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针对已有脉冲涡流集总参数模型的不足,建立了具有一般性的脉冲涡流集总参数模型.首先将导体试件中的脉冲涡流场等效为一簇沿深度方向排开的同轴等半径的涡流环;然后建立了涡流随时间和空间分布的偏微分矩阵方程,推导了涡流回线的电阻、自感与互感计算公式;接着阐述了系统矩阵的特征值和特征向量的物理意义;最后使用有限差分法求解了模型实例的矩阵方程,并进行了实验验证.该模型推导、求解简单,适用于任意厚度的被测试件,能准确地模拟瞬态涡流场的扩散过程,也能预知试件厚度变化时线圈感应电压的变化情况.
Aiming at the insufficiency of the existing model of pulsed eddy current lumped parameter, a general pulsed eddy current lumped parameter model is established.Firstly, the pulse eddy current field in the conductor specimen is equivalent to a cluster of coaxial equivalent radii along the depth direction Then the partial differential matrix equation of eddy current with time and space distribution is established, and the formula of resistance, self inductance and mutual inductance of the eddy current loop is deduced. Then the physical meaning of eigenvalues and eigenvectors of the system matrix is expounded. Finally, The finite difference method is used to solve the matrix equation of the model example and the experimental verification is carried out.The model is simple to be solved and applicable to the test piece with arbitrary thickness and can exactly simulate the diffusion process of the transient eddy current field, Changes in the thickness of the coil when the induced voltage changes.