Sensitivity predictions of geometric parameters on engagement impacts of face gear drives

Face gear dynamics is one of study focuses of face gear drives, and addressed by many scholars. However, an engagement impact force calculation solution of face gear drives is not to be constructed, and some design suggestions for face gear drives considered engagement impact effects are also not to be extracted. Thus, in this study, an engagement impact force calculation solution of face gear drives is constructed, and a conversion solution between engagement impact energy and static transmission errors is proposed. Furthermore, based on a four DOF dynamic model formulated, the dynamic behavior difference of face gear drives between without and with engagement impacts is simulated, and sensitivity predictions of geometric parameters on engagement impacts are discussed. According to the limited analytic results in the issue, some design suggestions for face gear drives associated with lower engagement impacts are obtained. These contributions should improve the design of face gear drives in the future

Determination of intrinsic physical properties of porous media by applying Bayesian Optimization to inverse problems in Laplace NMR relaxometry

Nuclear magnetic resonance (NMR) longitudinal (T1) and transverse (T2) relaxation time distributions are widely used for the characterization of porous media. Subject to simplifying assumptions predictions about pore size, permeability and fluid content can be made. Numerical forward models based on high-resolution images are employed to naturally incorporate structural heterogeneity and diffusive motion without limiting assumptions, offering alternate interpretation approaches. Extracting the required multiple intrinsic parameters of the system poses an ill-conditioned inverse problem where multiple scales are covered by the underlying microstructure. Three general and robust inverse solution workflows (ISW) utilizing Bayesian optimization for the inverse problem of estimation of intrinsic physical quantities from the integration of pore-scale forward modeling and experimental measurements of macroscopic system responses are developed. A single-task ISW identifies multiple intrinsic properties for a single core by minimization of the deviation between simulated and measured T2 distributions. A multi-task ISW efficiently identifies the same set of unknown quantities for different cores by leveraging information from completed tasks using transfer learning. Finally, a dual-task ISW inspired by the multi-task ISW incorporates transfer learning for the simultaneous statistical modeling of T1 and T2 distributions, providing robust estimates of T1 and T2 intrinsic properties. A multi-modal search strategy comprising the multi-start L-BFGS-B optimizer and the social-learning particle swarm optimizer, and a multi-modal solution analysis procedure are applied in these workflows for the identification of non-unique solution sets. The performance of the single-task ISW is demonstrated on T2 relaxation responses of a Bentheimer sandstone, extracting three physical parameters simultaneously, and the results facilitate the multi-task ISW to study the spatial variability of the three physical quantities of three Bentheimer sandstone cored from two different blocks. The performance of the dual-task ISW is demonstrated on the identification of the five physical quantities with two extra T1 related unknowns. The effect of SNR on the identified parameter values is demonstrated. Inverse solution workflows enable the use of classical interpretation techniques and local analysis of responses based on numerical simulation

Constructed solutions of face gear dynamics associated with engagement impact energy decay

Face gear drives are focused by many researchers, due to several strong-points versus traditional spiral bevel gear drives. However, calculation solutions of face gear dynamics associated with engagement impact energy decay are not to be constructed, according to the limited published issues. Thus, in the study, a calculation solution of engagement impact energy decay of face gear drives is proposed, a face gear dynamic model is established, and the dynamic mesh forces of an example case of face gear drives without engagement impacts as well as with engagement impacts and engagement impact suppressions are simulated. The results indicate the fidelity of the proposed calculation solutions of face gear dynamics associated with engagement impact energy decay could be accepted. These contributions would improve the developments of face gear drive modifications and engineering applications of face gear drives in the future

Analytical impact of the sliding friction on mesh stiffness of spur gear drives based on Ishikawa model

Mesh stiffness always is a studying focus of gear dynamics. In the issue, a solution for the calculation of mesh stiffness considering the sliding friction effect is constructed, and the influence of the sliding friction on mesh stiffness is analyzed. Further, the analytical results indicate mesh stiffness is sensitive to the sliding friction in poorly lubricating conditions specially. These contributions would not only simplify the calculation of mesh stiffness associated with the sliding friction but also be good for assessing the dynamic behaviors of spur gear drives in some special operating condition

Differences of dynamic behaviors of face gear drives between time varying and average mesh stiffness

Face gear dynamics is one of important studies of face gear drives. However, differences of dynamic behaviors of face gear drives between time varying and average mesh stiffness are not to be discussed. Thus, in this study, a mesh stiffness calculation solution of face gear drives is constructed, which is based on the proposed equivalent face gear teeth, and a four DOF dynamic model of face gear drives is formulated. Furthermore, differences of dynamic behaviors of face gear drives between time varying and average mesh stiffness are investigated. The result indicates instantaneous impacts are existed at start engagement points of face gear drives

Calculation of static transmission errors associated with thermo-elastic coupling contacts of spur gears

The static transmission error is one of the key incentives of gear dynamics and addressed by many scholars. However, the traditional calculation method of static transmission errors of spur gears does not take into account the influence of thermo-elastic coupling caused by the gear temperature field, and it limits the accuracy of the dynamic characteristic analysis. Thus, in this study, the calculation method of static transmission errors associated with thermo-elastic coupling is proposed. Furthermore, the differences between static transmission errors associated with thermo-elastic coupling contacts and traditional method of gear is discussed. The study is helpful to improve the accuracy of dynamic analysis of gear transmission system

Solutions of active vibration suppression associated with web structures on face gear drives

Vibration suppression of face gear drives is always one of study focuses of face gear dynamics. Thus, in the study, a solution of active vibration suppression associated with web structures on face gear drives is proposed, and an example case of face gear drives associated with the proposed solution is simulated. The results indicate effects of the proposed solution on face gear dynamic behaviors are significant. These contributions would benefit to improve face gear vibration suppression studies

Effect predictions of star pinion geometry phase adjustments on dynamic load sharing behaviors of differential face gear trains

Face gear drives, which are suggested to be used in input stage gear drives of helicopter main gear boxes, are focused by many scholars. However, differential face gear trains, which can be employed in output stage gear drives of coaxial helicopter main gear boxes, are not to be addressed by researchers, and dynamic load sharing design solutions of differential face gear trains are yet to be investigated. Thus, in the study, a star pinion geometry phase adjustment solution, which is not to change drive ratios of differential face gear trains versus traditional geometry parameter adjustment solutions, is proposed, and a six DOF torsion dynamic model associated with four star pinions is established. Furthermore, dynamic load sharing behaviors of two version differential face gear trains are discussed, and the effects of star pinion geometry phase adjustments on two version differential face gear trains are predicted. The analytic results indicate the effects of the proposed star pinion geometry phase adjustments on dynamic load sharing behaviors of two version differential face gear trains are significant. These contributions would benefit to improve dynamic load sharing designs and engineering applications of differential face gear trains in the future

Influence comparisons of two version tooth profile modifications on face gear dynamic behaviors

Face gear drives in first-stage gear drives of helicopter main gearboxes occupy several strong points versus traditional spiral bevel gear drives, and are addressed by many scholars. However, face gear vibration suppressions, such as calculation solutions of face gear dynamics associated with tooth profile modifications and influences of tooth profile modifications on face gear dynamic behaviors, are not to be investigated, according to the limited published issues. Thus, in the study, influence mechanisms of two version tooth profile modifications, namely, linear addendum modifications of face gears and arcuate dedendum modifications of pinions, on face gear dynamic base parameters, such as mesh stiffness and static transmission errors, are discussed, and calculation solutions of two version tooth profile modifications are constructed. Meanwhile, an equivalent evaluation solution between linear addendum modifications of face gears and arcuate dedendum modifications of pinions is proposed, and a four degree-of-freedom dynamic model of face gear drives is established. Furthermore, dynamic behaviors of an example case of face gear drives associated with two version tooth profile modifications are simulated. The results indicate dynamic behavior crises of face gear drives would not to be caused by two version tooth profile modifications, and when two version tooth profile modifications are equivalent, the effect of linear addendum modifications of face gears on dynamic mesh force suppressions at whole frequencies is better than that caused by arcuate dedendum modifications of pinions, while, as for mesh frequency, the dynamic mesh force suppression effect caused by arcuate dedendum modifications of pinions is better, and considered dynamic mesh force suppression average values associated with two version tooth profile modifications, arcuate dedendum modifications of pinions are recommended. These contributions would improve modification developments and engineering applications of face gear drives in the future

Construction of 12 DOFs spur gear coupling dynamic model

A 12-degree-of-freedom (DOF) spur gear dynamic model is constructed, which is coupled by the mesh gear pair and the gearbox. The construction method of spur gear coupling dynamic model, based on lumped mass method, is better than finite element method, due to higher modeling efficiency. The work would be benefit to spur gear coupling dynamic modeling and analyses