Theory Of Gearing Research Articles

Dynamics Analysis of Cycloidal Speed Reducers With Pinwheel and Nonpinwheel Designs

Cycloidal speed reducers are composed primarily of an eccentric shaft, output parts, and a set comprising a cycloidal gear and pinwheel with pins or a cycloidal gear and cycloid internal gear. This paper investigates the contact and collision conditions of these components, as well as their stress variations during the transmission process. To do so, a system dynamics analysis model of a cycloidal speed reducer is constructed, together with dynamics analysis models for two design types: A traditional pinwheel design and a nonpinwheel design (i.e., a design in which a cycloid internal gear replaces the pinwheel). Based on the theory of gearing, a mathematical model of the pinwheel with pins, cycloidal gear, and cycloid internal gear is then built from which the component geometry can be derived. These dynamics analysis models, constructed concurrently, are used to investigate the components' movements and stress variations, and determine the differences between the transmission mechanisms. The results indicate that the nonpinwheel design effectively reduces vibration, stress value, and stress fluctuation, thereby enhancing performance. An additional torsion test further suggests that the nonpinwheel design's output rate is superior to that of the traditional pinwheel design.

Numerical simulation of gear surface hardening using the finite element method

This paper was devoted to presenting a systematic approach based on finite element method to numerical analysis of gear surface hardening with the consideration of the contact problem. After the contact finite element method theory of gear and rack was introduced, the numerical analysis of gear surface hardening was discussed in detail. The element selection of gear–rack hardening layer based on finite element method was proposed, the algorithm characteristics of gear–rack elastic–plastic contact problems were also put forward, and the material properties and constitutive relations of gear–rack hardening layer were then discussed in detail. The gear–rack elastic–plastic contact analysis results were discussed, and the experimental results with the laser treatment were analyzed with the microstructure changes of the laser hardening layer to measure the performance of the hardening layer. The wear simulating test of gear results in improving the wear resistance greatly, and this surface hardening treatment has been officially put into engineering application.

Nonlinear dynamics modeling and analysis of transmission error of wind turbine planetary gear system

In this paper, a type of planetary gear system in the wind turbine was studied by taking into account the actual conditions where the planetary gear system works. A nonlinear multi-gap planetary gear system finite element method model was established, and the engagement stress, the displacement, and the velocity curve with time of nodes of the planetary gear system were obtained by using explicit dynamic solution method. Under different speeds and different load, the variation of planetary gear system dynamic transmission error was then studied combined with the theory of gearing. The results showed that it is different from the dynamic transmission error of planetary gear system and planetary gear. Time-varying mesh stiffness of sun gear and the ring gear are also different along with their speed change. There are some correlation among time-varying mesh stiffness, meshing impact stress, and dynamic transmission errors. Therefore, it is suggested that the meshing stiffness and impact stress effect on the dynamic transmission error should be considered in the study of transmission error of wind turbine planetary gear system.

Study of optimal strategy and linkage-model for external non-circular helical gears shaping

As an efficient manufacturing method for gears, shaping technology developed for non-circular helical gears will greatly break through the dilemma of their applications; especially for those gears with part of pitch curves being concave, being not able to be hobbed. Two fundamental linkage-models for external non-circular helical gears were built based on the meshing theory of non-circular gears in this article. According to four linkage methods in plane and two kinds of additional rotation in vertical direction, eight shaping strategies and their practical linkage-models (1)–(8) were developed. Taking a three-order elliptic helical gear as an example, the kinematic characteristics of the eight practical linkage-models were analyzed, which reveals that equal arc-length of gear billet (models (3) and (4)) have the highest accuracy under a given efficiency. The dynamic characteristics of models (3) and (4) were analyzed, which shows that model (4) (equal arc-length of gear billet and additional rotation on shaper cutter) is better in performance, and is an optimal one. The optimal linkage-model was demonstrated to be valid by a virtual shaping, and be able to shape those non-circular helical gears with part of pitch curves being concave. Moreover, the accuracy among every gear tooth is uniform. The theory developed and the results of the virtual shaping were illustrated with a shaping experiment. The train of thought and the results will be useful for any external non-circular helical gears with free pitch curves.

Modeling and Manufacture of a PC-Type Single-Screw Compressor Rotor

This study aimed to effectively design, manufacture and simulate a single-screw compressor. In this paper, a mathematical model of a pc-type single-screw compressor was developed. The pc-type single-screw compressor was assembled using two gate rotors, a screw rotor and a frame. First, the mathematical model of a conical tooth was designed and a gate rotor equation was obtained through coordinate transformation. Then, the coordinate systems between the gate rotor and the screw rotor were set up. Using a homogeneous coordinate transformation matrix, the family of gate rotor surfaces was obtained. Based on gear theory, the equations of meshing between the gate rotor and screw rotor were determined. Substituting the equation of meshing into the family of gate rotor surfaces, the gate rotor and the screw rotor were generated and their geometrical model illustrated using a software package. Based on the developed mathematical models, the contact lines and stress analysis between the gate rotor and screw rotor were displayed. An edge contact between the gate and screw rotors was found, indicating the necessity of a plastic or a composite material to encircle the conical surface. A computer-aided manufacturing software package was used to simulate the manufacture of the screw rotor.

Meshing Analysis of Quadruple-Arc Profile Bevel Gears in the Process of Cutting Tooth

Based on the theory of quadruple-arc gears and the bevel gears process principle, meshing analysis of quadruple-arc profile bevel gears in the process of cutting tooth is carried out. The surface equation of generating gear and the equation of action line in the process of cutting tooth as well as the general tooth surface equation of quadruple-arc profile bevel gears are obtained.

Dynamics of High-Speed Precision Geared Rotor Systems

Gears are one of the most widely applied precision machine elements in power transmission systems employed in automotive, aerospace, marine, rail and industrial applications because of their reliability, precision, efficiency and versatility. Fundamentally, gears provide a very practical mechanism to transmit motion and mechanical power between two rotating shafts. However, their performance and accuracy are often hampered by tooth failure, vibrations and whine noise. This is most acute in high-speed, high power density geared rotor systems, which is the primary scope of this paper. The present study focuses on the development of a gear pair mathematical model for use to analyze the dynamics of power transmission systems. The theory includes the gear mesh representation derived from results of the quasi-static tooth contact analysis. This proposed gear mesh theory comprising of transmission error, mesh point, mesh stiffness and line-of-action nonlinear, time-varying parameters can be easily incorporated into a variety of transmission system models ranging from the lumped parameter type to detailed finite element representation. The gear dynamic analysis performed led to the discovery of the out-of-phase gear pair torsion modes that are responsible for much of the mechanical problems seen in gearing applications. The paper concludes with a discussion on effectual design approaches to minimize the influence of gear dynamics and to mitigate gear failure in practical power transmission systems.

Applications of the Exponential Function of the Euclidean Motion Group to the Theory of Gearing

The present paper provides a first step to a new approach to the theory of gearing, which uses modern differential geometry in order to ensure a strict and coordinate-independent formulation. Here, we are mainly concerned with a basic equation, namely, the equation of meshing, of two rotating surfaces in mesh. Since we are able to solve this equation by the time parameter, we derive parameterizations of the mating pinion from a bevel gear as well as a parameterization for gears produced by special machine tools.

Gearbox Fault Simulation and Analysis Based on Virtual Prototype Technology

Simulation study of the failure of gearbox system using virtual prototype technology and analysis of its vibration signal is a foreword topic in recent years. This paper established a rigid-flexible coupling model of gearbox system using SolidWorks, ANSYS and ADAMS. Then, make simulation under the following three conditions: normal, gear fault and bearing outer ring fault. Next, make time domain and frequency domain analysis of the simulated fault signal using MATLAB. Simulation results are consistent with gear vibration mechanism and signal modulation theory, which verified correctness and feasibility of virtual prototype technology in gearbox fault simulation. Lay foundation for gearbox fault diagnosis.

Dynamic Analysis of Less-Teeth Gear Transmission System

According to the less-teeth gear design theory, the FEM model of less-teeth gear system was established, and its dynamic contact characteristic was analyzed, then dynamic contact simulation was realized. Laws of contact area, contact stress and tooth stress change over time were got, which can be used for the gear profile modification and dynamic characteristics optimization design of the less-teeth gear system.

Gear Strength Optimization Analysis of Automobile Gearbox Based on the Software of MASTA

Automobile gear, as key part of automobile gearbox, bears the torque of automobile transmission, whose strength will directly affect the transmission efficiency of automobile gearbox and the service life of transmission system. On the basis of gear transmission theory, This paper focuses on gear pair of an automobile transmission as the research object, with the help of the professional transmission system software of MASTA, to realize the gear meshing analysis of the automobile gearbox, establish the simulation model of the automobile gearbox, simulate the actual load condition to complete the process analysis of the gear transmission. Finally, the strength optimization analysis of gear pair is implemented to obtain the reasonable gear design, which is more close to the gear meshing transmission process. There are great benefits to improve the overall performance of the automobile gearbox, effectively reduce the test cost, shorten development cycle, and optimize product structure. Therefore, it will provide guidance for the development and application of new transmission gear in the future, and present a new perspective and approach for the optimization analysis of gear strength.

The Edge Effect and Longitudinal Modification of Involute Gear Drive Used in Automobile

Via combining parameterized modeling function of Pro/E with gear mesh principle, the accurate 3-D crowning modification models of involute gears used in automobile are made. The edge effect in meshing process of the gear pair is validated by finite element method. The longitudinal corrections of a gear pair are designed combining crowning technology of roller bearings with the characteristic of gear mesh and using gear mesh principle and contact mechanics theory. Then it is testified by FEA that the maximum stresses of the gears can be reduced effectively since longitudinal correction can avoid the edge effect in the meshing process of the gear pair.

Decoupled Cable-Driven Grasper Design Based on Planetary Gear Theory

Decoupled Cable-Driven Grasper Design Based on Planetary Gear Theory

Machining Simulation of Equal Base Circle Bevel Gear Using Disc Cutter

The purpose of this paper is achieve machining the equal base circle bevel gear with a disc cutter. Based on the equal base circle bevel gear theory, By solving coordinate values of the disk cutter section, made tool model in VERICUT environment. By planning disc cutter machining path , the disc cutter trajectory is obtained, simulated the NC machining to a equal base circle bevel gear using VERICUT software. The results show that machining this gear in NC machine can be realized using disk cutter.

An invariant approach for curvature analysis of conjugate surfaces

Curvature analysis of conjugate surfaces is important and difficult in the theory of gearing. By introducing a rotation tensor for rigid-body motion and a surface curvature tensor for the curvatures of surface, tensor expressions of curvature relations between conjugate surfaces of line contact and point contact are directly obtained based on tensor analysis. Especially the result of point contact shows a clear explanation for Litvin's local synthesis. When involving practical computation, convenient reference coordinate systems can be chosen and the methods and tools for matrix computation can be employed. Application to generation, local synthesis and tooth contact analysis of face-milled spiral bevel gears is presented. The proposed invariant approach and the obtained results can be applied to design, manufacture and simulation of other complex surfaces.

Study of <i>V/H/J</i> of Pointing-Lapping for Hypoid Gears

Pointing-lapping is a lapping way for modifying tooth surface defects of hypoid gears. For numerical control, V/H/J calculation principle of pointing-lapping of hypoid gears is introduced. According to mesh relations and coordinate relations, 8 nonlinear equations are formed on the basis of mesh theory of hypoid gears. V/H/J can be got by solving the nonlinear equations, which can be finished easily by computation program. The accuracy of the calculation principle has been proved by tooth surface contact pattern test in Y9550 roll checking machine.

Determination of the Most Dangerous Meshing Point for Modified-Hourglass Worm Drives

A type of modified-hourglass worm gear drive, frequently called type-II worm gearing for short, has various favorable meshing features. Its sole shortcoming is the undercutting of the worm wheel. By adopting a slight modification, this problem can be overcome due to the removal of a part of one subconjugate area containing the curvature interference limit line. To measure how effectively the undercutting is avoided, a strategy to determine the meshing point in the most severe condition is proposed for a type-II worm drive. The strategy presented consists of two steps. The first step is to establish a system of nonlinear equations in five variables in accordance with the theory of gearing. The second step is to solve the system of nonlinear equations by a numerical iteration method to ascertain the meshing point required. A numerical example is presented to verify the validity and feasibility of the proposed scheme.

Research on Meshing Theory and Simulation of Noninvolute Beveloid Gears with Crossed Axes

Crossed axes noninvolute beveloid gears meshing with line contact has been studied in this paper. The engagement equation and tooth profile equation have been presented by applying the theory of gearing. Meanwhile the tooth profile errors and axial errors have been calculated by means of numerical analysis and provided a theoretical way to calculate the induced normal curvature along the normal direction of the contact line in this paper.

Design of the conjugated straight-line internal gear pairs for fluid power gear machines

The conjugated straight-line internal gear pair, including a pinion with straight-line profile and an internal gear with profile conjugated to the pinion profile, is the key components to the conjugated straight-line internal gear pumps. Truninger [ Truninger gear pump. Patent 3491698, USA, 1970] pointed that this kind of gear pairs leads to a very small trapped volume, which is 10 times smaller than that of the conventional involute internal gear pumps. Therefore, it can yield significant reduction in noise levels of the pumps. However, to the authors’ knowledge, there is no research on the design of these gear pairs until now. First, our study describes the straight-line profile of the pinion mathematically with definitions of some geometric parameters. Second, according to the theory of gearing, the mathematical models of the rack-cutter and the conjugated internal gear are derived. Then, the condition to avoid overcutting is obtained for the generation of the pinion by a rack-cutter. Finally, the condition to avoid interference in the internal gear pair is derived as a non-linear equation system and an algorithm is developed to find a numerical solution. Two examples are presented to demonstrate how to determine tooth numbers of the internal gears for avoiding interference. It is hoped that the study in this article should be helpful to the designers of the conjugated straight-line internal gear pairs. Moreover, it could provide a prepared knowledge for the researchers to investigate the performances of the fluid power gear machines, pumps, and motors, with the conjugated straight-line internal gear pumps.

The Modification and Design Method of Large Gear

Due to the difficulty in large gear modification, a method that modifying gear tooth in the processing through correcting gear cutter was proposed. In this paper, modification theory of large gear and design method of gear cutter were introduced in detail. Based on gear meshing theory, the tooth equation of large gear was deduced from the equation of correcting cutter. The processing was simulated by using Matlab software, and it verified the validity of theoretical analysis.