Helical Gear Transmission Research Articles

Advancing high-speed train gearbox durability: enhanced bearing load and contact stress through transition from helical to herringbone gears

High-speed trains typically utilize helical gear transmissions, which significantly impact the bearing load capacity and fatigue service performance of the gearbox bearings. This paper focuses on the gearbox bearings, establishing dynamic models for both helical gear and herringbone gear transmissions in high-speed trains. The modeling particularly emphasizes the precision of the bearings at the gearbox’s pinion and gear wheels. Using this model, a comparative analysis is conducted on the bearing loads and contact stresses of the gearbox bearings under uniform-speed operation between the two gear transmissions. The findings reveal that the helical gear transmission generates axial forces leading to severe load imbalance on the bearings at both sides of the large gear, and this imbalance intensifies with the increase in train speed. Consequently, this results in a significant increase in contact stress on the bearings on one side. The adoption of herringbone gear transmission effectively suppresses axial forces, resolving the load imbalance issue and substantially reducing the contact stress on the originally biased side of the bearings. The study demonstrates that employing herringbone gear transmission can significantly enhance the service performance of high-speed train gearbox bearings, thereby extending their service life.

Robust modification optimization for helical gear mounting errors based on contact ratio

Mounting errors are a disruptive factor in gear utilization. This paper investigates the contribution of mounting error components in helical gears to the helix slope deviation using the involute equations. A model of the helical gear transmission system has been established, by which the impact of mounting errors on the loaded transmission error and contact ratio of the bevel gear transmission was studied using the Loaded Tooth Contact Analysis method. A bench test was then casted as a verification of this model. A methodology was proposed for optimizing the micro modification of helical gear flanks based on contact ratio control. Robust optimization of the mounting error was achieved by reducing the contact ratio under commonly used torques compared to the contact ratio at the local minimum of the loaded peak-to-peak transmission error. This approach has been demonstrated to enhance the robustness of gear transmission against mounting errors and torque fluctuations.

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.

Towards Condition Monitoring: Fabrication and Finite Element Analysis of A Helical Gear Transmission Rig for Fault Simulation

Towards Condition Monitoring: Fabrication and Finite Element Analysis of A Helical Gear Transmission Rig for Fault Simulation

Nonlinear dynamics simulation of the helical gear transmission system for high-speed train

Considering the bending-torsional-axial-coupled vibration of the helical gear transmission system, a 10 degrees of freedom high-speed train gear transmission system model, including motor and load, is established based on the lumped parameter method. In addition, the potential energy method based on the slicing principle is used to accurately calculate the time-varying meshing stiffness of helical gears. Furthermore, the influence of geometric parameters of helical gears on the time-varying meshing stiffness is studied, and the impact of time-varying meshing stiffness on the system is further investigated. Meanwhile, by analyzing the dynamic phenomena of the system under different parameter excitations under different parameter excitations, the influence of internal and external excitation parameters such as gear speed, wheel rail creep force, support stiffness, and support damping on the stability of high-speed train gear transmission system is deeply studied.

Vibration nonstationary representation of the railway vehicle's gear system considering spalling failure under variable speed conditions: Numerical modeling and field testing

The nonstationary representation of spalling faults in the helical gear transmission system of railway vehicles remains unclear under variable speed conditions, and the selection of sensitive features in faults recognition has been confirmed as a problem to be addressed in this field. Thus, a vehicle-track coupled model with a helical gear transmission system was built in this study, which considered the spalling faults and employed field testing data to verify the model. The model was adopted to analyze the non-stationary representation of a helical gear system with spalling faults in the translational directions under variable speed conditions. Subsequently, the data originating from the simulation and field testing were adopted in this study, such that the ReliefF-MSVM (Multi-class SVM) algorithm was driven to sift the sensitive features in the translational directions and obtain the optimal sensitive features and diagnostic direction. The result achieved with the sensitive features selected suggested that the vertical statistical characterization of the helical gear transmission system of railway vehicles exhibited low dimensionality and high robustness, and the diagnostic results were optimal. This study can provide a theoretical reference for dynamics analysis, health monitoring, and fault diagnosis in the helical gear system of railway vehicles.

Dynamics model and vibrational response analysis of helical gear-rotor-bearing transmission system

As a core component of wind turbines, wind power gear speed increasers often work in harsh environments, so it is necessary to study the vibration characteristics of gear transmission systems. Taking a wind turbine gearbox high-speed stage helical gear transmission system as the research object, the dynamics model of multi-degree-of-freedom helical gear-rotor-bearing transmission system is established by the lumped parameter method and solved by Runge-Kutta method, taking into account the tooth side clearance of the gear, transmission error, eccentricity and support force of the nonlinear bearing. The effects of input torque, transmission error and tooth side clearance on the vibration characteristic response of the helical gear train were analyzed. The relationship between the trend of amplitude change in each direction of the gear and the trend of change in the major frequency components was analyzed under the conditions of changing internal and external excitation. The results show that torsional vibration dominates in the system. As the input torque increases, the vibration amplitude of the driving and driven gears decreases, and the frequency amplitude decreases significantly at multiple locations. Gear transmission errors and changes in tooth side clearance have significant effects on gear vibration amplitudes, but are sensitive only to the meshing frequency. The trend of gear vibration amplitude caused by the change of external excitation of the gear set is synchronized with the trend of main frequency amplitude in the corresponding direction, while the change of vibration amplitude caused by internal excitation is consistent with the trend of mesh frequency amplitude in the corresponding direction. The results of this paper can pave a certain foundation for the design and fault diagnosis of wind power gearbox transmission system.

Research on Noise Reduction Modification Design of High Speed EMU Traction Arc Toothed Cylindrical Gears

Aiming at the deficiencies of the traction helical gear transmission system when the EMU is running at high speed, this paper proposes and designs a kind of arc toothed cylindrical gear adapted to the traction of higher speed EMU. A parametric arc toothed cylindrical gear model was constructed using CREO, and its dynamic contact characteristics and acoustic response characteristics were analyzed under sustained operating conditions using the finite element boundary element method. The design of a tooth profile combined with the radius of the arc toothed line of the comprehensive trimming program put forward a virtual trimming prototype method through MATLAB and CREO reconstruction gear, and trimming before and after the gear transmission simulation experiments occurred for comparison and analysis. This study shows that the traction arc toothed cylindrical gear comprehensive modification method proposed in this study achieves better dynamic performance optimization, effectively reduces the contact stress and radiation noise of the gear transmission, and provides a theoretical basis for the development of a new generation of high-speed EMU stock traction drive systems.

Influence of idler misalignment fault on contact and dynamic characteristics of helical gear

Due to the advantages of stable helical gear transmission, it is widely used in industry, agriculture, and national defense. Shaft misalignment has a great influence on the vibration, bearing capacity, and life of gear transmission. Based on the idler wheel drive system as the research object, according to the principle of gear meshing, the helical gear time-varying contact wire length model was deduced. The dynamic model of the gear transmission system with faults is established considering the faults of the idler's center distance error and angle error, and the influence law of idler misalignment fault on the vibration of the idler transmission system is revealed. On this basis, the finite element model under angle error is established to analyze the contact stress of the tooth surface under different faults and reveal the contact stress distribution law of the tooth surface. The results show that the misalignment fault will change the length of the helical gear contact line. When the gear shaft misaligns, it will increase the axial force of the gear and increase the axial vibration of the gear. Moreover, the angle error will cause uneven load distribution on the tooth surface of the helical gear, which will reduce the contact area of the gear and increase the contact stress. The phenomenon of off-load of gear accelerates the wear of the gear tooth surface and shortens the life of the gear. The study of idler misalignment fault is of great significance for prolonging the life of gear and providing the basis for gear fault diagnosis.

Calculation of the deformation values of the ammortizer in the compound angle gear transmission

The article presents the method of calculating the axial deformations of the rubber bush used in the bevel gear with the recommended composition and the formulas for determining the axial deformations. Based on the analysis of the connection graphs, the recommended values of its parameters were determined. The article presents the results of an analysis of the design features and disadvantages of cylindrical gears. An effective design scheme for a helical cylindrical gear transmission with elastic elements has been developed, allowing it to absorb peak values of oscillations of torques and axial force components arising from the meshing of wheel teeth, as well as cycling noise indicators.

Multi-objective optimization model of transmission error of nonlinear dynamic load of double helical gears

Abstract In order to address the impact of reduced transmission stability and reliability caused by volume reduction on the quality of gear transmission, this article proposes a multi-objective optimization model for nonlinear dynamic load transmission errors of double helical gears. This study aims to introduce a multi-objective design method for gear transmission, using the volume and smooth reliability of helical gears as objective functions, and establish a multi-objective optimization design mathematical model for helical cylindrical gear transmission. In order to solve this multi-objective optimization problem, we utilized the optimization toolbox in the scientific calculation software MATLAB with examples. The results show that after the joint optimization design of volume and coincidence degree, it is calculated that the volume after the joint optimization design is still 2.2624 × 107 mm3, and the coincidence degree is 5.9908. After rounding, the design result is m n = 3 , Z 1 = 31 , β = 20 ∘ , Ψ d = 1.2 {m}_{{\rm{n}}}=3,{Z}_{1}=31,\beta ={20}^{\circ },{\Psi }_{{\rm{d}}}=1.2 . The optimization design results show that the joint optimization design with the minimum volume and the maximum coincidence as the objective function can reduce the volume and improve the output stability of the helical gear.

Dynamic Analysis of the Helical Gear Transmission System in Electric Vehicles with a Large Helix Angle

Sliding friction is an important excitation for the vibration and noise of a transmission system. However, in cases where the helix angle of the helical gear is large, the dynamic characteristics of the transmission system in an electric vehicle caused by friction excitation have not been explored explicitly. In this study, the helix angle of helical gears is 30.5 degrees. A mesh stiffness calculation algorithm is derived. A dynamic model of a Motor Two-Stage helical gear transmission system in an electric vehicle at a constant speed is established. A bench test is carried out to verify the model. A friction model is employed. The dynamic characteristics are analysed after considering the friction and the axial stiffness component. The friction makes the vibration in the x direction increase. The vibration in the y direction is suppressed by friction. The vibration in the z direction has a small change. The components in the frequency domain also change. The axial stiffness components only make the vibration and the meshing force increase in the time domain. This indicates that friction needs to be considered when dynamic characteristics are analysed. The study is good for the reduction of vibration and noise. This may provide a theoretical base for the condition monitoring of the gear system in electric vehicles.

Initial impact force analysis and simulation of planetary helical gear transmission

The planetary gear transmission is widely used because of its advantages such as large transmission ratio and high transmission efficiency. But at the moment of starting, there is a speed difference between driving gear and driven wheel due to the backlash between the teeth, this will easily cause the initial collision and impact force, which seriously affect the life of gear transmission, even lead to tooth surface pitting and root fracture failure, therefore, it is necessary to conduct a quantitative analysis of the initial collision. Based on the gear meshing principle and the system dynamics theory, the analytical calculation formula of initial impact force for the internal and external meshing gear pair was derived. The impact simulation analysis model of planetary helical gear transmission was established based on the finite element LS-DYNA, and the simulation analysis results were compared with the analytical calculation results, which verified the correctness of the analytical calculation model. This paper reveals the impact collision mechanism and studies the influence law of the speed and temperature on the impact force, thus laying a good theoretical foundation for the dynamic modification design of the planetary gear transmission and preventing the failure of the gear teeth from impact collision.

Dynamic characteristics of helical gear with root crack and friction

Helical gear transmission is smooth and has many advantages. However, long-term operation will cause root cracks, which will reduce the time-varying meshing stiffness (TVMS) of the gears, increase the transmission error (LSTE), and reduce the load distribution ratio (Lsr). According to the slice method and the energy method, a TVMS calculation model for a helical gear pair with cracks was established, and the effects of the crack initiation width, termination width, effective contact length and crack propagation angle on the gear were studied. Then, the changes of TVMS, LSTE, and Lsr under the time-varying friction and crack are considered. Build failure dynamics model, and fourth-order Runge-Kutta solution for vibration and amplitude-frequency characteristics. And wavelet transform and variational mode decomposition (VMD) are used to analyze the vibration signal, and statistical indicators are used to analyze the sensitivity of vibration. The results show that the TVMS with tooth root cracks will gradually decrease, LSTE will increase, the Lsr will decrease, and the vibration displacement (VD) will increase. When the two faults are combined, due to the damping characteristics of friction, the TVMS will increase, the LSTE and the VD will decrease. This offers a theoretical foundation for studying the dynamic characteristics of the coupling of gear cracks and friction faults, as well as vibration and noise reduction.

A lumped parameter and CFD combined approach for the lubrication analysis of a helical gear transmission

This paper proposes a combined 1D-3D approach for the lubrication analysis of a standard transmission including two helical gears. A lumped parameter model of the entire lubrication system is developed to predict the flow distribution within the circuit and the localized pressure drops along the lines. This model considers the geometrical features of the real system, and it combines the experimental characteristic curves of the main hydraulic components. The steady-state condition is investigated, and the corresponding lubrication flow is provided as a boundary condition for a three-dimensional CFD model. The overset mesh method is employed to address the instantaneous position of the gears in the contact region and the Volume of Fluid (VOF) model assesses the multi-phase phenomenon. The turbulent behavior of the flow is described by the two-equation realizable k-ε model, and the incompressible assumption is made for both oil and air. The effect of different nozzles configurations on the lubrication efficiency is analyzed and the internal system fluid-dynamics is investigated to point out the oil path. The numerical results are discussed in terms of the volume fraction of oil on the gears teeth, the passive torques at the shafts and the associated power losses under specific operating conditions.

Vibration Analysis of Two-Stage Helical Gear Transmission with Cracked Fault Based on an Improved Mesh Stiffness Model

The crack fault has an important influence on the vibration characteristics of the transmission system. This paper is devoted to analyzing fault mechanism and dynamic characteristics of transmission with gear crack, which provides the basis for crack diagnosis and monitoring of helical gear in two-stage transmission system. For this purpose, an improved calculation method of time-varying meshing stiffness with crack fault is proposed considering the axial force of the helical gear. The influence of crack depths and angles on stiffness is analyzed. Based on this, the dynamic model of the two-stage helical gear transmission system is established using the lumped mass method. The influence of crack parameters on the characteristics of the transmission system is studied. In order to better diagnose the crack fault of the helical gear, the statistical index in time domain is calculated and the sensitivity to crack fault is analyzed. It is shown that the stiffness decreases by 25%, and the vibration acceleration increases by 8.3% after the axial force component is considered into the stiffness of the crack gear pair. The meshing stiffness decreases with the increase of crack depths and crack angles. The dynamic model is verified by rig test. Periodic impact exists in the system. The time of entering meshing of the cracked tooth and the time of complete disengagement is observed in the residual signal. In the frequency domain, there appear sidebands on the mesh frequency of the first gear pairs and its harmonics, the second gear mesh frequency and its harmonic frequencies. There is a little influence on the vibration acceleration of the driven gear of the second-stage. According to the signals in the frequency domain and the time domain, we can tell at which stage the gear is cracked. While through the time required for the crack tooth from engagement to disengagement completely, we can tell which gear is cracked. The sensitivity of skewness, impulse factor and kurtosis to crack fault decreases successively. The results provide theoretical basis for crack fault diagnosis of a two-stage helical gear transmission system.

Optimal Vibration Suppression Modification Method for High-Speed Helical Gear Transmission of Battery Electric Vehicles under Full Working Conditions

To improve the working performance of battery electric vehicle (BEV) high-speed helical gear transmission under full working conditions, combined with Tooth Contact Analysis (TCA) and Loaded Tooth Contact Analysis (LTCA), the vibration model of single-stage helical gear bending-torsion-axis-swing coupling system considering time-varying mesh stiffness was established. The genetic algorithm was used to optimize the tooth surface with the objective of minimizing the mean value of the vibration acceleration at full working conditions. Finally, a high-speed helical gear transmission system in a BEV gearbox was taken as a simulation example and the best-modified tooth surface at full working conditions was obtained. Experiment and simulation results show that the proposed calculation method of time-varying meshing stiffness is accurate, and tooth surface modification can effectively suppress the vibration of high-speed helical gear transmission in BEV; compared to the optimally modified tooth surface under a single load, the optimal modified tooth surface under full working conditions has a better vibration reduction effect over the entire working range.

Optimal design of high efficiency double helical gear based on dynamics model

A 16-degree-of-freedom dynamic model for the load contact analysis of a double helical gear considering sliding friction is established. The dynamic equation is solved by the Runge–Kutta method to obtain the vibration displacement. The method combines the friction coefficient model based on the elastohydrodynamic lubrication theory with the dynamic model, which provides a theoretical basis for the calculation of the power loss of the transmission system. Moreover, the sensitivity analysis of the parameters that affect the transmission efficiency is carried out, and an optimization method of meshing efficiency is proposed without reducing the bending strength of the gears. This method can directly guide the design of the double helical gear transmission system.

Fault simulation and forecast of helical cylindrical gear of reducer based on ADAMS

Aiming at the problems that the dynamic speed and meshing force of the helical cylindrical gear of the reducer are difficult to actually measure and the test cost is high, the helical cylindrical gear transmission system of a crane reducer is used as the research object, and the 3D modeling software Solid Works is used to establish the assembly model of the gear transmission system, import the dynamic simulation software ADAMS to establish simulation model, and perform simulation analysis on it. The simulation results show that the gear speed is stable after acceleration, which is basically close to the theoretical calculation value; meshing at different multiples the gear meshing force amplitude is different at different frequencies. As the frequency multiplier increases, the amplitude shows a downward trend. Finally, Ensemble Empirical Mode Decomposition (EEMD) sample entropy and Extreme Learning Machine (ELM) are used for fault prediction to verify the effectiveness of this method. The above can provide a certain reference basis for the condition monitoring and fault prediction of the gearbox of metallurgical cranes, so as to ensure the safe operation of the crane.

Development of a Test Bench for Transmission Efficiency of Small Modulus Worm Helical Gears

Worm helical gear transmission falls between lever transmission and inclined transmission in principle. There is large relative sliding speed between the conjugate tooth surfaces, and the transmission efficiency is low. To accurately grasp the changing law of worm helical gear transmission efficiency and propose an effective efficiency improvement method, this paper designed and built a transmission efficiency test bench for small modulus worm helical gear transmission pair.