Structure design and performance analysis of self-driving articulated arm coordinate measuring machine

To solve the problem that the traditional articulated arm coordinate measuring machine cannot measure automatically, a self-driven articulated arm coordinate measuring machine (AACMM) is proposed. The length of the connecting rods of the AACMM was allocated according to the design indicators. The AACMM virtual prototype was assembled based on the joint module selection and joint component design, and its measurement space range was also verified. The AACMM ideal measurement model was established based on MDH methodology. The static deformation of the structure and the influence of the dynamic flexible deformation on the positioning error of the probe of the measuring machine was analyzed, respectively. The results show that the measurement space range of the AACMM designed in this paper can meet the design index of the measuring radius. The probe position error caused by static deformation of the measuring machine after structural optimization was reduced by an order of magnitude. The positioning error of the probe caused by the dynamic deformation of the AACMM structure meets the positioning accuracy index. In the constant-speed touch measurement stage, the instantaneous position error of the probe changes linearly with time, and the optimal touch speed (6.6 mm/s, 6.4 mm/s) exists to minimize the probe positioning error. During the variable-speed approach stage, the influence of angular acceleration and velocity of each joint on the positioning error of the probe can be negligible when AACMM in the typical posture. In the extreme posture, , the inertial force of the measuring machine structure and the instantaneous position error of the probe are the smallest with the optimal joint angular acceleration ( ) and angular velocity ( ). The structural design and positioning error performance analysis of self-driving AACMM can provide a theoretical research foundation for subsequent trajectory planning and error compensation modeling.

Static deformation of a multilayered magneto-electro-elastic half-space structures due to vertical inner loading

The static deformation in a multilayered magneto-electro-elastic half-space under vertical inner loading is calculated using a vector function system approach and a stiffness matrix method. Firstly, the displacement, stress, and inner loading are expanded using the vector function system, and the N-type and L&M-type problems related to the expansion coefficient are constructed. Secondly, the stable stiffness matrix method is used to solve the expansion coefficients of the L&M-type problem. After introducing the boundary condition and the discontinuity of the stress caused by inner loading, the displacement and stress are calculated through adaptive Gaussian quadrature. Finally, the numerical examples considering the circular load and point load are designed and analyzed, respectively.

Static analysis model of a non-pneumatic tire with elastic spokes contacting with rigid ground

An analytical model of a non-pneumatic tire is proposed to study the static deformation responses of a non-pneumatic tire in contact with a rigid ground. The tire consists of a shear band which is formed by an annular beam, and elastic spokes that connect the shear band to the rigid hub of the tire. The shear band is modeled using a Timoshenko beam. The spokes are modeled by linear springs, which are distributed evenly in circumferential direction. Governing equations of the model were derived using a theoretical analysis. The shear band static deformation was obtained based on the discussion of the relationship between spoke stiffness and the parameters of the shear band. A finite element model was developed to verify the accuracy of the model. As a part of the results from this study, a parametric analysis of quantities of interest for the tire is presented, which can be used in improving the optimal design of non-pneumatic tires. This scheme offers a holonomic solution for the complicated differential equations and gives a computationally efficient tool for rapid analyzing and designing such systems.

Application of exponential functions in weighted residuals method in structural mechanics. Part II: static and vibration analysis of rectangular plate

The paper is continuation of our efforts on application of the properly constructed sets of exponential functions as the trial (basic) functions in weighted residuals method, WRM, on example of classical tasks of structural mechanics. The purpose of this paper is justification of new method’s efficiency as opposed to getting new results. So, static deformation and free vibration of isotropic thin – walled plate are considered here. Another peculiarity of paper is choice of weight (test) functions, where three options are investigated: it is the same as trial one (Galerkin method); it is taken as results of application of differential operator to trial function (least square method); it equals to the second derivative of trial function with respect to both x and y coordinate (moment method). Solution is considered as product of two independent sets of functions with respect to x or y coordinates. Each set is the combination of five consequent exponential functions, where coefficient at first function is equal to one, and four other coefficients are to satisfy two boundary conditions at each opposite boundary. The only arbitrary value in this method is the scaling factor at exponents, the reasonable range of which was carefully investigated and was shown to have a negligible impact on results. Static deformation was investigated on example of simple supported plate when outer loading is either symmetrical and concentrated near the center or is shifted to any corner point. It was demonstrated that results converge to correct solution much quickly than in classical Navier method, while moment method seems to be a best choice. Then method was applied to free vibration analysis, and again the accuracy of results on frequencies and mode shape were excellent even at small number of terms. At last the vibration of relatively complicated case of clamped – clamped plate was analyzed and very encouraged results as to efficiency and accuracy were achieved.

New insight into the stability and dynamics of fluid-conveying supported pipes with small geometric imperfections

In several previous studies, it was reported that a supported pipe with small geometric imperfections would lose stability when the internal flow velocity became sufficiently high. Recently, however, it has become clear that this conclusion may be at best incomplete. A reevaluation of the problem is undertaken here by essentially considering the flow-induced static deformation of a pipe. With the aid of the absolute nodal coordinate formulation (ANCF) and the extended Lagrange equations for dynamical systems containing non-material volumes, the nonlinear governing equations of a pipe with three different geometric imperfections are introduced and formulated. Based on extensive numerical calculations, the static equilibrium configuration, the stability, and the nonlinear dynamics of the considered pipe system are determined and analyzed. The results show that for a supported pipe with the geometric imperfection of a half sinusoidal wave, the dynamical system could not lose stability even if the flow velocity reaches an extremely high value of 40. However, for a supported pipe with the geometric imperfection of one or one and a half sinusoidal waves, the first-mode buckling instability would take place at high flow velocity. Moreover, based on a further parametric analysis, the effects of the amplitude of the geometric imperfection and the aspect ratio of the pipe on the static deformation, the critical flow velocity for buckling instability, and the nonlinear responses of the supported pipes with geometric imperfections are analyzed.

Research on the dynamic identification method of weak parts in cantilever structures

Determining the weak parts of a structure is one of the key issues in the field of machine tool stiffness improvement. However, studies show that overcoming the static deformation with acquisition difficulty is a complex problem in practical structures. This study considers the machine tool cantilever structure, as a cantilever beam and bar structure, where the objective is to propose a weakness index, to identify the weak part, using system reconstruction to extract the measured static deformation data and the fitting data. Stiffness reduction is used to simulate weak parts, while the effectiveness of the method is evaluated, in the case of various weakness values and of different noise levels, using the finite element simulation approach. The validity of the proposed method is illustrated through comparison of the theoretical results to the experimental ones, using the cantilever structure of a test machine tool. The research content provides some means of improving the machining accuracy of machine tools.

Three-dimensional modeling of static deformation of arbitrary functionally graded multilayered multiferroic composites plates with weakly and highly conducting imperfect interfaces

In this paper, a three-dimensional static deformation of arbitrary functionally graded multilayered multiferroic composites plates with weakly and highly conducting imperfect interfaces is derived. The magnetoelectroelastic properties of each layer of the composite plates have been assumed varying throughout the thickness direction. The imperfect interfaces between the layers are assumed to be mechanically compliant, dielectrically and magnetically weakly or highly conducting. In each layer, the state-space approach is firstly applied leading to space variable. Cauchy’s problem and adapted Runge-Kutta numerical procedure is used to solve the established state-space equation. The elaborated semi-analytical solution has been propagated throughout the multilayered multiferroic composites plates using the propagator matrix method and accounting the transfers matrices at each imperfect interface. The developed formulas have been programmed and the numerical obtained results have been well compared with available ones. For the computation process, the piezoelectric material [Formula: see text] and piezomagnetic material [Formula: see text] are used. In addition, these numerical tests showed that the proposed solution is in good agreement with the available 3D asymptotic approach, the modified Pagano method, the pseudo-Stroh formalism, the finite elements method and the Peano series solution. Furthermore, the effects of mechanically compliant, dielectrically and magnetically weakly or highly conducting imperfect interface on the static response and the magnetoelectric coupling coefficient of the functionally graded multilayered multiferroic composites plates for various configurations have been also analyzed. It has been carried out that, the bending response and the magnetoelectric coupling coefficient of the multiferroic composites plates remarkably depend on the kind of imperfect interface, the used sequences as well as on the loadings conditions namely mechanical, electric or magnetic, respectively.