Theory and experimental research on spiral bevel gear by double-side milling method

In this paper, a double-side milling method on spiral bevel gear is proposed. First, according to the tooth taper processed by double-side milling method, the influence of dedendum angle on the tooth taper was researched. Taking cut parameters into comprehensive consideration, the geometric parameters were designed through the inclination of root line and modified mean point in which machine setting parameters calculated was selected. Only the modified mean point met the meshing equation, and the error of pressure angle would increase as far away from the modified mean point in tooth line. The error would lead to bias in contact. A helical correction motion was introduced and the influence of helical motion coefficient on tooth surface topology was studied. Based on the meshing performance, a suitable coefficient was calculated. Finally, an example was illustrated. The experimental results were consistent with the theoretical analysis. The validity of the proposed method is verified.

Geometry and parameter design of novel circular arc helical gears for parallel-axis transmission

Based on the space curve meshing equation, in this article, a geometry design of a novel circular arc helical gear mechanism with pure rolling for parallel transmission was presented. Different from conventional circular arc gears, the meshing points of circular arc helical gears were limited at the instantaneous centre of rotation. The parameter equations describing the contact curves for both the driving gear and the driven gear were deduced from the space curve meshing equation, and parameter equations of the concave–convex circular arc profiles were established both for internal meshing and external meshing. Furthermore, a formula for the contact ratio was presented, and the impact factors influencing the contact ratio were discussed. Then, the parameter design was presented for the geometry parameters of tooth profiles, such as normal pitch, tooth height and tooth thickness. Using the deduced equations, several numerical examples were then considered, and prototype samples were produced to experimentally validate the contact ratio equation and the theoretical kinematic performance. The circular arc helical gear mechanism investigated in this study showed a high gear transmission performance such as a pure rolling meshing, a high contact ratio and a large comprehensive strength, when considering engineering applications.

Theoretical Research on Load Capacity of Double-Roller Enveloping End Face Engagement Worm Gear

The calculation of load capacity is the key problem of worm's analysis. Taking the double-roller enveloping end face engagement worm gear as an example, a method for the numerical analysis of capacity was proposed based on finite element theory and fatigue analysis. Based on the meshing theory, the meshing equation was derived, and the accurate mathematical model for tooth surface of worm gear was established. Then the finite element modeling of worm gear was to analyze the contact stress and stress-strain effect. Finally, applying the safe life calculation method, the factors of fatigue life of worm gear were analyzed and researched. The researched result indicate that the worm gear has a quite good mesh performance when the worm meshing teeth have eight pairs. Under the same condition, with the analysis of the model's strength and finite elements performed, it was confirmed that the load capacity of end face engagement worm gear has an obvious improvement by comparison of that of enveloping hourglass worm gear, further, the maximum tooth root stress was only 6.5% of enveloping hourglass worm'. Meanwhile, the load distribution is in a declining invert L shape. And the fatigue life of end face engagement of worm gear pair could be attained 10 cycles. Therefore, this study results provided the theoretical basis and industrial applications value for transient analysis of end face engagement of worm gear and manufacturing constantly in the future.

The Equation of the Contact Line of the Involute Curvilinear-Tooth Cylindrical Gear Pump for the Agricultural Tractor

In order to derive the equation of the contact line of the involute curvilinear-tooth cylindrical gear pump for the agricultural tractor, the tooth surface of the involute curvilinear-tooth cylindrical gear is firstly generated as that of the spur or helical gear. Then the equation of the tooth surface is derived from changing the settings and orientations of the coordinate systems after the equation of the tooth profile in an arbitrary radial section is calculated by the methods of differential geometry. Based on the equation of the tooth surface, the meshing equation of the two gears is further acquired and then the equation of the contact line. Finally, the tooth surface and the contact line are simulated with mathematical software. The results suggests that the contact line between two curvilinear-tooth cylindrical gears is an arc line in the surface of action; and this line, shaped as an arc line in the generating plane of the tooth surface, is longer than that of the spur or helical gear with the same face width.

Contact Trace of Internal Meshing Double Circular-Arc Spiral Bevel Gears

The meshing contact analysis of double circular-arc spiral bevel gears for nutation drive is considered. Based on gear meshing theory, the mathematical models and meshing equation of the double circular-arc spiral bevel gears are developed. The contact trace satisfies the tooth surface equations and meshing equation simultaneously, and then the contact trace is solved by using mathematical software. The analysis of tooth surface contact pressure is simulated by finite element analysis software.

Geometry design and mathematical model of a new kind of gear transmission with circular arc tooth profiles based on curve contact analysis

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.

Contact Strength of Toroidal Drive with Cylindrical Teeth

The meshing equation of the toroidal drive with cylindrical tooth was established based on space meshing theory, and the formula of contact stress between planet and worm or the toroidal internal gear are derived. Major influence factors were analyzed and forecasted. The contact stress is sensitive to the tooth number of planet center distance and planet radius. Finally, the calculation method of contact strength of toroidal drive was given.

Analysis and Manufacture of Skew Bevel Gears with Spherical Involute

Skew bevel gears are fundamental element of transmission system. Processing quality of skew bevel gears has impact on the performance of system. An accurate processing method of tooth surface of skew bevel gears with spherical involute is proposed. According to the space meshing theory, the meshing equation of skew bevel gears is built by the theory of coordinate transform. And the generating principle of generation line of tooth surface about skew bevel gears is studied. In terms of the formation theory of tooth surface, moving process model of milling processing is established. And the generation line is as chord of face circular cutters to cut the tooth surface. Machining of the profile of skew bevel gears is performed using three axes linkage by the method. Finally, the transmission experiment proves that this method can improve dynamics and strength characteristics.

Calculation Equation of Tooth Face of Shaping Gear for Logarithmic Spiral Bevel Gear

According to the processing principle of the spiral bevel gear, analyzed the relative motion of cutter and workpiece in process. Combing the feature of logarithmic spiral bevel gear, this paper took the advantage of the gyration vector expansion to derivate the tooth surface equation of logarithmic spiral bevel gear shaping gear and deduced the meshing equation.

A generalized space curve meshing equation for arbitrary intersecting gear

This article derives the space curve meshing equations for arbitrary intersecting gear mechanism, which could achieve continuous and smooth transmission between arbitrary angle intersecting axes, and then establishes the central curves equations of the driving and driven tines on the basis of space curve meshing equations. According to the equations, a calculation example is given and material prototype samples are made to experimentally validate the kinematic performance. The result shows that if the central curve of the driving tine is a circular helix, the central curve of the driven tine is close to a conical helix. This article will supply a basic theory for the application of the arbitrary intersecting gear mechanism in various areas.