The Effect of the Elastic Compliance of Actuator Components on the Dynamics of a Robot

Kinematic and dynamic control problems for a pedestal-mounted robot with a multilink arm are formulated. The robot is considered a system of perfectly rigid bodies controlled by a combined actuating system. The mathematical model of robot dynamics accounts for the elastic properties of actuator components based on the formalism of Lagrange equations of the second kind. The effect of the elastic compliance of the actuator components on the dynamics of manipulator links and actuator motors is discussed. A robot with a two-link arm is considered as an example     

光刻投影物镜光学元件运动学支撑结构的设计与分析

为了实现曝光工作过程中深紫外投影光刻物镜的动态稳定性,设计了一种能够消除温度和应变影响的光学元件运动学支撑结构,研究了如何利用该支撑结构消除温度变化和外界应变对光学元件面形的影响。首先,计算单个支座的径向柔度,并与有限元分析结果进行比较。然后,分析在不同温度载荷和外界应变工况下光学元件上、下表面面形的变化,并与三点胶粘固定支撑方式下的结果进行了比较。计算结果表明：通过理论公式推导的支座径向柔度与仿真结果的误差绝对值小于2．2％;温度升高0．1℃时光学元件上下表面面形RMS值小于0．36nm;平面度公差5μm时面形RMS值小于0．05nm。与三点胶粘固定方式相比,运动学支撑方式能够有效消除温度变化和外界应变对光学元件表面面形的影响．     

Spectral decomposition of the compliance fourth-rank tensor for orthotropic materials

Summary The compliance tensor related to orthotropic media is spectrally decomposed and its characteristic values are determined. Further, its idempotent tensors are estimated, giving rise to energy orthogonal states of stress and strain, thus decomposing the elastic potential in discrete elements. It is proven that the essential parameters, required for a complete characterisation of the elastic properties of an orthotropic medium, are the six eigenvalues of the compliance tensor, together with a set of three dimensionless parameters, the eigenangles θ, ϕ and ω. In addition, the intervals of variation of these eigenangles with respect to different values of the elastic constants are presented. Furthermore, bounds on Poisson's ratios are obtained by imposing the thermodynamical constraint on the eigenvalues to be strictly positive, as specified from the positive-definite character of the elastic potential. Finally, the conditions are investigated under which a family of orthotropic media behaves like a transversely isotropic or an isotropic one. Received 5 January 1999; accepted for publication 22 June 1999     

Creep behavior of amorphous ethylene–styrene interpolymers in the glass transition region

The viscoelastic behavior of amorphous ethylene–styrene interpolymers (ESIs) was studied in the glass transition region. The creep behavior at temperatures from 15°C below the glass transition temperature (T_g) to T_g was determined for three amorphous ESIs. These three copolymers with 62, 69, and 72 wt % styrene had glass transition temperatures of 11, 23, and 33°C, respectively, as determined by DMTA at 1 Hz. Time–temperature superposition master curves were constructed from creep curves for each polymer. The temperature dependence of the shift factors was well described by the WLF equation. Using the T_g determined by DMTA at 1 Hz as a reference temperature, C₁ and C₂ constants for the Williams, Landel, and Ferry (WLF) equation were calculated as approximately 7 and 40 K, respectively. The master curves were used to obtain the retardation time spectrum and the plateau compliance. The entanglement molecular weight obtained from the plateau compliance increased with increasing styrene content as 1,600, 1,870, and 2,040, respectively. The entanglement molecular weight of the ESIs was much closer to that of polyethylene (1,390) than to that of polystyrene (18,700); this was attributed to the unique chain microstructure of these ESIs with no styrene–styrene dyads. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 2373–2382, 1999     

仪器柔度标定误差对两种压入测试方法的精度影响

针对目前最具代表性的两种压入测试方法:Oliver-Pharr方法和Ma方法,通过有限元数值模拟分析了仪器柔度标定误差对测试精度的影响.结果表明仪器柔度的标定精度直接影响压入测试结果的准确度,尤其是当材料较软且压入深度较大时更为显著;对同一材料,压入载荷越大,由仪器柔度标定误差引入的压入测试结果误差越大;在同一压入深度下,针对不同材料,由仪器柔度标定误差引入的压入测试结果误差差别不大;就测试方法而言,Ma方法具有比Oliver-Pharr方法更高的精度和更低的仪器柔度敏感性.     

Mathematical and numerical approaches to a one-dimensional dynamic thermoviscoelastic contact problem

In this paper, we propose numerical schemes for solving a nonlinear system which consists of a coupled partial differential equations and two conditions, called normal compliance contact condition and Barber’s heat exchange condition. The convergence of numerical trajectories is shown by using a time discretization and passing the limit of the time step size. The uniqueness of the weak solution is proved as well. We derive the extensive form of an energy balance which will be a criterion to examine numerical stability. An example is provided to present and discuss numerical results.     

The study of the dynamic contact in ultrasonic motor

In this paper, we consider a mathematical model which describes the dynamic contact between an elastic body and an obstacle. The process is assumed to be dynamic and the contact is modeled with the normal compliance. We present a variational formulation of the problem and prove the existence and the uniqueness of a weak solution. An efficient numerical method is presented to analyze this dynamic contact. This approach exploits the augmented Lagrangian concept and a special time integration algorithm. This is exploited to study the dynamic contact between the rotor and the stator inside an ultrasonic motor SHINSEI USR 60. Numerical results are presented and show the interest of this method to forecast the origin of the principal failure mode of this motor.     

Discontinuous Galerkin Methods for Solving a Frictional Contact Problem with Normal Compliance

Abstract

Several discontinuous Galerkin (DG) methods are introduced for solving a frictional contact problem with normal compliance, which is modeled as a quasi-variational inequality. Consistency, boundedness, and stability are established for the DG methods. Two numerical examples are presented to illustrate the performance of the DG methods.