Influence of milling vibration on blade machining error under thermodynamic coupling

Abstract

In the process of impeller machining, the blades of the impeller vibrate under the thermodynamic coupling effect encountered during the milling process, leading to a reduction in the machining precision. To reduce the machining error, the influence of blade vibration on the machining error under the effect of thermodynamic coupling effect was analyzed in this study. First, a milling-temperature-field model of the blades was established to determine the internal force and torque required for milling. The dynamic milling force at any position on the blade was obtained based on the Navier–Stokes solution method, and this force was used as the excitation source in the milling dynamic model. A nonlinear dynamic model of a three-degree-of-freedom blade milling system under the thermodynamic coupling effect was established based on the Kirchhoff law–Lagrange method, and simplified into a single-degree-of-freedom model, and an analytical solution for the three-direction vibration displacement at any point on the blade was obtained using the Galerkin method. Based on the vibration response at each position point on the blade, the spectrum and phase plane at each position point under different working conditions were analyzed based on the Fourier transform and phase plane method. Subsequently, a prediction model for the machining error caused by the blade milling vibration was established based on the coordinate transformation of the cutter tooth and workpiece motion chain. The effective values of the milling-edge vibration displacement within one cycle of tool rotation was proposed to represent the vibration displacement of milling edge at position point. Finally, an experiment was conducted on a five-axis CNC machine tool to study the effect of blade milling vibration on machining errors under the action of thermodynamic coupling. The experimental results showed that the errors in the predicted blade milling vibration in the three-direction and predicted machining error were less than 18% and 20%, respectively. The proposed method can effectively predict machining error caused by blade milling vibration.