Composite error modeling and optimized proportional compensation method for CMM based on DPCNN and key error analysis

Addressing the complexity of composite error coupling modeling and compensation for coordinate measuring machines (CMM), this paper proposes a collaborative optimization method for error element modeling and compensation. Traditional composite error models typically separate and integrate errors using function approximation approaches, which result in limited prediction accuracy under varying temperature conditions. As a result, a deep pyramid convolutional neural network (DPCNN) model is constructed. It achieves a nonlinear mapping from position and temperature parameters to composite errors. The complexity and low accuracy issues of composite error modeling are resolved. To address the limitations of conventional coupling effect evaluation methods, an improved sensitivity analysis method is employed to quantify error coupling effects. Geometric errors are classified based on first-order sensitivity. It avoids issues arising from small differences between total and first-order indices that hinder the evaluation of coupling effects. The improved method enables a clearer analysis of coupling effects while reducing computational complexity and cost. To mitigate the influence of error coupling and enhance compensation efficiency and accuracy, an error proportion compensation approach is proposed. The compensation ratio is calculated using the error distribution characteristics output by the DPCNN, thereby enabling targeted adjustment of key error components. Experimental results show that this strategy enhances compensation accuracy while reducing the number of compensation terms. Compared with traditional methods, the compensation accuracy is improved by 48.42%. This study demonstrates the practical impact of precise error modeling on compensation strategies and provides a systematic solution for multi-source coupled error analysis.