Transmission Error Of Spur Gears Research Articles

Investigation of High-Speed Dynamic Transmission Error Testing Using Gear Strain

The difficulties of testing the dynamic transmission errors of gears in complex environments, such as high-speed operations or situations with oil contamination, and the limited variety of available testing methods have been recognized as issues which this study endeavors to tackle. In this study, a testing method for evaluating high-speed dynamic transmission errors of spur gears through the use of strain sensors is proposed. To reduce the interference of environmental noise on testing signals, physical measures, such as the use of copper foil to shield signal wires and the grounding of data acquisition equipment, were implemented during the testing process. Utilizing wavelet decomposition to distinguish between the high- and low-frequency components of the testing signals, the transmission error of gears during high-speed operation was calculated. After confirming the feasibility of the stress–strain stiffness approach in gear transmission error testing using the magnetic grid method, tests on modified and non-modified gears at various speeds and loads were carried out. The two types of test data were processed and evaluated to determine the effect of speed and load on gear dynamic transmission error. It was possible to conduct research on the testing technique of gear dynamic transmission errors utilizing strain sensors, which provides a new, fast, simple, and practical testing strategy for gear transmission error testing.

Influence of profile modification on the transmission error of spur gears under surface wear

The load distribution, transmission error, and time-varying meshing stiffness of spur gears are all influenced by the teeth dimensions and profiles shape. Any modification on the teeth geometry, as a profile relief frequently used to avoid the mesh-in impact, will affect all these parameters and the entire dynamic behavior of the gearset. In addition, due to the friction between contacting surfaces, wear arises at the teeth flanks. This causes the shape of the meshing profiles to change, which will affect the load distribution and the transmission error for the subsequent meshing cycles. And this new load distribution causes a surfaces wear different form that of the previous meshing cycle. Consequently, the wear depth increase is different at any contact point —because the load and sliding velocity are different— and at any meshing cycle as well —because the load distribution changes with the accumulated wear—. And all the above is also influenced by the profile modification the teeth were manufactured with. In this paper, a simple, analytic model of meshing stiffness, load sharing, and transmission error for spur gears with profile modifications including the influence of surfaces wear is presented. The evolution of the transmission error with the number of wear cycles is studied, and the optimal profile modification for minimizing the dynamic load induced by the transmission error is investigated.

Analysis of the Transmission Error of Spur Gears Depending on the Finite Element Analysis Condition

Finite element analysis is widely used to predict the structural stability and tooth contact performance of gears. This study focused on the effect of finite element modeling conditions of a spur gear on the simulation result and the model simplification. The gear body and teeth, teeth width, configuration of mesh, frictional coefficient, and simulation time interval (gear mesh cycle division) were selected for model simplification for gear analysis. The static transmission error during a single-gear mesh cycle was calculated to represent the performance of the gear, and the elapsed time was measured as a simplification factor. Contact stress distribution was also checked. The differences in maximum transmission error and elapsed time depending on the model simplification methods were analyzed. After all simplification methods were estimated, an optimal combination of the methods was defined, and the result was compared with that of the most detailed modeling methods.

Influence of Surface Pitting and Friction Coefficient on the Static Transmission Error in Spur Gears

Influence of Surface Pitting and Friction Coefficient on the Static Transmission Error in Spur Gears

Tooth friction force and transmission error of spur gears due to sliding friction

This study investigated the tooth friction force and transmission error (TE) of spur gears due to sliding friction under quasi-static condition. The sliding velocity and friction force of spur gears and mesh compliance during meshing were calculated. The load–deformation relations between the tooth normal load, tooth errors, and mesh compliance, and moment equilibrium equation, including friction force, were derived. The friction force, tooth load, and TE of unmodified and linear tip-relief modified spur gears were analyzed by using the derived equations. Results indicated that the friction force, tooth load, and TE increased during approach and decreased in recess regardless of tooth modification, particularly in the single-mesh region. Friction caused larger peak-to-peak change of TE than that without friction. Xu’s friction coefficient generated smooth TE and tooth load transitions near the pitch point, and BK’s friction coefficient remained approximately constant, except for the sharp increase in tooth load and TE near the pitch point.

Calculation of static transmission errors associated with thermo-elastic coupling contacts of spur gears

The static transmission error is one of the key incentives of gear dynamics and addressed by many scholars. However, the traditional calculation method of static transmission errors of spur gears does not take into account the influence of thermo-elastic coupling caused by the gear temperature field, and it limits the accuracy of the dynamic characteristic analysis. Thus, in this study, the calculation method of static transmission errors associated with thermo-elastic coupling is proposed. Furthermore, the differences between static transmission errors associated with thermo-elastic coupling contacts and traditional method of gear is discussed. The study is helpful to improve the accuracy of dynamic analysis of gear transmission system.

Static and Dynamic Transmissin Error in Spur Gears

In high precision and heavily loaded spur gears the effect of gear errors is negligible, so the periodic variation of tooth stiffness is the principal cause of noise and vibration. High contact ratio spur gears could be used to exclude or reduce the variation of tooth stiffness. The analysis of static and dynamic transmission error of spur gears cut with stan- dard tools of 20° profile angle is presented in this paper. A simple method to design spur gears with a contact ratio nearly 2.0 is used. It consists of increasing the number of teeth on mating gears and simultaneously introducing negative profile shift in order to provide the same center distance. Computer programs to calculate static and dynamic transmission error of gears under load have been developed. The analysis of gears using these programs showed that gears with high contact ratio have much less static and dynamic transmission error than standard gears.

Diagnoses of the operational errors of a threaded-wheel grinder in the grinding of spur gears using kinematic transmission errors

The kinematic transmission errors of spur gears can be detected by a single flank rolling test. This rolling test can be performed very quickly and requires little operator skill, so it is suitable for the diagnoses of manufacturing errors. This paper uses the conjugate shape generation method to construct the mathematical model of tooth profiles of spur gears that were ground in a threaded-wheel gear-grinder with operational errors. A single flank rolling test simulator is developed to investigate the relationships between the operational errors and the kinematic transmission errors. The diagnostic equations are derived using this simulator. The validity of this simulator is verified experimentally.

Discussion: “Optimum Profile Modifications for the Minimization of Static Transmission Errors of Spur Gears” (Tavakoli, M. S., and Houser, D. R., 1986, ASME J. Mech. Transm. Autom. Des., 108, pp. 86–94)

Discussion: “Optimum Profile Modifications for the Minimization of Static Transmission Errors of Spur Gears” (Tavakoli, M. S., and Houser, D. R., 1986, ASME J. Mech. Transm. Autom. Des., 108, pp. 86–94)

Optimum Profile Modifications for the Minimization of Static Transmission Errors of Spur Gears

A procedure for computing static transmission errors and tooth load sharing was developed for low and high contact ratio internal and external spur gears. A suitable optimization algorithm was used to minimize any combination of the harmonics of gear mesh frequency components of the static transmission error. Different combinations of tip and root relief may be used to achieve optimization. These include varying the starting point of relief and varying the magnitude of relief, and selecting the gear and/or the pinion teeth to be tip and/or root-relieved. Also, there exists an option for using either linear or parabolic relief. In addition to the presentation of optimal profile modifications, the effects of off-design loads, nonoptimum modifications, and random spacing errors are presented.

Closure to “Discussion of ‘Optimum Profile Modifications for the Minimization of Static Transmission Errors of Spur Gears’” (1986, ASME J. Mech. Transm. Autom. Des., 108, p. 94)

Closure to “Discussion of ‘Optimum Profile Modifications for the Minimization of Static Transmission Errors of Spur Gears’” (1986, ASME J. Mech. Transm. Autom. Des., 108, p. 94)

A method of measuring transmission error in spur gears of 1:1 ratio

The transmission error of a pair of spur gears is detected by an optical method and recorded continuously as a function of time. Measurement of the alternating component of the error is repeatable within ?5 ? 10-5 in., and of the mean value within ?1 ? 10-4 in., at base circle radius, at any speed in the range 0-6000 rev min-1 and at any load within the capacity of the gears. Records are taken on photographic paper wrapped round a drum which rotates with one of the gears being tested. In this way the wavelength of record per cycle of tooth-engagement is made independent of speed and comparison of static and dynamic behaviour is facilitated. The method of measurement is applicable only to a pair of gears with the same number of teeth.