A finishing method for the continuous generation of spur face gears with shaving cutters

https://doi.org/10.1016/j.ijmecsci.2020.106020Get rights and content

Highlights

  • A method of continuous generation of spur face gears is proposed.

  • The cause of the mid-concave based on LTCA is analyzed.

  • The method slows down the error of the mid-concave.

  • A lot of dislocation lines generated in tooth surfaces.

  • The residual stress increased when compared with grinding.

Abstract

Face gear drives have been widely applied in power transmission, but the finishing of continuous generation is a difficult problem. This is mainly because the teeth of face gears are on a plane, which leads to interference by worm grinding. Hence, a shaving method for face gears is proposed in this paper. This work studies the theory of face gear shaving, the causes of mid-concave phenomena based on load tooth contact analysis (LTCA), a solution for the modification coefficient of the shaving cutter and a control method for the cutter location point. The experimental results show that the maximum machining error is 12.7μm, that many generating lines appear and that the residual stress increases by 49.2% in comparison with that of the grinding tooth surface. The present study suggests that the shaving method for spur face gears can not only achieve the finishing of continuous generation but also improve the surface integrity of the gear.

Introduction

The spur face gear drive is a kind of meshing transmission mechanism consisting of a cylindrical gear and a bevel gear. It can transmit motion and torque between intersecting and alternating axes and has the great advantages of a small volume, light weight, high load-carrying capacity, lack of axial force and excellent split power [1] in comparison with the traditional spiral bevel gear drive. The face gear drive has been applied widely because these characteristics are in line with the development requirements of aviation equipment for the future. For instance, it has been successfully applied in an Apache power split system to obtain a 40% smaller volume, 35% larger load-carrying capacity and 56% longer time between overhauls (TBO) as a consequence [2].

Manufacturing a face gear is a key technical problem in the field of face gear transmission. Scholars around the world have proposed a variety of machining methods in view of the high-order characteristics of face gear tooth surfaces. In the field of face gear shaping research, Litvin [3] proposed a new type of gear shaping method for face gears. The phenomenon of root undercutting and tipping during processing was analysed, and the occurrence conditions were studied. The point contact was achieved by a localized bearing contact to guarantee the gear ratio. Nan et al. [4] proposed a new modelling method with Boolean operations based on meshing theory. The feasibility and accuracy of this tooth surface extraction modelling method was verified by shaping simulation. Then, the change regularity of the tooth surface was analysed by the cross-section method. Li et al. [5] studied the relative position of the theoretical shaping surface and processing surface of face gears with computer programs. The results were verified by a shaping experiment. In the field of face gear milling research, Yang et al. [6] studied the numerically controlled (NC) milling method of face gears, established a milling machining model for face gears, calculated the swing angle and feed amount of tools during the milling process, and proved the correctness of the machining method through VERICUT simulation. Tang et al. [7] proposed a plunging processing method with multi-group envelopes and derived a mathematical formula for the plug mill in copying the profile of the cutter. According to numerical control manufacturing techniques, the NC code based on the face gear machining equation was obtained, and a simulation and experiment were conducted. Zhou et al. [8] established a new calculation method for an envelope surface according to the geometric characteristics of the shaper tooth surface, which enabled the mathematical model of the face gear tooth surface to be expressed in explicit form. This has great reference value for face gear manufacturing. Wang et al. [9], [10] analysed the milling mechanism of face gears for the five-axis computer numerical control milling machine and deduced the milling cutter profile equation. The influence of the installation error on the machining accuracy was studied, and a compensation method for the face gear machining parameters was proposed. Zhou et al. [11] proposed a novel geometric analysis to bridge the gap between the CAD and computer numerical control (CNC) milling methods for spur face gears. A comprehensive algorithm was studied to generate tool paths by choosing the largest allowable cutters without interference. The results showed that the method was feasible by both simulation and experiment. Guo et al. [12] studied a method of making the generating surfaces of the circular cutters approximate the theoretical reference shaper as closely as possible by introducing a cutter profile tilt angle. Six different design parameters were considered in order to investigate the influence on the contact patterns of the gear tooth surfaces. The results showed that surface deviations can lead to edge contacts, interference, and high stress concentrations. Contact patterns and stresses can be made as good as the standard geometry of face gears through the appropriate design parameters. Shi et al. [13] investigated a mathematical model of a dressing wheel with a general profile modification based on the worm grinding method of face gears. The minimal transmissionerror without edge contacts was obtained by comparing different parameters for the profile modification of the dressing wheel based on the above method. The method was validated with simulations. In the field of face gear hobbing research, Li et al. [14] studied a worm of a hobbing or grinding wheel for the face gear. The equation of the axis section of the worm and the equation of the tooth form of the worm were deduced, and the undercut of the worm was analysed. Then, the track of the contact point between the worm and face gear was analysed. Gao et al. [15] designed a base worm used for the hob, derived the equations describing the worm thread surface, and analysed the derivation and avoidance of singularities in the base worm thread surface. Finally, the law of the base worm radius, the module of the shaper, the number of teeth and the pressure angle at the singularity point were determined. Wu et al. [16] established the hobbing surface equation for the face gear and analysed the hobbing tooth surface constraint conditions for dedendum undercutting. The exact assembly and machining simulation were completed by using the program, which validated the hob correctness. Zhang et al. [17] proposed a scheme for cutting face gears with an internal gear elliptical sphericity hob. The deviations of the face gears cut by the elliptical sphericity hob and by a shaper were very small in simulations. The surface errors gradually decreased with increasing hob radius. This hobbing method is reasonable. Wang et al. [18] proposed a precision generating hobbing method for face gears with an assembly spherical hob. The basic spherical hob worm was designed based on an analysis of the evolution from the cylindrical gear to the spherical hob. According to the tooth equations, the development method of the assembly spherical hob was analysed. An error analysis model was established, and the impacts of each error on the gear tooth surface were analysed. The assembly spherical hob was manufactured, and the gear hobbing test was completed. Li et al. [19] proposed a method of using a flying cutter to manufacture a worm-face gear to obtain its precise tooth surface. Flying cutter machining was used to determine the cutter trajectories, which verified the correctness of the method. Finally, simulations and experiments were carried out to verify the feasibility of the method. In addition, other face gear processing methods have been studied. Tang et al. [20] proposed the processing method of planing for a spur face gear with a 4-axis CNC planer. Based on theoretical research on the profiling curves of planer tools, the planing method was verified by the results of the simulation processing test on VERICUT software. Tan et al. [21] proposed a face-gear forging die that can be used for near-net forge face gears. The face gear was cut to specification using a wire electrical discharge machining (EDM) process based on the theory that the complex, curved surfaces of the face gear teeth could be mathematically approximated with a ruled surface. Zhang et al. [22] proposed a method of rapid prototyping technology for the investment casting of spur face gears. A test model was built based on the principle of rapid casting, and the processing parameters were obtained by experiments. The detection results showed that the roughness was 4.52μm, and the process is feasible. Dong et al. [23], Wang et al. [24] and Bai et al. [25] studied the methods of additive manufacturing for offset face gears and arc face gears. Face gear samples were manufactured based on the principle of additive manufacturing. However, the precision and surface quality of face gears need to be improved to satisfy the material and processing parameters. Lin et al. [26] proposed a method of additive manufacturing as the primary process for face gears, which is used to obtain the blanks of the face gear. The results suggested that the material wastage and number of processes were greatly reduced, and the precision was within the scope of permission. Thus, this method was proven to be effective. Wang et al. [27] studied a novel method of using laser cladding as the primary process for improving the anti-sticking performance and wear process of offset face gears. The accuracy of the laser cladding surface of the face gears and the feasibility of the method were verified by the process of detection. Huang et al. [28] proposed a rapid high-precision batch manufacturing method for spur face gears by electrochemical machining, which addressed technical defects in face gear milling. The detection results showed that the cost was reduced by 70% and the cycles by 75% in comparison with NC milling. Peng et al. [29] studied the theory of manufacturing face gears by plane cutters and proposed the method of adding additional movement to achieve the accurate simulation of the involute profile based on the method of Gleason. The results showed that the maximum error was 1.05μm, and the method has the advantage of practicability.

The processing methods mentioned above result in a rough finish. An increasing number of scholars have become involved in the research on face gear fine finishing technology to improve the machining accuracy of face gear tooth surfaces. In the field of face gear grinding research, Litvin [30] established a theory of face gear grinding, designed a special grinding wheel, and applied the patent apparatus and method for precision grinding face gears, which promoted face gear processing technology from rough to fine finishing. Litvin et al. [31] proposed a new method for the generation of face gears by the application of a grinding worm. Tooth contact analysis and stress analysis were performed, and the results confirmed the existence of a longitudinal bearing contact, avoidance of edge contacts, and reduction of contact stresses. Shen et al. [32] presented a method of using two-parameter worm grinding to form the face gear. A helical face gear was formed via a two-parameter worm envelope, and the two-parameter enveloping and envelope formation processes were analysed. The computer visualization results showed that an ideal face gear tooth surface was obtained. Tang et al. [33] developed a progressive grinding method, established a mathematical model of a parabolic rack cutter, spur gear cutter, disk wheel and modified spur face gear, and built a calculation model of the swing angle range of the complete grinding of the profile. Finally, a simulation processing test based on VERICUT software verified the feasibility and correctness of the method. Wang et al. [34] proposed a grinding method with a disk wheel and analysed the influence of the wheel trajectory and the installation error on the tooth surface deviation of face gears. The error factor of dressing the disk wheel with a diamond wheel was studied simultaneously, and a method of reducing the error by adjusting the tool position was ultimately proposed. Zhong et al. [35] discussed the deviation of an offset face gear manufactured by an involute disk wheel as a cutting tool. The equations for an offset face gear including machining deviation were derived. Zhou et al. [36] proposed a grinding method for face gears manufactured by a disk wheel and established a numerical model for determining the envelope residuals of the ground face gear surfaces to determine the grinding tracks of the disk wheel. The effectiveness of the proposed grinding method was illustrated by the simulation of four different cases of face gears. Cui et al. [37] introduced a new method for calculating the face gear tooth surface in the case of worm wheel installation errors and proposed the method of assuming the tool surface as the error surface, where the actual tool installation position error is introduced into the equation of the virtual shaper cutter. When they were compared, the face gear tooth surface machined in VERICUT software and the real process were found to be coincident, which proved the validity and feasibility of this new method. Wang et al. [38] studied an efficient processing method for face gears by grinding compound honing. The honing gear was manufactured by a shaped wheel covered with cubic boron nitride (CBN), and flexible coupling was installed between the spindle of the machine tool and the honing gear to eliminate the influence of installation errors on the surface quality. The maximum error was 15.1μm by experiment. Ming et al. [39] built a model of the grinding surface roughness of face gears based on the mathematical formula of the residual height of the motion trajectory of abrasive grains. The experimental results suggested that the mathematical model was reasonable, and the effects of the disk wheel spindle speed and the feed velocity of the disk wheel were more obvious than those of the abrasive code. Shen et al. [40] developed an optimization method to optimize the execution motions for the generating motion of the grinding process based on investigations of the design and generation of face gears with double-crowned tooth geometry. With this method, longitudinal crowned gear tooth flanks were generated precisely. The feasibility of the proposed method was validated by numerical examples. Stadtfeld [41] proposed a coniface grinding method for face gears, and it used a straight line disk wheel with a tool inclination to grind face gears. The method has been applied to the phoenix gear grinding machine. This method is a large step forward in the standardization of face gear cutters. Stadtfeld [42] described the manufacturing method in the USA and Europe and extended this technology in the American Gear Manufacturers Association (AGMA). Mao et al. [43] commented on the new method of Stadtfeld in China and said that the tool path should be optimized in order to optimize the meshing performance. This method has the property of a quasi-conjugate. Stadtfeld [42] proposed a continuous method for manufacturing face gears based on the above method. The proposed tool was a face cutter that performed a continuous indexing motion with equal rotation of the cutter and face gears during one gear rotation, which produced straight lines along the face width of the face gear.

The fine finishing methods above are discrete processing methods. That is, face gear surfaces are generated one by one, which results in low efficiency because of the long clearance time and high noise because of the poor dividing movement of the machine tool. Therefore, high efficiency and excellent surface quality have gradually become the research hotspots for face gear drives. The shaving method is popular in the field of gear finishing, as it has the advantages of high efficiency, high precision and low cost [44]. Shen [45], [46] analysed the kinematics of the shaving process for helical face gears and implemented it on a universal 5-axis CNC machine with a grooved shaving cutter. Additionally, helical face gear surfaces were generated in VERICUT software by the cutter tooth geometry designed, and the perfect morphology was obtained. Radzevich [47] proposed a novel modified scheme and an effective computer representation for the design of a plunge shaving cutter, which could be used on Gleason’s new Genesis (TM) 130SV CNC shaving machine. Hsu et al. [48] proposed a mathematical model that summarized instantaneous cutting marks and estimated the final shaved tooth surface of the work gear, which also provided guidance for designing the geometric data for a plunge shaving cutter to satisfy the even contact condition. According to [49], the conventional methods for decreasing the mid-concave error are negative displacement shaving [50] and balanced shaving [51]. In this paper, the method of negative displacement is used from a cost perspective.

However, there is currently little research on shaving methods for spur face gears in the published literature. This paper makes several contributions to the field of shaving methods for face gears. First, the feasibility of spur face gear shaving is analysed from the perspective of the generating and cutting motions. Second, coordinate systems for shaving based on physical location are designed, and the tooth surfaces of the shaving cutter and spur face gear are constructed. Third, the causes of mid-concave phenomena are analysed based on load tooth contact analysis, and mid-concave error is decreased by the method of distortion. Finally, the proposed method is successfully used to machine spur face gears according to the control equations of cutter points.

The paper is organized as follows: the feasible analysis and theoretical derivation of spur face gear shaving are presented in Sections 2 and 3, the investigation of LTCA and experiments with spur face gear shaving are presented in Sections 4 and 5, and Section 6 gives the conclusions.

Section snippets

Formation mechanism for tooth surfaces

A spur face gear drive’s left flank and right flank are symmetric along the radial direction of the face gears, and the drive can transmit motion and torque between orthogonal and non-orthogonal axes [1]. A 3D model of a spur face gear drive is shown in Fig. 1. γ is the included angle between the face gear and pinion along their rotational axes. A spur face gear drive with axes at right angles (γ=90) is the research object of this paper.

The tooth surface of spur face gears is generated by an

Mathematical model of shaving cutters

The rotary shaving cutter is an involute helical gear [44]. It meshes with the shaper cutter at staggered axes, and the involute tooth profile is enveloped by the normal sectional tooth profile as in Fig. 5. The coordinate system Ss(Os, Xs, Ys, Zs) represents the position of the shaving cutter, and Sc(Oc, Xc, Yc, Zc) represents the position of the virtual shaper cutter. Ec is the vertical distance between Xs and Zc. β is the included angle of Xs and Zc, and it is equal to the reference helix

Three-dimensional model of face gears

The spur face gear parameters selected are derived from the face gear transmission system project of the tank studied. According to the drive ratio, the tooth number of the pinions is 24, which accords with the theoretical number for the axial section. Its design parameters are detailed in Part 1 of Table 1. According to [3], the tooth number of the involved tools selected is 1 ~ 3 more than the tooth number of the pinions to avoid edge contact. Thus, the tooth number of the shaving cutters is

Overview of experiments

The shaving cutter was customized with the modification coefficient 1.2232mm, and the gear shaving machine is shown in Fig. 12 (****). The shaving parameter set is 0.2 mm/r (feed amount). The selection of the feed amount is related to the rigidity of the fixture and the ability to correct pre-shaving errors while shaving. If the feed amount is too small, the machined tooth surface will be squeezed, the material will not be removed, and the pre-shaving errors will not be corrected. If it is too

Conclusions

In summary, this paper studies a shaving method for spur face gears with shaving cutters that achieves continuous generation. The conclusions are as follows:

  • (1)

    There is a relative speed between the shaving cutter and spur face gear while meshing that can remove the tooth surface material. According to the shaving tooth meshing principle, the shaving tooth surface obtained is the standard tooth surface of spur face gears, which means that they can mesh properly. The result shows that it is feasible

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This work was supported by the Innovative Research Project of Basic Products of the State Administration of Science, Technology and Industry for National Defense [Grant Number: 237099000000170006] and the National Key Research and Development Project [Grant Number: 2019YFB2004400] and the National Natural Science Foundation of China [Grant Number: U1937603].

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