A Three-Dimensional Topography Model of Rough Surfaces with High Computational Convergence

doi:10.7652/xjtuxb202106017

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A Three-Dimensional Topography Model of Rough Surfaces with High Computational Convergence

更新时间：2025-07-09

- A Three-Dimensional Topography Model of Rough Surfaces with High Computational Convergence
- Vol. 55, Issue 6, Pages: 141-149(2021)
- 作者机构：
  
  华北理工大学机械工程学院,河北,唐山,063210
- 作者简介：
- 基金信息：
- DOI：10.7652/xjtuxb202106017
  CLC： TH114
- Online First：10 June 2021，
  
  Published：2021
- 稿件说明：
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A Three-Dimensional Topography Model of Rough Surfaces with High Computational Convergence[J]. 2021, 55(6): 141-149.
DOI：

A Three-Dimensional Topography Model of Rough Surfaces with High Computational Convergence[J]. 2021, 55(6): 141-149. DOI： 10.7652/xjtuxb202106017.

摘要

针对现有机械加工面三维形貌模型不能有效反映曲面宏观与微观综合特征以及在接触、润滑等分析时计算收敛性差等问题

提出了一种计算收敛性较好的曲面三维形貌模型。基于微分几何理论

采用矢量函数表征曲面的轮廓尺寸以及曲率等宏观特征; 基于分形理论

采用Weierstrass-Mandelbrot(W-M)函数表征微凸体高度与分布以及纹理方向等微观特征

将矢量函数与W-M函数叠加

构建了曲面的三维形貌模型。为解决计算收敛性问题

通过滤波对粗糙表面进行平滑处理

在保留原有表面形貌特征前提下获得了连续可导粗糙表面

通过弹流润滑分析进行对比可知

滤波后的模型计算收敛性提升明显。应用Matlab对构建的三维粗糙面进行仿真

验证了模型对粗糙曲面形貌的有效表征能力。为检验模型的应用性

以RV减速器中的关键零件摆线轮为例

构建了摆线轮轮齿的齿面模型

模型能完整反映摆线轮轮齿的宏观轮廓与微观形貌

将得到的摆线轮齿形貌模型应用到混合润滑分析中

得到的分析结果与采用试验采集的粗糙面的分析结果一致

关键参数误差不高于3%

但计算时间大幅缩短

计算效率提升55.7%。调整粗糙曲面模型参数

可以快速得到不同的粗糙面参与相关的分析对比

能为机械结合面的宏观轮廓与表面形貌的优化设计提供依据。

Abstract

A 3D topography model of surfaces with better calculation convergence is proposed to solve the problems that the existing three-dimensional surface model of machined surface cannot effectively reflect macro and micro comprehensive characteristics of surface

and the calculation convergence is poor in contact and lubrication analysis. Based on the theory of differential geometry

vector functions are used to characterize the macroscopic features such as contour size and curvature of the surface. Based on the fractal theory

the W-M function is used to characterize the microfeatures such as the height and distribution of asperity and the texture direction. Then the vector function and the W-M function are superimposed to construct a three-dimensional surface topography model. In order to solve the problem of calculation convergence

the rough surface is smoothed by filtering

and the continuous and differentiable rough surface is obtained on the premise of retaining the original surface topography. Through comparison of the elastohydrodynamic lubrication analysis

it is found that the calculation convergence of the filtered model is significantly improved. Matlab is used to simulate the constructed three-dimensional rough surface

and the result verifies the effective characterization ability of the model for rough surface morphology. In order to test the applicability of the model

the cycloidal gear

a key part of the RV reducer

is taken as an example to construct the tooth surface model of the cycloidal gear. The model can completely reflect the macroscopic profile and microscopic appearance of the cycloidal gear teeth. The obtained cycloid gear tooth profile model is applied to the mixed lubrication analysis

and the obtained analysis results are consistent with those obtained by using the rough surfaces collected by experiment. The errors of the key parameters are less than 3%

but the calculation time is greatly shortened. The calculation efficiency in the example is improved by 55.7%. By adjusting the parameters of the rough surface model

different rough surfaces can be quickly obtained to participate in the relevant analysis and comparison

which can provide a basis for the optimization design of the macroscopic profile and surface topography of the mechanical joint surfaces.

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Keywords

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