Kriging模型在齿面磨损预测中的应用

Wear prediction of gear surface with Kriging model

为快速准确地对齿面磨损进行预测,考虑双齿啮合区的载荷分配并用Kriging方法建立了新的磨损数值仿真模型.基于Winkler弹性模型和轮齿啮合原理得到磨损量计算所需要的压力分布及啮合速度,在确定压力分布时考虑了由磨损带来间隙的影响,并对所需的载荷进行了动态分配;基于Archard磨损模型推导齿轮的磨损量数值仿真模型,得到了不同磨损次数下轮廓各个啮合点处的磨损深度;用Kriging方法和人工神经网络方法构建磨损与齿轮参数的关系代理模型,研究不同初始样本量下代理模型的逼近程度和拟合优度.算例计算结果表明:磨损量随磨损次数增加逐渐累积,参与啮合的齿廓各个位置的磨损量均不相同,节点处最小,越靠近齿根越大,主动轮(小齿轮)大于从动轮(大齿轮);综合比较3个初始样本量训练得到的Kriging模型表明,最小样本量为100时逼近程度和拟合优度都满足要求,并可预测未来的磨损量.采用Kriging模型具有较高的计算效率和精度,克服了磨损数值仿真模型计算耗时长的不足.

To predict gear wear rapidly and accurately,a new wear numerical simulation model is established considering distributed load between double tooth meshing area based on Kriging method. The distributed pressure and meshing speed,which should be obtained before calculating wear depth,are obtained based on the Winkler surface model and gear meshing theory. The Load to determine distributed pressure is distributed dynamically considering the effect of clearance caused by wear. Based on Archard＇s wear model,the calculation wear model of spur gear is derived,and the wear depth of each meshing points on tooth profile under the different wear cycles are obtained. A surrogate model which can describe the relation between wear and gear parameters is constructed based on the Kriging and artificial neural network method,the approximation level and goodness of fit among different Kriging models with different samples are studied. As shown in a numerical example,the wear depth tends to accumulate as wear cycles and are varying over the teeth flanks with minimum wear at the pitch and increase as the meshing point moves towards the root. By comparison of three Kriging models with different original sample numbers,the minimum sample number is 100 if the approximation level and goodness of fit meet the demands. The Kriging model has high computational efficiency and accuracy and can overcome time-consuming defect.