Theoretical Explanation for Lower Order Harmonic Resonance Phenomenon of Three-Ring Gear Transmissions

Dynamic investigations revealed that lower order harmonic resonance phenomenon exists in the three ring gear transmission. That is, when the input speed is close to 1/3, 1/6, 1/9,…, 1/3 n of the primary natural frequency of the transmission, the loads on the bearings and gears are especially high. This paper explained this phenomenon from the viewpoint of parametric resonance in terms of perturbation technique. A conclusion was drawn that the basic reason for this phenomenon is the primary resonance caused by forcing excitation and parametric resonance caused by parametric change.

Design of Pinion Machine Tool-settings for Spiral Bevel Gears by Controlling Contact Path and Transmission Errors

This paper proposes a new approach to design pinion machine tool-settings for spiral bevel gears by controlling contact path and transmission errors. It is based on the satisfaction of contact condition of three given control points on the tooth surface. The three meshing points are controlled to be on a predesigned straight contact path that meets the pre-designed parabolic function of transmission errors. Designed separately, the magnitude of transmission errors and the orientation of the contact path are subjected to precise control. In addition, in order to meet the manufacturing requirements, we suggest to modify the values of blank offset, one of the pinion machine tool-settings, and redesign pinion ma- chine tool-settings to ensure that the magnitude and the geometry of transmission errors should not be influenced apart from minor effects on the predesigned straight contact path. The proposed approach together with its ideas has been proven by a numerical example and the manufacturing practice of a pair of spiral bevel gears.

Design and Analysis of Power and Transmission System of Downhole Pure Electric Command Vehicle

Electric vehicles use electric motors, which turn electrical energy into mechanical energy. As electric motors are conventionally used in all the industry, it is an established development site. It’s a mature technology with ideal power and torque curves for vehicular operation. Conventional vehicles use oil and gas as fuel or energy storage. Although they also have an excellent economic impact, the continuous use of oil and gas threatened the world’s reservation of total oil and gas. Also, they emit carbon dioxide and some toxic ingredients through the vehicle’s tailpipe, which causes the greenhouse effect and seriously impacts the environment. So, as an alternative, electric car refers to a green technology of decarbonization with zero emission of greenhouse gases through the tailpipe. So, they can remove the problem of greenhouse gas emissions and solve the world’s remaining non-renewable energy storage problem. Pure electric vehicles (PEV) can be applied in all spheres, but their special implementation can only be seen in downhole operations. They are used for low noise and less pollution in the downhole process. In this study, the basic structure of the pure electric command vehicle is studied, the main components of the command vehicle power system, namely the selection of the drive motor and the power battery, are analyzed, and the main parameters of the drive motor and the power battery are designed and calculated. The checking calculation results show that the power and transmission system developed in this paper meets the design requirements, and the design scheme is feasible and reasonable.

Design of Linear Functional Noncircular Gear with High Contact Ratio Used in Continuously Variable Transmission

Continuously variable transmission(CVT)of noncircular gear has the technical advantages of large bearing capacity and high transmission efficiency.The key technology of CVT with noncircular gear has been broken through some countries,and is in the stage of deep application research.Although the characteristics and design methods of noncircular gear pairs have been continuously studied in China,the noncircular gear CVT is still in the preliminary exploration and research stage.The linear functional noncircular gear pair,whose transmission ratio is a linear function in the working section,to realize continuously variable transmission was the research object in this paper.According to the required transmission ratio in the working section,the transmission ratio function in the non-working section was constructed by using a polynomial.And then the influence of pitch curve parameters in the working section on which in the non-working section was also analyzed to obtain the pitch curve suitable for transmission of this gear pair.In addition,for improving the stability and bearing capacity of gear transmission,the noncircular gear pair transmission with high contact ratio was designed.Furthermore,the accurate value of the contact tooth length was calculated based on the gear principle and the characteristics of the involute tooth profile,from this the contact tooth length error was calculated by comparing the accurate value with its actual value obtained by the rolling experiment.Finally,an indirect method to verify the contact ratio by detecting the contact length error of the tooth profile was proposed.

Geometry Design and Tooth Contact Analysis of Crossed Beveloid Gears for Marine Transmissions

Beveloid gears,also known as conical gears,gain more and more importance in industry practice due to their abilities for power transmission between parallel,intersected and crossed axis.However,this type of gearing with crossed axes has no common plane of action which results in a point contact and low tooth durability.Therefore,a geometry design approach assuming line contact is developed to analyze the tooth engagement process of crossed beveloid gears with small shaft angle for marine transmission applications.The loaded gear tooth contact behavior is simulated by applying a quasi-static analysis to study the effects of gearing parameters on mesh characteristics.Using the proposed method,a series of sensitivity analyses to examine the effects of critical gearing parameters such as shaft angle,cone angle,helix angle and profile-shift coefficient on the theoretical gear mesh is performed.The parametric analysis of pitch cone design shows that the dominant design parameters represented by the angle between the first principle directions（FPD） and normal angular factor are more sensitive to the shaft and cone angles than they are to the helix angle.The theoretical contact path is highly sensitive to the profile-shift coefficient,which is determined from the theoretical tooth contact analysis.The FPD angle is found to change the distribution of contact pattern,contact pressure and root stress as well as the translational transmission error and the variation of the mesh stiffness significantly.The contact pattern is clearly different between the drive and coast sides due to different designed FPD angles.Finally,a practical experimental setup for marine transmission is performed and tooth bearing test is conducted to demonstrate the proposed design procedure.The experimental result compared well with the simulation.Results of this study yield a better understanding of the geometry design and loaded gear mesh characteristics for crossed beveloid gears used in marine transmission.

Effect of static transmission error on dynamic responses of spiral bevel gears

The effect of static transmission error on nonlinear dynamic response of the spiral bevel gear system combining with time-varying stiffness and backlash was investigated.Firstly,two different control equations of the spiral bevel gear model were adopted,where the static transmission error was expressed in two patterns as predesigned parabolic function and sine function of transmission errors.The dynamic response,bifurcation map,time domain response,phase curve and Poincare map were obtained by applying the explicit Runge-Kutta integration routine with variable-step.A comparative study was carried out and some profound phenomena were detected.The results show that there are many different kinds of tooth rattling phenomena at low speed.With the increase of speed,the system enters into stable motion without any rattling in the region(0.72,1.64),which indicates that the system with predesigned parabolic function of transmission error has preferable capability at high speed.

Research on stepless transmission utilizing noncircular gears

In view of the lack of systemic analysis for stepless transmission using noncircular gears, two basic noncircular gear units, an addition unit adopting differential mechanism and a multiplication unit applying a fixed gear train, are proposed. Then, the design methods of the noncircular gear pair of each unit, transmission ratio relationship, rotation angle relationship and key parameters with specific physical meanings are studied. The adjusting properties, composing strategy and varying range of transmission ratio etc. are investigated in detail for each unit. Following this, several examples of using a noncircular gear pair in the units and their manipulation technique are introduced.

Design and Experimental Research on Seedling Pick-Up Mechanism of Planetary Gear Train with Combined Non-circular Gear Transmission

Currently, transplanting mechanisms for dryland plug seedlings in China are mainly semiautomatic and have low efficiency. The rotary seedling pick-up mechanism with a planetary gear train for non-uniform intermittent transmission, and a concave and convex locking arc device, has a large rigid impact. To solve these problems, according to the design requirements for a dryland plug seedling transplanting mechanism, a rotary seedling pick-up mechanism of a planetary gear train with combined non-circular gear transmission of incomplete eccentric circular and noncircular gears was proposed. This has the characteristics of two-times greater fluctuation of the transmission ratio in a cycle, and can achieve a non-uniform continuous drive. Through analysis of the working principle of the seedling pick-up mechanism, its kinematics model was established. The human–computer interaction optimization method and self-developed computer-aided analysis and optimization software were used to obtain a set of parameters that satisfy the operation requirements of the seedling pick-up mechanism. According to the optimized parameters, the structure of the seedling pick-up mechanism was designed, a virtual prototype of the mechanism was created, and a physical prototype was manufactured. A virtual motion simulation of the mechanism was performed, high-speed photographic kinematics tests were conducted, and the kinematic properties of the physical prototype were investigated, whereby the correctness of the theoretical model and the optimized design of the mechanism were verified. Further, laboratory seedling pick-up tests were conducted. The success ratio of seedling pick-up was 93.8% when the seedling pick-up efficiency of the mechanism was 60 plants per minute per row, indicating that the mechanism has a high efficiency and success ratio for seedling pick-up and can be applied to a dryland plug seedling transplanter.

Analysis of Mixed Model in Gear Transmission Based on ADAMS

The traditional method of mechanical gear driving simulation includes gear pair method and solid to solid contact method. The former has higher solving efficiency but lower results accuracy; the latter usually obtains higher precision of results while the calculation process is complex, also it is not easy to converge. Currently, most of the researches are focused on the description of geometric models and the definition of boundary conditions. However, none of them can solve the problems fundamentally. To improve the simulation efficiency while ensure the results with high accuracy, a mixed model method which uses gear tooth profiles to take the place of the solid gear to simulate gear movement is presented under these circumstances. In the process of modeling, build the solid models of the mechanism in the SolidWorks firstly; Then collect the point coordinates of outline curves of the gear using SolidWorks API and create fit curves in Adams based on the point coordinates; Next, adjust the position of those fitting curves according to the position of the contact area; Finally, define the loading conditions, boundary conditions and simulation parameters. The method provides gear shape information by tooth profile curves; simulates the mesh process through tooth profile curve to curve contact and offer mass as well as inertia data via solid gear models. This simulation process combines the two models to complete the gear driving analysis. In order to verify the validity of the method presented, both theoretical derivation and numerical simulation on a runaway escapement are conducted. The results show that the computational efficiency of the mixed model method is 1.4 times over the traditional method which contains solid to solid contact. Meanwhile, the simulation results are more closely to theoretical calculations. Consequently, mixed model method has a high application value regarding to the study of the dynamics of gear mechanism.

Modeling and Calculation of Impact Friction Caused by Corner Contact in Gear Transmission

Corner contact in gear pair causes vibration and noise,which has attracted many attentions.However,teeth errors and deformation make it difficulty to determine the point situated at corner contact and study the mechanism of teeth impact friction in the current researches.Based on the mechanism of corner contact,the process of corner contact is divided into two stages of impact and scratch,and the calculation model including gear equivalent error-combined deformation is established along the line of action.According to the distributive law,gear equivalent error is synthesized by base pitch error,normal backlash and tooth profile modification on the line of action.The combined tooth compliance of the first point lying in corner contact before the normal path is inversed along the line of action,on basis of the theory of engagement and the curve of tooth synthetic complianceload-history.Combined secondarily the equivalent error with the combined deflection,the position standard of the point situated at corner contact is probed.Then the impact positions and forces,from the beginning to the end during corner contact before the normal path,are calculated accurately.Due to the above results,the lash model during corner contact is founded,and the impact force and frictional coefficient are quantified.A numerical example is performed and the averaged impact friction coefficient based on the presented calculation method is validated.This research obtains the results which could be referenced to understand the complex mechanism of teeth impact friction and quantitative calculation of the friction force and coefficient,and to gear exact design for tribology.

Automatic Scallion Seedling Feeding Mechanism with an Asymmetrical High-order Transmission Gear Train

The current automatic scallion-transplanting machine is a complicated mechanism composed of two linkage mechanisms and two band carriers.It delivers seedlings ine ciently because of the movement limitations of the linkage mechanism.This paper proposes a new high-order non-circular gear train for an automatic scallion-seedling feeding mechanism.The proposed gear train has an asymmetrical transmission ratio;i.e.,its transmission ratio varies.This allows the mechanism’s execution component to move in a long displacement and rotate in a large rotation angle.The long displacement enables the execution component to reach the designed working position,and the large rotation angle allows it to feed a scallion in the required pose.A mathematical model for calculating the asymmetrical transmission ratio was established according to the closure requirements and the full-cycle motion of the driven gear pitch curve.Then,the parameter-design model of the new seedling-feeding mechanism was established,based on precise pose points and trajectory-shape control points.Moreover,an aided-design program was developed to obtain the parameter-solution domain of the scallion-seedling feeding mechanism.The mechanism parameters,which met the seedling-feeding function,were optimized to determine the transmission ratio,using a program and a kinematic simulation.Finally,a prototype of the mechanism was produced,and a seedling-feeding experiment was carried out.One-thousand seedlings were tested at a rate of 100 seedlings per minute,and the statistical success rate was 93.4%.Thus,the automatic scallion-seedling feeding mechanism significantly improves the e ciency of automatically transplanting scallions.

Effect of Tooth Profile Modification on Vibration of Power Split Gear Transmission System

Based on Newton ' s second law,the bend-torsion-shaft coupling nonlinear dynamic model and equations of power split gear transmission system are established.According to the principle of tooth profile modification,the tooth profile modification is considered as time-varying gear backlash function acting along the line of action.Then the dynamic functions are solved by using Runge-Kutta numerical method.After analyzing the effect of tooth profile modification quantity( TPMQ) and relative tooth profile modification length( TPML) to the nonlinear dynamic characteristics of power split gear transmission,the following conclusions are drawn:1 The TPMQ of a certain stage transmission affects the vibration of its own stage more significantly than the other stage,and the coupling effect between two stages can be ignored usually in the modification design;2 If the first stage TPMLs are less than 0.3,the influence of the first stage TPMLs to the first stage transmission vibration is much more greatly than the influence of the second stage TPMLs to the first stage transmission vibration,or else both the first and second stage TPMLs affect the first stage transmission vibration largely.The same is true for the second stage TPMLs,and the cutoff value is 0.2;3 The TPMQ affects the vibration of power split gear transmission system more principally than the TPML,and should be top-priority in the modification design.

Super-harmonic resonance of gear transmission system under stick-slip vibration in high-speed train

This work deals with super-harmonic responses and the stabilities of a gear transmission system of a high-speed train under the stick-slip oscillation of the wheel-set.The dynamic model of the system is developed with consideration on the factors including the time-varying system stiffness,the transmission error,the tooth backlash and the self-excited excitation of the wheel-set.The frequency-response equation of the system at super-harmonic resonance is obtained by the multiple scales method,and the stabilities of the system are analyzed using the perturbation theory.Complex nonlinear behaviors of the system including multi-valued solutions,jump phenomenon,hardening stiffness are found.The effects of the equivalent damping and the loads of the system under the stick-slip oscillation are analyzed.It shows that the change of the load can obviously influence the resonance frequency of the system and have little effect on the steady-state response amplitude of the system.The damping of the system has a negative effect,opposite to the load.The synthetic damping of the system composed of meshing damping and equivalent damping may be less than zero when the wheel-set has a large slippage,and the system loses its stability owing to the Hopf bifurcation.Analytical results are validated by numerical simulations.

A novel method to predict static transmission error for spur gear pair based on accuracy grade

This paper proposes a novel method to predict the spur gear pair’s static transmission error based on the accuracy grade,in which manufacturing errors(MEs),assembly errors(AEs),tooth deflections(TDs)and profile modifications(PMs)are considered.For the prediction,a discrete gear model for generating the error tooth profile based on the ISO accuracy grade is presented.Then,the gear model and a tooth deflection model for calculating the tooth compliance on gear meshing are coupled with the transmission error model to make the prediction by checking the interference status between gear and pinion.The prediction method is validated by comparison with the experimental results from the literature,and a set of cases are simulated to study the effects of MEs,AEs,TDs and PMs on the static transmission error.In addition,the time-varying backlash caused by both MEs and AEs,and the contact ratio under load conditions are also investigated.The results show that the novel method can effectively predict the range of the static transmission error under different accuracy grades.The prediction results can provide references for the selection of gear design parameters and the optimization of transmission performance in the design stage of gear systems.

Dynamic Simulation for Rigid-Flexible Coupling Model of Gear Transmission System Based on ADAMS

The influence of the flexible body for the motion of gear transmission system is analyzed and the foundation for a more accurate assessment of gear transmission system is established when it has battle damage faults. By using Pro / E software,the virtual prototype model of gear transmission system in the speed reducer is established,and the rigid model and rigid-flexible coupling model are simulated respectively in ADAMS to obtain the data of gear meshing force. It can be concluded that rigid-flexible coupling model can reflect the real motion better than rigid model by comparing the simulation data of two models.

Dynamic Fatigue Reliability Analysis of Transmission Gear Considering Failure Dependence

Multiple failuremodes and strength degradation are usually inherent in the gear transmission system,which brings new challenges for conducting fatigue reliability analysis and design.This paper proposes a novel dynamic fatigue reliability analysis method for failure dependence and strength degradation based on the combination of theCopula function and Gamma process.Firstly,the dynamic simulation model of the gear transmission system is established to obtain the dynamic stress-time history.The Gamma process is then used to describe the strength degradation to establish the dynamic stress-strength interference model.The marginal distribution functions of tooth contact fatigue and dedendumbending fatigue are calculated respectively based on the dynamic interferencemodel.Finally,the joint distribution of the two failure modes can be obtained by the t-Copula function to characterize the failure dependence,and so the dynamic fatigue reliability considering failure dependence can be estimated.The effectiveness of the proposed method is illustrated with examples.The results reveal the temporal law of reliability and the effects of failure dependence on dynamic fatigue reliability.

Gear Transmission Fault Classification using Deep Neural Networks and Classifier Level Sensor Fusion

Gear transmissions are widely used in industrial drive systems.Fault diagnosis of gear transmissions is important for maintaining the system performance,reducing the maintenance cost,and providing a safe working environment.This paper presents a novel fault diagnosis approach for gear transmissions based on convolutional neural networks(CNNs)and decision-level sensor fusion.In the proposed approach,a CNN is first utilized to classify the faults of a gear transmission based on the acquired signals from each of the sensors.Raw sensory data is sent directly into the CNN models without manual feature extraction.Then,classifier level sensor fusion is carried out to achieve improved classification accuracy by fusing the classification results from the CNN models.Experimental study is conducted,which shows the superior performance of the developed method in the classification of different gear transmission conditions in an automated industrial machine.The presented approach also achieves end-to-end learning that ean be applied to the fault elassification of a gear transmission under various operating eonditions and with signals from different types of sensors.

Theoretical calculation and experimental study on the load distribution coefficient (LDC) of three-ring gear reducer

In this paper, primary manufacturing and assembling errors of three-ring gear reducer （TRGR） are analyzed. TRGR is a new transmission type whose eccentric phase difference between middle ring plate and side ring plates is 120°, Its mass of middle ring plate is equal to that of side ring plate or 180°, and its inass of middle ring plate is twice of that of side ring plate, which affects load distribution between ring plates. The primary manufacturing and assembling errors include eccentric error of eccentric sheath E111, internal gear plate E1 and output external gear E11. A new theoretical method is presented in this paper, which converts load on ring plates into the dedendum bending stress of ring plate to calculate load distribution coefficient （ LDC ）, by means of gap element method （GEM）, one of finite element method （FEM）. The theoretical calculation and experimental study, which measures ring plate dedendum bending stress by means of sticking strain gauges on the dedendum of middle ring plate internal gear and side ring plate internal gears, are presented. The theoretical calculation and comparison with experiment result of LDC are implemented an two kinds of three-ring gear reducers whose eccentric phase difference between eccentric sheaths is 120° and 180°respectively. The research indicates that the result of theoretical calculation is consistent with that of experimental study. That is to say, the theoretical calculation method is feasible.

Excitation Prediction by Dynamic Transmission Error under Sliding Friction in Helical Gear System

Monte Carlo method was adopted to calculate the meshing error considering the manufacture error and assembly error of the meshing point along the time-varying contact line for helical gear pair. The flexural-torsion-axis dynamic model coupled was established under the tooth friction force and solved by the perturbation method to compute real dynamic tooth load. The change laws of the friction force and friction torque were obtained in a meshing period. The transmission error formulation was analyzed to introduce meshing excitations. The maximum dynamic transmission error, the maximum meshing force and the maximum dynamic factor were calculated under different speeds, external loads and damping factors. The conclusions can provide theoretical basis for the gear design especially in tooth profile correction.

Efficiency Evaluation of Continuously Variable Transmissions Including a Planetary Gear Train

With their advantages, continuously variable transmissions have gained more popularity in the last decade by their use in mechanical transmission systems. The present paper aims to analysis the efficiency of the transmission based on the mechanical efficiency of the planetary gear train integrated in such transmission. In this analysis, we consider the mechanical efficiency of the transmission has been determined considering how the efficiency of the CVT members changes as a function of the operating conditions. The efficiency of the planetary gear train as a function of the configuration, speeds in his three input/output shafts, and also with respect to the power flow type. Results are compared with those obtained from other methods performance evaluation of the transmission, available in the literature.