Involute Gear Research Articles

Recent developments on an interferometric multilateration measurement system for large volume coordinate metrology

A mobile multilateration measurement system developed at the Physikalisch-Technische Bundesanstalt (PTB) around 2010 has been thoroughly investigated and refined to gain better performance with smaller uncertainties even when applied to the calibration of large complex workpieces. The mathematical background of multilateration and the propagation of uncertainties for the algorithms involved is explained in detail. Using the example of simple 1D and 2D measuring tasks, the influence of certain parameters characterizing the setup of the measurement system on the overall uncertainty is quantified. A strategy is developed to incorporate multi-stylus measurements which are often inevitable when workpieces feature complex shapes. The findings are verified on a large involute gear which is 2 m in diameter. All measurements are performed on PTB’s large coordinate measuring machine with a working range of .

DESIGN OF A COMPUTER-AIDED GEAR MANUFACTURING TOOL – RACK-SHAPED CUTTER

In this work, the calculation of Maag gear shaper cutter parameters is performed for spur gears with helical teeth in three variants – straight-tooth tool with machine offset, helical-tooth tool without machine offset and helical-tooth tool with machine offset. It is therefore a prerequisite that the manufactured involute gearing has helical teeth for each variant. The created CAD program is universal and can be used for construction in other combinations as well. The tool clamping angles on the tool holder, the cutting geometry of the cutter and the characteristic of the gearing are introduced into the calculation. The output of the work will be then calculated individual parameters of the Maag shaping cutter in the tooling system, necessary for its construction. The calculation are performed in program T-Flex CAD and the summary output is graphical 2D/3D representation of the rack-shaped cutter in its base, normal and side planes, always in a different design based on the change of the tool input data and gearing characteristic. The analysis of the tool´s involute profile was solved by vector calculus and matrices and by rotating the tool in the chosen coordinate systems. The specific calculation of the tool parameters will be solved using goniometric functions.

Forecasting of the contact endurance of hardened teeth and the load capacity of involute gear transmissions based on the limit state criterion of the material

Forecasting of surface contact stress and load capacity of cemented and nitrocarburized involute gears using the criterion of the limit state of the material based on the results of known reliable tests is considered. Keywords: involute gear transmission, contact endurance, load capacity, limit state criterion, forecasting. vkorotkin@sfedu.ru

A Novel Measurement Standard for Surface Roughness on Involute Gears

Although manufacturers of coordinate measurement systems and gear measurement systems already provide instruments that enable an end-of-line-monitoring of the roughness properties of gears, the roughness measurement on gear flanks still lacks traceability with respect to the standardised SI-units. There is still a gap between well standardised roughness measurements on planar surfaces and gear measurements on involutes. This gap is bridged by a novel physical measurement standard (PMS), also referred to as material measure, for roughness measurements on involute gears that has been developed at the Physikalisch-Technische Bundesanstalt (PTB). The necessary transformations between the systems of roughness and gear measurements have been implemented. The measurement standard itself represents calibrated roughness values for the parameters Ra, Rz, Rq, Rk, Rpk and Rvk and Mr1 and Mr2. Furthermore, the PMS can be measured both with classic profilometers as well as gear measurement systems with integrated roughness probes.

Numerical analysis of meshing heating of involute spur gear

Involute spur gears generate heat due to tooth surface meshing friction. Excessive temperature rising affects transmission accuracy and reduces work reliability.. By establishing the normalized coordinates of the meshing curve and based on the frictional heat generation theory, the mathematical analysis model of the meshing surface heating is studied, the factors affecting the average heat flux density of meshing are explored, and the distribution law of these factors along the normalized coordinate of the meshing is analysed. The analysis shows that the tangential velocity of the meshing point and the half-bandwidth of the time domain contact have the greatest influence on the average heat flow density; the average heat flow density distribution of the driving wheel and the driven wheel are similar. The heat flow density of the driving wheel is greater than that of the driven wheel. Tooth shape modification minimizes tooth surface meshing contact stress, reduces meshing heat generation, controls temperature rise and improves transmission reliability.

Alternative methods of verifying the reconstructed outline of a non-standard spur gear

Common methods of checking a gear that have been designed in reverse engineering are, for example, measurement with a modular caliper or disc micrometer. However, although these methods are among the most accurate, they allow only one or a few of the selected geometric parameters to be measured. The paper presents alternative methods of verification of the reconstructed outline of a very non-standard involute gear with the parameters m = 4.98, α = 26.325 °, x = 0.0695, y = 0.795, c* = 0.383. These methods are less accurate than the classic ones, but they allow for a comprehensive check of the entire outline of the reconstructed tooth. They are often used in industrial practice. However, here, in addition to the methodology, a short tolerance analysis was also carried out, which may to some extent compensate for the aforementioned measurement inaccuracy. The method consists in using the potential of a spreadsheet and CAD technique to generate an involute outline of a gear tooth whose geometry is recreated.

Issues related to an attempt to recreate the geometry of a non-standard spur gear

Modern machine manufacturers are making the design and technology of their products more and more complicated. This is to protect against a frequently used practice at customers, i.e. making extra parts on your own. This is because entrepreneurs often cannot afford to order expensive original spare parts and - using reverse engineering - prepare working drawings and commission the components to be made in their own machine park or externally from local suppliers. However, the matter is more complex in the case of gears, which so far have been designed on the basis of the selection of standard geometric parameters. A small modification of one or more of these parameters is enough and it becomes very difficult to recreate the geometry of such a gear. This paper presents the issues related to the reverse engineering of a spur involute gear with very non-standard parameters m = 4.98, α = 26.325 °, x = 0.0695, y = 0.795, c* = 0.383. Further metrological steps were proposed that should be taken to correctly identify at least the fact that the test object is not a part produced by standard modular tools (Fellows cutter, Maag rack cutter, worm cutter, etc.). The work also includes short graphical analyzes of the recreated geometry.

Contact Stresses and Dynamic Analysis of involute Spur Gear with FEM Approach

Abstract: This paper investigates the characteristics of a gear system including contact stresses, bending stresses, and the transmission errors of gears in mesh. The objective of this paper is to compare values of contact stress and dynamic analysis obtained by theoretical hertz equation with the ANSYS result. A two stage spur gear box has been designed for material handling application by manual calculation and then performs contact stress and dynamic Simulation to ensure its reliable working. The results of the two-dimensional Finite Element Method (FEM) analysis from ANSYS and theoretical results are well comparable. Keywords: involute, spur gear, contact stress, dynamic analysis, finite element analysis

Research on diagnostic method for broken tooth fault of reducer with involute helical gear

This article takes the reducer with the involute helical gear as the research object, the diagnostic method of the broken tooth fault and the deterioration trend is researched by vibration spectrum graph, demodulation waveform graph, time domain waveform graph, demodulation spectrum graph. The research results show that vibration spectrum graph has the worst guidance for the broken tooth fault of the involute helical gear reducer, demodulation waveform graph has the poor guidance in the initial stage of the broken tooth fault, with the deepening of the severity of the fault, the fault characteristics of the waveform gradually become obvious, time domain waveform graph and demodulation spectrum graph are the effective means to discover the initial fault and monitor the fault changes.

Design, modeling and FEA analysis of internal symmetric and asymmetric involute spur gears

Recently, internal gears become widely used and highly required according to its ability to transmit large torque to weight ratio, high bending strength, smooth transmission, low noise, and low vibration. Therefore, internal gears are strongly recommended in particular “planetary gear transmission systems”. In this paper, internal involute spur gears are designed based on conventional approach of involute gears. Matlab is used to attain the points of internal gear and to get the main parameters of internal tooth profile, these points have been read by AutoCad to have two dimensional tooth profile. Finite element analysis using Ansys is achieved to analyze and compared the strength of three types of internal gears, Symmetric (20° - 20°) that has been chose to be the standard case, Asymmetric (14.5° - 35°) and Corrected Asymmetric (14.5° - 35°). Tetrahedral type patch conforming method with element size1mm have been chose for fine meshing. The internal gear is fixed supported from the outer ring then, 6500 N.m torque is applied at the rotating axis of the pinion. The bending stresses are calculated based on Von-Mises theory using (FEA). Finally, this study is presented to demonstrate the superiority of internal asymmetric tooth and improve and optimize this significant type of gears.

Contact Damping and Stiffness Calculation Model for Rough Surface Considering Lubrication in Involute Spur Gear

The contact properties of an interface are crucial to the performance of equipment, and it is necessary to study the contact damping and contact stiffness, especially in the case of mixed lubrication. A calculation model for contact damping and contact stiffness considering lubrication was proposed on the basis of the KE contact model and mixed elastohydrodynamic lubrication theory. Both the damping and the stiffness were composed of the oil film portion and the asperity contact portion. Since the damping and the stiffness of oil film mainly depended on the film thickness and the pressure, which can be obtained with the mixed lubrication model, another crucial point was to figure out the contribution of asperity contact. Ignoring the effect of the tangential deformation, the stiffness and the load determined with the normal deformation of the asperity were obtained. Then, the contact damping and the contact stiffness considering lubrication could be derived. Finally, the model was applied to the study of contact damping and stiffness of the involute spur gear.

Acoustical behavior of loss-optimized involute gears

The progressing electrification of vehicle drive systems focuses more and more on efficient high-speed concepts. Increasing the motor speed leads to a higher power density of the electrified power train and thereby to an increased range for battery electric vehicles. The high rotational speeds cause new challenges in designing gearboxes regarding the efficiency and the acoustical behavior. Most present gearings in conventional vehicles are designed with high tooth depths to ensure low noise excitation behavior combined with the best possible efficiency. By changing the gear geometry to smaller tooth depths with higher pressure angles, it is possible to further decrease gear losses. However, the loss-optimized gear geometry must not jeopardize the beneficial acoustical behavior. In theoretical studies, the acoustical behavior of loss-optimized gears are investigated and compared to gearings designed according to the state of the art. Design calculations of the excitations of all ideal gears without deviations are on similar levels. However, application of such gear geometries faces severe challenges because the sensitivity to manufacturing deviations may be high. In this paper, simulation results and test results between low-NVH gears and loss-optimized gears are documented and analyzed.

Meshing performance investigations of involute worm and helical gear drive based on counterpart rack

Meshing performance investigations of involute worm and helical gear drive based on counterpart rack

Geometric Design and Kinematics Analysis of Non-Circular Planetary Gear Train with Cycloid Profile

This research presents a method to design a non-circular planetary gear. Therein the satellite gear block consists of eccentric cycloidal gear and elliptical cycloidal gear, which have been given. The mathematical equations of two ring non-circular gears are set up according to the gearing theory considering the undercutting conditions. A numerical calculation program was written in Matlab to calculate and dynamically analyze this planetary gear. The examples presented in the paper clarified the design steps of the method. The simulation results show that the non-circular cycloidal gear can overcome the irregular tooth phenomenon on the traditional non-circular involute gear, and when it is necessary to design infinitely variable speed converters with large amplitudes, the coefficient λ should be adjusted rather than the coefficient μ.

Effect of structural design parameters on nonlinear dynamic characteristics of the gear transmission

The calculation of time-varying meshing stiffness caused by the alternate contacting of the gear tooth is an essential prerequisite to obtain real and effective nonlinear dynamic characteristics of the transmission system, so that the significance of which cannot be overemphasized. Accordingly, this work proposes an improved method to get meshing stiffness with taking fillet-foundation and gear rim deflection into consideration. Compared to the traditional potential energy method, the proposed method has more superior accuracy and performance, and its effectiveness has been further verified by the finite element analytical model. After that, an ideal eight degree of freedoms (DOFs) dynamic model of one stage mass-spring-damper involute spur gear, including lateral and torsional motions, is established to study the dynamic characteristics. Due to the complexity of the gear system operating conditions, we also investigate the influence of various parameters including hub bore radius, transmitting load, and rotation speed on dynamic features, especially in heavy-load and high-speed conditions. From the results, it can be concluded that these parameters will play a prominent role in the spur gear pair dynamic behaviors, providing a certain guidance for gear design.

Effect of Profile Modification on Noise in Involute Gear Pair

Ensuring regular movement and power transmission in gear wheels is possible with a suitable tooth profile. Although involute profiles have a structure that can provide conjugate movement in accordance with the law of gearing, transmission errors that cause vibration and noise occur due to the flexibility of the elements in the gear system under dynamic conditions. Transmission errors occur depend-ing on many parameters from production to the oil and lubrication system. In this study, the vibration and noise state generated during transmission in gears were investigated in relation to geometric parameters. In the reference gear pair as-sumption, the noise levels were evaluated for the four cases created due to the change of different geometric parameters. The effect of profile modification on vibration and noise was addressed, and optimum profile modification parameters for the reference gear pair were analyzed with KISSsoft commercial software. The effects of geometric parameters and profile modification on noise level are shown in graphs. With the application of the Tip Relief method, a significant de-crease in the noise level has been observed.

Research on an Optimized Hob to Increase the Bending Strength of Involute Gears by Changing the Root Fillet Profile

An optimized hob to increase the bending strength of involute gears by changing the root fillet profile is presented in this paper. The maximum bending stress which determines the service life of a gear in many applications depends on stress concentration caused by the gear root fillet. Better control of the root fillet can result in gears with higher bending strength. The optimised hob tool is a modification based on the standard hob tool, with constant normal base pitch, but a different pressure angle and module, which will generate a different gear root fillet area. The comparison analysis demonstrates that the gear generated by the optimised hob has higher bending strength than that generated by the common standard hob. For analysis and validation of results, three methods of predicting bending stress - ISO standard, three-dimensional tooth contact analysis (3D-TCA) method, and finite element analysis (FEA) are applied and discussed.

Investigation on the high-cycle tooth bending fatigue and thermo-mechanical behavior of polymer gears with a progressive curved path of contact

A systematic combination of experimental and numerical methods was employed in a comprehensive study on the high-cycle tooth bending fatigue of polymer gears with a progressive curved path of contact (S-gears). A polymer/polymer combination was tested where the drive gear was made of POM and the driven one from PA 66. Gears were tested at three different torque levels, i.e. 0.6 Nm, 0.8 Nm, and 1.0 Nm, with no additional lubrication and until gear failure. S-gear pairs showed increased durability over the involute gear pairs. A 100% pronounced lifespan increase was observed at the tested load 0.6 Nm.

Geometry design and dynamic analysis of a modified cycloid reducer with epitrochoid tooth profile

This study proposes a design method for a modified cycloid reducer with an epitrochoid tooth profile. The reducer used here has one contact pattern and non-pin rollers like a planocentric reducer. This feature makes the designed reducer easier to be manufactured compared to conventional cycloid reducers, which are difficult to manufacture due to tolerances. The tooth profile characteristics for nine different design scenarios for the cycloid reducer were analyzed with respect to the tooth thickness ratio and the distance from the center of the rolling circle. It was observed that the inflection point, which was calculated from the radius of curvature, was a major factor influencing the design of the cycloidal tooth profiles. A mathematical model for the force analysis of the designed reducer was developed, and variations in force distribution between the internal and external gears as well as the efficiency of the cycloid reducer were calculated according to different coefficients of friction. Involute and cycloid gears with a difference of one tooth between the internal and external gears were designed and manufactured, and finite element analysis showed that the cycloid gear had higher rigidity than the involute gear.

Mathematical modelling of power skiving for general profile based on numerical enveloping

Power skiving is an effective generating machining method for internal parts like gears with respect its high productivity. The general mathematic modelling for power skiving is the basis for cutting tools design, machining precision evaluation, and machining process optimization. Currently, mainly studies are focus on the involute gear machining with adopting the analytical enveloping equation. However, these analytical methods have failed to deal with overcutting for general profile skiving tasks. Moreover, little attention has been devoted to investigate the power skiving process with taking variable configuration parameters, which is significant to control the machined surface topography. Herein, we introduce a mathematic modelling method for power skiving with general profile based on the numerical discrete enveloping. Firstly, the basic mathematic model of power skiving is established, in which the center distance is formulated as polynomial of time. By transforming the power skiving into a forming machining of the swept volume of cutting edge, a numerical algorithm is designed to distinguish the machined transverse profile via the discrete enveloping ideology. Especially, the precise instant contact curve is extracted according to the feed motion speed inversely. Finally, simulations for involute gear and cycloid wheel are carried out to verify the effectiveness of this method and investigate the influence of variable radial motions on the machined slot surface topography. The results validate capability of this method on simulate the dynamic power skiving process for general desire profiles and evaluate the machined results.