Helical Gear Model Research Articles

Evaluation of Scuffing Load Capacity of Helical Gear Based on the Tribo‐Dynamic Model

ABSTRACTThe scuffing load capacity of gear is closely related to the meshing temperature rise of tooth surface. The key to predict the temperature rise is to establish an accurate meshing temperature rise model. In the paper, a tribo‐dynamic model of helical gear is established through coupling of tooth surface lubrication parameters, and the influence of temperature rise on ambient temperature during meshing process is considered. Then, the effects of oil supply temperature, input speed and torque on tooth surface temperature rise, film thickness, friction excitation and gear dynamic characteristics are discussed. The results show that the temperature rise of the gear is higher during the engaging‐in and engaging‐out regions. Meanwhile, there is local high temperature at the end of the contact line due to the end effect. The vibration of gear along the off‐line‐of‐action direction is mainly determined by friction excitation. With the increase of oil supply temperature, input speed and torque, the risk of scuffing failure increases and the influence of oil supply temperature and input load is more significant. The conclusions of this paper may provide some valuable suggestions for the anti‐gluing failure design of gear in engineering.

Improved analytical model for calculating mesh stiffness and transmission error of helical gears considering root curve: Theoretical analysis and experiments

A modified algorithm is proposed in this study to correct time-varying mesh stiffness (TVMS) and transmission error (TE) in helical gears considering tooth root transition curve. The parametric model of helical gear is established by using the meshing principle of helical gear and hob in order to obtain the accurate tooth root transition curve. Moreover, a TE test rig is set up to compare the theoretical and experimental results. The results of the improved algorithm are very similar to the experimental results compared to the traditional model, and the relative error of TE is also small. In this study, the effect of multi-parameters (e.g. pressure angle, meshing position, transverse contact ratio, and overlap ratio) on TE are investigated by comparing theory with experimental analysis. Through the analysis of parameters, it has been established that an elevation in pressure angle leads to a decrease in TE, followed by an increase. In the event that the meshing position is situated closer to the nodal point, the TE slightly decreases. Moreover, as the transverse contact ratio and overlap ratio increase, the TVMS increases, while the TE decreases. When the overlap ratio approaches an odd multiple of 0.5, the TE displays a significant peak.

Tribological characteristics evaluation of a helical gear pair based on the tribo‐dynamic model

AbstractIn this paper, a tribo‐dynamic model of a helical gear is established. For the lubrication sub‐model, a finite line thermal elastohydrodynamic lubrication model of helical gear is adopted. The lateral vibration, axial vibration of gear and torsional vibration of the gear shaft are considered in the dynamic sub‐model. Results show that the tribological parameters of helical gear under the tribo‐dynamic model deviate significantly from that of the quasi‐static model, especially in the engaging‐in region of tooth pair. The friction excitation mainly affects the vibration along the off‐line‐of‐action direction of the gears. The influence of operating conditions on the tribological and dynamic properties of a helical gear pair is significant, especially in the case related to the characteristic frequency of gears.

A Tribo‐Dynamic Model of a Helical Gear Pair Based on the Finite Line Contact Theory

In this article, a finite line contact tribo‐dynamics model of helical gears is established by coupling the tooth surface friction, friction moment, and vibration velocity. To obtain convergent results, a cycle iteration strategy is adopted to solve the two submodels, the dynamic model and the thermal elastohydrodynamic lubrication model. The parameters obtained from the dynamic model such as the dynamic load, dynamic transmission error, and instantaneous speed of the teeth surfaces are used as the boundary conditions for solving the lubrication model. Meanwhile, the friction force and friction moment obtained by the lubrication model are used as parametric excitations of the dynamic model. Based on the proposed model, the influence of dynamic effect, thermal effect, rotational speed, and tooth surface roughness on the tribological and dynamic properties of helical gears are discussed. The results show that the tribological and dynamic parameters deviate significantly from the quasistatic values, especially at the characteristic speed. The vibration along the off‐line‐of‐action direction is obviously affected by the friction excitation. As the rotational speed increases, the friction coefficient and friction force decrease as well as the vibration of the gear pair along the off‐line‐of‐action direction weakens. In addition, the surface roughness has the greatest influence on the vibration of the off‐line‐of‐action direction in all directions of gear vibrations.

Design and finite element analysis of AISI 4340 alloy steel helical gear

The present study aims at design, modeling, modal analysis, static analysis and harmonic analysis of helical gear of AISI 4340 material. The dimensions of helical gear are obtained through comprehensive theoretical design procedure. Three dimensional model of helical gear was created by three dimensional modeling software. Ansys workbench finite element tool was used for harmonic analysis, static structural analysis and modal analysis of designed helical gear. Helical gears are commonly used components in power transmission system. Helical gears play a vital role in transmitting motion and power. Gear teeth are usually subjected to root bending stresses and tooth contact stresses. Study of these stresses during designing helical gear is very important. Hence numerical analysis of AISI 4340 helical gear is done using numerical analysis software tool to check the designed gear met the application requirement or not.

A revised method to calculate time-varying mesh stiffness of helical gear

Time-varying mesh stiffness (TVMS) of gear plays vital role in analysing dynamic characteristic of gear transmission. So accurately evaluating the TVMS is important and essential. In this paper, a revised method to calculate the TVMS of helical gear is proposed. Based on slice method, the helical gear is sliced into pieces along the tooth width direction. The proposed method corrects the fillet foundation stiffness within multi-tooth in contact and considers the non-linearity and load-dependence of the Hertzian contact stiffness. The effect of the axial mesh force is considered. Finally, an equivalent helical gear model is established in ANSYS to study the mesh stiffness. The results show the proposed method has high effectiveness compared with FEM (finite element method).

Simulation analysis of gear contact stress in reduction gearbox

In this paper, the contact stress of reducer gears is simulated and analyzed, and the assembly error is considered. Application of three-dimensional modeling software SolidWorks helical gear model is set up, and carried out in accordance with the working condition of two kinds of error assembly, including the backlash error and axis parallelism error, and the finite element analysis software ANSYS, the contact surface and tooth root, the contact stress of the online statics and dynamics analysis, it is concluded that the stress under two kinds of error and change situation, the size of the summary analysis of the influence on gear transmission, in the future has reference and guiding significance to the actual production of gear assembly. Combining the powerful modeling function of CAD software with CAE, it embodies the integration of CAD and CAE technology.

The Load Distribution with Modification and Misalignment and Thermal Elastohydrodynamic Lubrication Simulation of Helical Gears

A non-uniform model of the load per unit of length distribution of helical gear with modification and misalignment was proposed based on the meshing stiffness, transmission error, and load-balanced equation. The distribution of unit-lineload, transmission error (TE), and contact press of any point on the contact plane were calculated by the numerical method. The feature coordinate system was put forward to implement the helical preliminary design and strength rating.The thermal elastohydrodynamic lubrication (EHL) model of helical gear was established, and the pressure, film, and temperature fields were obtained from the thermal EHL model.The maximum contact temperature and minimum film thickness solved by thermal EHL were applied to check the scuffing load capacity. The highest flash temperature and thinnest film occur in the dedendum of the pinion. The thermal EHL method to evaluate the scuffing load capacity is effective.

Design And FEM Analysis of Helical Gear

In this paper the problem of the failure of gear in speed reduction gearbox developed by Laxmi Hydraulic Pump (LHP) Pvt Ltd, Solapur is resolved by replacing the existing material by a material SAE8620. The Gear and Pinion using AGMA and FEM analysis Method. In the gear design, the bending stress and surface strength of the gear tooth are considered to be one of the main factors to the failure of the gear. In this paper bending and contact stresses are calculated by using analytical method as well as Finite Element Method. To estimate bending stress modified Lewis beam strength method is used as well as AGMA method. Software is used to generate the 3-D solid model of helical gear. Ansys software package is used to analyze the bending stress. Contact stresses are calculated using modified AGMA contact stress method. Ansys software package is used to analyze the contact stress and bending stress. The main objective of this study has to investigate the stresses induced by gear tooth profile. Finally, the results obtained by theoretical analysis and Finite Element Analysis are compared to check the correctness. Estimated stress is used to calculate module of gear which can withstand easily at given loading conditions. A conclusion has arrived on the material which is best suited for helical gear based on the results.

Analysis of vibration characteristic for helical gear under hydrodynamic conditions

Based on the elasto-hydrodynamic lubrication theory, a 2-degree-of-freedom nonlinear dynamic model of helical gears with double-sided film is proposed, in which the minimum film thickness behaves as a function of load parameters, lubricant parameters, and the geometry of the contact. Then, the comparison of the hysteresis loops in different gear models shows the soundness of the presented model. Using numerical method, the time evolution of lubricant normal force, minimum film thickness, and lubricant stiffness is obtained in order to demonstrate the influence of the driving torque and pinion’s velocity. The results obtained in this article can contribute to the root cause for the gear vibration and show that the hydrodynamic flank friction has almost no influence on the gear system.

Calculation of Meshing Efficiency of Helical Gear Based on Double Integral Method

The meshing efficiency of helical gear transmission is calculated by using the method of double integral. The external involute helical gear meshing is taken and the model of helical gears is simplified by the idea of differential. The instantaneous efficiency equation of a meshing point is derived, and further more the rectangular coordinate system of meshing zone of helical gears is established. The average meshing efficiency of helical gears is achieved by using double integral method. Then, the influence of design parameters is studied and the efficiency formula is verified by comparing the theoretical results with relevant experimental data, which can provide a theoretical basis for decide the design parameters.

Coupled lateral-torsional-axial vibrations of a helical gear-rotor-bearing system

Considering the axial and radial loads, a math- ematical model of angular contact ball bearing is deduced with Hertz contact theory. With the coupling effects of lateral, torsional and axial vibrations taken into account, a lumped-parameter nonlinear dynamic model of helical gear- rotor-bearing system (HGRBS) is established to obtain the transmission system dynamic response to the changes of dif- ferent parameters. The vibration differential equations of the drive system are derived through the Lagrange equation, which considers the kinetic and potential energies, the dis- sipative function and the internal/external excitation. Based on the Runge-Kutta numerical method, the dynamics of the HGRBS is investigated, which describes vibration proper- ties of HGRBS more comprehensively. The results show that the vibration amplitudes have obvious fluctuation, and the frequency multiplication and random frequency compo- nents become increasingly obvious with changing rotational speed and eccentricity at gear and bearing positions. Ax- ial vibration of the HGRBS also has some fluctuations. The bearing has self-variable stiffness frequency, which should be avoided in engineering design. In addition, the bearing clearance needs little attention due to its slightly discernible effect on vibration response. It is suggested that a careful examination should be made in modelling the nonlinear dy- namic behavior of a helical gear-rotor-bearing system.

The Influence of the Pinion-Shaft Deflection on the Dynamic Characteristics of Helical Gear Pairs

This study presents a dynamic model of helical gears for analyzing the effect of pinion-shaft flexibility on the dynamic behavior of helical gears. In the analysis, the time-varying mesh stiffness is determined in relation with the geometry of the gear pair and incorporates the deflection of the pinion–shaft. A comparison analysis is presented for the dynamic transmission error response of gear pairs supported with a rigid and a flexible shaft system. The results show that the pinion-shaft deflection must be included in the dynamic analysis since they can strongly affect the dynamic characteristics of helical gear pairs.

The Design and Finite Element Analysis for Crane Turntable Gear Based on Pro/E and ANSYS

The use of Pro/E and their respective advantages ANSYS software product design and engineering analysis to solve the case, first of all in the Pro/E, the completion of three-dimensional helical gear design, and then in the Pro/MECHANICA completed finite element model of helical gear, and then into ANSYS for finite element analysis of bevel gear calculation and simulation, finite element analysis of the final results of optimization design model is presented recommendations for improvement. The product design and engineering analysis method has some reference value in engineering design.

Finite Element Analysis of Impact of Root Fillet on Bending Stress for Helical Gear of Automotive Transmission

On the basis of the analysis of special demand of helical gear of automotive transmission, gear precision modeling and finite element analysis of bending stress were carried out in this paper. In UG three-dimensional modeling environment, helical gear model was generated and imported into ANSYS software. Then the meshing on the geometric model and influence on gear strength with different radius of root fillet were discussed. The paper provided certain methods to guide the gear parametric design, strength analysis and improve optimization design efficiency of transmission gear parts.

Finite Element Analysis of Flexural Strength for Helical Gear of Automotive Transmission

On the basis of the analysis of special demand of helical gear of automotive transmission, gear precision modeling and finite element analysis of flexural strength were carried out in this paper. In UG three-dimensional modeling environment, helical gear model was generated and imported into ANSYS software through data exchange interface. Then meshed on the geometric model, discussed the tooth contact area and the detrimental loading position, and compared the influence on gear strength with different tooth root fillet radius. The paper provided certain methods to guide the gear parametric design, strength analysis and improving optimization design efficiency of transmission gear parts.

Dynamic Behavior of Helical Gears with Effects of Shaft and Bearing Flexibilities

This study presents a numerical model of helical gears to consider the effects of shaft and bearing flexibility. A primary feature of this study is that the time-varying mesh stiffness is not just determined by the geometry of gear pair but also updated for each iteration according to the change of center distance. The effects of shaft and bearing flexibilities are discussed by comparing the dynamic response of gear pairs supported with a rigid and a flexible bearing-shaft system. The results show that the pressure angle and contact ratio are significantly changed due to the center-distance variation of gears and the gear pair with a flexible bearing-shaft system has much larger vibration. Finally, experimental tests are conducted to validate the proposed model. The predicted results show good agreement with the experimental data.

Research on Natural Characteristics of Helical Gear in Gearbox for Wind Turbine Generator

The three-dimensional helical gear model based on the geometric parameters is created by using software called PROE3.0. The natural characteristics of helical gear are analyzed by using the finite element method. The natural frequency of the helical gear is calculated by the software ANSYS and the principal mode of vibration is discussed. There are four vibration modes, which are circular vibration, torsional vibration, radial vibration and umbrella vibration. The phenomenon of resonance of the helical gear can be avoided by choosing suitable parameters and changing the natural frequency of the helical gear.

토크 변동에 의한 백래시를 가진 헬리컬 기어의 비선형 동적 해석

Backlashes of gears provide gears for good lubrication and for removal of the interference between teeth by the wear and manufacturing errors. The backlash is the strong nonlinear factor to gears. This study deals with nonlinear modeling of helical gears with backlash. Excitation of helical gears comes from torque variation, the tooth surface error, and the periodical change of mesh stiffness. To study the effect of torque fluctuation, equation of motion for the single degree of freedom torsional model of helical gears with the periodical change of mesh stiffness and the backlash was derived. The Newmark beta method and the Newton-Raphson method were used to obtain the nonlinear behaviors of mesh forces of helical gears. All excitation frequencies initially caused the tooth separation and single-sided impacts of the gear pair and eventually led to the normal tooth contact. However, some special excitation frequencies caused the single-sided impacts in the entire time as well as the initial time. Damping increase reduced the duration of single-sided impacts, and the backlash increase caused those in the entire time domain.

Numerical simulation and experimental verification of carburizing-quenching process of SCr420H steel helical gear

Using DEFORM 2D ver. 9.0 and 3D ver. 6.0, a finite-element model was developed to study the prediction accuracy for the modeling of carburized-quenched helical gear. The helical gear model incorporates phase transformation kinetics during heating, carburizing, diffusing and quenching process. Carbon- and temperature-dependent material properties of austenite, martensite and bainite including transformation-induced volume change, latent heat and transformation plasticity are considered in calculating the stress–strain distribution. The total strain is divided into individual strain which are thermal, elastic, plastic, phase transformation and transformation plastic strain, respectively. There are 2 thermal boundary conditions employed which are uniform heat transfer coefficient (HTC) that is estimated from an oil-quenched silver probe by using the lumped-heat capacity method, and zone-based HTC that is estimated from an oil-quenched SUS304 gear blank by using the iterative modification method. The aim of this study is to evaluate the prediction accuracy of the simulated results when both methods of HTC are employed. The results of the simulation and experiment e.g., cooling curves, cooling rate curves, radial displacement, hardness, diffused carbon layer, residual stress and strain distribution are presented. The summary is that although zone-based HTC gives a more accurate prediction of thermal history than uniform HTC, it does not give significant accuracy in the prediction of hardness, distortion and residual stress.