外文翻译模板.doc

本科毕业设计（论文）外文翻译题 目 插座面板注塑模具设计 姓 名 陈小勇 专 业 机械设计制造及其自动化学 号 201233467 指导教师 李玉龙 郑州科技学院机械工程学院二一六年三月参数化建模滚珠丝杠主轴达塔拉米莫塔格罗光费尔摘 要产品开发过程的数值优化可以成功地应用于产品设计的早期阶段。在滚珠丝杠驱动器很常见的情况下，动态现象大多数根据滚珠丝杠本身的几何形状而定。轴向和扭转刚度相同的丝杠，最大速度和加速度不仅取决于伺服电机，也取决于丝杆直径，凹槽斜率和球半径。此外联轴器的设计参数影响使优化变得更加困难。为了捕捉这些影响，有效的数据（通常是有限元或MBS）模型是必要的。在这项工作中，一个新的更准确和有效的计算滚珠丝杠主轴轴向和扭转刚度被提出。我们分析得到描绘的丝杠几何参数对大多数刚度的依赖关系的参数方程。此外，我们增加一个确定函数的分析模型，从而提高了准确性。在许多例子帮助下，所提出的分析模型针对有限元模型和目录数据进行了验证。1 绪论滚珠丝杠主轴的轴向和扭转刚度中对滚珠丝杠驱动器动态特性起着重要作用，因为它基本上决定了滚珠丝杠驱动器的第一个和第二个特征值。当用有限元建模时，滚珠丝杠驱动器的螺纹通常被忽略并且一些平均直径被用来建立简化的滚珠丝杆模型。因此，关键是得到最接近的平均直径。在大多数关于前人建模与仿真下，滚珠丝杆传动建模集中在滚珠丝刚螺母和滚珠丝杠主轴部件。 Jarosch比较了不同类型的滚珠丝杠，但考虑到主轴简化为圆柱体，直径等于主轴外径，从而忽视了削减主轴螺纹。随着了解的实际轴向和单位长度的螺杆扭转刚度，平均直径可以被计算为 （1） （2）杨氏模量和剪切模量分别为E和G。平均直径总是比主轴外径小。对于每个刚度我们得到两个不同的平均直径。这取决于每个应用的平均直径的最好选择。这两个直径也可以做到线性组合。一般滚珠丝杠制造商提供轴向刚度数据，但没有扭转刚度。基于这个原因我们使用有限元法（FEM）来计算两者滚珠丝杠主轴轴向和扭转刚度。使用完全参数化的有限元计算模型，我们也可以不用滚珠丝杠主轴刚度。此外，由于参数范围是不离散的，我们可以结合使用滚珠丝杠驱动器参数优化模型。这种方法的困难是如何有效地计算轴向和扭转刚度。有些作品提供了计算扭曲梁的性能计算方法，但只适用于抗弯刚度或弯曲特征频率，它的作用对滚珠丝杠驱动器是不太重要的。2 详细的参数化有限元模型图1是我们描述的三维滚珠丝杠生成方法。在有限元软件ANSYS宏的帮助下，这个过程是全自动的。我们的滚珠丝杠几何模型是参数化的，因此可以生成任意几何形状。这几何模型描述是以下六个参数：主轴直径d1，主轴直径d2，滚珠槽半径Rs，主轴间距Ph，主轴长度Ls和螺纹nT的数量。由于生产商不提供滚珠槽半径的数据，但提供滚珠直径Dw，我们使用了振荡确定滚珠槽半径的关系：.这样的计算模型刚度可以非常准确的，但也很昂贵。为了减少自由度数提高精度，我们划分滚珠丝杠在核心筒（0.9d2）和带螺纹圆柱。建成线性，弹性和杨氏的弹性模量与泊松比=0.3的模型。图.1滚珠丝杠主轴建模与ANSYS为了计算滚珠丝杠轴向和扭转刚度，我们需要滚珠丝杠的轴向力和扭矩一个滚珠丝杠应用在两个不同的静态载荷步。滚珠丝杠的另一端必须在同一方向的限制，以防止刚体运动。同时滚珠丝杠两端应该能够在径向方向自由地转动。表面上制约两个单一节点（TARGE170元素），我们运用这些制约因素和力。制约和节点力分布在滚珠丝杠的一端，只有轴向和切向方向（CONTA174）通过接触节点，见图.2。3 目录数据比较为了验证我们的模型，我们产生的40种不同的Bosch-Rexroth滚珠丝杠主轴的模型。轴向刚度仿真结果与由Bosch-Rexroth提供的目录资料相比，提供了数据。作为对比的基准，我们使用的轴向刚度的分析方程，DINISO3408-4符合，主轴长度为： （3）公称直径d0、滚珠和滚珠凹槽之间的接触角。分析数值和产品目录显示，没有依赖主轴螺距。但是，主轴螺距确定了有限元模型。此外，如果我们区分产品目录和分析数值之间有限元和分析数值之间的偏差，我们可以看到产品目录的数据显示的最小的偏差。这可以解释产品目录值仅仅是圆形的分析值。图.2应用约束和滚珠丝杠轴轴向力4 滚珠丝杠分析模型 我们计划推出一滚珠丝杠传动的分析模型，捕捉螺纹的作用。拥有一个精确的分析方法来计算滚珠丝杠刚度的分析方程，并且优先考虑有效率的参数模型，而不是有限元模型，因为那需要大量的迭代。4.1 主要思想对于一个无扭曲统一长度的等截面A和惯性力矩I的主轴，轴向和扭转刚度的分析方程为： （4） （5）横截面面积为A，极惯性矩为I。滚珠丝杠有固定截面，这截面沿着滚珠丝杠螺纹角为，根据纵坐标Z和主轴间距Ph0确定： . （6）螺纹数量的影响丝杠的刚度。在我们的分析方法中，我们假设丝杠轴径A和扭转刚度I正比和，并且和Ph0相乘： （7） （8）从公式7和8我们可以看出，我们分析推导滚珠丝杠主轴的刚度的两个步骤：- 分析推导A和I- 数值计算确定f（Ph0）4.2 分析推导截面特性滚珠丝杠螺纹横截面面积的范围为： （9）另一条曲线（钟形曲线图.3）的形状取决于参数 d2，Rs和Ph0。在我们的推导中，我们认为在大多数情况下，螺纹的轮廓用哥特式形状。这种简化只导致滚珠丝杠刚度的小偏差。为了得到一个钟形解析函数，在图.3中我们削减扭曲的圆柱体。图.3确定滚珠丝杠横截面积曲线平面垂直于丝杠的纵向轴。忽略了扭曲的圆柱体曲率我们就可以简化，并且生成的段可近似于椭圆形： （10）螺纹斜率Ap： （11）切割曲线的结果由切割直线Y0=0切割椭圆得到： （12）表示为： （13）我们简化公式12： （14）为了计算丝杠横截面面积，我们需要圆（9）和钟形曲线（14）的交点（r0| U0）。由于交叉点是在圆内，很明显， （15）角等于（9）和（14）： （16）丝杠截面面积可分为Ac和Ak区域，如图.4。Ac包括一个涵盖角2()的圆形机构，这样我们得到： （17）由曲线（14）包涵在0和U0之间（由于相对于X轴对称）可以计算AK区域： （18）经过一番计算，我们得到： （19）第一和第二积分可以很容易地使用标准的积分公式计算。第三个积分较为复杂，所以我们用数学符号求解： （20） 图.4包围的丝杠截面面积使用公式19和20，我们得到AK： （21）类似于横截面积，我们划分极惯性矩在两附加的部分：Ic和Ik区域。第一部分是圆的转动惯量： （22）对其余区域Ak 转动惯量，可以计算为： （23）公式24类似18它可以得出同一组的其他公式19和20。经过一番计算，我们得到的极惯性矩： （24）我们比较公式，得到22和25横截面的所有的参数设置数值计算值。提出了错误的百分比，如图. 5。对于最大的错误在于以下0.16，这是微不足道的，而我的最大错误是较高的，但仍低于0.52。4.3 主轴间距因素对于一个给定d1，d2，rs和NT的滚珠丝杆，螺距影响的刚度可以分为两类：截面的影响和扭转量的影响。截面的解析表示为公式22和25。扭曲影响的正式表达Ph0通过公式7和8得到。函数f（Ph0）是未知的但我们期望的特定值f（0）=1和f（）= 1转换为无螺距的影响，而对一些螺距的中间点的影响将达到最大。Fisher分布符合这些条件的最小的参数。鉴于这些考虑，我们提出以下螺距函数： （25）图.5 解析和数值计算滚珠丝杠第一部分计算面积A和极惯性I的误差百分比这类似于Fisher的分布。这个函数的主要缺点是系数的M，N，A和B是在转弯的最高点Ph0max|fmax。我们给予不同的10和300d1的螺距。在参数化有限元模型中，我们可以计算出f（Ph0）的不同值，如图. 6。有限元计算结果得出了最相近的，反过来又得到M，N的系数a和b的值： （26）图6 间距影响函数和其数值拟和我们使用曲线拟合来确定m，n。得到的最佳拟合为m = 297.89, n= 299.32, a = 0.10 and b =-0.09，见图.6。间距的识别方法提供了两个参数的良好效果，但效率不高，因为它需要大量的有限元模型。5 结论随着拟定分析方法的帮助，滚珠丝杠驱动器的刚度计算变得比其他的标准方法更有效率，如有限元法或简单的目录数据。实际上，我们引入分析函数作为一个Matlab功能。这个函数会得到丝杠的几何和材料的数据作为参数，并计算在忽略不计滚珠丝杠轴向和扭转刚度的情况下，比其他已知分析方法具有更高的精度。首次我们知道滚珠丝杠扭转刚度的精确信息，这普遍被生产厂家普遍忽视。在一个机床工具模型中（通常梁单元），计算的刚度可以被用来生成简单而有效的滚珠丝杠有限元模型，从而提高有限元模型的整体效率。但是解析的主轴间距因素仍然可以捕捉改进，使获得更广泛的参数范围也是有可能的。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 Youngs 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 Youngs 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 constraints and forces with the help of surface based constraints on two single pilot nodes (TARGE170). The constraints and forces of the pilot nodes are distributed to the end areas of the ball screw through contact nodes (CONTA174) only in axial and tangential direction, see Fig. 2.3 .Comparison with catalog dataIn order to validate our model we generated 40 different models of Bosch-Rexroth screw spindles. The simulation results of the axial stiffness can be compared with catalog data which is provided by Bosch-Rexroth. As a reference for the comparison we use the analytical equation for axial stiffness, which can be found in DIN ISO 3408-4, for unity length spindle: (3)with d0 nominal diameter and a contact angle between ball and ball groove. Both analytical values and catalog values shows, other as expected, no dependence on the spindle pitch. But the influence of spindle pitch is confirmed by the FE simulation. Furthermore if we concentrate on the percental deviation between catalog and analytical values and between FEM and analytical values respectively, we can see that the catalog data show the smallest deviation. This could be explained by the fact, that the catalog values are just rounded analytical values.Fig. 2 Applying constraints and forces to the ball screw spindle4. Analytical model of ball screwsIn our approach we intend to derive an analytical model of the ball screw drive, capable of capturing theweakening effect of the thread. Having an accurate analytical method to compute the stiffness of ball screws also have a practical application in optimization, where efficient parameter models are preferred instead of FiniteElement models due to the large amount of iterations needed.4.1 Main ideaFor an untwisted volume of length of unity with constant cross section A and polar moment of inertia I, the axial and torsion stiffness can be computed by （4）and （5）respectively, A cross section area and I polar moment of inertia. Ball screws do have constant cross section but this cross section is twisted along the screw with angle u which is depending on the longitudinal coordinate z and the spindle pitch Ph0 : . （6）The amount of twist influence the stiffness of the screw . In our analytical approach we suppose that the axial and torsional stiffness of the screw is proportional to the A and I, respectively, whereas the influence of the twist is a multiplying function of Ph0 : （7） and （8）From Eqs. 7 and 8 we can see, that we can divide the analytical derivation of ball screw spindle stiffness in two steps: analytical derivation of A and I numerical identification of f(Ph0)4.2 Analytical derivation of cross section propertiesFor a one threaded screw the cross section area is bounded by the circle （9）and by another curve (bell shaped curve in Fig. 3, which shape depends on the parameters d2, rs, and Ph0 . In our derivation we consider a round thread profile although today in most cases a gothic profile is used. This simplification should only induce a small deviation to the true stiffness of ball screws. To get an analytical function for the bell shaped curve in Fig. 3 we cut the twisted cylinder in Fig.Fig. 3 Delimiting curves of the ball screw cross section areaWith a plane perpendicular to the longitudinal axis of the screw. Ignoring the curvature of the twisted cylinder we can simplify the problem and the resulting section can be approximated by an ellipse: （10）with ap the thread slope: （11）The cutting curve results by cutting the ellipse (10) with the line y0 = 0: （12）With the notations （13）we simplify Eq. 12 to （14）To compute the cross section area of the screw we need the intersection point (r0|u0) of the circle (9) and the bell shaped curve (14). Since the intersection point is lying on the circle it is obvious that （15）The angle results by equating (9) with (14): （16）The cross section area of the screw can be divided into area Ac and AK, like in Fig. 4. Area AC is a circle sector of spanning angle 2(p-u0) so we get: （17）Area AK can be computed by direct integration of the curve (14) between 0 and u0 (due to symmetry with respect to the x axis): （18）After some calculations we get: （19）The first and second integral can be easily calculated using standard integration formulas. The third integral is more complicated and we compute it with a symbolic mathematic solver: （20）Fig. 4 Bounding of the cross section area of screw spindleUsing Eqs. 19 and 20 we get for Ak: （21）Analogous to the cross section area we divide the polar moment of inertia in two additive parts: area IC and IK. The first part is the moment of inertia of the circle sector: （22）The moment of inertia of the remaining area Ak can be computed with （23）Equation 24 is similar to Eq. 18 and it can be solved with the same set of additional Eqs. 19 and 20. After some calculations we get for the polar moment of inertia （24）We compared Eqs. 22 and 25 with the numerically computed values for the cross sections of all the parameter sets. The percental error is presented in Fig. 5. The maximal error for A lies below 0.16%, which is negligible, whereas the maximum error for I is higher but still below 0.52%.4.3 Spindle pitch influenceThe pitch influence on stiffness for a given ball screw of fixed d1, d2, rs and nT can be divided in two categories: influence of the cross section and influence of the amount of twist. The influence of the cross section is expressed analytically by Eqs 22 and 25. The influence of twist is formally expressed by the function f（Ph0） in Eqs 7 and 8. The function f Ph0 is unknown but we expect the particular values f(0) = 1 and f() = 1, which translates to no pitch influence, whereas for some intermediate value of pitch the influence will reach a maximum. The Fisher distribution fulfills these conditions with an minimum of parameters, 10. In light of these considerations we propose the following pitch influence function: （25）Fig. 5 Percental deviation between analytically and numerically computed area A and polar moment of inertia I of ball screw sectionwhich is similar to the Fisher distribution. The main disadvantage of this function is that the coefficients m, n, a and b are in turn unknown functions of the maximum point Ph0 max|fmax. We varied the pitch between 10% and 300% of d