摘要
轿车车身的尺寸偏差直接影响到整车外观、行驶风噪声、关门效果甚至整车平顺性,车身尺寸偏差大小不仅依赖车身制造过程控制,而且取决于车身设计阶段的工艺设计。因此,车身装配偏差分析与公差设计方法研究具有重要意义。然而,车身装配过程中零件间的多约束特征和多装配顺序影响,使得车身装配偏差累积规律十分复杂,传统尺寸链分析方法需要建立尺寸链方程,难以适应车身三维偏差分析;同时,传统的蒙特卡洛求解方法计算效率低下,难以应用于这种复杂车身产品的公差综合。为此,本文开展面向车身装配的三维偏差模型及求解方法研究,旨在提高车身公差设计水平。
本文首先针对车身装配多约束特征及多装配顺序的特点,建立基于确定性定位分析的车身装配三维偏差模型;然后,研究偏差模型线性化求解方法和基于矩方法的二次化求解方法;最后,以三维偏差建模和求解方法作为核心算法,开发复杂车身装配三维公差分析系统,并应用于实例。主要研究工作及创新点如下:
(1)基于确定性定位分析的车身三维偏差模型
传统的尺寸链模型需要建立尺寸链,难以应用于车身产品这种多约束、多装配顺序的装配偏差分析过程。本文提出一种新的车身装配三维偏差模型建模方法。该模型首先将车身装配多约束条件转化为确定性约束定位条件,根据给定的装配顺序将装配过程分解为一系列单个零件的确定性定位;然后,以零件偏差、夹具偏差的耦合偏差为输入,建立考虑定位点二阶几何信息的零件确定性定位分析模型。最后采用一系列确定性定位分析建立车身装配偏差分析模型。
(2)三维偏差模型的线性化求解方法
传统的蒙特卡洛仿真计算效率低,难以应用于复杂车身装配公差设计这样需求大量迭代运算的场合,本文提出一种高效率的线性化求解方法。首先,对于非线性隐式模型,采用隐式求导和一阶泰勒级数展开得到确定性定位分析模型的输入输出间线性关系。然后,利用数理统计理论,建立输入输出统计参数的显式表达式,实现装配公差的线性化求解;最后,通过与蒙特卡洛方法的比较,验证了线性化方法的有效性和计算效率。该方法无需解大量非线性方程组,计算效率显著提高;
(3)三维偏差模型的二次化求解方法
线性方法只能应用于装配偏差模型非线性程度较低的场合,针对模型较强非线性或零件尺寸为非正态分布的场合,本文进一步提出基于矩方法的确定性定位分析模型的二次化求解方法。首先,对确定性定位分析模型进行二次泰勒级数展开,采用有限差分法与牛顿-拉尔森法得到一阶、二阶及二阶混合敏感度矩阵;然后,根据零件偏差的前四阶矩计算零件定位偏差的均值和标准差,并分析了二次化方法的计算精度和效率;最后,通过与线性方法及蒙特卡洛方法的对比验证方法的有效性。该方法可应用于非线性模型或非正态分布输入,可对非线性隐式模型进行敏感度分析。
(4)三维偏差分析软件系统开发
以三维偏差模型及求解方法为核心算法,采用Visual C++为开发工具,开发车身三维复杂装配偏差分析系统AVAS。系统采用基于功能的三层式结构,分别为算法层,数据层和用户层。采用车大灯安装和车门安装两个典型实例对系统及核心算法进行验证,将分析结果分别与三坐标实测数据及3DCS分析结果进行对比分析。系统具有如下特点:不依赖于其他CAD软件;可选择线性化方法或二次化求解方法进行公差分析,与采用蒙特卡洛相比效率更高;可在同一模型中计算多条装配顺序而无需重新建模。
The dimensional variation of auto-body has a direct effect on appearance, wind noise, shutdown of door and so on. The dimensional variation of auto-body not only depend on manufacturing process control, but also on the the process design. So it has great significance about the research of the variation analsysi of auto-body assembly. However, the characteristics that the multiple constraints and sequences in the auto-body assembly make the error stack-up very complex and it is difficult to search dimension-loop by utilizing the traditional dimension loop model in the 3-D variation analysis and synthesis in auto-body. Meanwhile, for the auto-body composed by great mounts of parts, the traditional Monte Carlo Simulation is time-consuming. So, the 3-D variation modeling and analysis is developed for auto-body assembly to raise the tolerance design of auto-body in this paper.
According to the characteristic of multiple constraits and sequence, a 3-D assembly variation model based on deterministic locating is presented firstly; then the linearized and quadratic analysis method of the 3-D variation model is developed; finally based on the variation model and analysis method, a software prototype of 3-D variation analysis in auto-body is developed. The main research work and method are as follows:
(1) The auto-body assembly has the characteristics of the multiple constraints and sequences, it is difficult to search dimension-loop by utilizing the traditional dimension loop model for the 3-D variation analysis。
The deformation of auto-body assembly is very small and it can be consider as rigid body. A new 3-D variation model is presented in this paper, the hierarchical assembly process is decomposed to a series of deterministic locating of single part in this model. Firstly, the multiple constraints is transferred to deterministic locating; then the part variation and jig variation is taken as input to develop the model of deterministic locating by considering the quadratic geometry of constraints.
(2) The linearized method of 3-D variation model
Because the traditional Monte Carlo simulation is time-consuming, and can not be applied to tolerance synthesis, a linearized method is presented in this paper. At first, for nonlinear assembly function, the implicit differentiation and multi-variables Tayler Series Expansion are used to obtain the linear relationship between input and output. Then the stability and computational complexity are investigated to determint is application range. Finally this method is applied in case study to compare to Monte Carlo simulation. The presented method is efficient by avoiding resolving nonlinear equations, and in general applications, the relationship between input and output of assembly function is linear and closely linear, the linearized method can obtain enough accuracy.
(3) The quadratic method of 3-D variation model
In case that the assembly function is nonlinear, or the part dimension is not follow Gaussion distribution (for example, the position tolerance of hole can be consider as Rayley distribution), the application of Method of Moments in the nonlinear implicit assembly function is presented.
Firstly the nonlinear implicit function is expanded by 2nd Taylor Series Expansion, and the finite differential method and Newton-Raphson method are utilized to obtain the 1st order, 2nd order and 2nd order mixed sensitivity matrix, then the mean, variance, skewness and kurtosis of part dimension are take as input to obtain the mean and variance of assembly diemension; and then the accuracy and computational complexity are investigated; finally it is compared to linearized method and Monte Carlo Simulation. The application of Method of Moments in the nolinear implicit function is a general method, and can be further extended to other fields, such as finite element analysis.
(4) The development of 3D tolerance analysis software
Based on the presented variation model and analysis method, by using C++, a 3D tolerance analysis software for auto-body assembly, AVAS, is developed and this software has applied for registration. The system adopts a functional 3-hierarchical structure: the data layer, algorithm layer and user layer. The Headlamp assembly and Auto-door assembly are utilized to validate the AVAS system and the core algorithm, the results is compared to the meament data and 3DCS software. It has the followed merits: independent with other exist CAD software; AVAS can choose linearized method in tolerance analysis to obtain higher efficiency as compared to the Monte Carlo Simulation; AVAS can deal with two or more assembly sequence in one model.
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