(四川省冶金研究所，成都 610081)
摘 要: 在实际冲杯过程中会产生数个制耳(通常为4个或8个)，且每个制耳不一定都一样高，传统的制耳率计算公式是由算术平均法推导出来的。通过数学推导和论证发现这种计算方法误差很大，且自相矛盾。由此提出新的设想：每个制耳对平均制耳率的贡献是不一样的，并以制耳的相对高度作为加权系数，从而推导出新的平均制耳率计算公式。经验算，该公式的计算精确度更高，并发现传统的平均制耳率计算公式只是新公式中当每个制耳大小相等时的一个特例。
关键字: 冲杯 制耳 制耳率
（Sichuan Institute of Metallurgy Research, Chengdu 610081, P. R. China）
Abstract:There are several(usually 4 or 8) earings formed in the practical cupping process, and the earings may be different in height. The conventional calculation formulae for earing ratio were derived from the arithmetic mean method, and through mathematical derivation and demonstration, it was found that this method has very large error and contradicts itself. Assuming that the contributions of each earing to the earing ratio is different, and the relative heights are used as weight coefficients, a new calculation formula for earing ratio has been derived. Computation checking showed that the new formula has higher precision than the conventional formulae and the conventional calculation formulae are only the specific case of the new one when the earings are equivalent.
Key words: cupping: earing; earing ratio
