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In order to improve the coupling vibration response characteristics of the reducer system, the model of the gear transmission system is established by using the Masta software. Secondly, the finite element model of the differential case and the reducer case is introduced for coupling, the noise waterfall diagram of the reducer under various working conditions is obtained through NVH (Noise, Vibration and Harshness) analysis, and the noise slice diagram and dynamic response curve of it under various operating conditions are further obtained. Finally, the influence of the pressure angle, helix angle and tooth width on dynamic response of the gear transmission system is studied and optimized. The results show that the dynamic meshing force of each operating condition of the reducer system after optimization is reduced, and the noise radiation is greatly reduced, which provides a theoretical basis for the vibration reduction and noise reduction design of the reducer.

The influence of elastohydrodynamic lubrication (EHL) to the spur gear profile modification is considered for the first time, and a new method of spur gear profile modification is proposed using gear EHL friction pair meshing stiffness to replace gear meshing stiffness to calculate the maximum modification amount. Based on the EHL theory and by simplifying the EHL film into linearized spring and damping, a tribology-dynamics coupling model of line contact friction pair is established and the stiffness of tooth surface EHL friction pair is obtained by numerical method; the gear meshing stiffness and the meshing stiffness of gear EHL friction pair are calculated respectively using the definition of ISO gear meshing stiffness and the maximum modification amount is calculated based on two different gear meshing stiffness; through Creo, the meshing models of a standard gear pair, an ISO method modified gear pair and an EHL friction pair stiffness modified gear pair are established respectively. Dynamic meshing force, angular acceleration and transmission error of the three kinds of gear pairs are simulated and compared using Adams and Romax. The values of maximum modification amount calculated based on the stiffness of the EHL friction pair are compared with the values of modification amount of some engineering actual modified gears. The results show that the gear stiffness decreases significantly when taking into account the effect of EHL, which leads to an increase in the maximum gear modification amount. The modification effect based on the stiffness of the EHL friction pair is better than that when using the ISO method and the gear dynamic performance and transmission performance is improved significantly. And the theoretical calculation values of the modification amount are also closer to the values of actual modification amount of the engineering gear.

• A vibration signal separation method is proposed through parameter identification. • A novel vibration signal model is built by utilizing the mode shape of ring gear. • A vibration signal calculation method is derived from the elastic theory of ring. • The influences of unequal load sharing and meshing position errors are studied. The gearbox vibration signal of a planetary gear set contains multiple components caused by different excitations. Separating the gearbox vibration signal to decouple its components can provide core information for operational status monitoring. In this paper, we propose an indirect gearbox vibration signal separation method based on parameter identification. A novel vibration signal model is established using the modal shape of ring gear. A parameter identification method is adopted to determine the parameters of the vibration signal model. The vibration signal components are reconstructed based on the vibration signal model and identified parameters. To evaluate the performance of the proposed method, a ring gear response calculation method derived from the elastic theory of ring gear is presented. The influences of unequal load sharing and meshing position errors on vibration signals are studied through numerical simulations using the calculation method. Experiments are conducted in a planetary gear set test rig. Comparisons between the experimental results obtained by the separation and calculation methods indicate the effectiveness of the proposed separation method. [ABSTRACT FROM AUTHOR]

The determination of meshing force and the load sharing ratio of gear teeth is critical to predict the dynamic behavior or the load capacity of gear transmissions. In the previous literature, the dynamic meshing force is usually calculated based on the traditional dynamic model, which ignores the different effects of the meshing characteristics of each pair of teeth on the dynamic behavior of the gear system. In this work, a new calculation method of dynamic meshing force is proposed based on the new dynamic model considering the meshing state of multiple pairs of teeth. The difference between the traditional calculation method and the new calculation method of dynamic meshing force is analyzed. Based on the new dynamic model and new calculation method of dynamic meshing force, the influence of different factors on dynamic response and dynamic meshing force are further discussed. The results show that, compared with the traditional calculation method, this new method can be used to effectively calculate the dynamic meshing force and the load sharing ratio of each pair of teeth with different meshing characteristics. The presented method for the calculation of the dynamic meshing force and the load sharing ratio provides an important reference for analyzing and predicting the dynamic behavior or the load capacity of spur gears, especially the high contact ratio (HCR) gears with contact ratio more than two. [ABSTRACT FROM AUTHOR]

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The double motor hybrid vehicle distributes the power on both sides through the parallel planetary gear mechanism. The meshing force of the two rows of planetary gears affects each other， resulting in the increase of dynamic load coefficient and vibration excitation. The harmonic analysis method is used to obtain the frequency ratio of meshing force under multiple working conditions， so as to establish RBF neural network model， and a prediction of meshing force in a certain working range is carried out. The maximum meshing force and dynamic load coefficient are calculated on the prediction results， and the meshing force is proportional to the difference between speed ratio and output torque ratio minus 1， and the dynamic load coefficient on the low-speed side is greater than that on the high-speed side， which can be expressed as a multiple or reciprocal multiple relationship. It provides a theoretical basis for the study of dynamics of hybrid vehicles with dual motors.

A improved torsional nonlinear dynamic model of double-helical star gearing system of Geared Turbofan (GTF) aero-engine is established, considering multiple nonlinear parameters and the effect of tool withdrawal groove that connect helical gears on both sides of double-helical gear. The dynamic responses of the system are solved by Runge–Kutta numerical integration method. The results reveal that the double-helical star gearing system exhibits abundant torsional nonlinear behaviors, which were illustrated by the evolution curve of dynamic meshing force and load sharing coefficient under varying rotational speed, gear backflash and width of groove, with either side of helical gear pairs in double-helical gear system are considered and illustrated, respectively, which can be hardly seen in previous research and worth being analyzed for better understanding of undesirable torsional dynamic motion for the double-helical gear system and therefore provide a reference for the design and control of gear system. [ABSTRACT FROM AUTHOR]

When gears change their distance along the off-line of action (OLOA) direction, this affects the distance between the working surfaces of the meshing teeth along the line of action (LOA). This effect is usually neglected in studies. To include this effect precise equations are derived for spur gears. The analysis is carried out for the general case of spur gears with shifted profiles frequently used in the industry. The influence of OLOA gear displacement on LOA direction is also a function of gears parameters. An analysis is conducted, and the impact of parameters such as module, pressure angle, gear ratio, and the number of teeth is determined. As an example, a simulation of a 12 DOF analytical model is presented. The movement of gears along OLOA is caused by a frictional force that can be high during tooth degradation e.g. scuffing. Results show that when the movement of gears along the OLOA direction is significant, its influence on the distance between the mating teeth should not be neglected. [ABSTRACT FROM AUTHOR]

In order to accurately predict the wear distribution of involute spline pairs, a nonlin ear dynamic meshing force formula of involute spline pairs is proposed considering the multi tooth meshing behavior of involute spline pairs, the equations are solved by runge-kutta method after the rigid body displacement is eliminated and dimensionless, finally, the influ ence of different mass eccentricity on the nonlinear dynamic meshing force is analyzed. The results show that the amplitude of nonlinear dynamic meshing force increases with the in crease of mass eccentricity, the running state of the spline pair gradually changes from stable to unstable and the range of the dynamic load coefficient gradually increases. and its maxi mum value also increases, which indicates that the vibration of the system is intensified, and it is easy to cause the failure of the spline. This paper analyzes the change rules of dynamic meshing force with mass eccentricity, which provides a theoretical support for the design of aviation spline pairs with high strength and high reliability, as well as an accurate dynamic force calculation method for wear prediction. [ABSTRACT FROM AUTHOR]

The determination of meshing force and the load sharing ratio of gear teeth is critical to predict the dynamic behavior or the load capacity of gear transmissions. In the previous literature, the dynamic meshing force is usually calculated based on the traditional dynamic model, which ignores the different effects of the meshing characteristics of each pair of teeth on the dynamic behavior of the gear system. In this work, a new calculation method of dynamic meshing force is proposed based on the new dynamic model considering the meshing state of multiple pairs of teeth. The difference between the traditional calculation method and the new calculation method of dynamic meshing force is analyzed. Based on the new dynamic model and new calculation method of dynamic meshing force, the influence of different factors on dynamic response and dynamic meshing force are further discussed. The results show that, compared with the traditional calculation method, this new method can be used to effectively calculate the dynamic meshing force and the load sharing ratio of each pair of teeth with different meshing characteristics. The presented method for the calculation of the dynamic meshing force and the load sharing ratio provides an important reference for analyzing and predicting the dynamic behavior or the load capacity of spur gears, especially the high contact ratio (HCR) gears with contact ratio more than two.

This work presents a nonlinear dynamic model considering the multi-tooth meshing behaviour and mass eccentricity of an involute spline coupling to tackle the serious problem of involute spline failure, in aviation power transmission systems. The dynamic meshing force is calculated for the same. Based on this, the influence of different mass eccentricities on the nonlinear dynamic response of the spline coupling was investigated in aero-engines. The results show that when the mass eccentricity is small, its impact on the system is insignificant. When the eccentricity reaches a certain value, the quasi-periodic and chaotic state appears alternately. Meanwhile, it can be concluded that the acceleration-frequency spectrum during the multi-periodic phase is an approximation of the working frequency with the accuracy affected by multiple teeth engagements. This was validated by the vibration experiments of the involute spline coupling. The proposed model, which considers the multi-tooth meshing behaviour and the mass eccentricity provides a reference model for the dynamic analysis of similar structures. The nonlinear dynamic response results attained lay a good theoretical foundation for fretting damage analysis and precise designs for involute spline couplings. [ABSTRACT FROM AUTHOR]

This study relates to the research on improving analytical models of gears. A new analytical model of gear shaft with 5 DOF was proposed. Equations of vibration were derived without small-angle approximation and were presented in a form that could be implemented in Simulink. In order to determine the effect of the additional DOF, four popular models having 2 DOF, 4 DOF, 6 DOF and 8 DOF were investigated, too. The proposed model has 12 DOF in total. This number of DOF could be increased; this, however, would result in a greater difference between the considered models, thus making it more difficult to evaluate the impact of the additional DOF of shafts. As a benchmark, the dynamic meshing force in the considered analytical models was calculated. Simulations were carried out with and without friction. Additionally, for the 12 DOF model, the effects of the position of the centre of gear and the centre of mass were investigated. [ABSTRACT FROM AUTHOR]

Highlights • Establishing a dynamic model of the gear pair with multi-state mesh and time-varying parameters. • Considering teeth separation and back-side tooth meshing. • Investigating variations of the dynamic meshing force under multiple meshing states. • Mutation of the reverse dynamic meshing force will cause the change of the meshing state. • Effects of system parameters on the vibro-impact properties are analyzed numerically. Abstract Backlash-induced variations may lead to teeth separation and back-side tooth mesh in lightly loaded geared drive. Effects of teeth separation and back-side tooth mesh are considered. The dynamic model of a spur gear pair under multi-state meshing conditions such as teeth separation, drive- and back-side tooth mesh is established based on the gear transmission principle and forces acting on teeth. Time-varying meshing stiffness, time-varying friction, load distribution, comprehensive transmission error and backlash are included in the model. Variations of the dynamic meshing force of the system under different meshing states are analyzed numerically. The dynamic meshing force affects the meshing state of the system significantly. Furthermore, the effects of load, backlash and comprehensive transmission error on meshing states and vibro-impact properties of the system are studied by defining three different Poincaré maps, where bifurcation diagrams, top Lyapunov exponent diagrams (TLE), phase portraits are used. Results indicate that the complicated phenomena such as drive-side impact, teeth separation and back-side impact gradually occur with the decrease of the load or the increase of the comprehensive error. However, these phenomena always exist with the increase in backlash. This study provides a theoretical reference for the optimization of gears. [ABSTRACT FROM AUTHOR]

Highlights • Dynamic meshing force and blunt effects are quantitatively investigated. • Threshold for crack ductile propagation is analytically calculated and verified. • Bluntness can lead to a modest increase in applied load for crack propagation. • Crack can have three propagation ways under various upload and contact ratios. • The crack propagation way is related to the stress at crack tip and stacking fault. Abstract This work investigates the dynamic meshing force and blunt effects on atomistic scale ductile-brittle behavior of the crack in bcc iron through molecular dynamics. Two engineering factors including upload ratio and contact ratio are introduced to reveal the effects of force amplitude and distribution. Under different upload and contact ratios, normal stress fields are diverse and crack can propagate in ductile-to-brittle, weak ductile, and strong ductile ways. The increase of blunt layer leads to modest increase in critical applied load for crack ductile propagation, but it leads to obvious enhancement of crack toughness during single-tooth meshing. [ABSTRACT FROM AUTHOR]

• A hybrid model for evaluating the mesh stiffness of spalled HCRS gear is proposed. • The impact of the spall bottom features on HCRS gear dynamics is investigated. Tooth spall defects are one of the most common types of gear failures. The impact of the bottom features of the tooth spall on the dynamic properties of high-contact-ratio spur (HCRS) gears is investigated in this work. Considering the load sharing ratio, coupling structure effects, and nonlinear contact stiffness, a hybrid model was developed for evaluating the mesh stiffness of the HCRS gear, and a torsional dynamic model of the HCRS gear pair was built. The dynamic transmission errors and dynamic meshing forces are acquired by solving the above model; based on the dynamic responses of the healthy HCRS gear, the dynamic characteristics of two different spalled gear systems were compared. The results revealed that the proposed mesh stiffness model is effective within 5% calculation errors. The bottom shape of the tooth spall has important effects on the mesh stiffness but limited influence on the gear dynamic response. This study is expected to provide a theoretical foundation for future research on spall defect diagnosis in gear transmission devices. [ABSTRACT FROM AUTHOR]

Abstract: Effects of the friction and dynamic backlash on the multi-degree of freedom nonlinear dynamic gear transmission system, which incorporate time varying stiffness, are investigated. Firstly, the relationship between gear central distance error and backlash is deduced and the dynamic backlash is defined, subsequently a multi-degree of freedom nonlinear dynamic gear transmission system is developed with dynamic backlash, friction and time varying stiffness. The nonlinear dynamic system is solved by the Runge–Kutta method. The results show that the friction force may enlarge the displacement magnitude and affect the high frequency parts significantly in frequency domain at low speed. But the RMS of the steady response is reduced on the effect of friction. The difference between the constant backlash and the dynamic backlash models is also discussed. The system may enter into previous chaotic motion due to the effect of dynamic backlash. Finally, no impact motion, single-side impact motion and double-side impact motion are also predicted in the new dynamic backlash model. [Copyright &y& Elsevier]

A face-gear drive system has been extensively used in important transmission devices with strict requirements for size and weight such as helicopter reducer and so on. Its dynamic characteristics directly affect the stability and reliability of the equipment. A piecewise torsional-bending-pendular nonlinear dynamics model of the face-gear drive system is established to study its nonlinear dynamics and dynamic characteristics. The multi-state engagements including drive-side teeth engaging, teeth disengagement, back-side teeth engaging, and alternate engaging between single-teeth pair and double-teeth pairs caused by the couple of the backlash and the contact ratio being greater than 1.0 is considered. The change of the dynamic engaging force and load distribution ratio for the system is analyzed by numerical results under three different states engagement. The effects of the load coefficient, meshing frequency and the comprehensive transmission error on the dynamic characteristics and nonlinear dynamics of the system are studied based on three different Poincaré mappings defined by bifurcation diagrams, top Lyapunov exponent diagrams, phase portraits and variation curve of the dynamic engaging force. Results show that the complex phenomena such as teeth disengagement, drive-side and back-side impact occur with alternating meshing of the single and double pair teeth via the change of studied parameters. The research is helpful for the optimization of the face-gear drives. [ABSTRACT FROM AUTHOR]

• The coupling modeling method between multistage gear-rotor and box is proposed. • Condensed stiffness matrix of box is extracted by static substructure method. • Coupled box modeling reduces the vibration level of gearbox. • It's helpful for lightweight design of the gearbox considering housing flexibility. The coupling dynamic model of the multistage gears transmission subsystem and the box subsystem is established. The static substructure method is used to extract the dynamic model parameters of the box. Study of the dynamic behavior of the gearbox coupling system shows, the acceleration of the rotors are mainly excited by gear meshing frequency and its harmonic, meshing frequency of the high-speed gears has a more obvious excitation effect on the system, gear meshing excitation is the cause of the rotor's acceleration. It shows that the coupling model which is closer to the actual situation is helpful to the lightweight design of the system. The frequency amplitude of the low frequency region is significantly higher than the amplitude of the high frequency region for bearing force, which indicates that the external excitation caused by the cutting load is the main reason for the dynamic force of the system. [ABSTRACT FROM AUTHOR]