation efficiency, which makes it suitable for applications in the stiffness optimization of parallel manipulators. Proposed method had been applied to the parallel alignment mechanism in China’s large space telescope and verified by dynamic experiments.

Stiffness Evaluation of an Adsorption Robot for Large-Scale Structural Parts Processing

Abstract Efficient and economical processing of large-scale structural parts is in increasing need and is also a challenging issue. In this paper, an adsorption machining robot for processing of large-scale structural parts is presented. It has potential advantages in flexible, efficient, and economical processing of large-scale structural parts because of the adsorption ability. Stiffness is one of the most important performance for machining robots. In order to investigate the stiffness of the robot in the workspace, the kinematics of the adsorption manipulator, the five-axis machining manipulator, and the adsorption machining robot is derived step by step. Then with the help of finite element analysis (FEA), a stiffness modeling method considering the compliance of the base is proposed. A stiffness isotropy index is put forward to evaluate the robot’s overall stiffness performance by taking all possible working conditions into consideration. Based on the index, stiffness evaluation in the reachable workspace is carried out and an optimized workspace is identified considering the overall stiffness magnitude, stiffness isotropy, and workspace volume, which will be used in the machining process. The stiffness modeling method and stiffness isotropy index proposed in the paper are universal and can be applied to other parallel robots.

Accurate Stiffness Modeling Method for Flexure Hinges with a Complex Contour Curve

Background: Flexure hinges have certain advantages, such as a simple structure, smooth movement, no need for lubrication, frictionless movement and high precision. The flexure hinge’s transfer of force and displacement relies on its deformation. Thus, stiffness is an important index for evaluating hinge flexibility. Objective: Stiffness analysis of the flexure hinges is necessary to be performed. This paper aims to present a unified stiffness model solving method of the flexible hinges with complex contour curves. Methods: The transfer matrix of a flexure hinge was derived based on balance equations and the virtual work principle with consideration of axial, shear, and bending deformations. The element stiffness matrix of a flexure hinge was obtained from the relationship between the transfer and stiffness matrices. In this manner, the unified formula of element stiffness of a general flexure hinge was established. By using this method, rigidity models of parabolic, corner-filled, and the right circular flexure hinge have been deduced. By taking the right circular flexure hinge as an example, the results obtained using this method were compared with those of methods provided in other studies and the finite element results. Results and Conclusion: The comparison results revealed that the proposed method increases the rigidity accuracy because the effect of the uneven distribution coefficient of shear stress was considered. The stiffness error was within 7%, which demonstrates the validity of this method. In contrast to the other methods, the proposed method can be applied by determining the first integral element stiffness of a common flexible hinge. Moreover, the proposed method provides better commonality, flexibility, and ease of programming. In particular, it is much easier for the flexure hinges with a complex contour curve. Transitivity can be used to calculate the rigidity after the flexure hinge has been divided into subunits, thus making it unnecessary to convert to the global coordinate system.

Computational study of pitting defect influence on mesh stiffness for straight beveloid gear

As the representation for the effects of contact and bending elasticity gear tooth, variational mesh stiffness is an important source of excitation for gear vibration. Aiming to get the numerical method of calculating mesh stiffness of the irregular taperred tooth profile, an efficient slice-based mesh stiffness modeling method is introduced for straight beveloid gear pair with and without the pitting corrosion defect. The deformation for tooth fillet and transient curve part are considered to improve the calculation accuracy. The FEM model is used to verify the results obtained by the proposed model and showed that the peak error is only 3.2%. Then the effects of different sizes and locations of pitting defects are analyzed. Results show that the size of pitting defect is a significant influencing factor for mesh stiffness. The mesh stiffness is reduced by 28.3% as the radius of pitting defect increases from 1 mm to 5 mm. For the impacts of pitting defect locations, the mesh stiffness has a noticeable fluctuation when the pitting defect is close to tooth root. While the pitting defect is shfited from root to a certain height, the mean mesh stiffness is decreased by 2.2% and the fluctuating value is decreased by 24.6%.The distance between pitting corrosion center and transverse plane has a little influence on the mesh stiffness.

Stiffness modeling of overconstrained parallel mechanisms under considering gravity and external payloads

Difficulty and complexity of stiffness modeling of parallel mechanisms will be greatly increased under considering gravity of limbs. This paper presents a general method for stiffness modeling of overconstrained parallel mechanisms under considering gravity of all moving components and external payloads. First, the expression of the end joint reaction of a limb is derived based on screw theory and special equilibrium equations. Second, an approach to stiffness modeling of a limb under its end joint reaction and own gravity is presented based on the Castigliano's second theorem associated with strain energy. Third, stiffness modeling of the whole mechanism is performed based on the static equilibrium equation of the moving platform, the base-point method and the established limb stiffness models. Finally, two typical numerical examples show that computational results obtained from the proposed method are very closed to those obtained from finite element analysis (FEA) models, illustrating the effectiveness of the proposed method.

Static analysis on a 2(3PUS+S) parallel manipulator with two moving platforms

The stiffness of a novel 2(3PUS+S) parallel manipulator with two moving platforms was investigated in this study. In the stiffness evaluation, the two moving platforms of the manipulator were driven through three linear modules and the load force on the drive joint was large. The corresponding parts of the two moving platforms were divided into independent subsystems and were integrated through a stiffness modeling method of a serial system to establish the overall stiffness model of the 2(3PUS+S) parallel manipulator. During modeling, elastic deformations on the joint lever and lead screw were involved, the joint lever was simplified as a supported beam, and the axial and torsional stiffness of the lead screw were considered. Numerical analysis on the established stiffness model was validated, and virtual experiments were conducted. Results indicate that the stiffness performance of the 2(3PUS+S) parallel manipulator changes with the variation of structural parameters and moving platform positions. To ensure the minimum stiffness under the required trajectory, the length of the joint lever and the ratio of the moving platform radius to the base platform should be appropriately reduced. Comparisons between the results from the numerical analysis and virtual experiments verified the accuracy of the established stiffness model.

A method for stiffness modeling of 3R2T overconstrained parallel robotic mechanisms based on screw theory and strain energy

Stiffness (or compliance) performances of three-rotation and two-translation (3R2T) overconstrained parallel mechanisms have an important influence on their applications in bio-inspired robots with precision operations. However, it is difficult to build stiffness models of the class of mechanisms due to fairly complicated structures, and an effective and efficient modeling method has not been reported. This paper presents an approach to stiffness modeling of 3R2T overconstrained parallel robotic mechanisms. First, expressions of applied wrenches exerted on limbs and joints of a mechanism under an external load are solved based on screw theory. Then, the stiffness matrix of a limb is derived by applying Castigliano’s second theorem to strain energy of the limb, which is solved by introducing a strategy of structural decomposition. Third, the stiffness model of a mechanism is built based on stiffness matrices of all limbs and the principle of virtual work on the moving platform. Finally, the effectiveness of the proposed method is verified based on the fact that the computational compliance matrices are very close to those from finite element analysis (FEA) models. The proposed method can be used to build conveniently stiffness models with high accuracy for 3R2T overconstrained parallel mechanisms in precision positioning applications.

Stiffness analysis of overconstrained parallel manipulators

The paper presents a new stiffness modeling method for overconstrained parallel manipulators with flexible links and compliant actuating joints. It is based on a multidimensional lumped-parameter model that replaces the link flexibility by localized 6-dof virtual springs that describe both translational/rotational compliance and the coupling between them. In contrast to other works, the method involves a FEA-based link stiffness evaluation and employs a new solution strategy of the kinetostatic equations for the unloaded manipulator configuration, which allows computing the stiffness matrix for the overconstrained architectures, including singular manipulator postures. The advantages of the developed technique are confirmed by application examples, which deal with comparative stiffness analysis of two translational parallel manipulators of 3-PUU and 3-PRPaR architectures. Accuracy of the proposed approach was evaluated for a case study, which focuses on stiffness analysis of Orthoglide parallel manipulator.

Analytical Method for Stiffness Modeling of the Tricept Robot

Analytical Method for Stiffness Modeling of the Tricept Robot