预紧力与粗糙度对拉杆弯曲振动特性影响的研究

微小型涡喷发动机的离心叶轮轴向长度相比转轴长度不可忽略,可将其看作拉杆转子结构。为研究该拉杆转子结构的弯曲振动特性,建立了包含连接面的简支梁数学模型,应用结合面接触分形理论,推导了预紧力、粗糙度对拉杆弯曲振动特性的数学关系。通过算例研究,得出了预紧力、粗糙度对拉杆弯曲振动特性的影响趋势。结果表明:连接面所需的最小预紧力随着粗糙度的增加呈指数增长;仅考虑连接面刚度变化的情况下,拉杆固有频率与对数坐标下的预紧力之间呈S型曲线关系,粗糙度值越大,S曲线的潜伏期越长;同时考虑预紧力对连接面刚度和拉杆抗弯刚度的影响,当粗糙度较小时,拉杆固有频率随预紧力上升而上升;粗糙度较大或预紧力较大时,拉杆固有频率随预紧力上升而下降。

Lateral vibration characteristics of a rod-fastening rotor considering the tightening force and roughness

A micro turbine engine rotor could be considered as a rod fastening rotor, since the disc thickness of its centrifugal impeller is not negligible compared with the rotor length.To gain an insight into the rotor lateral vibration characteristics, a simply supported Bernoulli-Euler beam including connecting surfaces was built.By means of the fractal contacting theory, the mathematical expression for describing the effects of the tightening force and surface roughness on the lateral vibration were derived, and the effect trends were clearly expounded by case studys.It shows that the needed minimal tightening force for connecting surfaces rises exponentially with roughness.Considering only the change of joint stiffness, the rotor natural frequencies vary along an S-shape curve with the increase of exponential tightening force.Furthermore, the more the roughness, the longer the incubation period of the S-shape curve.Considering both the changes of joint stiffness and rotor lateral stiffness, when the roughness and tightening force are small, the natural frequencies increase with the tightening force, on the contrary, the natural frequencies fall with the tightening force.