Tooth Flank Research Articles

A precision generating hobbing method for face-gear based on worm hob

In order to improve the machining accuracy and production efficiency of face-gear, a method of face-gear generating hobbing by worm is provided in this paper. The principle of face-gear hobbing worm is analyzed, and the mathematical model of the worm is presented based on the principle and the theory of meshing. Taking the hobbing needs into account, the special machine tool is provided, and the movement control method of face-gear hobbing by the worm on the machine tool is proposed. The equation of face-gear tooth surface is calculated, and the 3-D model of face-gear is established based on CATIA software. To reduce the face-gear tooth profile errors induced by ratio errors, an error analysis model of face-gear hobbing is established. The experiment is carried out, and the completed specimen is detected by Coordinate Measuring Machining (CMM). The processing parameter is amended according to the tooth flank detection results, and the maximum normal deviation of the whole tooth surface of the face-gear specimen is improved from 243.2 µm to 61.0 µm. Experiment results demonstrate that the method of face-gear hobbing by worm is an effective approach to achieve the precision face-gear with high dimensional accuracy.

Simulation and optimization of computer numerical control-milling model for machining a spiral bevel gear with new tooth flank

Distinguished with the traditional tooth flank of spiral bevel gears, an accurate spherical involute tooth profile is of obvious advantages for the design and manufacture. For obtaining the gear model with enough tooth flank accuracy, simulation and optimization methodologies of computer numerical control-milling model are proposed. Initially, it gives an identification of the spherical involute tooth flank based on an improved formation theory. A universal simulation machining of the universal multi-axis computer numerical control-milling center is proposed to obtain an initial model. Then, in order to get/for getting improved tooth flank accuracy of the initial gear model, it presents some optimization methods included in the applications which are (1) non-uniform rational B-spline reconstruction by the Skinning method and (2) an overall interpolation based on Energy method. Finally, some given numerical examples are utilized to verify the form error of tooth flank. In addition, a closed-loop experiment scheme is provided to verify the validity of proposed methods.

Geometry and contact characteristics of torus involute gears

Aimed at overcoming high sensitivity to machining or mounting error of line-contact conjugate surfaces, a novel torus involute gear drive is proposed which can compensate large axial misalignments and possess good meshing characteristics without lead correction. The torus involute gear is essentially a special spur gear with continuous shifting in the second order. Based on the processing principle of the torus involute gears, their mathematical models are established according to the corresponding imaginary rack cutter. In order to provide the approach to choose proper designing parameters, geometry characteristics of the torus involute gear are investigated: condition equations of tooth undercutting for a convex torus involute gear and tooth pointing for a concave torus involute gear are formulated utilizing the developed mathematical models, and the approach to checking tooth flank interference is provided. Contact characteristics of the gear set is studied through tooth contact analysis and finite element analysis. The simulated results produce useful information about tooth contact pattern, stress distribution, and transmission errors of the gear set.

Backlash Decrease System of Reducers/Gearboxes in Feed Kinematical Linkage Structure of CNC Machine Tools

Feed kinematic linkages of the CNC machine tools are built in camted cycle (closed loop) and their structures include reducers/gearboxes. as well. Because of the mechanical backlash between the flanks of the teeth of gearings, disturbances occur in the performance of a kinematic linkage as a whole (in terms of speed and position loops), thus leading to instability. This work presents a new system for decreasing the mechanical backlash that is based on a new type of cylindrical gearings with tapered teeth, allowing the backlash adjustment between the flanks of the joint teeth. The modality of acting in terms of decreasing the backlash on a reducer in the structure of a feed kinematic linkage is also detailed.

The meshing angular velocity and tangential contact force simulation for logarithmic spiral bevel gear based on Hertz elastic contact theory

To obtain the change tendency of output angular velocity and tangential contact force of a gear when the pinion under the step input during meshing of a new type of spiral bevel gear, which is a logarithmic spiral bevel gear, the tooth flank equation of logarithmic spiral bevel gear is deduced based on the formation mechanism of the tooth flank formation. A three-dimensional model of a pair of logarithmic spiral bevel gears whose number of teeth was 37:9, with modules being 4.5 mm, normal pressure angle being 20 degrees and spiral angle being 35 degrees were built and assembled. Based on Hertz elastic contact theory, the calculation formulas and parameters sets of contact force for conventional spiral bevel gear meshing simulation and logarithmic spiral bevel gear meshing simulation were done. Consider the dynamic simulation about meshing angular velocity and tangential contact force for conventional spiral bevel gear meshing and logarithmic spiral bevel gear meshing, respectively. Finally, by analyzing and comparing the simulation data, the results show that under the same input conditions, the fluctuation of the gear angular velocity and tangential contact force of logarithmic spiral bevel gear meshing are smaller than the conventional spiral bevel gear. That is, the transmission stationary of logarithmic spiral bevel gear meshing is superior to conventional spiral bevel gear.

Influence of Tip Relief Profile Modification on Involute Spur Gear Stress

This paper deals with the effects of linear tip profile modification on tooth root and tooth flank stress of involute spur gears. The increase in tooth flank stress due to tip profile modification is potentially hazardous due to increased risk of micro pitting initiation. The amount of required tip relief profile modification depends on the amount of tooth elastic deformation that needs to be compensated. In order to study the effects of linear tip profile modification on gear stress, two matching finite element models of involute spur gear pairs have been created, and tip relief profile modification has been applied to one pair. Tooth root and tooth flank stresses for both gear pairs have been compared in order to establish the effect of tip relief profile modification on gear stress.

Evaluation of a high-precision gear measuring machine for helix measurement using helix and wedge artifacts

High-precision gears are required for advanced motion and power transmission. The reliability of the measured value becomes important as the gear accuracy increases, and the establishment of a traceability system is needed. Therefore, a high-precision gear measuring machine (GMM) with a smaller uncertainty is expected to improve the gear calibration uncertainty. For this purpose, we developed a prototype of a high-precision GMM that adopts a direct drive mechanism and other features. Then, the high measurement capability of the developed GMM was verified using gear artifacts. Recently, some new measurement methods using simple shapes such as spheres and planes have been proposed as standards. We have verified the tooth profile measurement using a sphere artifact and reported the results that the developed GMM had a high capability in tooth profile measurement. Therefore, we attempted to devise a new evaluation method for helix measurement using a wedge artifact (WA) whose plane was treated as the tooth flank, and the high measurement capability of the developed GMM was verified. The results will provide a part of information to fully assess measurement uncertainty as our future work. This paper describes the evaluation results of the developed GMM for helix measurement using both a helix artifact and the WA, and discusses the effectiveness of the WA as a new artifact to evaluate the GMMs.

Wpływ skrajnej krawędzi frezu ślimakowego na kształtowanie boku zęba ślimacznicy

Wpływ skrajnej krawędzi frezu ślimakowego na kształtowanie boku zęba ślimacznicy

Gear Flank Modification Using a Variable Lead Grinding Worm Method on a Computer Numerical Control Gear Grinding Machine

Tooth crowning of a ground helical gear is usually done by adjusting the radial feed with respect to the axial feed of the grinding worm on the modern CNC gear grinding machine. However, when the amount of crowning and the helical angle of the gear are large, this method always results in a twisted tooth flank. Hence, in this paper, we propose a tooth flank crowning method for helical gears, which uses a diagonal (combined tangential and axial) feed on a grinding machine with a variable lead grinding worm (VLGW) obtained by adjusting the axial feed of the dressing disk with respect to the rotation angle of the grinding worm. Since all the required corrective motions for the proposed VLGW method are existing CNC controlled axes on modern gear grinding machines, it can easily be implemented without extra cost to modify the grinder hardware. Three numerical examples are presented to show the validation of the proposed method and its ability to reduce tooth flank twist even in the case of a large helical angle, with a particularly significant reduction on a crowned helical gear.

Micro tooth surface topography of face-milled hypoid gears

An accurate kinematic model of the face-milling process of hypoid gears has been developed in order to compute the micro tooth surface topography, generated by successive cuts of the head-cutter cutting edges, as they come into contact with the gear blank. The instantaneous gear tooth surface point has been determined at each point on each active cutting edge and from this it has been possible to predict the tooth surface roughness experienced during the machining process. The paper presents a description of the theoretical gear cutting model and the method to calculate the generated roughness of gear tooth flank. The effectiveness of the presented method is demonstrated by using a hypoid gear example.

Contact Pattern Analysis: Simulation of a Laser-Assisted Thermographic Approach

The contact pattern, defined as the area where gear teeth come into contact during their meshing, is a crucial quality feature of gears. If the size and location of the contact pattern are wrong, the gear meshing properties can be significantly affected (e.g., lifetime, noise). Despite several disadvantages, the so-called “paste method” is established as a method to analyse contact patterns. Here, a new measuring approach is examined using the Finite Elements Method (FEM). It is based on the heating-up of one tooth flank with a powerful laser, a subsequent partial transfer of the heat to a meshing tooth of the second gear wheel and finally capturing the heat distribution on that flank as an infrared image shortly afterwards. The thermal image should correspond to the contact pattern of that individual combination of teeth. A numerical analysis shows that at medium- and large-sized gears the achievable temperature increase will be high enough to be detected with modern infrared cameras.

Experimental and numerical study of tooth finishing processes contribution to gear noise

The contribution of gear tooth flank surface micro-finish on gear noise has not yet been taken into consideration. This paper is devoted to study the simultaneous effect of tooth roughness and lubricant viscosity on automotive gear vibrations. The vibrations performances were evaluated on an instrumented test rig under both dry and wet conditions. A non-destructive replication technique coupled to 3D optical measures was used to acquire the flanks topographies, which were characterized using multiscale decomposition. A three-dimensional finite element simulation of a helical gear was performed to assess the micro-scales impact on gear noise. Numerical representative surfaces morphologies were introduced into the simulation and compared through the transmission error calculation. Results have shown gear noise dependence on tooth finishing processes.

Surface fitting of an involute spur gear tooth flank roughness measurement to its nominal shape

Abstract A method for fitting a topography measured on an involute spur gear tooth flank to its nominal shape is proposed, so that the exact position along the length of the tooth from which the measured surface originates can be determined, and so that the nominal shape of the surface can be subtracted prior to roughness parameters calculation.

Compensation method for the alignment angle error in pitch deviation measurement

When measuring the tooth flank of an involute helical gear by gear measuring center (GMC), the alignment angle error of a gear axis, which was caused by the assembly error and manufacturing error of the GMC, will affect the measurement accuracy of pitch deviation of the gear tooth flank. Based on the model of the involute helical gear and the tooth flank measurement theory, a method is proposed to compensate the alignment angle error that is included in the measurement results of pitch deviation, without changing the initial measurement method of the GMC. Simulation experiments are done to verify the compensation method and the results show that after compensation, the alignment angle error of the gear axis included in measurement results of pitch deviation declines significantly, more than 90% of the alignment angle errors are compensated, and the residual alignment angle errors in pitch deviation measurement results are less than 0.1 μm. It shows that the proposed method can improve the measurement accuracy of the GMC when measuring the pitch deviation of involute helical gear.

Accurate modification methodology of universal machine tool settings for spiral bevel and hypoid gears

Universal machine tool settings with higher-order motion coefficients are developed to make accurate modification considering the actual machine geometric error compensation for spiral bevel and hypoid gears. First, the universal machine tool settings are exploited for the identification of the real tooth flank form error. Furthermore, the error sensitivity analysis method and an improved Levenberg–Marquardt algorithm with a trust-region strategy are utilized to obtain the solution of modification amount. Finally, a higher-order modification methodology for the universal machine tool settings is proposed which mainly covers three vital parts: (a) optimized selection of the modification settings, (b) modification of universal machine tool settings, and (c) machine geometric error compensation. Especially, a higher-accuracy fitting method for the form error tooth flank is investigated. Some numerical examples verify that the tooth flank form error after higher-order modification can reach less than 0.5 µm or even a smaller one, and the position error after compensating process spindle can be reduced from 0.0044861° to 0.0009232°. In addition, given experimental result can validate the feasibility of the proposed methodology.

Precision compensation method for tooth flank measurement error of hypoid gear

When measuring the tooth flank of hypoid gear, the measurement datum surface (the large end surface of the gear) does not always coincide with the design bases (the theoretical mounting distance), and this non-coincidence error would affect the tooth flank measurement results. Based on the measurement theory of the hypoid gear tooth flank, a precision matching method of the theoretical tooth surface and the measured tooth surface is designed, the objective function of the tooth flank matching method is established, and the search iterative method was used to calculate the compensation value of the measurement error of the tooth flank, when the two gear tooth surface is most accurately matched. As the mounting distance of the hypoid gear changes, two experiments are done to verify the proposed method. The experiment results show that, for different tooth flank of the measured gear, the measuring error of the tooth flank along Z-axis dropped significantly after compensated by this method, more than 80% of the error along Z-axis are compensated. It is obvious that this method could improve the measurement accuracy of the tooth flank form of hypoid gear.

Development of a gear measuring device using DFRP method

This paper presents the double-flank rack probe (DFRP) method to measure the accuracy relevant to flanks of gear teeth. In DFRP method, both left and right flanks of the gear to be measured are in mesh with a rack probe to measure pitch and profile deviations on the left and right flanks simultaneously. A gear measuring device (GMD) using DFRP method is developed. The evaluation method for pitch and profile deviations, the structure of the measuring system, and the key mechanical parts are introduced. Repeatability experimental results of the device is less than 2μm, and the results compared to the gear measuring machine (GMM) Klingelnberg P26 shows that this device have consistency with GMM and can be used for the measurement of the accuracy relevant to flanks of gear teeth.

Load Capacity of Dynamically Loaded Gears with Different Case-Hardened Depth

This article describes load capacity of dynamically loaded gears, more precisely describes the mechanical pulsation tests of carburized gears with different thickness of case-hardened depth and case-hardening technology, i.e. addition or removal of certain steps during the case-hardening process of the tooth flank and foot root. The comparison was made on six different process chemical-heat treatment, in two thicknesses of case-hardened depth and two pressure angles. Results are shown and compared in a Wöhler’s curve.

Accurate nonlinear modeling and computing of grinding machine settings modification considering spatial geometric errors for hypoid gears

The machine settings modification is a primary optimization stage in optimization design of the tooth form error flank. Spatial geometric errors (SGEs) as a main error source play an important role in affecting the precision of the actual CNC process, especially the grinding. Based on nonlinear analysis and application of computational algorithm, a new accurate grinding machine settings modification methodology considering the SGEs is proposed for manufacturing hypoid gears with a high level of accuracy. Firstly, the functional relationships between machine settings and SGEs of a six-axis CNC grinding machine tool are established. Then, an accurate modification objective function taking into account the residual tooth form error is investigated as a nonlinear least square problem, and a trust region algorithm with dogleg step is proposed to obtain accurate modification variations. After the SGEs are measured and compensated, the modification of grinding machine settings is accomplished. Finally, the practical application of a closed-loop modification process is presented to verify the good accuracy of the modification methodology by the proposed algorithm.

Influence of different combined severe shot peening and laser surface melting treatments on the fatigue performance of 20CrMnTi steel gear

In this paper, the effect of severe shot peening combined with laser melting (LSMSSP for short) on the fatigue resistance of 20CrMiTi steel gears is investigated in comparison with the effect of traditional shot peening on the fatigue resistance of the laser surface melted (LSMTSP for short) 20CrMiTi steel gear. The surface characteristics of the gear have been analyzed by a scanning electron microscope (SEM) and an X-ray diffractometer (XRD). The Forschungsstelle für Zahnräder und Getriebebau (FZG) back-to-back spur gear test rig was used for fatigue experiments. Experimental results showed that the residual stresses, full width at half maximum (FWHM), microhardness and retained austenite of the LSMSSP gears and LSMTSP gear were entirely different. Although the LSMSSP gears had higher surface roughness than the LSMTSP gear, the LSMSSP gears still had better fatigue resistance than the LSMTSP gear and laser surface melted gear. The nanocrystallized surface layer on the gear tooth flank created by severe shot peening might be a very important factor for improving the fatigue property of the LSMSSP gears.