Systematic Elastostatic Stiffness Model of Over-Constrained Parallel Manipulators Without Additional Constraint Equations

The establishment of an elastostatic stiffness model for over constrained parallel manipulators(PMs),particularly those with over constrained subclosed loops,poses a challenge while ensuring numerical stability.This study addresses this issue by proposing a systematic elastostatic stiffness model based on matrix structural analysis(MSA)and independent displacement coordinates(IDCs)extraction techniques.To begin,the closed-loop PM is transformed into an open-loop PM by eliminating constraints.A subassembly element is then introduced,which considers the flexibility of both rods and joints.This approach helps circumvent the numerical instability typically encountered with traditional constraint equations.The IDCs and analytical constraint equations of nodes constrained by various joints are summarized in the appendix,utilizing multipoint constraint theory and singularity analysis,all unified within a single coordinate frame.Subsequently,the open-loop mechanism is efficiently closed by referencing the constraint equations presented in the appendix,alongside its elastostatic model.The proposed method proves to be both modeling and computationally efficient due to the comprehensive summary of the constraint equations in the Appendix,eliminating the need for additional equations.An example utilizing an over constrained subclosed loops demonstrate the application of the proposed method.In conclusion,the model proposed in this study enriches the theory of elastostatic stiffness modeling of PMs and provides an effective solution for stiffness modeling challenges they present.

Torsional stiffness modeling and optimization of the rubber torsion bushing for a light tracked vehicle

Taking the rubber torsion bushing of a certain type of all-terrain tracked vehicle as the research object,a theoretical model of torsional stiffness was proposed according to the non-linear characteristics of rubber components and structural feature of the suspension. Simulations were carried out under different working conditions to obtain root mean square of vertical weighted acceleration as the evaluation index for ride performance of the all-terrain tracked vehicle,with a dynamics model of the whole vehicle based on the theoretical model of the torsional stiffness and standard road roughness as excitation input. Response surface method was used to establish the parametric optimization model of the torsional stiffness. The evaluation index showed that ride performance of the vehicle with optimized torsional stiffness model of suspension was improved compared with previous model fromexperiment. The torsional stiffness model of rubber bushing provided a theoretical basis for the design of the rubber torsion bushing in light tracked vehicles.

Semi-analytical Stiffness Model of Bolted Joints in Machine Tools Considering the Coupling Effect

This study proposes an improved semi-analytical approach for contact stiffness modeling of bolted joints in a machine tool system.First,nonlinear contact stress distribution within a single-bolted joint is obtained from the simulation results of finite element analysis software.Second,employing the Hertz contact theory and fractal theory,the contact stiffness model of a single asperity is formulated,affording analytical expressions for normal and tangential contact stiffnesses of a single-bolted joint by integrating multi-asperities in the contact area.Subsequently,considering two test specimens as illustrations,the mode shapes and natural frequencies of the proposed model and modal analysis tests are compared,and the influence of coupling effects between two adjacent bolts is illustrated.The maximum error in the natural frequencies of the proposed approach is<2.73%relative to the experimental results.Finally,the measurements of frequency response functions on a box-in-box precision horizontal machine tool are conducted to demonstrate the accuracy and efficiency of the proposed model.The proposed model is highly efficient in revealing the influence of microcontact factors on the contact stiffness of bolted joints and in guiding the optimal functional design of bolt arrangements under the framework of virtual machine tools.

Stiffness Degradation Modeling for Composite Wind Turbine Blades Based on Full-Scale Fatigue Testing

In order to provide more insights into the damage propagation composite wind turbine blades(blade)under cyclic fatigue loading,a stiffness degradation model for blade is proposed based on the full-scale fatigue testing of a blade.A novel non-linear fatigue damage accumulation model is proposed using the damage assessment theories of composite laminates for the first time.Then,a stiffness degradation model is established based on the correlation of fatigue damage and residual stiffness of the composite laminates.Finally,a stiffness degradation model for the blade is presented based on the full-scale fatigue testing.The scientific rationale of the proposed stiffness model of blade is verified by using full-scale fatigue test data of blade with a total length of 52.5 m.The results indicate that the proposed stiffness degradation model of the blade agrees well with the fatigue testing results of this blade.This work provides a basis for evaluating the fatigue damage and lifetime of blade under cyclic fatigue loading.

A New Modification to Shear Lag Model as Applied to Stiffness and Yield Strength of Short Fiber Reinforced Metal Matrix Composites

A new modification for the shear lag model is given and the expressions for the stiffness and yield Strength of short fiber metal matri×composite are derived. These expressions are then compared with our experimental data in a SiCw/Al-Li T6 composite and the published experimental data on different SiCw/Al T6 composites and also compared with the previous shear lag models and the other theoretical models.

Static analysis of ultra-thin beams based on a semi-continuum model

A linear semi-continuum model with discrete atomic layers in the thickness direction was developed to investigate the bending behaviors of ultra-thin beams with nanoscale thickness.The theoretical results show that the deflection of an ultra-thin beam may be enhanced or reduced due to different relaxation coefficients.If the relaxation coefficient is greater/less than one,the deflection of micro/nano-scale structures is enhanced/reduced in comparison with macro-scale structures.So,two opposite types of size-dependent behaviors are observed and they are mainly caused by the relaxation coefficients.Comparisons with the classical continuum model,exact nonlocal stress model and finite element model （FEM） verify the validity of the present semi-continuum model.In particular,an explanation is proposed in the debate whether the bending stiffness of a micro/nano-scale beam should be greater or weaker as compared with the macro-scale structures.The characteristics of bending stiffness are proved to be associated with the relaxation coefficients.

聚酯缆动力学行为计算方法研究

The dynamic stiffness of polyester rope presents a complex mechanical performance,and the search for an appropriate calculation method to simulate this property is important.Distorted simulation results eventually yield inaccurate line tension and vessel offset predictions,with the inaccuracy of vessel offset being particularly large.This paper proposes a flexible calculation method for the dynamic behavior of polyester rope based on the dynamic stiffness model.A real-time varying stiffness model of polyester rope is employed to simulate tension response through rope strain monitoring.Consequently,a simulation program is developed,and related case studies are conducted to explore the differences between the proposed method and analytical procedure of the DNV standard.Orcaflex is used to simulate the results of the latter procedure for comparison.Results show the convenience and straightforwardness of the procedure in the selection of an approximate dynamic stiffness model for polyester rope,which leads to an engineering-oriented approach.However,the proposed method is related to line property,which can directly reflect the dynamic behavior of polyester rope.Thus,a flexible calculation method may provide a reference for the simulation of the dynamic response of polyester mooring systems.

A novel stiffness optimization model of space telescopic boom based on locking mechanism

The deployable telescopic boom,whose mass and stiffness play crucial roles,is extensively used in the design of space-deployable structures.However,the most existing optimal design that neglects the influence of the locking mechanisms in boom joints cannot raise the whole stiffness while reducing the boom mass.To tackle this challenge,a novel optimization model,which utilizes the arrangement of the locking mechanisms to achieve synchronous improvement of the stiffness and mass,is proposed.The proposed optimization model incorporates a novel joint stiffness model developed based on an equivalent parallel mechanism that enables the consideration of multiple internal stiffness factors of the locking mechanisms and tubes,resulting in more accurate representations of the joint stiffness behavior.Comparative analysis shows that the proposed stiffness model achieves more than at least 11% improved accuracy compared with existing models.Furthermore,case verification shows that the proposed optimization model can improve stiffness while effectively reducing mass,and it is applied in boom optimization design.

Fatigue behavior of basalt-aramid and basalt-carbon hybrid fiber reinforced polymer sheets

In order to study the fatigue failure mode and fatigue life laws of basalt-aramid and basalt-carbon hybrid fiber reinforced polymer （ FRP ） sheets, fatigue experiments are carried out, considering two hybrid ratios of 1 ： 1 and 2：1 under different stress levels from 0.6 to 0.95. The results show that fractures occur first in carbon fibers or aramid fibers for the specimens with hybrid ratio of 1： 1, namely B1A1 and B1C1, while a fracture occurs first in basalt fibers for the specimens with a hybrid ratio of 2： 1, namely B2A1 and B2C1. The fatigue lives of the hybrid FRP sheets increase with the improvement of the content of carbon fibers or aramid fibers, and the influence of the carbon fibers content improvement to fatigue life is more significant. The fatigue performance of B2A1 is relatively worse, while the fatigue performance of B1C1 and B2C1 is relatively better. Finally, a new fatigue stiffness degradation model with dual variables and double inflection points is presented, which is applicable to both hybrid and normal FRP sheets.

Static Stability Analysis of a Single Planar Object Grasped by a.Multifingered Hand

In this study, the static stability of the grasp of a single planar object is analyzed using the potential energy method. In previous papers, we considered cases in which individual fingers were replaced by a multidimensional translational spring model, in which each finger is constructed with prismatic joints. Human hands and the most developed mechanical hands are constructed with revolute joints. In this paper, the effects of fingertip rotation and a revolute joint spring model are investigated. A grasp stiffness matrix is analytically derived by considering not only frictional rolling contact but also frictionless sliding contact. The difl＇erence between the frictional stiffness matrix and the frictionless one is analytically obtained. The effect of local curvature at contact points is analytically derived. The grasp displacement directions affected by the change in curvature and the contact condition are also obtained. The derived stiffness matrix of the revolute joint model is compared with that of the prismatic joint model, and then the stiffness relation is clarified. The gravity effect of the object is also considered. The effectiveness of our method is demonstrated through numerical examples. The stability is evaluated by the eigenvalues of the grasp stiffness matrix, and the grasp displacement direction is obtained by the corresponding eigenvectors. The effect of joint angle is also discussed.

Rice stem lodging properties and bending modeling under the influence of circadian temperature difference

Under diurnal temperature stress,the vascular bundle content of mature rice stems will change which will cause a change in the modulus of elasticity.Therefore,the rice stems will collapse with the reduction in bending resistance because of the change in the modulus of elasticity.In order to reveal the distribution of vascular bundle gradients in rice stems under different climatic temperatures and explore the locations where stems are prone to bending and the form of stem damage,this study established a model of stem stiffness under free loading based on observing microstructure of the rice.The lodging characteristics of rice stems was explored seldom in different environmental temperatures from a micro structure of rice stems.So,the statistical analysis and t-tests were carried out on stems 1 to 4 in combination for cantilever bending tests at room temperature on stem internodes 3,versus three-point bending tests at-10℃ to 65℃ temperature treatment.Results showed that the bending resistance of the stem can be well predicted by using the vascular bundle distribution regression model and the variable stiffness mechanical model.The bending resistance of No.3 stem was established by using the results obtained from the three-point bending test in a temperature range between 10℃-65℃.The correction coefficient TF of stem bending resistance under temperature difference induced stress was established based on the Gauss regression model.Statistical analysis showed that the bending resistance of No.3 stem was relatively large in a temperature range of 16℃-34℃.This study elucidated the variations of the mechanical properties of rice stems under temperature difference induced stress and provided a theoretical foundation for understanding the lodging characteristics of rice during mechanized harvesting.

Torsional dynamic response of tapered pile considering compaction effect and stress diffusion effect

Considering both the compaction effect of pile surrounding soil and the stress diffusion effect of pile end soil,this paper theoretically investigates the torsional vibration characteristics of tapered pile.Utilizing the complex stiffness transfer model to simulate compaction effect and tapered fictitious soil pile model to simulate stress diffusion,the analytical solution for the torsional impedance at tapered pile top is obtained by virtue of Laplace transform technique and impedance transfer method.Based on the present solution,a parametric study is conducted to investigate the rationality of the present solution and the influence of soil and pile properties on the torsional vibration characteristics of tapered pile embedded in layered soil.The results show that,both the compaction effect and stress diffusion effect have significant influence on the torsional vibration characteristics of tapered pile,and these two factors should be considered during the dynamic design of pile foundation.

Complex dynamics of a harmonically excited structure coupled with a nonlinear energy sink

Nonlinear behaviors are investigated for a structure coupled with a nonlinear energy sink. The structure is linear and subject to a harmonic excitation, modeled as a forced single-degree-of-freedom oscillator. The nonlinear energy sink is modeled as an oscillator consisting of a mass,a nonlinear spring, and a linear damper. Based on the numerical solutions, global bifurcation diagrams are presented to reveal the coexistence of periodic and chaotic motions for varying nonlinear energy sink mass and stiffness. Chaos is numerically identified via phase trajectories, power spectra,and Poincaré maps. Amplitude-frequency response curves are predicted by the method of harmonic balance for periodic steady-state responses. Their stabilities are analyzed.The Hopf bifurcation and the saddle-node bifurcation are determined. The investigation demonstrates that a nonlinear energy sink may create dynamic complexity.

An efficient design tool based on FEM for evaluating effects of components properties and operating conditions on interaction of tire with rigid road

It is noted that any variation in operating conditions has a considerable effect on the tire/road interaction. Furthermore,choosing a range of proper values for carcass stiffness is very essential for both tire safety and effective driving action. In this work,an elaborated 3D model fully compliant with the geometrical size of radial tire 185/60 R15 is worked up, for evaluating the effects of components properties and working conditions on deformation and stress/strain fields created inside the tire. For the simulation, the tire structure is assumed to be composed of tread, carcass ply, and bead. The mechanical behavior of rubber as main component of tire is described by Mooney-Rivlin material model. The comparison of the obtained results and laboratory tests demonstrates the validity and high accuracy of analysis.

Natural Frequency of Planetary Transmission with Thin-Walled Ring Gear on Elastic Supports

A lumped parameter-rigid elastic coupled dynamic model of two-stage planetary gears for a hybrid car is established through the inter-stage coupled method,in which the supports of the ring gear of planet set Ⅱ are represented as an elastic foundation with radial and tangential uniform distributed stiffness,and the ring gear of planet set Ⅱ is modeled as an elastic continuum body. The natural frequencies based on the eigenvalue problem of dynamic model of planetary transmission are solved and the associated vibration modes are discussed. The rules are revealed which are the influences of the ring gear elastic supports stiffness and rim thickness on natural frequencies of planetary transmission. The theoretical analysis indicates that the vibration modes of planetary transmission with thin-walled ring gear on elastic supports are classified into seven types: Ⅰ/Ⅱ stage coupled rotational mode,Ⅰ stage translational mode,Ⅰ stage planet mode,Ⅱ stage translational mode,Ⅱ stage degenerate planet mode,Ⅱ stage distinct planet mode and purely ring gear mode. For each vibration mode, its properties are summarized. The numerical solutions show that the elastic supports stiffness and rim thickness of the ring gear of planet set Ⅱ have different influences on natural frequencies.

Stiffness of a 3-degree of freedom translational parallel kinematic machine

In this paper, a typical 3-degree of freedom （3- DOF） translational parallel kinematic machine （PKM） is studied and analyzed whose tool platform has only translations along X-, Y- and Z-axes. It consists of three limbs, each of which have arm and forearm with prismatic- revolute-revolute-revolute （PRRR）joints. Inverse kine- matics analysis is carried out to find the slider coordinates and joint angles for a given position of tool platform. Stiffness modeling is done based on the compliance matrices of arm and forearm of each limb. Using the stiffness modeling the variations of minimum and max- imum translational stiffness in the workspaee are analyzed. For various architectural parameters of the 3-DOF PKM the tendency of variations on the minimum and maximum stiffness over the entire workspace is studied; and also the deflections of the tool platform along X, Y, and Z directions with respect to various forces are presented.

Viscoelastic plastic continuous physical model of a magnetorheological damper applied in the high speed train

In the preliminary design stage of high-speed train smart suspension,a simple,yet accurate magnetorheological(MR)damper model whose parameters have clear physical meaning is needed.Based on the working mechanism analysis and the dynamic behavior study of the MR damper,a new consecutive viscoelastic plastics(VEP)model is proposed.A methodology to find the parameters of the proposed model directly has been proposed.The comparison with experimental results indicates that the proposed model could adequately characterize the intrinsic nonlinear behavior of the MR damper,including the hysteretic behavior,roll-off phenomenon,and the variation of the hysteresis width in terms of the frequency and magnitude of excitation.The results of experimental testing prove that the accuracy of the proposed model is higher than that of the phenomenological model while only containing four undetermined parameters with clear physical meaning.Moreover,based on the proposed VEP model,a nonlinear stiffness VEP(nkVEP)model is developed with higher precision in the hysteretic region.The nkVEP model,which can reproduce the behavior of the damper with fluctuating input current,is developed.The proposed model could predict accurately the response of the MR damper in a wide range of frequency and displacement.

A calibration and compensation method for an industrial robot with high accuracy harmonic reducers

Industrial serial robots need high stiffness to keep absolute pose accuracy and meet the requirements in practical applications. However, the weak stiffness feature of robot joints and the payloads affected on robot end-effector, which will also increase the pose error of robot. Especially, the existing calibration methods often consider under no-payload condition without discussing the payload state. In this paper, we report a new industrial serial robot composed by a new harmonic reducer: Model-Y, based on high accuracy and high stiffness, and a kinematic parameter calibration algorithm which is based on a harmonic reducer forcedeformation model. To decrease the accuracy effects of payload, an iterative calibration method for kinematic parameters with payload situation was proposed. Simulation and experiments are conducted to verify the effectiveness of the proposed calibration method using the self-developed industrial serial robot. The results show a remarkably improved accuracy in absolute position and orientation with the robot's payload range. The position mean error has 70% decreased to 0.1 mm and the orientation mean error diminished to less than 0.01° after calibration with compensation. Additionally, online linear and circular tests are carried out to evaluate the position error of the robot during large-scale spatial and low-speed continuous movement. The accuracy is consistent with the previous calibration results, indicating the effectiveness and advantages of the proposed strategy in this article.

High Efficient Numerical Simulation of Infrared Radiation from a Hot Exhaust Nozzle

A coupled model,capable of simulating transonic flow,solid heat conduction,species transport,and gas radiation,is developed that provides better computational treatment of infrared radiation from hot exhaust nozzles.The modeling of gas radiation is based on a statistical narrow-band correlated-k analysis,whose parameters are deduced from the HITEMP line-by-line database.To improve computational efficiency,several methods are employed.A mixed analytical-numerical algorithm is described for the stiffness of the two-equation turbulence model and an alternating direction implicit pretreatment for the ill-conditioned matrix appearing in the coupled problem of flow and solid heat conduction.Moreover,an improved multigrid method and a symmetry plane treatment of the radiation transfer-energy equations are also introduced.Four numerical simulations are given to confirm the efficiency and accuracy of the numerical method.Finally,an account of the aerothermodynamics and infrared characteristics for two types of nozzles are presented.The infrared radiation intensity of the Chevron ejecting nozzle is clearly smaller than that of the common axisymmetric ejecting nozzle.All computations can be performed on a personal computer.