Gear Error Research Articles

The Gap Nonlinear Characteristics of Gear Transmission System under External Excitation

For the study of nonlinear dynamic characteristics of a pair of gears in an external torque under gear meshing error excitation, we will establish two degrees of freedom nonlinear torsional vibration model. The use of Matlab / Simulink for numerical simulation solves the nonlinear dynamic model of the gear gap. Study the dynamic characteristics of the system in a certain domain of parameters on external incentive conditions, as well as external motivation of gear transmission system dynamic characteristics influence. The results have important practical value for future engineering practice on gear transmission system's dynamic design, and have important theoretical significance for complex gear transmission system dynamics study.

Application of Error Separation Technique on the Virtual Detector of Gear Error

On the foundation of conventional double-flank gear rolling tester, a virtual detector of gear error taking personal computer as the core is developed with the use of virtual instrument technology. Systematic error is analyzed through error separation technique. The structure of the detecting system , the design of the system software based on LabVIEW, and the separation of different radial component deviations of gear are presented.

Tooth Profile Modification and its Effect on Spur Gear Pair Vibration in Presence of Localized Tooth Defect

AbstractVibration induced by gears includes important data about gearbox condition. We can use dynamic modeling of gear vibration for increasing our information about vibration generating mechanisms in gearboxes and dynamic behavior of gearbox in the presence of some kind of gear defects. In this paper a six degree-of-freedom nonlinear dynamic model including different gear errors and defects is developed for investigation of effects of tooth localized defect and profile modifications on overall gear dynamics. Interactions between tooth modifications and profile error are studied and the role of profile modification in dynamic response when a localized defect is incurred by a tooth is shown. It is indicated that although profile modifications and profile errors are micro-geometrical, they have considerable effects on vibrations of gear pair. Especially for the case of root relieved teeth that is shown to be more effective in reduction of vibration in the presence of tooth localized defect. Finally, the simulation results are compared with results from literature and the model is verified.

표준기어를 이용한 기어 프로파일 정밀측정 알고리즘에 관한 연구

In this paper, a method to control the noise and vibration of a standard gear transmitting mechanical power in the transmission insides, to things regarding a way to inspect the gear which was processed minutely. In an algorithm used to accurately measure a work gear, the measurements of the master gear are considered as the basis. The existing method considers one rotation of the standard gear and monitor gear, and that carried out mastering work in frequency ways. In this study, an algorithm to measure standard gear and monitor gear is proposed along with methods to calculate an error of the monitor gear and to significantly increase the precision of gear measurement. Further, the algorithm is fast and is expected to be capable of accurately measuring for mastering processing.

Experiment Research and Analysis of Transmission Error of Gears

Through testing the errors of spur gear and helical gears, transmission error curve of non-grinding gear is drawn. The effect factors on gear transmission error are found. The transmission error effect factors of all kinds of gear high-low frequency are analyzed. It is obtained that gear kinematic error is the evaluating guideline of transmission precision. Experimental results shows that error of gear axial offset and gear frequency period have less effect on gear transmission kinematic error. While gear backlash and face width direction error have more obvious effect on kinematic error. The results provides reasonable theory basis for determining gear cutting precision.

Analysis of Nonlinear Dynamic Accuracy on RV Transmission System <sup></sup>

RV (Rotate Vector) transmission is a new precision transmission system. In order to improve its accuracy, we study the RV transmission system. It is researched in comprehensive factors including displacement errors, elastic deformation (static transmission error, design transmission error), gear meshing errors, backlash of gear, time-varying mesh stiffness, mesh damping, bearing stiffness, torsional stiffness of input shaft, etc. The mathematical and mechanical model of dynamic transmission accuracy is established by the concentrated mass method and the dynamic substructure method. Then, the meshing force of each part is analyzed in RV reducer. The motion differential equation of RV drive system is obtained, which lays the foundation for the calculation and analysis of the transmission error.

Method of On-Machine Spacing-Tooth Measuring Large Gear Pitch Accumulated Errors and Technology of Compensating a Geometric Eccentric

The method of on-machine measuring pitch accumulated errors of large gears is much convenient and there are no dimension limits of measured gears. The technology of non-synchro-drive and synchro-measurement is utilized to ensure continuous measurement. The spacing-tooth method of measuring pitch accumulated errors of large gears is used to decrease measuring errors. The technology of compensating a geometric eccentric is applied in data treatment, and the high accurate measurement is carried out

Effects of Eccentricity on Transmission Errors of Trochoidal Gears

This article deals with the effects of eccentricity on transmission errors of trochoidal gears (consisting of a roller gear and cam gear). For the tests, three types of roller gears and three types of cam gears (which had different eccentricity) were used. The experimental results showed that the peak to peak values of transmission errors had a tendency to be greater under a larger eccentricity. The measured transmission error waveforms fluctuated with periods 1/fr, 1/fc and 1/zrfr (in which fr and fc are the rotational frequencies of the roller gears and cam gears, while zr is the number of rollers). The peaks with nfr (n = 1, 2, 3, …), nfc, nzrfr, nzrfr ± mfr (m = 1, 2, 3, …) and nzrfr ± mfc appeared in the measured transmission error spectra. The amplitudes of peaks with fr and nzrfr ± mfr increased as er increased, while the amplitudes of peaks with fc and nzrfr ± mfc increased as ec increased. The transmission errors of test gears with eccentricity were estimated by the multibody analysis (MBA). A reasonable correlation exits between the calculated results obtained by the MBA and the measured experimental results.

Investigation and strategies for precision of miniaturized robots with micro gears

PurposeEconomic, flexible and efficient micro production needs new miniaturized automation equipment (desktop factories). Micro assembly processes make demands on precision of miniaturized robots used in desktop factories and the driving concepts, as well as miniaturized machine elements. The purpose of this paper is to investigate miniaturized drives using micro harmonic drive gears, which are promising driving concepts.Design/methodology/approachThe analysis of the miniaturized precision robot Parvus (using micro harmonic drive gears) shows a good repeatability but also room for improvement concerning the path accuracy. Thereby the transmission error of the micro gears is identified as main disturbing influence concerning the robot's precision characteristics. Owing to the size reduction of the micro harmonic drive gear and the slightly different working principle compared to larger harmonic drive gears, the transmission error are more pronounced. Therefore, it is necessary to discuss approaches to compensate for this effect.FindingsA very promising approach is the use of a simplified model of the kinematic error within the robot control to compensate for this disturbing effect. Measurement data of the transmission error is mathematically transformed into the frequency domain and filtered to the most important frequency modes of the function. These modes are used to build up a simplified mathematic model of the gear transmission error. A final test using this model as compensation function demonstrates that it is possible to reduce the transmission error of the micro gears by more than 50 percent.Originality/valueThe paper presents the first investigation into compensation of the transmission error of micro harmonic drive gears.

Axial error of gears and the tooth stress state in involute gear systems

Simulation of the stress state of the recess in the teeth of straight-tooth involute gear systems with skewing of the gear axes indicates that the standard calculations overstate the load capacity of the system. An effective longitudinal modification of the tooth surface is presented.

Analysis of Static Load Sharing in Star Gearing

In order to analyze the sharing mechanism of marine high-speed star gearing system, a static mechanical model is presented in the paper, in which manufacturing errors, assembly errors, bearing errors and tooth thickness error are all considered. In consideration of equivalent mesh error and static balance of floating components, the load sharing coefficient of the system in different kinds of errors was obtained. And the sensitivities of the load sharing coefficient on different types of errors are analyzed. The result shows that the effects of the eccentric error of sun and tooth thickness error of star gear upon load sharing coefficient are larger than those of the other errors. The influences on load sharing coefficient of each error have cumulative effects. The research has provided a useful reference for improving the load sharing capability of marine star gearing system.

Dynamic Analysis of Combined Gear Drive

Combined gear drive is a common transmission form for high power drive systems. In order to study its behaviors of redundant drive, which improve the system reliability but lead to a problem of inter-excitation of vibrations, dynamic analysis becomes very necessary. First, considering the influences of gear meshing errors, backlashes and time-varying meshing stiffness, a nonlinear dynamic model of sixteen degrees of freedom is developed by using lumped parameter method. Then a nonlinear differential equation set is derived for calculating the steady-state forced response to the internal sinusoidal excitation. After that, time history wave of displacement responses, phase graphs, Poincaré maps and FFT (Fast Fourier Transform) spectra are analyzed. Finally, some useful conclusions are obtained.

An Initial Assessment of the Accuracy of the Gear Trains in the Antikythera Mechanism

The article examines the accuracy of the gear trains of the Antikythera Mechanism, an ancient Greek device that was possibly used as an astronomical calculator. The author analyzes the placement of the mechanism's gear teeth. Mathematical models of gear train accuracy are provided, with the author noting the standard deviations in the trains. Because of the gear errors present in the Mechanism, the author concludes that it was probably used more for display or education purposes than for actual astronomical calculation.

Torsional Vibration of Machines with Gear Errors

Vibration and noise induced by errors and faults in gear meshes are key concerns for the performance of many rotating machines and the prediction of developing faults. Of particular concern are displacement errors in the gear mesh and for rigid gears these may be modelled to give a linear set of differential equations with forced excitation. Other faults, such as backlash or friction, may also arise and give non-linear models with rich dynamics. This paper considers the particular case of gear errors modelled as a Fourier series based on the tooth meshing frequency, leading immediately to non-linear equations of motion, even without the presence of other non-linear phenomena. By considering the perturbed response this system may be modelled as a parametrically excited system. This paper motivates the analysis, derives the equations of motion for the case of a single gear mesh, and provides example response simulations of a boiler feed pump including phase portraits and power spectra.

Modified-Roll Profile Correction for a Gear Shaping Cutter Made by the Lengthwise-Reciprocating Grinding Process

The tooth profile error of a gear shaping cutter made by the lengthwise-reciprocating grinding process (LRGP) is usually corrected by modifying the grinding wheel profile. However, such grinding wheel modification cannot eliminate the twisting profile error along the face of the shaping cutter. A kinematic modified roll motion for generating a shaping cutter is proposed to minimize such twisted profile errors even after cutter resharpening. The tooth profile errors of the work gears generated by the shaping cutter with various resharpening depths are represented as a novel topographic error map. Based on the error map and its sensitivity matrix, the roll ratio between the shaping cutter and the grinding wheel stroke is modified to reduce the twisted profile error as illustrated by the numerical examples. Combining this modified roll motion modification and the grinding wheel profile correction, the high accuracy resharpening depth of the LRGP helical shaping cutter is increased.

Research on Multi-Motor Synchronization Control Based on the Ring Coupling Strategy for Cutterhead Driving System of Shield Machines

With the research object of cutterhead rotation electric drive system, influencing factors of the system synchronous coordination and the multi-motor torque synchronization control strategy is studied. The paper analyzes the dynamics of the cutterhead rotary motors-driving system, discusses the interaction mechanism between motors and gear nonlinear transmission unit, and then the mathematical model of the cutterhead rotary driving system with consideration of gear frequency cycle error and backlash is presented. Based on that, the multi-drive synchronization control based on the ring coupling strategy is given. Simulation results using Matlab platform show the effectiveness of the proposed strategy.

The Measurement and Evaluation Method of Global Error of Spiral Bevel Gear

This paper offers a method of spiral bevel gear’s global error measurement and evaluation based on three-coordinate measurement according to the characteristics of spiral bevel gear. The 3d solid modeling built in UG was regarded as the gear’s ideal factor of measure and error evaluation; the values of the measured points in the real gear tooth surface by CMM were regarded as the gear’s real factor. The global error of spiral bevel gear was reflected by the difference surface which was fitted by the deviation between real tooth surface and theoretical tooth surface. This method is very effective and feasible by measuring and evaluating the automobile rear axle’s driven gear.

Research on Real Tooth Surface Deviation Correction of Spiral Bevel Gear Based on Truncated Singular Value Decomposition

According to structure of traditional milling machine, the tooth surface error identification model of forming processing spiral bevel gear is established by the 4×4 Denavit-Hartenberg homogeneous transformation matrix, the gear meshing theory and so on. In view of the present commonly used least squares method’s solution defects, the truncated singular value decomposition (TSVD) and the L curve method are proposed to solve the identification model and the solution method accuracy was verified by the example and experiment. The results show that the gear concave average error is at 0.01498mm before correction, and the average error will drop down to 0.00084mm after using this method correction, and the error corrects 94.4%. The gear convex average error is at 0.00846mm before correction and the average error will drop down to 0.00176mm after using this method correction and the error corrects 79.2%.

Shaping Principle in Hobbing and Analysis on Errors of Involute Gear Tooth Surfaces

An involute helical surface is one of the surfaces widely used in engineering. There are four characteristics lines ( involute, helix, straight generatrix, pathofcontact) on it. On the basis of characteristic lines, the shaping principle in hobbing is studied, the error characteristics and their interrelations are analyzed. The analysis formula of involute gear tooth surface errors is given for spur gears and helical gears.

The Installation Eccentricity Error Compensation Technology for Gear Based on CNC Gear Measuring Center

In order to decrease the influence of installation eccentricity on gear error evaluation and to raise its accuracy, a compensation algorithm for installation eccentricity is proposed and a compensation model of installation eccentricity is established. A new installation eccentricity parameter identification method determined with involute equations is also raised. Installation Eccentricity parameters are gained through measuring points on involute profile with the method of unconstrained parameter identification. Taking involute profile evaluation as an example, the eccentricity compensation model is introduced into the error evaluation of CNC Gear Measuring Center. The experiment shows that the compensation model raised in this paper can compensate for evaluation results of the involute gear whose eccentricity value is within 2/3 of the total measurement range of the probe and lead it into the non-eccentricity condition, and the most installation eccentricity value that can be compensated in the experiment is 300 μm. The proposition of this compensation method not only improves the accuracy of gear evaluation, but also lowers the requirements on installation accuracy of the gear.