热膨胀系数同弹性模量数学模型分析

为满足超精密加工对精度的要求，从机理角度分析了材料的热膨胀系数和弹性模量，建立了二者关系的数学模型。结果表明：材料热膨胀和材料弹性模量的物理本质都同原子间作用力密勿相关，只是二者的原子间发生作用的起固有别。材料的热膨胀是因温度升高，原子振幅加大，引起原子间斥力增加，平衡距离加大，原子间仍是平衡状态；而弹性模量是两原子受到外力作用，偏离平衡位置，双子间是引力(斥力)状态，该引力(斥力)值同外界作用力平衡。

Analysis of Relation of Coefficient of Thermal Expansion and Elastic Modulus

This paper offers a mathematics model of relationship of material coefficient of thermal expansion and elastic modulus on mechanism, for sufficient condition of precision process. Result indicates that physics essence of material coefficient of thermal expansion and elastic modulus is closely related to the action of atoms, but differences occur in origin reason of their action. When temperature rises, atoms swing and expulsive force increase and balance distance increases, thus causing material coefficient of thermal expansion, and this time atoms is in balance state; but elastic modulus is different. Two atoms, acted by outside force, deviate balance place; gravitation (repulsion) in two atoms is balance with outside force action.