Application of Fractional Derivatives in Thermal Analysis of Disk Brakes
Application of Fractional Derivatives in Thermal Analysis of Disk Brakes
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DOI：
10.1007/s11071-004-3755-7
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发表时间：
2004-12
影响因子：
5.6
通讯作者：
O. Agrawal
中科院分区：
文献类型：
--
作者：
O. Agrawal
本文提出了一种用于盘式制动器热分析的分数阶导数法。在这项研究中，问题被理想化为一维。该公式包含分数阶半积分和导数表达式，为计算摩擦表面温度和热流密度随时间的变化提供了一种简便的方法。给定热通量，该公式提供了一种计算表面温度的方法，并且给定表面温度，它提供了一种计算表面热通量的方法。提出了一种最小二乘法来平滑温度曲线，并消除/减少由于测量误差引起的温度统计变化的影响。结果表明，整数幂级数的方法来考虑简单的多项式最小二乘的目的可能会导致显着的错误。相反，这里考虑的多项式包含分数幂项。该配方扩展到帐户从侧表面的对流热损失。使用模拟实验，它也表明，本配方预测准确的表面热通量值。本研究的结果比较以及与分析和实验结果。
This paper presents a Fractional Derivative Approach for thermal analysis of disk brakes. In this research, the problem is idealized as one-dimensional. The formulation developed contains fractional semi integral and derivative expressions, which provide an easy approach to compute friction surface temperature and heat flux as functions of time. Given the heat flux, the formulation provides a means to compute the surface temperature, and given the surface temperature, it provides a means to compute surface heat flux. A least square method is presented to smooth out the temperature curve and eliminate/reduce the effect of statistical variations in temperature due to measurement errors. It is shown that the integer power series approach to consider simple polynomials for least square purposes can lead to significant error. In contrast, the polynomials considered here contain fractional power terms. The formulation is extended to account for convective heat loss from the side surfaces. Using a simulated experiment, it is also shown that the present formulation predicts accurate values for the surface heat flux. Results of this study compare well with analytical and experimental results.