Numerical Algorithm of Non-circular Gear’s Tooth Profile Based on Jarvis March

Purpose Crossed helical gears have point contact and their surfaces are subject to high surface stress. Contact stress and root tooth stress are the most common sources of failure in crossed helical gear. This paper aims to study the load-carrying capacity and performance of crossed helical gear teeth with different gear tooth profiles. To overcome defects and reduce the sensitivity to small shaft angle changes. The combined tooth profile is designed to reduce the bending stresses, contact stresses and tooth deflection, and prevent pinion failure in the gearbox. Design/methodology/approach The principle of the method is a line contact is introduced instead of a point contact between two teeth in mesh with each other. The tooth surface of the helical gear is designed and cut by a modified tool. Higher normal pressure angles like 25° and 35° are used. The modified involute is accomplished to eliminate interference between the teeth. Engineering software packages have been applied to generate all crossed helical gears gear profiles. The modification is compounding curves consisting of an epicycloid-involute-hypocycloid gear teeth profile generated by the cutter modified. Findings The stresses in the crossed helical gear teeth profile were reduced by increasing the normal pressure angle values. Using a 35° pressure angle the enhancement percentage in contact stress and teeth fillet region will be about 29.345% and 15.421%, respectively. The best enhancement in a gear’s resistance is the epicycloid-involute-hypocycloid gear teeth profile. The enhancement was 32.610% and 18.588%. The skew in line of action in skewed helical gear will be sensitive when the crossing angles are small. Their teeth surface tends to be easily worn out; however, the wearing process will be reduced by using a proposed gear teeth profile. Practical implications The gear teeth to be modified are cut by a shaper process. The modifying rack cutter of this study can be used as a reference for creating a different helical gears sample. The helical teeth surface is modified to become an envelope of the other. This makes an original point contact change into a line contact. The epicycloid-involute-hypocycloid gear teeth profile is preferred for a higher contact ratio and a large load capacity. This work explicitly introduces a new method of kinematic consideration to improve the load capacity of crossed helical gear. Originality/value This paper showed some novel results by the unique shape of the rack-cutter designed to generate different helical angles and different gear positions. In the future, it will make valuable contributions to the further development of the dynamic performance of a crossed helical gear system through the study in the field of using asymmetric teeth profiles of helical gears with tip relief as the manner to enhance the crossed helical gear performance. Investigation of crossed helical gear by applying a predesigned parabolic function of transmission error enables the absorption of linear discontinuous functions caused by misalignment.

Deproximating Tredgold's Approximation

This paper brings forward a new type of the tooth profile of noncircular gear—constant pressure angle involute tooth profile, and realizes its wire-electrode cutting. By the design of CAD and CAM, this paper shortens the design time of the noncircular gear and improved the design accuracy of the noncircular gear. By the research of the constant pressure angle involute tooth profile of noncircular gear, this paper has improved the transmission accuracy of the noncircular gear. By the research of the technology of wire-electrode cutting, this paper has improved the manufacturing accuracy of the noncircular gear.

A non-circular planetary gears train beating-up mechanism was proposed, the ideal kinematic curve of beating-up rockshaft was constructed and the reverse model of the pitch curve of non-circular gears was established based on the ideal kinematic curve. When the first-level non-circular gears were set as elliptical gears, the maximum swinging angle of the sley and the influence of the elliptical gears' eccentricity on the concavo-convex characteristic of the second-level non-circular gears were analyzed. Provided with a set of parameters, the pitch curves and tooth profiles of the second-level non-circular gears were determined by reverse method. The result has shown that non-circular planetary gears train beating-up mechanism can meet the requirements of beating-up process.

We investigated the effect of swelling of polyamide gear on the gear accuracy and noise generation. For the influence of swelling on the gear accuracy, we examined the changes in the tooth profile and tooth trace of test gear by water immersion test. Gear swelling caused large negative pressure angle errors on the tooth profiles of test gear and the error increased with the immersion time. Changes in the tooth profile were approximately similar in each tooth of the test gear. For the influence of swelling on the gear noise, we examined by comparing the noise of swelled gear and that of non-swelled gear using a gear tester. In this study, we attached a polyamide gear to the driven shaft and a steel gear to the driving shaft, and carried out gear tests under the conditions of tangential force F/b = 6.5, 13.0, 19.6 N/mm (the nominal load torque = 19.6, 39.2, 58.8 Nm). The change in tooth profile due to swelling influenced the noise generation, however the influence was limitative and swelling had no very influence on the gear noise generation except for the case operated under low load condition.

A hybrid strategy is proposed to meet the challenge of obtaining the profile of micro gear teeth with a small modulus. Firstly, the contact probe segmentally obtained the falling flank profiles with an auxiliary lifting mechanism to avoid interference when it climbs on the rising slope. Then, the noncontact chromatic confocal displacement sensor efficiently acquired the gear peak positions to carry out the two-point error separation with the gear peak positions from the probe measurement. Finally, actual experiments were carried out to obtain the profile of a harmonic drive flexspline. Compared with the commercial ultraprecise profiler, the proposed method provides measurement results with a deviation of less than 20 μm. In conclusion, the hybrid strategy is feasible and accurate for drawing the micro gear teeth profile without any collision between the measuring probes and the measured workpiece.

This paper aims to propose a design method for tooth profiles of spur gears based on given line of action. A simplified derivation of the mathematical model of tooth profiles is introduced according to the meshing theory. Tooth profiles of spur gears, using a parabola as line of action, is established. The result shows that it will be better to control the performances of a gear set by specifying the shape of the line of action rather than specifying tooth profiles of mating gear.

A simple but accurate combined computationaland graphical method for creating drawings and solid models of standard involute gears is presented. The method is predicated on the fact that the gear tooth angle at the base circle is fixed for a gear of specified module or size. As the contact point moves along the involute curve from the base circle point through the pitch point to the addendum circle point; the involute and gear tooth contact angles change continuously but their sum is fixed at the value it was at the base circle. This allows the coordinates of points on the involute curve to be generated analytically without employing the roll angle as current available methods. The generated data can be implemented in any computer design drafting (CDD) package platform to create an accurate gear tooth profile. The computations are done with Microsoft Excel which generates the graphical data for the gear tooth profile that are used in the CDD package. The required inputs to the Excel spreadsheet are the gear module size, the pressure angle, the number of teeth and the radial number of steps. A gearset example is considered and created with this method. The solid model of the example gearset in mesh and 2D drawing of the pinion are presented.

Continuously variable transmission (CVT) of noncircular gear has the technical advantages of large bearing capacity and high transmission efficiency. The key technology of CVT with noncircular gear has been broken through some countries, and is in the stage of deep application research. Although the characteristics and design methods of noncircular gear pairs have been continuously studied in China, the noncircular gear CVT is still in the preliminary exploration and research stage. The linear functional noncircular gear pair, whose transmission ratio is a linear function in the working section, to realize continuously variable transmission was the research object in this paper. According to the required transmission ratio in the working section, the transmission ratio function in the non-working section was constructed by using a polynomial. And then the influence of pitch curve parameters in the working section on which in the non-working section was also analyzed to obtain the pitch curve suitable for transmission of this gear pair. In addition, for improving the stability and bearing capacity of gear transmission, the noncircular gear pair transmission with high contact ratio was designed. Furthermore, the accurate value of the contact tooth length was calculated based on the gear principle and the characteristics of the involute tooth profile, from this the contact tooth length error was calculated by comparing the accurate value with its actual value obtained by the rolling experiment. Finally, an indirect method to verify the contact ratio by detecting the contact length error of the tooth profile was proposed.

We have successfully developed a tooth profile which enables a spur gear having zero relative curvature at contact points under the engagement through the concave/convex pattern of contact and further enables a single flank of the tooth profile to have the infinite number of points where the relative curvature and specific sliding are zero values. We have given a name of “LogiX” to this tooth profile. A W-N (Wildhaber-Novikov) tooth profi¨le has been known as that having the concave/convex pattern of contact. The tooth profile, however, is applied only to a helical gear due to its feature of a point contact. While, on the LogiX tooth profile, an improvement has been made so that a pair of spur gears having the tooth profile may contact each other through the concave/convex pattern of a line-contact which cannot be achieved by the W-N tooth profile. Therefore, the LogiX tooth profile has realized a spur gear whose surface durability is as high as that of the W-N tooth profile. Since the results of durability tests show slightly higher than an involute one, it is expected that a new type heavy duty gear of this tooth profile puts into practical use. Furthermore, the tooth profile will have the possibility of creating the new era in the history of tooth profile theory.

A new meshing relationship for gear drive to characterize the conjugation geometry is studied in this paper based on conjugate curves. Conjugate curves are described as two smooth curves always keep continuous and tangent contact with each other in given contact direction under motion law. The general principle of curve meshing is developed for the given spatial or plane curve. The meshing equation along arbitrary direction of contact angle is derived. The properties of geometric and motion of the contact of conjugate curves are discussed. According to the equidistance-enveloping method, tubular meshing surfaces are proposed to build up circular arc tooth profiles, which inherit all properties of conjugate curves. The geometry design and mathematical model of the gears are established. Three types of contact pattern of tooth profiles are generated: convex-to-convex, convex-to-plane and convex-to-concave. A calculation example for convex-to-concave tooth profiles of gears is provided. Theoretical and numerical results demonstrate the feasibility and correctness of proposed conjugate curves theory and it lays the foundation for the design of high performance gear transmission.

On a gear tooth surface, there may be some certain points which contact twice with its mating gear tooth surface. This phenomenon is called secondary action. In this paper, applying this phenomenon in cycloid drive, a new type of double-enveloping cycloid drive is generated based on gear geometry theory, and the torsional stiffness is calculated. The new conjugated tooth profile is composed by an external cycloid tooth profile and a new generated internal ring gear tooth profile. The main characteristic of the new tooth profile is that there are double contact lines simultaneously between on tooth pair in a certain meshing area. In this paper, firstly the generation method of the new conjugated tooth profile is present, and the meshing characteristics are investigated. Secondly, the torsional stiffness calculation model for double-enveloping cycloid drive is established. The normal stiffness, the arm length of the meshing force and the torsional stiffness are calculated. Finally, based on a numerical example, the calculation results are present, and the torsional stiffness of double-enveloping cycloid drive is compared with that of the conventional cycloid drive both on single tooth pair and whole gear mesh.

In harmonic gear transmission, the influence of meshing transmission tooth profile on its performance is particularly prominent. In order to improve the meshing transmission performance of harmonic gear transmission significantly, in this paper, the modified tooth profile of common tangent cycloid is adopted as the tooth profile of the flexible gear. The exact conjugate theory based on envelope method is applied to study the conjugate region and the conjugate tooth profile of harmonic drive with the novel cycloid tooth, and the influence of the tooth parameters on the conjugate characteristics. Through research, two conjugate regions with different sizes exist in harmonic gear transmission with cycloid modified tooth, and there is a double-conjugated tooth profile that takes into account both the “secondary conjugation phenomenon” and the “two-point conjugation phenomenon”. Besides, the meshing arc length of tooth profile is longer, the conjugate area is larger, and the bearing performance in transmission is excellent.KeywordsMechanical engineeringTooth profileCycloid harmonics

A new W-N gear tooth profile is developed. The gear developed has an addendum of circular arc and a dedendum of involute curve. This particular tooth profile is believed to solve the problem of conventional W-N gear profile—that is, the profile is sensitive to center distance variations. No pitting on the gear was observed even after 1 × 107 revolutions cycle during the laboratory test using a pair of gear having specified values of Mn (normal module) = 4, β (helix angle) = 30 deg, and Lloyd’s K factor at 8 MPa.

This article introduces a method to calculate contours of form cutters for machining helical gears from given gear tooth profiles. It is essential to find a relationship between the cutter contour and the gear profile in order to carry out the calculation. The method introduced in this article uses contact points between the cutter rotary surface and the gear tooth surface to establish the relationship. A minimum distance principle is applied. Equations for the calculation are derived and an example is given.