Face Gear Meshing Research Articles

Time-varying Reliability Analysis of Contact Fatigue Strength for Nutation Face Gear Transmission

Background: Nutation face gear transmission is a patent about a new type of transmission based on meshing between two face gears. It replaces spur gear with internal face gear to form a “faceface” meshing gear pair and actualizes its deceleration function by combining the nutation principle, which has the advantages of both face gear and nutation drive. Objective: The purpose of this paper is to establish the time-varying reliability calculation model of contact fatigue strength based on fractal contact theory, so as to improve the reliability, safe service and further optimization design of the nutation face gear transmission. Methods: The time-varying uncertainties of the contact stress and the allowable contact stress of the face gear teeth are analyzed respectively, and then the time-varying reliability model of the contact fatigue strength is established. Finally, the drift rate and fluctuation rate of each random variable are simulated using the Monte Carlo simulation method to obtain the time-varying reliability of the contact fatigue strength for the nutation face gear drive. Results: The results show that the general trend of geometric Brownian motion locus of each random variable is consistent with the actual situation. Conclusion: For the given example of the nutation face gear transmission device, the reliability of the contact fatigue strength of the planetary face gear meshing with the fixed face gear and the rotating face gear within one year is calculated to be 0.9912 and 0.9856 respectively, and the maximum vibration noise is about 68dB, which meets the expected value.

Dynamic characteristics of the face gear transmission system based on a rotor-shaft-bearing model with multiple nodes

A multi-node dynamic model is proposed for the gear system composed of face gear meshing, rigid gear rotors, flexible shafts and deformable bearings, and the model is applied to investigate the characteristics of the system. Firstly, as the existing vector formula of angular velocity ignores the torsional deformation, a new formula including torsion, bending and translation is derived, and accordingly the motion equations of rotors and beam elements are formulated. The gyroscopic effect is considered in the gear rotors and shaft beams. Then, the node equation of face gear meshing is derived according to the characteristics of face gear drives, in which the gear backlash, meshing damping, time-varying mesh stiffness and transmission error excitation is involved. Finally, the dynamic model of the face geared rotor-shaft-bearing system is established with nodes assembled. The natural characteristics and the dynamic responses are investigated. Moreover, the proposed model is compared with the lumped parameter model and applied to explore the dynamic responses to variable support stiffness and support spans. Results indicate that the parameters of input shaft have enormous influence on dynamic responses rather than that of output shaft, and the influence mainly comes from the support close to meshing.

Contact stress and bending stress calculation model of spur face gear drive based on orthogonal test

As the stress of gears determines the reliability of transmission, the stress research of face gear drive has great significance from the perspective of both theory and practice. The finite element model of orthogonal spur face gear meshing is attained via root-top section lofting method. The geometry parameters (include modulus, teeth number of face gear, teeth number of pinion and pressure angle) and transmission parameter (nominal contact force) are considered in the stress modeling. This paper, respectively established the empirical equations for contact stress and bending stress of face gear and pinion through stepwise regression by using single factor test and orthogonal test. The empirical equations have been validated by comparing them with results obtained from FEA.

Parametric Instability of Face-Gear Drives Meshing With Multiple Spur Pinions

This paper studies the dynamic behaviors for face-gear drives meshing with multiple spur pinions by using the model of a spinning disk with time-varying mesh loads that result from the unique face-gear meshing kinematics and nonunity contact-ratio. The system stability is assessed with respect to intersecting pinion shaft angles and pinion gear properties. The results provide information about parametric instability for dynamic-based design of multipinion/face-gear drives. This investigation also provides stabilization methods for pre-installed systems via gear radii and tooth numbers for a given intersecting pinion shaft angle.

The Application of Tooth Contact Analysis in the Shaper Modification for Face-gear

To get ideal position of contact area for face-gear drives, we researched beginningly the rack-cutter modification, setted up equation of tooth surface of parabolic rack-cutter. According to the machining coordinate systems of shaper and the gear geometry and applied theory. The surface equation of shaper was established by using the equation of rack-cutter tooth surface and matrix for coordinate transform; The gear teeth surface equation of face-gear was got base on machining coordinate systems and the surface equation of shaper. Comprehensively considered the meshing relation among shaper, pinion and face-gear, the coordinate systems of meshing analysis were founded; The equations of meshing contact points for face-gear drives were established; Recurring to the technology of computer simulation, the effects between the face-gear meshing contact path and shaper modification were researched through the computational examples. So, The position of contact area for face-gear drives is controlled.

Research on Meshing of Face Gear Drive under Errors of Alignment and Machining

The coordinate systems for cutting face gears and for meshing of face gear drive with involute cylindrical pinion. The tooth surface equation of face gear with machining errors is deviated, such as change of shaft angle, change of shortest distance between face gear and cutter tool axes, helix angle of cutter tool. Tooth contact analysis applied in the paper considered with the alignment error of the driving system. The tooth contact path and the transmission error of the face gear drive were simulated through the tooth contact analysis for different alignment errors and machining errors. The simulation results indicate that all of the alignment errors and machining error don’t cause transmission error except helix angle error of the cutting tool. The errors will bring the shift of the contact path on gear teeth. The shift of bearing contact can be reduced by combination of different errors of alignment or machining.

Analysis and Optimization of the Loaded Meshing of Face Gears

This paper presents a method of simulating loaded face gear meshing. A brief description of the software developed is given in the first part. It simulates the loaded behavior of face gear meshing and provides information such as the instantaneous pressure distribution across the entire width of the teeth in contact and loaded transmission error. Analytical simulations are used to define the geometry and study the unloaded kinematics. This method permits very precise results in a very short time. In the second part of the paper, a comparison between point and line contacts is made for loaded meshing. Further computations calculate assembling-error sensitivity for the two types of contact. The best performance is achieved with the line contact, but it is very sensitive to misalignment. The last part of the paper presents a method for pinion crowning to improve optimization of the line contact case. The aim is to obtain the best loading of face gear meshing in order to avoid line contact sensitivity due to misalignment.

普通ホブで歯切りしたフェースギヤとこれを用いた自動割出装置

The study deals with the development of a new type face gear and the application. The face gear can be easily hobbed by use of a conventional narrow gear hob without any special attachment. Geometrical dimensions and form of face gears are analysed, and face gears were actually produced. The face gear meshing with involute spur gears or helical pinions has advantages of easy setting and smooth mating. Together with applications to robot hand, radial-feed screw cutting device and reel for fishing, the automatic circular index table developed in combination with two different face gears is explained, making use of features of the face gears.