Construction of conical axoids on the basis of congruent spherical ellipses

Purpose: To carry out the transition from a cylindrical gear in which the centroids are congruent ellipses with centres of rotation in the foci, to a bevel gear on the basic of congruent spherical ellipses. Design/methodology/approach: Congruent ellipses with centres of rotation in the foci serve as centroids for the design of cylindrical gears with non-circular wheels. The article analytically shows that the analogues of ellipses on the plane - congruent spherical ellipses are the basis for the construction of the axoids of the corresponding bevel gears. An analogue of the centre-to-centre distance for ellipses in the plane is the angle between the axes of rotation of conical axoids. Findings: Based on the equality of the arcs of ellipses, the dependence of the angle of rotation of one axoid on the angle of rotation of another is found. Graphs of this dependence for separate cases are given. It is shown under what conditions the axes of axoids intersect at right angle. The parametric equations of spherical ellipses and corresponding axoids are given. They were used to construct spherical ellipses and corresponding conical axoids for different cases. For gears with right angle between the axes, separate positions of the axoids with different angles of their rotation around their axes are constructed. Practical implications: Spherical ellipses are directing curves for the construction of the corresponding conical axoids. Originality/value: The paper shows that congruent spherical ellipses act as centroids for the design of axoids of bevel gears. They roll one by one without sliding, rotating around axes that intersect in the centre of the sphere. To design such gears, it is important to know the interdependence between the geometric parameters, especially for common gears with a right angle between the axes.

PROCESSING OF HARDENED CYLINDRICAL GEAR WHEELS OF THE CUTTING GEARBOX OF THE COMBINE UKD 200-500

The article discusses the latest developments of unique technological methods of gear milling of cylindrical gears for preliminary blade gear processing of hardened cylindrical gears of the cutting reducer of the UKD200-500 coal mining harvester for the final gear grinding of gear teeth with modulus m = 16 mm, with hardness HRC 56 ... 62. The peculiarity of the design of special hob cutters is that a circle passing through the lower boundary points of the involute is used as the palloid of the machine gearing of the tool and part. Pre-cutting the teeth of hardened wheels with carbide milling cutters allows you to remove the main allowance for the final gear grinding.

Research and Manufacturing of Oval Gear Pair Applied in Rotor of a Roots Type Compressor

This study presents a method of shaping the tooth profile of an oval gear pair with the modified cycloid profile of the ellipse. The driving oval gear was shaped by a rack cutter with the profile of an improved cycloid, and the tooth profile of the driven oval gear was shaped by a shaper cutter to ensure that gear pair will mesh accurately with a function of transmission ratio. Mathematical model of the oval gear pair was established according to the theory of the non-circular gear with consideration to the conditions of the design parameters to avoid undercutting and tooth distribution of the oval gear. An improved pair of cycloid oval gears is designed and manufactured according to the results of the theoretical calculation. Furthermore, this gear pair is specifically applied to a Roots-type compressor to demonstrate its applicability in special cases where the traditional cylindrical gear pair cannot be replaced.

Lubrication Effect of the Nozzle Layout for Arc Tooth Cylindrical Gears

In order to study the influence of fuel injection nozzle arrangement on the lubrication effect of arc tooth cylindrical gear, a model of fuel injection lubrication was established, and computational fluid dynamics (CFD) software was used for simulation calculation. The focus on the influence of gear parameters, oil jet conditions and nozzle layout on gear lubrication performance is studied. The results show that reducing the oil jet distance not only improves the lubrication performance of the gear but also reduces the offset of the oil jet streamline. The reasonable of nozzle layout is the premise of ensuring better lubrication conditions, and the best nozzle layout scheme is obtained through data comparison analysis. The lubrication effect decreases when the nozzle angle is offset. The lubrication effect does not change when the nozzle is horizontally offset by a distance of 0.5 module in the direction of the pinion, and the lubrication performance is degraded when the distance exceeds 0.5 module. Finally, the influence of nozzle diameter on lubrication is analyzed, the lubrication effect is directly proportional to the nozzle diameter.

Analytical solution to contact characteristics for a variable hyperbolic circular-arc-tooth-trace cylindrical gear

The variable hyperbolic circular-arc-tooth-trace (VH-CATT) cylindrical gear is a new type of gear. In order to research the contact characteristics of the VH-CATT cylindrical gear, tooth surface mathematical models of this kind of gear pair are derived based on the forming principle of the rotating double-edged cutting method with great cutter head in this regard. Then, according to the differential geometry theory and Hertz theory, the formula of the induced normal curvature and equation of the contact ellipse are derived based on the condition of continuous tangency of two meshing surfaces, which proves that the contact form of VH-CATT cylindrical gear is point contact. The present work establishes analytical solutions to research the effect of different parameters for the contact characteristic of the VH-CATT cylindrical gear by incorporating elastic deformation on the tooth surface, which have shown that the module, tooth number and cutter radius have a crucial effect on the induced normal curvature and contact ellipse of the VH-CATT cylindrical gear in the direction of tooth trace and tooth profile. Moreover, a theoretical analysis solution, a finite element analysis and the gear tooth contact pattern are carried out to verify the correctness of the computerized model and to investigate the contact type of the gear; it is verified that the contact form on the concave surface of the driving VH-CATT cylindrical gear rotates from dedendum at the heel to the addendum at toe and is an instantaneous oblique ellipse due to elastic deformation of the contact tooth profile, and the connecting line of the ellipse center is the contact trace path. It is indicated that the research results are beneficial for research on tooth break reduction, pitting, wear resistance and fatigue life improvement of the VH-CATT cylindrical gear. The results also have a certain reference value for development of the VH-CATT cylindrical gear.

Comparative Study on Transmission Performance of Manganese Phosphate Coated Gears

As an important part of transmission systems, coatings can improve the physical properties of gear surface. It is meaningful to research the effect of coating on the transmission performance of gears. In this paper, eight-degree-of-freedom dynamic response model of helical cylindrical gear is established considering friction, and the influence of friction factors on dynamic response is explored. The tribological properties and lubrication characteristics of the coating are investigated and compared with uncoated. The transmission performances of manganese phosphate conversion coated gears are studied experimentally. The results show that the coefficients of friction of Mn–P[C] coatings are reduced by 19%, the average amplitude and root mean square of vibration acceleration are obviously decreased, and the transmission efficiency is improved. The manganese phosphate conversion coating is beneficial to the transmission performance of gears.