Differential equation solution of shaping curves for narrow steps in cross wedge rolling
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摘要: 為了解決目前軋齊理論應用于窄臺階軋齊曲線求解時精確性不足的問題,同時為了進一步了解軋齊成形本質,通過改進幾何模型,分析并給出各影響因素之間關系函數,將軋齊曲線求解問題描述成為微分方程初值問題.通過軟件編程應用數值方法進行求解,得到窄臺階軋齊曲線函數的離散值.使用有限元模擬計算及軋制試驗的方法,將計算結果與文獻作對比.通過對比分析模擬和實驗結果中臺階面的尺寸,證明該解法不但是成立的,而且有利于成形更加精確的內側較窄直角臺階.Abstract: Existing methods are not accurate enough to apply in the solution of shaping curves for narrow steps in cross wedge rolling.In order to solve this problem and explore the shaping essence,the curve solution was described as the initial value problem of a differential equation by improving the previous geometric model and analyzing the relationships among various factors in shaping processes.A numerical method by mathematical programming software was used to solve the discrete results of the shaping curves.Through simulation and practice experiments,the calculated results were compared with data in literatures.The comparison of step size obviously shows that this method is not only able to be established,but also better than previous methods on the shaping accuracy of narrow steps.
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Key words:
- cross wedge rolling /
- step shaping /
- differential equations /
- numerical methods
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