Abstract:As one of the inherited displacement excitation sources which are related to the gear vibration and noise problems, gear transmission error always consists of two parts: gear tooth geometric error and tooth elastic deformation under transmitted load. The gear tooth geometric errors were directly employed as the displacement excitations in previous papers, which are not accurate. In this paper, a new method is developed to transform the gear tooth errors (TEs) to be the appropriate dynamic excitations through t… Show more
“…In this case, the vibration responses of the double-helical gear set are dominated by the gear mesh frequency components. It means that the double-helical gear set has the same vibration characteristics as other types of (spur and helical) gear transmission system (Han and Chu, 2014; Chen and Shao, 2014). Figure 4.(a) 3D spectrum and (b) order spectrum with respect to vibration velocity at bearing #1 in X-direction.…”
Section: Numerical Analysis and Discussionmentioning
Theoretical analysis is conducted to investigate the nonlinear vibration response in a double-helical gear set under the influence of staggering, single pitch error and cumulative pitch error. A dynamic model of the double-helical gear set is established considering the axial deflection of shaft and gyroscopic effect, and the natural frequencies, mode shapes and critical speeds for the gear set with axial degree and gyroscopic effect are calculated. Moreover, several cases are numerically simulated after consideration of time varying mesh stiffness and gear backlash, and then some general results are deduced about the influences of staggering, single pitch error and cumulative pitch error on vibration intensity and gear teeth impact. Although the pitch error is modeled as a lower frequency excitation, high natural frequencies and modes are excited, especially when the double-helical gear pair operates under high speed condition. Comparisons are listed which are useful for understanding the high speed performance of a high speed gear set.
“…In this case, the vibration responses of the double-helical gear set are dominated by the gear mesh frequency components. It means that the double-helical gear set has the same vibration characteristics as other types of (spur and helical) gear transmission system (Han and Chu, 2014; Chen and Shao, 2014). Figure 4.(a) 3D spectrum and (b) order spectrum with respect to vibration velocity at bearing #1 in X-direction.…”
Section: Numerical Analysis and Discussionmentioning
Theoretical analysis is conducted to investigate the nonlinear vibration response in a double-helical gear set under the influence of staggering, single pitch error and cumulative pitch error. A dynamic model of the double-helical gear set is established considering the axial deflection of shaft and gyroscopic effect, and the natural frequencies, mode shapes and critical speeds for the gear set with axial degree and gyroscopic effect are calculated. Moreover, several cases are numerically simulated after consideration of time varying mesh stiffness and gear backlash, and then some general results are deduced about the influences of staggering, single pitch error and cumulative pitch error on vibration intensity and gear teeth impact. Although the pitch error is modeled as a lower frequency excitation, high natural frequencies and modes are excited, especially when the double-helical gear pair operates under high speed condition. Comparisons are listed which are useful for understanding the high speed performance of a high speed gear set.
“…e planetary gear dynamic model investigated in this paper is a one-stage PGT as shown in Figure 3 [31]. It contains a sun gear (s), a carrier (c), a ring gear (r), and N planets (p).…”
This paper aims at investigating the effects of tooth profile modification (TPM) on the dynamic response of planetary gear train (PGT). A numerical model is carried out to calculate two major excitation sources of PGT, time-varying mesh stiffness (TVMS), and transmission errors (TEs). On this basis, a linear time-varying dynamic model of a PGT considering TVMS, TEs, and TPM is developed. Dynamic deviation factor is further introduced to describe the dynamic response of the PGT. In this paper, TPM is only applied to the external meshes firstly. Effects of TPM parameters, such as amount of TPM, normalized modification angle, and modification curve, on the excitation sources and dynamic response of the PGT are discussed in detail. Subsequently, investigation on the effects of TPM only applied to internal meshes is conducted. Finally, with the aim to obtain the optimal TPM for the minimization of dynamic load of PGT in both external and internal gear meshes, the genetic algorithm (GA) is employed. This research may shed light upon design optimization of PGT with respect to improvement of vibration performance by means of optimized TPM.
“…In this method, the contour equations of fault shapes were added to the model, and the effect of fault shapes on the TVMS was discovered, and then the result was compared with that obtained from the FEM. The simulation model was improved by Chen and Ma [18][19][20] for quantifying the TVMS and understanding the influence of tooth profile modification on the TVMS. The meshing process of gear pairs was regarded as the contact of two cylinders by Wu [21], who then proposed a calculation method to guide research on non-uniform wear.…”
For the analysis on the deformation of flexible ring gears in spur gear pairs, the complete flexible ring is discretized, and the boundary condition is added to the connecting points to develop a calculation method for the flexible deformation. The ovality index is used to describe the deformation degree of flexible ring gears, then the influences of ring-gear width and the spalling defects on the flexible deformation of ring gears are discussed. The result shows that the flexible deformation of ring gears is caused by the gear pair meshing force, and the deformed shape is close to an ellipse. In the single-tooth meshing interval of gear pairs, the main form of deformation is being stretched, and while in the double-tooth meshes, the main form is bending deformation. When the width of the ring gear rims is increased, the flexible deformation of the ring gears can be effectively suppressed, and the vibration amplitude of the gear pairs can be reduced. Additionally, when there is a localized spalling fault on gear pairs, the sudden changes in the deformation of flexible ring gears are generated by the shock of the meshing force. Finally, through the finite element analysis model and the experiment, the mathematical model of gear pairs with flexible rings is confirmed.
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