| Gear transmission is one of the most important transmission ways in mechanical equipment.The operating state of gear transmission system often directly affects the mechanical equipment.In the process of meshing,the tooth roots suffer periodic alternating force caused by alternating meshing of gear tooth pair,which easily induces the presence of crack.With the propagation of crack,gear tooth breakage may happen,which can lead to a major accident.Therefore,it has great significance to investigate the gear tooth crack feature for preventing the serious accident.Taking spur gear pairs as the research object,this paper established a revised analytical mesh stiffness calculation model for cracked gear pair considering the effects of extended tooth contact,reduction of fillet-foundation stiffness and installation error.The proposed model is effective for gear with profile modification and profile shifted gear.Based on a finite element(FE)model,time-varying mesh stiffness for thin-rimmed gear with crack propagation through the tooth and rim is obtained.Based on proposed mesh stiffness calculation model and dynamic model with six degrees of freedom(DOFs),a series of research works about the mesh stiffness excitations and vibration characteristic of the gear system have been carried on.The main contents include:(1)Based on energy method,a revised analytical model is established,in which the effects of one gear body shared by multi-tooth pairs in meshing and the flexibility of gear tooth are taken into account.By comparing with the results from traditional analytical model(TAM)and FE model,the results obtained from revised analytical model are more accuracy than those obtained by TVM and show great agreement with those of FE model.Mesh stiffness determined by TAM at multi-tooth engagement region is far high.The error is in that the meshing tooth pairs share the one gear body,which leads to the mesh stiffness in multi-tooth engagement higher than the actual condition.(2)Considering the reduction of fillet-foundation stiffess caused by gear crack,correction coefficient of fillet-foundation stiffness is determined by FE model.Mesh stiffness calculation models for cracked gear pair with tip relief and profile shift are proposed.And the effects of amount of tip relief,length of tip relief,modification coefficient and crack depth on mesh stiffness are investigated.The results indicate that mesh stiffness decreases due to the presence of crack;mean mesh stiffness,load sharing ratio,double-and single-tooth engagement are affected by profile modification and profile shift.(3)An improved mesh stiffness is also established considering the installation error.The effects of centre distance error and angular misalignment error on mesh stiffness are analyzed.The results show that mesh stiffness decreases under the presence of centre distance error and angular misalignment error.(4)A lumped mass model with six DOFs is established.Vibration responses of cracked gear pair,profile modification gear pair and profile shifted gear pair are obtained.By time-domain and frequency-domain analysis methods,vibration characteristic analysis of a cracked gear system considering the mesh stiffness excitation is carried out.In addition,simulated results of the cracked standard gear system are validated by analyzing the experimental signal.(5)Based on FE method,mesh stiffness for thin-rimmed gear is calculated.By using a lumped mass model,vibration response characteristics of a thin-rimmed gear pair with crack propagation through the tooth and rim are investigated.The results show that there exist three periods related to slots of the gear body in a rotating period of the thin-rimmed gear.For the healthy thin-rimmed gear,there exists not only meshing frequency and its harmonic components,but also combination frequencies of meshing frequency and rotational frequency.Vibration responses of gear with crack propagating through the rim are more severe than those of the gear with crack propagating through the tooth at the same crack level. |
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