钢球热处理过程中表层温差剧烈程度分析
The Steel Ball SurfaceTemperature Change Analysis
王小增，曾辉，杨久红
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作者单位：嘉应学院
中文关键字：热传导方程；球贝塞尔函数；钢球表层；温度变化
英文关键字：The heat conduction equation；Spherical bessel function；The steel ball surface；Temperature analysis
中文摘要：本文推导了钢球的热传导方程，采用球贝塞尔函数给出了钢球热传导方程的解答，并对不同半径钢球的热处理过程中不同时刻固定位置的温度变化剧烈程度进行分析计算，比较了不同半径钢球温度变化的剧烈程度，并对温度分布公式计算误差进行了分析。分析结果表明相同半径的钢球在加热开始时刻温度变化最为剧烈；对于不同半径的钢球，半径越小温度变化越剧烈；在钢球不同位置，温度误差为正弦波动，级数求和次数取30时误差小于1.2%。
英文摘要：The heat conduction equation of the steel ball is deduced. The Spherical Bessel function is adopted to solve the equation. The steel ball temperature’s change with the different radius is analyzed in the heat treatment process. The temperature change of the steel ball surface with different radius is compared. The error which is calculated by the temperature distribution formula is analyzed. The result show that the steel ball has more severe the temperature change at the beginning of time. The temperature error is the sine wave in the steel ball different radius, The error is 1.2% when the number of infinite series summation is 30.