Gear Pair Research Articles

Study on the Parameter Influences of Gear Tooth Profile Modification and Transmission Error Analysis

Gear transmission systems are widely used to transfer energy and motion and to guarantee the accuracy of the entire machine system. The modification technique is a common method that improves the gear profile and reduces the transmission error. Based on the parametric model, a modified gear can be established for the evaluation of static and dynamic characteristics. The influences of profile modification parameters and gear parameters are investigated while changing the rules of different kinds of factors. Based on sensitive parameters, a two-stage profile modification curve is proposed to improve the performance of gear pairs. Thus, considering the time-varying mesh stiffness and backlash, a novel, dynamic modified gear model is established to analyze the dynamic performance, such as the dynamic transmission error. Based on the proposed curve, the range and amplitude of the transmission error can be decreased. Additionally, the vibration displacement and noise can be reduced to improve the running characteristics.

A two-stage flank correction method for the continuous generation of face gears

Face gear pairs are particularly suitable for application in advanced equipment drivetrains with intersecting shafts. The continuous generation process of face gear tooth flanks using worms offers high machining efficiency, but achieving high accuracy in this process remains a considerable challenge. A two-stage flank correction method for face gears ground by worms on a computer numerical control (CNC) generator is proposed. This method comprehensively involves both the worm dressing and face gear grinding stages, considering the actual machine tool structure and constant offsets among its axes. Firstly, the machining kinematics for both stages are derived and the high-order tooth flank model of the face gears is developed. Secondly, the sensitivity of tooth flank deviations to variations in the kinematic coefficients is analyzed, and the deviations on both flanks of the tooth space generated with initial kinematics are measured. Finally, three cases of correction for the measured deviations are compared using the proposed method. Correcting only the grinding stage is effective and computationally inexpensive, and employing this case for manufacturing face gear tooth flank significantly reduces deviations.

A stiffness model for EHL contact on smooth/rough surfaces and its application in mesh stiffness calculation of the planetary gear set

A method for calculating time-varying mesh stiffness (TVMS) is proposed by developing a stiffness model for elastohydrodynamic lubrication (EHL) contact and integrating it into three-dimensional loaded tooth contact analysis (3D-LTCA). To enhance the accuracy and efficiency of the calculation, three projects have been implemented: Firstly, the contact deformation is modified, and the average slope is employed for calculating contact stiffness. Secondly, the lubricant film and EHL contact deformation are introduced into the deformation compatibility equations. Finally, the polynomial chaos expansion (PCE) surrogate model is employed to enhance computational efficiency. The proposed method is used to calculate TVMS of the planetary gear set, and the influence of speed, torque, and rough surface are analyzed. The results show that the previous method underestimating the TVMS of planet-ring gear pair in double-teeth meshing area under fluid lubrication, while the proposed method effectively addresses the issue. The different effects of the torque and speed on TVMS under mixed and fluid lubrication also have been revealed, emphasizing the significance of surface topography in gear meshing characteristics.

Research on optimal design method of dynamic stress parameters of helical gear based on orthogonal experimental design

Aiming at the reliability optimization design problem of two-grade helical cylindrical gear transmission system, the UG parameterized model based on expression and ADAMS dynamic simulation model under real working conditions are integrated in ISIGHT platform, and the distribution law of peak contact force on the tooth surface of helical gear pair in the transmission system at different meshing times is obtained. Considering the uncertainty of material properties, load conditions and geometric parameters, the sample set was generated according to the orthogonal experimental design method, and the Kriging approximation model was established. On this basis, the contact strength reliability of helical gear was analyzed. The mathematical model of meshing efficiency reliability optimization of helical gear pair was established and solved by Hooke-Jeeves Direct Search method. The results show that the meshing efficiency and reliability of the optimized helical gear pair are improved, and the peak value of the contact force is obviously reduced.

Meshing characteristic analysis of spur gear pair with tooth surface wear fault based on improved fractal method

Meshing characteristic analysis of spur gear pair with tooth surface wear fault based on improved fractal method

Mathematical Model and Analysis of Novel Bevel Gear with High Load-Capacity Based on the Geometric Elements

Load-capacity has always been one of the performances that is paid much attention to in the development of bevel gear transmission applications. Consequently, the mathematical model of novel bevel gear with high load-capacity based on geometric elements is proposed in this paper, which could be applied to the aviation, aerospace and other fields. In parallel, the design principle and design method of the novel bevel gear are introduced in detail. Subsequently, the conditions for tooth surface continuity and non-interference are derived. Furthermore, the model of novel bevel gear is established. Finally, the load-bearing characteristics are analyzed, revealing that an increase in the number of contact points could significantly enhance the load capacity of the bevel gear pairs. When the load torque applied to bevel gear II is 100 Nm, the contact pressure endured by the bevel gear pair with five-point contact is decreased by 41.37% compared to the bevel gear pair with single-point contact. When the number of contact points is the same, increasing the distance between the contact points could also reduce the contact stress. This provides strong theoretical support for the application of the bevel gear based on the geometric elements.

An improved tolerance analysis method for gear mechanisms considering form deviations and elastic-plastic contact behaviors

The contact quality between geometric features significantly affects the assembly accuracy and dynamic performance of mechanical products. However, accurate and efficient contact problem solving is currently a common challenge in the fields of tolerance analysis and tooth contact analysis (TCA). In this paper, a tolerance analysis method for gear mechanisms considering form deviations and elastic-plastic contact behaviors is proposed. Specifically, tolerance modeling of systematic and random deviations on tooth surfaces is represented by skin model shapes (SMS). Elastic-plastic contact behaviors including contact deformation, status, and stress distribution are modeled and calculated by a modified boundary element method (BEM). The accuracy and efficiency of this BEM algorithm are verified by comparing with the finite element method (FEM), indicating that the BEM can greatly improve the computational efficiency while maintaining high solution accuracy. A case study for a pair of spur gears demonstrates the significant effects of contact behaviors on transmission performance. This research provides an effective method to introduce mechanical contact behaviors in tolerance analysis of gear mechanisms. In addition, the contact simulation results can also be adopted in the analysis of vibration, reliability, and other aspects.

Modeling and contact analysis for spur gear pair with modification and localized crack failure

The modified teeth are deliberately manufactured to mitigate the stress concentration generated by offset components, which makes equipment more susceptible to localized failures. Therefore, this paper presents a model aimed at investigating the meshing characteristic of gear pair with modification and crack failure. In this model, the tooth deformation and force transmission are determined based on slice coupling theory. The torsional deformation of teeth produced by eccentric load distribution is considered and complemented to the calculation method. Finally, the approach is proven through the experimental tests and FE model. The result shows that when the equipment is operated in misalignment condition, eccentric load distribution, and stress concentration at tooth edge are generated, the meshing stiffness will be reduced drastically, which can be suppressed by appropriate modification, and the rapid decline of meshing stiffness is weakened by increasing the effective contact length. Although the contact stiffness would be further reduced by the crack failure and the tooth surface deformation is increased, it seems to alleviate the stress concentration and eccentric load effectively.

Mathematical model for mesh analysis of gear pair in gear-shaft-bearing systems with localized failure on raceway

To investigate the influence of bearing failures on the mesh characteristics of gear pairs, this paper presents a mathematical model for gear-shaft-bearing systems. Within this simulation method, the model of defective bearings and the contact analysis methodology of gear pairs are integrated into the system equations. Additionally, the coupling mechanism between system components is determined by addressing the misaligned shafts induced by asynchronous bearing vibrations. Furthermore, the torsional deformation of gear teeth generated by uneven load distribution is considered, and a calculation method for mesh stiffness in complex environments is developed. By employing the comprehensive model, the effect of raceway failures on the mesh behavior is lucidly explained, the real-time distribution of contact stress and load on the tooth surface can be obtained, and the optimal modification strategies for gears are formulated. Finally, the proposed model is confirmed through the finite element (FE) model and experimental observation, which provides a potent tool for the performance optimization of gearboxes.

A Computational Model for Analysing the Dry Rolling/Sliding Wear Behaviour of Polymer Gears Made of POM.

This study presents a computational model to determine the wear behaviour of polymer gears. Using PrePoMax finite element numerical calculation software, a proposed computational model was built to predict dry rolling/sliding wear behaviour based on Archard's wear model. This allows the calculation of the wear depth in each loading cycle with constant mesh updating using the finite element method. The developed computational model has been evaluated on a spur gear pair, where the pinion made of POM was meshed with a support gear made of steel. The computational results obtained were compared with the analytical results according to the VDI 2736 guidelines. Based on this comparison, it was concluded that the proposed computational model could be used to simulate the wear behaviour of contacting mechanical elements like gears, bearings, etc. The main advantage of the model, if compared to the standardised procedure according to the VDI 2736 guidelines, is the geometry updating after a chosen number of loading cycles, which enables a more accurate prediction of wear behaviour under rolling/sliding loading conditions.

Mesh Characteristic Analysis of Spiral Bevel Gear Pairs Considering Assembly Errors and Tooth Tip Chipping Faults

Due to machining errors, location inaccuracies, human error, and various other factors, it is challenging to avoid assembly errors during the production of spiral bevel gears (SBGs). When SBG assembly errors occur, it can cause the appearance of edge contact and may even lead to severe tooth tip chipping. In this study, we propose an improved method based on loaded tooth contact analysis (LTCA) to examine mesh characteristics, including time-varying mesh stiffness (TVMS), unloaded transmission error, and contact stress. Furthermore, we explore the effects of assembly errors and tooth tip chipping. Moreover, it is observed that assembly errors can alter the contact area of SBGs and potentially reduce the peak-to-peak value of TVMS. Additionally, the occurrence of tooth tip chipping decreases TVMS within the chipping region, lowers transmission error, and increases maximum contact stress. Notably, when assembly errors are present, the reduction in TVMS due to tooth tip chipping exceeds that of a properly assembled SBG pair.

The effect of floating spline parameter on the dynamic characteristic of encased differential planetary gear train

The load sharing performance of encased differential planetary system has a great impact on the operating performance and service life of the transmission system of the coaxial high speed helicopter. In order to improve the load-sharing performance of the gear pair, the influence of different floating spline structural parameters on the load sharing characteristics of the system was studied. Considering the manufacturing error, installation error, time varying meshing stiffness and other factors, the Lagrange equation is used to construct the dynamic model of encased differential planetary gear train with floating spline structure. The effects of input torque, spline clearance, spline shaft stiffness and spline friction coefficient on the load sharing performance of gear pairs were analyzed. The results show that the differential stage system has a better load sharing performance than the encased stage system. The increase of input torque helps to improve the load sharing performance of the system, and the improvement of the encased stage system is more obvious. The floating spline of sun gear of the encased stage has a greater impact on the load sharing performance of the system. Furthermore, increasing the floating spline clearance, reducing spline shaft stiffness or increasing the friction coefficient of the spline can improve the load sharing performance of the system overall.

Influence of gear modification on dynamic characteristics of star gearing system in geared turbofan (GTF) gearbox based on a closed-loop dynamic analysis method

The star gearing transmission system is a key component of a geared turbofan (GTF) aero-engine. Accurate prediction of the dynamic characteristics of the star gearing transmission system, especially after gear modification, is important for the design of high-performance engines. Firstly, this paper establishes a dynamic time-varying mesh stiffness (TVMS) and a comprehensive transmission error (TE) calculation model for herringbone gear pair considering changes in the meshing state. Then, the dynamic internal excitation calculation model is combined with the lumped parameter dynamic model of the system to form the “excitation–response–feedback” closed-loop coupling dynamic analysis method of the GTF star gearing system. Compared with traditional analysis methods, this method takes into account the effect of contact state changes on internal excitation during the calculation process and corrects internal excitation in real time. Finally, the effect of different topology modification schemes on the system's dynamic characteristics is investigated based on this method. The results show that the closed-loop coupled dynamics analysis method is able to capture contact state changes of the same gear pair at different moments and between different gear pairs at the same moment. Modified #2 is only to modify the planet gear. This scheme can effectively reduce the vibration displacement of the ring gear, and reduce the peak-to-peak value of the ring gear's vibration displacement in all directions by more than 70%. At the same time, the scheme also reduces the load-sharing coefficient of the internal and external meshing pairs of the system by 1.92% and 2.01%, respectively, and the peak-to-peak value of the dynamic factor of the internal and external meshing pairs can be reduced by 57.91% at most.

Stochastic uncertain lubrication in gear transmission subjected to tribodynamic loading

A stochastic uncertain tribodynamic model is established for a spur gear pair for the first time. The stochastic uncertainty of pinion rotation speed propagated to lubrication performance is investigated. The probability density function of the minimum lubricant film thickness hmin evolves over time periodically at interval of an engagement process. Correspondence between abrupt increase in meshing force and amplification of hmin uncertainty is found. Robust and reliable lubrication performance can be achieved by suppressing the hmin uncertainty and decreasing the lubrication failure probability. This can be done by increasing lubricant viscosity, and decreasing input torque and uncertainty level of input rotation speed. This work lays a solid foundation for robust and reliability based optimization for tribodynamic gear system.

Combining the Asymptotic Numerical Method with the Harmonic Balance Method to capture the nonlinear dynamics of spur gears

The present work proposes the Asymptotic Numerical Method (ANM) combined to the Harmonic Balance Method (HBM) as a valuable approach to solve the nonlinear dynamics of gear pairs. The ANM is a continuation method based on high-order Taylor series expansion of the computed solution branch. The HBM is a periodic solution representation method based on high-order Fourier series. Thanks to a quadratic recast of the equation of motion, the Taylor and Fourier series can be computed in a very efficient way and each step produces a continuous representation of the solution branch making the continuation very robust. By employing this method, the periodic solutions may be easily expressed with respect to both the shaft rotation frequency and the gear mesh frequency as the adoption of a high number of harmonics has negligible effects on the computational burden. Effectiveness and reliability of the method are proven by comparing the numerical results with that obtained from the Runge–Kutta time integration scheme and experimental data from literature. Afterwards, a comparison in terms of computational efficiency is performed. Finally, some considerations are drawn in order to highlights the main differences between the two methods within gear dynamics computation.

WEAR LOAD CAPACITY OF CROSSED HELICAL GEARS

The paper presents a wear load capacity of crossed helical gears (gear pair consists of a worm and a helical gear). Crossed helical gears are similar to worm gear pairs, and it is logical to extend the load capacity calculation approach of worm gears for the case of crossed helical gears. One of the disadvantages of crossed helical gear sets is very high running-in wear. The paper explains the transition between running-in and steady-state wear and proposes a joint wear calculation model. The paper outlines a proposal to extend the calculation method for wear load capacity from a worm gear pair to the case of crossed helical gears (a worm with a helical gear). This calculation method for determining the wear load capacity of crossed helical gears is verified for the cases when the wheel is of bronze CuSn12Ni2-C-GCB and sintered steel Fe1.5Cr0.2Mo.

Rounding theory and method for the pitch curves of the variable center distance non-circular gear pair based on working conditions

Rounding theory and method for the pitch curves of the variable center distance non-circular gear pair based on working conditions

Dynamic Characteristics Analysis of High-Speed Fixed-Axis Gear Pair with Spalling Fault for a Wind Turbine Gearbox Considering Friction and Flash Temperature

Dynamic Characteristics Analysis of High-Speed Fixed-Axis Gear Pair with Spalling Fault for a Wind Turbine Gearbox Considering Friction and Flash Temperature

Research on the Calculation Method for the Load Distribution of the Dual-Input Counter-Rotating Transmission System

In order to solve the problem of an uneven load distribution in a double-input and double-output gearbox, based on the small-displacement Jacobi spin theory and considering the manufacturing and assembly errors of the gearbox, a Jacobi spin analysis model of the gearbox was established. In order to improve the accuracy of the three-dimensional tolerance analysis of the gearbox, on the basis of the processing method of parallel chain of gears and shafts and box and shafts, the serialization method of parallel chain of meshing gear pairs is proposed, and the gearbox was established. For the three-dimensional tolerance analysis model, three-dimensional tolerance analysis was carried out on the side-clearance dimensions of double-input and double-output gearboxes, and the side clearance values under the extreme value method and Monte Carlo method were deduced and combined with the theoretical side clearance to obtain the range of the side clearance of the gearboxes. Elastic deflection analysis was carried out on the gearbox shaft system, and the compensation relationship between the elastic deflection and the side clearance was investigated, so as to calculate the range of the value of the gearbox uniform load coefficient from 1 to 1.259. The error between the theoretically calculated uniform load coefficient and the experimentally tested uniform load coefficient was 6.61%, which verifies the reasonableness of the load distribution method of double-input and double-output gearboxes calculated using three-dimensional tolerance analysis combined with the elastic deflection angle, and provides a theoretical basis for the optimal design of the uniform load of multi-branch input gearboxes.

Investigation of Gear Meshing Vibration and Meshing Impact Resonance Intensity Assessment

Abstract Gear drive is one of the most widely used transmission forms. Its vibration analysis plays an important role in design and operation. Considering the gear meshing resonance phenomenon (MRP), the paper analyzes the influences of rotating speed and load on meshing resonance intensity (MRI). Based on the gear meshing impact mechanism, meshing force variation during the engagement process were obtained. It was considered as meshing impacts exerted on the gear system. By comparing the maximum meshing force under different circumstances, it was found that rotating speeds and loads were positively related to meshing forces. The vibration signals with different load torques and rotating speeds obtained from the gear pair were analyzed. The experiment results showed that the intensity of meshing impact increased with the increases of both rotating speed and load. It was also observed that due to the MRP, the gear meshing frequency was modulated to the resonance frequency band as meshing impacts. Consequently, the resonance frequency band contained most of the energy of the meshing impact. An indicator called resonance energy ratio (RER) was defined to represent the proportion of resonance energy due to meshing impact. The simulation and experiment result show that the proposed RER indicator can well assess the intensity of the vibration. By comparing the RER values of 20 sets of gear vibration data, the influences of rotating speed and load on MRI were discussed. The result shows that the proposed method is helpful to the vibration assessment and condition monitoring in different operational states.