Stiffness Method Of Analysis Research Articles

Research on time-varying mesh stiffness analysis method of gears with local defective faults

Research on time-varying mesh stiffness analysis method of gears with local defective faults

Stiffness increase and homogenization by coupled robots

This article presents the explanation of higher than expected increase of stiffness of coupled robots in some geometric configurations against its expected simple addition. This phenomenon was named the vault principle for robots. In order to achieve that and to explore fully the consequences it was necessary to develop a new method for robot stiffness analysis. Single serial robot is compared with two serial robots mutually connected. Connected (coupled) robots are analyzed in five various topological configurations. The end effector stiffness field is evaluated at particular points of intersections of workspaces of five topological configurations in order to preserve the objectivity of the comparison. The new method for robot stiffness analysis is based on the evaluation of minimum/maximum values of principal axes of stiffness distribution determined by the singular value decomposition. The manimum/maximum values across the workspace are processed by average/median and used for computing homogeneity factor. It is a new integral criterion for robot topology configuration judgment. The direct implications of these findings are relevant to high-precision milling applications in cooperative robotic setups.

Time varying torsional stiffness analysis of RV reducer

The rotary vector reducer (RV reducer) is a key reduction mechanism for industrial robots, and its torsional stiffness directly determines positioning accuracy and dynamic characteristics. Unlike traditional time-varying torsional stiffness analysis methods considering limited factors and statics solution method, a time-varying torsional stiffness analysis method considering output torque variability and dynamic nonlinearity is proposed to assess the time-varying torsional stiffness of the reducer. Firstly, the rigid-flexible coupling multi-body dynamic model was built employing software ADAMS, with crank shaft and cycloidal gears being treated as flexible bodies. Its correctness was verified under standard condition through grey correlation theory and the torsional stiffness under different conditions was obtained, respectively. Secondly, a contact finite element model of the reducer was established, taking contact relationships between different shaft-gear-bearings into account. As a comparison, a rotating-join finite element model was also constructed. And their torsional stiffness under experimental condition was calculated. Finally, the torsional stiffness test was conducted to verify the accuracy of the three models under this condition. The results show that the time-varying torsional stiffness obtained by the proposed method is only 8.83% different from the test results and exhibiting a certain periodic pattern under standard conditions.

Stability Conditions and Stiffness Variability of General Tensegrity Systems with Kinematic Joints

Abstract Tensegrity systems represent promising candidate mechanisms with in-situ stiffness variability through changing the cables' prestress levels. However, prestress-based stiffness behaviors of tensegrity systems with arbitrary kinematic joints have not been analyzed systematically. This paper adopts the natural absolute coordinates for static modeling of tensegrity systems consisting of rigid members and tension elements. Then, a generic stiffness analysis method is developed to formulate the reduced-basis tangent stiffness matrix, which is found to include three parts: positive semi-definite material and geometric stiffness matrices, and an indefinite constraint stiffness matrix. Based on these findings, a systematic stability-checking procedure is derived to determine prestress and super stability, which are qualitative indicators of the softening and stiffening effects in different tensegrity systems. Then, we proceed to quantify the range of prestress-based stiffness variability by formulating semidefinite programming problems that numerically pinpoint the maximum and zero stiffness points. Furthermore, this paper reveals the composable nature of multiple self-stress states, enabling the composability of stiffness properties in mechanism designs. Several numerical examples verify the efficacy and versatility of the proposed method and demonstrate interesting stiffness behaviors of tensegrity systems with kinematic joints.

Nonlinear modeling and vibration response analysis of rod fastening rotor-bearing system with curvic coupling

Rod fastening combined rotor system (RFCR) are particularly popular in gas turbine rotor systems. The bolted connection introduces a discontinuity in this RFCR, which has a substantial influence on system performance.Traditional models of RFCR tend to neglect the influence of the connection structure, especially failing to fully consider the contribution of the curvic coupling to the rotor dynamics. To address this problem, this study proposes a new nonlinear analytical model of the rotor system, which focuses on the impact of the curvic coupling. This study provides a detailed analysis of the structural parameters and load forces of the curvic coupling. Based on this analysis, a mechanical model is created to assess how bolt preload and torque impact the stiffness of the curvic connection. The stiffness matrix of the curvic coupling is derived by the gear stiffness analysis method, and the accuracy of the model is confirmed using the finite element method. Furthermore, the model also considers the viscous and sliding state between the curvic coupling, which effectively describes the damping effect of the curvic coupling. On this basis, the motion control equations for the RFCR are formed, and a dynamic model considering the curvic connection in the RFCR system is introduced. The results show that the curvic coupling results in a decrease in stiffness and the occurrence of nonlinear damping phenomena in the RFCR.The RFCR exhibits a significant stiffness loss compared to the continuous rotor system, resulting in a decrease in the critical rotor speed. The nonlinear damping is mainly excited at high friction coefficient conditions and may lead to a self-excited vibration component in the rotor response at supercritical speeds. The negative impact of structural discontinuities on rotor dynamic performance can be reduced by increasing the bolt preload, decreasing the friction coefficient, and adjusting the amount of imbalance. This study offers a theoretical foundation for predicting curvic coupling-induced instability and serves as a reference for enhancing rotor system stability.

Influence of Prestress on Vibration Frequency of Beam String Structures Based on Exact Matrix Stiffness Method

Beam string structures (BSS) are frequently employed in large-span spatial structures due to their high load-carrying efficiency and elegant appearance. Owing to the neglect of the influence of prestress, the natural frequency of the BSS is often overestimated which could be crucial to the dynamic behavior of BSS. This paper presents an exact matrix stiffness analysis method (MSM) for investigating the relationship between prestress and the natural frequency of the planar BSS. A novel dynamic stiffness matrix of beam–columns considering the natural frequency and axial force is used to develop the MSM. The dynamic analysis of the structural vibration stability of BSS is performed by using the global structural stiffness matrix which is assembled from the element stiffness matrices in the global coordinate system. The proposed MSM with the exact dynamic element stiffness matrix for the dynamic analysis of the BSS is verified by comparing with previous results based on the finite element method. The illustrative examples demonstrate that the prestress in the cable has a negative effect on the natural frequency of the BSS and should be considered in the dynamic analysis. As the axial force increases from zero to the buckling load [Formula: see text], the natural frequency of the BSS decreases from the maximum vibration frequency to zero. The influence of prestress on the vibration frequencies of BSS is particularly significant when the prestress to balance the loads is large, especially in the case of large dead and live loads (e.g. floor slabs).

Numerical research on the connection stiffness of hinge-locked structures for a folding wing

Hinge-locked structures of the folding wing for high-speed vehicle contain gaps, contact and friction effects, and these factors increase the complexity of solving the local connection stiffness. In this paper, a finite element model and displacement vector equations of the folding structure are established, which provides a direct simulation method of connection stiffness. The influence of flexible deformation of the airfoil and the deflection of wing root are considered in the displacement vector equation. The effect of the clearance on the connection stiffness is discussed by adjusting the clearance between the shaft and sleeve. The load effect on stiffness is studied by varying the load distribution on the out-wing surface. The stiffness analysis method is finally established and meets the requirements of engineering design. The results show that the deformation of the hinge-locked structure is several times than that of the monolithic structure under the same load, which means that the stiffness is significantly reduced; the tension and compression asymmetric stiffness characteristics are also investigated; in addition, the increase of clearance between the hinge-locked structure shaft and wing holes decrease the connection stiffness; the load distribution on out-wing surface has no significant effect on the connection stiffness.

Workspace, stiffness analysis and design optimization of coupled active-passive multilink cable-driven space robots for on-orbit services

The use of space robots (SRs) for on-orbit services (OOSs) has been a hot research topic in recent years. However, the space unstructured environment (i.e.: confined spaces, multiple obstacles, and strong radiation interference) has greatly restricted the application of SRs. The coupled active-passive multilink cable-driven space robot (CAP-MCDSR) has the characteristics of slim body, flexible movement, and electromechanical separation, which is very suitable for extreme space environments. However, the dynamic and stiffness modeling of CAP-MCDSRs is challenging, due to the complex coupling among the active cables, passive cables, joints, and the end-effector. To deal with these problems, this paper proposes a workspace, stiffness analysis and design optimization method for such type of MCDSRs. Firstly, the multi-coupling kinematics relationships among the joint, cables and the end-effector are established. Based on hybrid series-parallel characteristics, the improved coupled active–passive (CAP) dynamic equation is derived. Then, the maximum workspace, the maximum stiffness, and the minimum cable tension are resolved, among them, the overall stiffness is the superposition of the stiffness produced by the active and the passive cable. Furthermore, the workspace, the stiffness, and the cable tension are analyzed by using the nonlinear optimization method (NOPM). Finally, an 8-DOF CAP-MCDSR experiment system is built to verify the proposed modeling and trajectory tracking methods. The proposed modeling and analysis results are very useful for practical space applications, such as designing a new CAP-MCDSR, or utilizing an existing CAP-MCDSR system.

AN INNOVATIVE BOUNDARY ELEMENT FORMULATION FOR BUILDING SLABS

Slab supported by beams (i.e. beam-slab floor) is a common practice in the construction of buildings. Modeling this slab type using the boundary element method (BEM) is an essential step to provide seamless frameworks for the analysis of buildings with complex geometries. However, one of the most challenging difficulties that have been facing research efforts in this area is its theoretical setting with limited applicability to practical building slabs. This limitation is addressed in this research work and a practical BEM-based formulation for the slab-beam floor is presented. The presented formulation discretizes the connection area between the slab, and beams and columns into cells (supporting cells). The centroids of these cells are used to carry out an additional collocation scheme which is required to solve the resulting system of equations. To generate the slab stiffness matrix, the generalized displacements that correspond to the supporting cells’ degrees of freedom are set to unity (one at a time). By assembling the generated slab stiffness matrix with beams and columns stiffness matrices using the stiffness analysis method, the overall stiffness matrix is obtained. Hooke’s law is then applied to calculate the generalized displacements and straining actions are obtained in the post-processing phase. The developed formulation is applied to an example to validate its results by comparing it with the analytical solution.

High-Precision Guide Stiffness Analysis Method for Micromechanism Based on the Boundary Element Method

The guide stiffness performance directly affects the motion of the micromechanism in accuracy and security. Therefore, it is crucial to analyze the guide stiffness precisely. In this paper, a high-precision guide stiffness analysis method for the micromechanism by the boundary element method (BEM) is proposed. The validity and accuracy of the analysis method are tested by a guide stiffness experiment. In order to ensure the accuracy and safety during the micromechanism motion, a guiding unit of the micromechanism was designed based on the guiding principle. The guiding unit can provide parasitic motion and additional force in the motion of the micromechanism. Then, the stiffness equations of the beam element are derived by the boundary element method. The stiffness equation of straight circular flexure hinge is analyzed by rigid discretization and rigid combination, and the guide stiffness of the mechanism is investigated by rigid combination. Finally, according to the actual situation, the stiffness matrix of the guide rail (Kb) was proposed, and the analytical value of the guide stiffness was calculated to be 22.2 N/μm. The guide stiffness performance experiment was completed, and the experimental value is 22.3 N/μm. Therefore, the error between the analysis method and the experimental results is 0.45%. This study provides a new method for the stiffness analysis of high-precision micromechanisms and presents a reference for the design and stiffness analysis of complex structures. This method is helpful for stiffness analysis of the microrotary mechanism with high accuracy.

Experimental and analytical investigation on the in-plane mechanical property of discretely connected precast RC floor diaphragm

Discretely connected precast reinforced concrete floor diaphragm (DCPCD) is a new-type untopped precast concrete floor system. Using slab joint connectors, instead of cast-in-situ concrete overlap layers on precast slab, to transmit slab joints inner forces caused by vertical and horizontal loads eliminates the need for wet works in construction site, thus leading to economical designs and high efficiency in installation. This paper presents the development and experimental evaluation of DCPCD subjected to in-plane low-cyclic reversed loading. Performance of the tested specimen was evaluated in terms of failure mode, in-plane deformation pattern, hysteretic curves, stiffness, ductility and energy dissipation capacity. The results show that DCPCD had high in-plane stiffness and good integrity, and the beam-to-slab connections and slab joints perform well during the test process. The ductility of the specimen is acceptable, while the energy dissipation is not that satisfactory, confirming that the elastic design method of precast RC diaphragms is rational. The shear and axial force distribution regularity of the tested specimen was analyzed, and the results indicate that internal force distribution is similar to that of the simply supported beam. The equivalent beam model theory was modified based on the measured tensile (compressive) stiffness of slab joint connectors and the actual load effect in the floor et al. It is demonstrated that the in-plane deformations determined by the modified calculation method agree well with the test results. Hence, the proposed in-plane stiffness analysis method is reliable and can be used for designing buildings adopting DCPCD.

Seismic Response of Multistory Buildings with Double Telescoping Self-Centering Energy-Dissipative Brace (DT-SCED)

Telescopic Self-Centering braces are one of the very successful examples of Self-Centering braces which perform well in seismic loading. In this study, a new example of Telescopic Self-Centering brace is introduced, which has superior features over other telescopic braces. These include: high axial load capacity, use of shorter cables in brace construction, simplicity of construction, use of separate cables for compressive and traction modes, less fatigue in cyclic loads and, allowing for more dynamic loading cycles. In this paper, a sample was designed with an axial force capacity of 300kN. Modeling of behavior (DT-SCED) was accurately expressed using numerical relationships. nonlinear incremental stiffness analysis method was also used to calculate the hysteresis brace behavior. The cyclic load test was applied to this brace and the result showed complete Self-Centering behavior. Then, a sample building with the double telescoping Self-Centering Energy-Dissipative Brace (DT-SCED) was subjected Single direction pushover analyses and the results are compared with the sample buildings with the Self-Centering Energy-Dissipative Bracing (SCED) and the Telescoping Self-Centering Energy-Dissipative Bracing (T-SCED). The results of the analysis and comparing with other samples confirm the seismic superiority of performance of the DT-SCED brace over other samples.

Method for Stiffness Analysis of Weak Bases Reinforced with Crushed Stone Cores

The article presents a method for stiffness analysis of the weak bases reinforced with crushed stone cores. Stiffness analysis of the bases reinforced with the geotechnogenic massif in the form of crushed stone cores showed that the maximum settlement of the compressible strata of the soil mass is far less than the maximum permissible value. This makes it possible to increase the design resistance of the base and to choose a more economical structure of the foundation.

Jacobian-based natural frequency analysis of parallel manipulators

The dynamic performance of a parallel manipulator is often limited by its natural frequencies. These frequencies are a result of the controlled actuator stiffness and the mechanical design. Typically, only the lowest natural frequencies are of interest. However, existing methods to analyze natural frequencies of parallel manipulators with flexible links have been developed in a high-dimensional generalized coordinate space. This paper presents a novel natural frequency analysis method for parallel manipulators that focuses on the lowest natural frequencies and which expresses the corresponding eigenmodes in an end-effector Cartesian reference frame. The analysis method combines a flexible-body stiffness analysis method with a rigid-body inertia analysis method. As an example, the two lowest natural frequencies of the Heli4 robot are modeled and measured over a range of controlled actuator stiffness values for a single pose. The results show that structural compliance in the mechanical parts of the Heli4 robot is significant for actuator stiffness values above roughly 1000 Nm/rad. For an actuator stiffness value of 4000 Nm/rad, consideration of the structural compliance reduces the maximum prediction error for the two lowest natural frequencies from 33% to 6%.

Research on Controllable Stiffness of Redundant Cable-Driven Parallel Robots

In this paper, to solve the problem of variable stiffness of cable-driven parallel robots (CDPR), a new static stiffness analysis and cable tension distribution method are proposed for studying the CDPRs’ controllable stiffness. First, a three-dimensional Hessian matrix of the structure matrix to position differential is deduced by introducing a line vector and differential transform, and a static stiffness model is established for analyzing the relationship between cable tension and the stiffness of the robots. Furthermore, a calculation algorithm for cable tension polygons based on Graham's Scan is introduced that effectively obtains the cable tension feasible region (CTFR) of CDPRs. Next, a method involving “the relationship between the external force and the pose change value of the moving-platform” is proposed to measure the variation of system stiffness. The CDPR's controllable stiffness is also analyzed based on the CTFR by considering the variation of each driving-cable's tension and each component of the moving-platform's pose. The results of experimental and theoretical analyses verify the correctness and efficacy of the proposed method. In addition, they show that the proposed method is computationally efficient and easily establishes the relationship between cable tension and the CDPR's controllable stiffness.

Characteristics of controllable stiffness for cable-driven parallel robots

Human-robot interaction include some safety threats to people or products from the robots due to their stiffness. The characteristics of controllable stiffness for cable-driven parallel robots are studied using a static stiffness analysis and cable tension distribution method. The robot kinematics and statics equations are used for the force analysis with the three-dimensional Hessian matrix of the structural matrix to position differential is deduced by introducing a line vector and a differential transform. Then, the static stiffness model is derived for the relationship between the cable tension and the robot stiffness. The robots stiffness is then controlled by analyzing the cable tension polygon and the cable tension distribution. Simulations show that this method can effectively control the robot stiffness. 摘要 在机器人与人交互过程中, 机器人可能因刚度过大而对人或产品产生安全威胁。该文提出索驱动并联机器人静态刚度分析及索力分配方法, 研究其可控刚度特性问题。首先, 通过建立运动学和静力学方程对机器人进行受力分析, 并通过引入线矢量和微分变换的方式, 推导出结构矩阵对位姿微分的三维Hessian矩阵, 建立静态刚度模型, 分析索力与机器人刚度间的关系; 其次, 给出索力多边形计算算法, 并研究索力分配方法, 完成机器人刚度的有效控制; 最后, 通过计算实例验证该方法正确性与有效性。结果表明：该方法可以有效控制机器人的系统刚度。

Stiffness modeling approach for a 3-DOF parallel manipulator with consideration of nonlinear joint stiffness

Considering the nonlinear characteristics of joint, this paper proposes a new comprehensive stiffness analysis method by combining finite element analysis and matrix structural analysis. Based on the force/moment equilibrium equations of a 3-DOF over-constrained parallel manipulator, a method for solving the internal forces of the joints is proposed. By calculating the stiffness of the bearing under the action of joint internal forces, the stiffness matrix of the revolute joint and the composite spherical joint can be derived. The FEA-based identification method for the stiffness matrix of multi-node components is proposed by importing the structural model into the finite element software for virtual experiments. Then, integrating the stiffness matrices of components and joints, the stiffness matrix of the whole manipulator can be derived and the theoretical stiffness computed from the stiffness model is mapped in the workspace. Finally, the stiffness analysis method is verified by experiments in the physical prototype.

A method for stiffness analysis of overconstrained parallel robotic mechanisms with Scara motion

This paper presents a general method for analyzing stiffness of overconstrained parallel robotic mechanisms with Scara motion. In the method, the stiffness model of a limb is derived by applying Castigliano's second theorem to strain energy of the limb with a structural decomposition strategy, and the stiffness matrix of a parallel mechanism is established based on stiffness models of limbs and the static equilibrium equation of the moving platform. Comparisons show that the stiffness model obtained from the proposed method is very close to the counterpart obtained from finite element analysis (FEA). In addition, a new index is proposed to evaluate stiffness performance of a parallel mechanism in a given configuration based on strain energy under external unit forces and moments. With this index, the dimensions of a parallel mechanism can be optimized and the path of a given task can be planned to obtain high stiffness.

Stiffness Analysis of General Folding Frame of Mobile Solar Wing of Inverted Type

The simulation experiment on the solar wings, under the situation of zero gravity, is an important part of the satellite’s ground work. With the development of space station and deep space exploration technology, the fold-expanding solar wing is being used more frequently, and there are higher requirements for its quality. As a result, the demand of the simulation experiment, which the solar wings worked on the ground with no gravity, also increase. In order to facilitate the comprehensive utilization of the test device, save space and improve the flexibility and speed of the test equipment, a new test device is provided, which is used for the unfoldment of mobile, retractable solar wings, working on the ground under zero gravity. In this paper, the calculation method for stiffness analysis is also given.

Virtual characterization of MDF fiber network

A virtual design method for medium density fiberboards (MDF) is proposed with the aim to optimize the fiber orientation and lay-up of MDF. The new method estimates the stiffness and strength by using microstructure models of the MDF fiber network. The virtual design is used to improve the manufacturing technology of MDF plates with multilayer oriented fiber structure. Experimental investigations of the mechanical behavior of MDF microstructure for various fiber geometries, glue content and distribution are complicated, time consuming and expensive. On the other side, virtual microstructure design allows to develop a new wood fiber based material with less experimental work. Microstructure models help to better understand the non-linear damage mechanical behavior of a wood fiber network depending on fiber geometrical parameters. Such parameters as crack distribution and fiber deformation on micro-scale level are complicated to experimentally measure, but possible to model using computer simulations. The virtual design tool requires less empirical data. The model takes into account information on average wood fiber orientation, fiber diameter, fiber length and mechanical properties of wood fiber cell wall and glue. The numerical method for strength and stiffness analysis of MDF microstructure was calibrated using standard MDF with non-oriented fibers. It turned out that this method gives precise results for MDF with oriented fibers and even with multilayer structure. The proposed virtual microstructure design tool can significantly improve and speed-up the optimization manufacturing technology of MDF and other wood fiber based composites.