Assembly Accuracy Analysis of Small Deformation of Flexible Body based on Differential Transformation
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摘要: 在产品设计阶段进行装配精度分析时通常以刚体假设为前提，往往忽略外部载荷、温度变化等载荷因素的影响. 在已存在制造误差、装配误差的情况下，载荷因素引起的零件变形会进一步影响装配精度. 因此，本文提出了一种同时考虑制造、装配误差和零件变形的装配精度分析模型. 该模型首先沿尺寸链将变形的公差特征离散化，在每个节点处建立并固结节点坐标系；然后提取节点的变形信息，对目标特征上的每个节点坐标系进行微分变换，实现误差与变形的综合；最后建立了线性化的综合误差分析模型. 研究结果表明：模型不仅克服了传统误差分析模型以刚体假设为前提的局限，得到了零件的局部变形对装配精度的影响，还可极大地减少装配系统几何建模与力学分析的难度和工作量.Abstract: Rigid body assumptions were usually used as the premise for assembly accuracy analysis during the product design stage, and the effects of load factors such as external loads and temperature changes were often ignored. In the case of manufacturing errors and assembly errors, the deformation of the part caused by the load factor would further affect the assembly accuracy. Therefore, an assembly accuracy analysis model that considered manufacturing , assembly errors, and part deformations simultaneously was proposed. Firstly, the model made the deformed Tolerance Features discretized along the dimensional chain, and established and consolidated the node coordinate system at each node. Then, the node's deformation information was extracted and differential transformation on each node coordinate system on the target feature was performed to achieve the error synthesis with deformation. Finally, a linearized comprehensive error analysis model was established. The results show that the model overcomes the limitations of the traditional error analysis model based on the assumption of rigid bodies, obtains the effect of the local deformation of parts on assembly accuracy, and also greatly reduce the difficulties and workload of geometric modeling and mechanical analysis.
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Key words:
- error analysis /
- small deformation /
- differential transformation /
- product design
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图 1 TF上的局部坐标系和节点坐标系
Figure 1. Local coordinate systems and node coordinate systems on TF
图 5 3种不同类型坐标系构成的尺寸链
Figure 5. Dimensional chain of three different types of coordinate systems
图 7 齿轮轴线端点变动凸包的形状与位置
Figure 7. Shape and position of convex hulls of the end point of gear shaft
表 1 齿轮轴线端点处的变形值
Table 1. Deformation value of the gear axis end
端点 输出轴的变形/mm 端点 中间轴的变形/mm X13 方向 Y13 方向 X15 方向 Y15 方向 A 0.07562 −0.2311 C −0.08983 0.13210 B 0.05764 −0.1631 D −0.07237 0.04538 
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