参数化建模滚珠丝杠主轴外文文献翻译、中英文翻译、外文翻译.doc

Parametric modeling of ball screw spindlesA. Dadalau • M. Mottahedi • K. Groh •A. VerlAbstract In the product development process numerical optimization can successfully be applied in the early product design stages. In the very common case of ball screw drives, the dynamical behavior is most depending on the geometrical shape of the ball screw itself. Properties like axial and torsional stiffness, moment of inertia, maximum velocity and acceleration are determined not only by the servo motor but also by screw diameter, slope and ball groove radius. Furthermore coupling effects between the design variables make the optimization task even more difficult. In order to capture these effects, efficient numerical (usually FEM or MBS) models are needed. In this work ，a new more accurate and efficient method of computing the axial and torsional stiffness of ball screw spindles is presented. We analytically derive parametric equations which depicts most of the dependencies of stiffness on geometrical parameters of the screw. Furthermore, we enhance the analytical model with an identified function, which increase the accuracy even more. The presented analytical model is validated against FEM model and catalog data with the help of numerous examples.1.IntroductionThe axial and torsional stiffness of ball screw spindles plays an important role in the dynamic behavior of ball screw drives, since it essentially determine the first and second eigenvalues of ball screw drives. When modeling ball screw drives with FEM the thread is usually ignored and some mean diameter is used to model a simplified ball screw. Therefore it is crucial to have knowledge about the best approximating mean diameter. Most of the previous work on modeling and simulating stiffness of ball screw drives concentrate on modeling the assembly between ball screw nut and ball screw spindle, which implies high accuracy modeling of contact. In Jarosch compares theoretical stiffness of different types of ball screws, but the spindle is taken into account simplified as an cylinder with diameter equal to the spindle outer diameter, thus ignoring the stiffness weakening due to spindle thread. With knowledge about the real axial kuz and torsional kuz stiffness of a screw of unit length, a mean diameter can be computed with the help of （1）and （2)Respectively, E Young’s modulus and G shear modulus. The mean diameter is always less than the spindle outer diameter. For each stiffness we get two different mean diameters. It depends on each application which mean diameter is the best to choose. A linear combination of the two diameters could also be done. In general ball screw manufacturers provide data for axial stiffness but not for torsional stiffness. For this reason we use the Finite Element Method (FEM) to compute both axial and torsional stiffness of ball screw spindles. By using a fully parameterized FE model we can also compute stiffness for not existing ball screw spindles. Furthermore since the parameter range is not discretized, we can use the model in conjunction with parameter optimization of ball screw drives. The difficulty here is how to efficiently compute the axial and torsional stiffness. Some works provide methods for computing properties of twisted beams but only for the bending stiffness or the bending eigenfrequencies , which role is less important in ball screw drives.2 Detailed parametric FE modelDepicts our generation method of 3D ball screw. The process is fully automated with the help of macros in the Finite Element software ANSYS. The geometry of our ball screw model is parametric, so arbitrarily geometries can be generated. The geometry is described by the following six parameters: spindle diameter d1, spindle core diameter d2, ball groove radius rs, spindle pitch Ph, spindle length Ls and number of threads nT. Since manufacturers does not provide data of the ball groove radius, but for the ball diameter Dw instead, we use the relationship for the oscillation to determine the ball groove radius:.Computing the stiffness with such a model can be very exact but also very time expensive. In order to minimize the number of degrees of freedom by maximizing the accuracy we divide the ball screw in a core cylinder (0.9d2) and threaded cylinder. The material is modeled as linear, elastic and isotropic with an Young’s modulus and a Poisson ratio v = 0.3.Fig. 1 Modeling of ball screw spindles with ANSYSIn order to compute the axial and torsional stiffness of the ball screw, we need to apply an axial force and a torsional moment to one ball screw end in two different statically load steps. The other end of the ball screw has to be constrained in the same directions in order to prevent rigid body motion. At the same time both end areas of the ball screw should be able to freely expand or contract in radial direction. We apply these c。