变速器壳体拓扑优化设计分析

介绍了变速器壳体设计的一般原则,简述了结构拓扑优化设计技术的基本功能,以实际开发项目中的变速器壳体技术设计为例,介绍了变速器设计的基本要求,提供了变速器壳体设计的一些经验数据,并阐述了壳体材料的选择和结构的工艺性.采用有限元分析方法,对变速器壳体进行拓扑优化分析,通过不同的拓扑优化方法,分析了先进设计方法的实现方式,为实现变速器合理优化设计提供了依据.     

NEW HMM ALGORITHM FOR TOPOLOGY OPTIMIZATION

0 INTRODUCTIONTwo types of algorithms are currently widely used instructure optimization. The first one is the optimization criteria(OC) method. The OC method can be understood directly, but it isdifficult to deduce different types of optimization criteri…     

拓扑优化方法在产品设计中的应用探索

许多工程活动中,都会遇到零件的形状和性能之间的关系.所要解决的基本问题比较典型:如果给定了零件的大致外形以及零件与周围环境的分界面,那么产品的最优形状是什么.这项任务就是拓扑优化.借助于ANSYS软件对载重汽车车架进行结构优化设计,这对拓扑优化设计理论在产品设计中的应用是一种尝试.     

电容式微加速度传感器微结构的拓扑优化

采用均匀化方法,以电容式微加速度传感器微结构的第一阶谐振频率为目标函数,以微结构的体积作为约束条件,建立了微结构的拓扑优化模型,对叉指式微加速度传感器微结构进行了拓扑优化设计,经计算获得满足体积约束并使第一阶谐振频率最大的微结构拓扑形式。计算结果表明该方法可以很好地解决微加速度传感器灵敏度和谐振频率这一对矛盾,在满足灵敏度的要求下提高微加速度传感器的测量范围上限,不失为一种先进的、有效的电容式微加速度传感器微结构的设计方法。     

Study of key algorithms in topology optimization

The theory of topology optimization based on the solid isotropic material with penalization model (SIMP) method is thoroughly analyzed in this paper. In order to solve complicated topology optimization problems, a hybrid solution algorithm based on the method of moving asymptotes (MMA) approach and the globally convergent version of the method of moving asymptotes (GCMMA) approach is proposed. The numerical instability, which always leads to a non-manufacturing result in topology optimization, is analyzed, along with current methods to control it. To eliminate the numerical instability of topology results, a convolution integral factor method is introduced. Meanwhile, an iteration procedure based on the hybrid solution algorithm and a method to eliminate numerical instability are developed. The proposed algorithms are verified with illustrative examples. The effect and function of the hybrid solution algorithm and the convolution radius in optimization are also discussed.     

Magnetic circuit design by topology optimization for Lorentz force maximization in a microspeaker

Bipolar magnets are common in most magnetic circuits, but circuit efficiency can be enhanced if multipolar magnets are used instead. However, the use of multipolar magnets is rare. In this investigation, the possibility of using multipolar magnets for maximizing the Lorentz force in a microspeaker is considered. The design problem of a multipolar magnetic circuit is formulated as a topology optimization problem. The circuit design region is discretized by finite elements, and a material state among a multipolar magnet, a yoke and air for every element is so determined as to maximize a desired Lorentz force component. Numerical results show that multipolar magnetic circuits obtained by the topology optimization outperform a conventional bipolar circuit.     

Crashworthiness design and evaluation on the leading-cab structure of rolling stock using topology optimization

The leading cab of the rolling stock receives the greatest impact when frontal crashes occur. It has a complex structure due to the concentrated loads it must resist, and a need exists to enhance its performance while minimizing the weight of the cab. Therefore, during the design phase, the optimal material arrangement to enhance structural capacity should be sought. Here, topology optimization is applied to the design of a protective shell frame to enhance crash energy absorption. The design performance during a crash is then compared with the original shell frame design. The crash analysis of this research is performed using a finite element model consisting of an optimized/initial protective shell frame. The frame is tested in an accident scenario (crash at 110 km/h against a movable rigid mass of 15 ton). The results of the crash analysis validate the use of topology optimization in the conceptual design phase.     

基于拓扑优化的加工中心十字滑台结构设计

基于零件结构静态和动态性能及轻量化的总体设计目标,利用结构拓扑优化方法完成了立式加工中心十字滑台的结构设计,解决了零件结构静、动刚度不足问题及质量过重导致的机床加速性能不良等问题。首先,详细分析了十字滑台的工况。其次,针对同时满足十字滑台具有良好的静动态性能并减轻其质量的设计需求,采用结构的柔度最小和基频最大为目标函数以及体积比为约束的多目标、多工况的结构拓扑优化方法,进行了十字滑台的结构拓扑优化设计,获得了其结构构型。最后,分析并对比了十字滑台新结构和原有结构的刚度、固有频率、质量及机床加速性能,验证了新结构具有良好的性能。     

Isogeometric topology optimization based on energy penalization for symmetric structure

We present an energy penalization method for isogeometric topology optimization using moving morphable components (ITO–MMC), propose an ITO–MMC with an additional bilateral or periodic symmetric constraint for symmetric structures, and then extend the proposed energy penalization method to an ITO–MMC with a symmetric constraint. The energy penalization method can solve the problems of numerical instability and convergence for the ITO–MMC and the ITO–MMC subjected to the structural symmetric constraint with asymmetric loads. Topology optimization problems of asymmetric, bilateral symmetric, and periodic symmetric structures are discussed to validate the effectiveness of the proposed energy penalization approach. Compared with the conventional ITO–MMC, the energy penalization method for the ITO–MMC can improve the convergence rate from 18.6% to 44.5% for the optimization of the asymmetric structure. For the ITO–MMC under a bilateral symmetric constraint, the proposed method can reduce the objective value by 5.6% and obtain a final optimized topology that has a clear boundary with decreased iterations. For the ITO–MMC under a periodic symmetric constraint, the proposed energy penalization method can dramatically reduce the number of iterations and obtain a speedup of more than 2.     

拓扑和形状集成优化设计

将拓扑优化、形状优化、有限元分析和计算机辅助设计加以有机集成,构建了优化设计模型;利用几何重构技术,拟合拓扑优化后的边界;在形状优化中,将设计变量定义为B样条曲线或曲面的控制顶点的运动,建立了边界节点移动速度场计算方法,有效地控制节点的运动,给出了相应的算法和计算表达式,寻求较快的搜索方向,以合理速度分布使形状变为最佳.通过设计实例,证明了文中模型的合理性和方法的有效性.     

具有应力和厚度约束的平面弹性体结构拓扑优化设计

研究了具有应力和厚度约束的弹性平面体结构拓扑优化问题。这类问题不同于一般意义的拓扑优化问题 ,其优化结果不仅得到最优拓扑 ,而且得到最优形状和尺寸。建立了这类问题的数学模型 ,给出了求解策略 ,算例表明算法是有效的     

Topology optimization of compressor bracket

Topology optimization is very useful engineering technique especially at the concept design stage. It is common habit to design depending on the designer’s experience at the early stage of product development. Structural analysis methodology of compressor bracket was verified on the static and dynamic loading condition with 2 bracket samples for the topology optimization base model. Topology optimization is able to produce reliable and satisfactory results with the verified structural model. Base bracket model for the topology optimization was modeled considering the interference with the adjacent vehicle parts. Objective function was to minimize combined compliance and the constraint was the first natural frequency over 250 Hz. Multiple load cases such as normal mode calculation and gravity load conditions with 3-axis direction were also applied for the optimization, expecting an even stress distribution and vibration durability performance. Commercial structural optimization code such as optistruct of Altair Engineering was used for the structural topology optimization. Optimization was converged after 14 iterations with the satisfaction of natural frequency constraint. New bracket shape was produced with the CATIA based on the topology optimization result. The new bracket from topology optimization result was compared with the traditional concept model and topology optimization base model under 4 load cases. 14 % 1’st natural frequency of new bracket with only 4 % mass increment increased compared to the concept model. 31 % mass decreased compared to the base model without the increment of stress under gravity load cases. It was analyzed thata new bracket would not fail during a vibration durability test, and these results were verified with a fabricated real sample under the durability condition.     

集装箱吊架结构优化设计

采用拓扑优化、形状优化和尺寸优化对集装箱吊架进行优化设计。首先利用基于变密度法的拓扑优化,以柔度最小为优化目标,体积分数作为约束条件,得到设计空间内最优的材料分布路径。然后根据得到的拓扑结构重新设计,并在局部再一次进行拓扑优化,改善局部的拓扑结构。利用最终得到的吊架的拓扑结构建立新的有限元模型,综合运用形状优化和尺寸优化;以质量最小为优化目标,吊架的刚度和强度为约束条件,实现吊架的减重。通过综合三种优化方法,不仅提高了吊架的性能,而且大大降低了吊架的质量。     

The role of S-Shape mapping functions in the SIMP approach for topology optimization

The SIMP (solid isotropic material with penalization) approach is perhaps the most popular density variable relaxation method in topology optimization. This method has been very successful in many applications, but the optimization solution convergence can be improved when new variables, not the direct density variables, are used as the design variables. In this work, we newly propose S-shape functions mapping the original density variables nonlinearly to new design variables. The main role of S-shape function is to push intermediate densities to either lower or upper bounds. In particular, this method works well with nonlinear mathematical programming methods. A method of feasible directions is chosen as a nonlinear mathematical programming method in order to show the effects of the S-shape scaling function on the solution convergence.     

智能寻位加工技术中一种新的寻位方法

智能寻位加工中的关键技术是工件寻位。文章对现有的工件寻位方法进行了分析,指出了它们的优缺点,并在此基础上提出了一种适合常规工件寻位的新方法,实验证明这种方法简洁实用,能够应用到寻位加工系统中去,实现常规工件的敏感制造。     

Multiple stiffness topology optimizations of continuum structures

This paper presents a new multi-objective topology optimization algorithm for continuum structures under multiple loading cases. An expert evaluation method of weights based on grey system theory is proposed to calculate the objective weights when the compromise programming approach is employed as a multi-objective optimization scheme converting the multi-objective problem to a single objective problem. A modified updating scheme with a self-adaptive move limit for design variables is also suggested, SIMP is regarded as density-stiffness interpolation scheme and the optimality criteria method is used as the optimizer. Numerical instabilities, such as checkerboards and mesh dependencies, are also discussed. The validities of these methods in this paper are demonstrated by some numerical applications.     

Independent continuous and mapping method of structural topology optimization based on the global stress approach

There are three difficulties in topology optimization of continuum structures. 1) The topology under multiple load case is more difficult to be optimized than under single load case, because the former becomes a multiple objective based on compliance objective functions. 2) With local constraints, such as an elemental stress limit, the topology is more difficult to be solved than with global constraints, such as the displacement or frequency limits, because the sensitivity analysis of the former has very expensive computation. 3) With the phenomenon of load illness, which is similar with stiffness illness in the structural analysis, it is not easy to get the reasonable final topological structure, because it is difficult to consider different influences between the loads with small forces and big forces, and some topology paths of transferring small forces may disappear during the iteration process. To overcome difficulties above, four measures are adopted. 1) Topology optimization model is established by independent continuous mapping (ICM) method. 2) Based on the von Mises strength theory, all elements’ stress constraints are transformed into a structural energy constraint. 3) The phenomenon of load illness is divided to classify into three cases. 4) A strategy based on strain energy is proposed to adopt ICM method with stress globalization, and the problems of the above mentioned three cases of load illness are solved in terms of different complementary approaches. Several numerical examples show that the topology path of transferring forces can be obtained more easily by substituting global strain energy constraints for local stresses constraints, and the problem of load illness can be solved well by the weighting method that takes the structural energy as a weighting coefficient.     

汽车车架的结构优化设计

这里以有限元结构分析和优化算法相结合为手段，以某型载货车车架为例，先对车架进行拓扑优化获得车架最优拓扑形式，根据车架最优拓扑形式确定横梁的数量及分布位置和纵梁的加强方式，得到车架的概念化设计。然后对横梁和纵梁的截面尺寸进行优化，建立了车架的力学模型，优化参数模型，优化数学模型，有限元模型，采用ANSYS参数化设计语言编制了优化设计程序，用ANSYS软件中的零阶优化方法获得最优设计，计算结果表明该优化设计方法的有效和高效，给出了汽车车架的计算机辅助优化设计的有效方法，该方法可广泛应用于车架的优化设计工程。     

基于进化元胞自动机的结构拓扑优化

实现元胞自动机算法自组织演化机制的关键是建立适合问题的局部规则。传统的方法是根据人们的经验或 其他算法得到的结果来建立局部规则,被称为局部间接规则。为了解决局部间接规则存在的局限性,计算量大等 缺点,提出用进化建立元胞自动机局部直接规则的方法。通过建立结构优化的多目标优化模型,用遗传算法寻求 最优的演化规则,得到适应相应问题的解。由仿真结果可见用遗传算法建立的元胞自动机局部直接规则对复杂系 统的自组织问题是很有效的。     

2MW风力发电机轮毂优化设计

优化设计是一种为了让自己的设计材料最省、支出最小的一种技术。通常,在设计中,会有许多的设计方案以供选择,如何从众多的方案中选择一个最好的方案,就需要有较好的设计方法。优化设计的方法有很多,而拓扑优化又称结构布局优化,是一种根据优化目标、载荷及约束而寻求结构材料最佳分配的优化方法。针对2MW风力发电机轮毂进行了拓扑优化,对比分析了优化前后轮毂的质量、及联合工况下的应力和变形,结果表明,联合工况下的应力及变形减小,动态应力最大值减小,动态强度提高;并在三维软件中重建模型,验证优化后模型进行工程实践的可行性。