护环外补液胀形的尺寸计算

护环是发电机组中最重要的零件之一，针对护环外补液胀形技术理论分析在指导实际生产的不足，利用塑性力学的变分原理，研究外补液胀形过程中护环毛坯形状尺寸的规律。预设护环外补液胀形运动学容许的速度场，通过马尔柯夫变分原理建立了真实速度场，解析式表明质点径向速度分量与半径成双曲线函数关系。由应变速率场求得应变增量场，并以体积不变条件作为补充方程，得到了内径与高度的微分方程，进而求解得到护环液压胀形过程中径向尺寸与高度的解析关系，试验结果与理论计算结果对比表明，该式可用于计算护环外补液胀形的瞬时尺寸。

Dimension Control for Hydraulic Expansion of Retaining Ring

The retaining ring is a key part in generator systems. As theoretical analysis on hy- draulic expansion of the retaining ring with additional liquid is inadequate, this paper applies varia- tion principles in plastic mechanics to the calculation of dimensional change during the hydraulic expansion of the retaining ring. Kinematically admissible velocity fields are assumed, and a real velocity field is established based on the Markov variation principle. The analytical expression in- dicates that a radial component of the particle velocity and its radius satisfy a hyperbolic relation. A differential equation of the internal radius and the billet height is obtained using a strain incre- ment field derived from a strain rate field and with the volume constancy condition as a complementary equation. An analytic relation between the radial dimension and the height of a particle during expansion can be acquired. Comparison between experiments and the theoretical calculation shows that the equation is applicable to the calculation of instantaneous dimension of the billet during hydraulic expansion of the retaining ring with an additional liquid.