Abstract Accurate machining in small-radius paths is a challenge associated with Wire Electrical Discharge Machining (WEDM). This article experimentally and theoretically analyzes the machining errors of the arced paths through successive machining stages. The machining errors of a three-stage WEDM on both straight and arced paths are first experimentally analyzed. Mathematical expressions are derived to relate new theoretical concepts, including spark angle and spark density, for each finishing stage on both straight and arced paths. Then, the effects of these concepts on machining errors of the finishing stages are determined. The causes of the machining errors of the first and second finishing stages on male and female arced paths are theoretically analyzed, and a novel mathematical methodology for the prediction of these errors is developed. The experimental machining errors of the first and second finishing stages on the different arced paths are compared and evaluated with related theoretical ones. Results reveal that the mathematical methodology predicts and compensates the machining errors of the first finishing stage with the accuracy of 78% and of the second finishing stage with the accuracy of 83%. There is a good improvement which can be employed in WEDM applications and to increase the wire electrical discharge (WED) machine capability.

中文翻译：

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线切割加工阶段小圆弧加工误差的理论与实验分析

摘要 小半径路径中的精确加工是线材放电加工 (WEDM) 相关的挑战。本文从实验和理论上分析了弧形路径通过连续加工阶段的加工误差。首先通过实验分析了三级 WEDM 在直线和圆弧路径上的加工误差。数学表达式被推导出来关联新的理论概念，包括火花角和火花密度，用于直线和弧形路径上的每个精加工阶段。然后，确定这些概念对精加工阶段的加工误差的影响。从理论上分析了公母弧形路径上第一和第二精加工阶段的加工误差的原因，并开发了一种预测这些误差的新数学方法。将不同圆弧路径上第一和第二精加工阶段的实验加工误差与相关理论进行比较和评估。结果表明，数学方法以 78% 的精度预测和补偿了第一精加工阶段的加工误差，并以 83% 的精度预测和补偿了第二精加工阶段的加工误差。有一个很好的改进，可用于 WEDM 应用并增加线放电 (WED) 机器的能力。结果表明，数学方法以 78% 的精度预测和补偿了第一精加工阶段的加工误差，并以 83% 的精度预测和补偿了第二精加工阶段的加工误差。有一个很好的改进，可用于 WEDM 应用并增加线放电 (WED) 机器的能力。结果表明，数学方法以 78% 的精度预测和补偿了第一精加工阶段的加工误差，并以 83% 的精度预测和补偿了第二精加工阶段的加工误差。有一个很好的改进，可用于 WEDM 应用并增加线放电 (WED) 机器的能力。