变速转子瞬时不平衡响应的精细算法

A Precise Integration Method on Transient Unbalance Response of Varying Velocity Rotor

针对变速转子瞬时不平衡响应计算积分精度不足的问题,基于传递矩阵法建立了考虑反对称陀螺力矩的变速转子瞬时不平衡响应线性运动微分方程,推导了适用于线性非定常系统的精细积分法,并通过仿真计算与Newmark-β法比较了变速转子模型下的积分计算效率和动力响应参数的瞬时不平衡识别精度。结果表明两种算法均具有较高的积分精度和计算效率,但是随着转速的增加,Newmark-β法的误差逐渐增大,而精细算法得到的瞬时不平衡响应信息与理论值保持一致。平衡效果显示了精细积分法能准确识别初始不平衡量,提高平衡精度。此外,通过真实不平衡转子在噪声影响下的试验结果进行了验证,发现升速过程中仿真结果与实际响应结果基本吻合。

In view of the disadvantages of integral precision in dynamic unbalance response of rotors,a linear differential equation with variable coefficient of motion based on transfer matrix method is established,in which the antisymmetric gyroscopic moment and acceleration process are exploited.An efficient algorithm based on precise integration method is formulated to calculate the nonstationary linear system.Integral computation efficiency and instantaneous imbalance identification precision are comparatively validated using the improved precise integration and Newmark-β method.The results show that both algorithms have high integral precision and computational efficiency,but the proposed method is efficient and estimates the response of parameters accurately during the whole accelerating process while the integral error of Newmark-β method is increased at a high rotation speed.The precise algorithm can improve balancing precision by identifying the initial unbalance accurately.In addition,this proposed algorithm is verified with an experimental rotor with both noise and unbalance.The simulation is in a good agreement with the measured values in the running-up procedure.