Cutter Interchangeability for Spiral-Bevel and Hypoid Gear Manufacturing

In the manufacturing of spiral-bevel and hypoid gears, circular cutter dimensions are usually based on the desired performance of a gear set. In large manufacturing operations, where several hundred gear geometries may have been cut over the years, the necessary cutter inventory may become quite large since the cutter diameters will differ from one geometry to another, which results in used storage space and associated costs in purchasing and maintaining the cutter parts. Interchangeability of cutters is therefore of significant interest to reduce cost while maintaining approved tooth geometries. An algorithm is presented which allows the use of a different cutter, either in diameter and/or pressure angle, to obtain the same tooth flank surface topography. A test case is presented to illustrate the usefulness of the method: the OB cutter diameter of an hypoid pinion is changed from 8.9500" to 9.1000". CMM results and the comparison of the bearing patterns before and after change show excellent correlation, and indicate that the new pinion can be used in place of the original pinion without performance or quality problems. Significant cost reductions may be obtained with the application of the method.

Meshing Stiffness and Tooth Root Stress for Internal Cylindrical Gears With Thin Rim

The main objective of this study is to quantify the influence of the deformation of the rim of an internal gear on the meshing stiffness and the stress distribution in tooth fillets. The 3D model used is based on a method derived from the Finite Prism Method. Tooth bending effects and contact deformations are processed simultaneously. Scientific use of the software has resulted in formulating an equation to calculate the maximal tension stress in the tooth root. This formula has been obtained by using the statistical design of experiment method.

Improving the Characteristics of Gear Pumps: Part A — Discharge

The main objective of this paper is to study the effect of gear geometry on the discharge of gear pumps. We have used gears of circular-arc tooth profile as gear pumps and have compared between these types of gearing and spur, helical gear pumps according to discharge. The chosen module change from 2 to 16 mm, number of teeth change from 8 to 20 teeth, pressure angle change from 10 to 30 deg, face width change from 20 to 120 mm, correction factor change from −1 to 1, helix angle change from 5 to 30 deg, and radii of curvature equal 1.4, 1.5, 2, 2.5, 2.75, and 3m are considered. The authors deduced that the tooth rack profile with radius of curvature equal 2.5, 2.75, 3m for all addendum circular arc tooth and convex-concave tooth profile, and derived equations representing the tooth profile, and calculated the points of intersections between curves of tooth profile. We drive the formulas for the volume of oil between adjacent teeth. Computer program has been prepared to calculate the discharge from the derived formulae with all variables for different types of gear pumps. Curves showing the change of discharge with module, number of teeth, pressure angle, face width, correction factor, helix angle, and radius of curvature are presented. The results show that: 1) The discharge increases with increasing module, number of teeth, positive correction factor, face width and radius of curvature of the tooth. 2) The discharge increases with increasing pressure angle to a certain value and then decreases with increasing pressure angle. 3) The discharge decreases with increasing helix angle. 4) The convex-concave circular-arc gears gives discharge higher than that of alla ddendum circular arc, spur, and helical gear pumps respectively. 5) A curve fitting of the results are done and the following formulae derived for the discharge of involute and circular arc gear pumps respectively: Q=A1bm2z0.895e0.065xe0.0033αe−0.0079βQ=A2bm2z0.91ρ10.669e−0.0047β

The Development of the Traction Drive Mechanism Made of the Plastic Magnet

This paper is the one that it was described to have developed the traction drive by using the plastic hard magnet. The plastics material was used to research by the following reasons. The plastics material can mold it. As a result, it processes complex and it is possible to make it to the magnet. In addition, it is possible to mass-produce, it is light, and it is also possible that the miniaturization reduces possible and the cost. Next, the mechanism of the traction drive is described. It rotates by being circumscribed by non-contact, and inscribing two plastic hard rings as if the gear. N pole and S pole are divided equally in the direction of the circumference of the ring. It becomes by these as if the match of the god with teeth and teeth. These devices are commonly called “Gear without teeth”. Some doughnut disks with a different outside diameter were produced. Each disk is made magnetism. Each disk was set, and assembled to one disk. The disk is molded with the plastic hard. The plastics material used the one that the ferrite powder was mixed with the polyacetal resin. Making to magnetism is possible by the magnetization technology. The mechanism, molding, making to magnetism, and the magnetic induction, etc. were examined in the experiment. The development of non-contact made of plastic hard traction drive device was proven to be possible by this research.

Kinematics of Meshing Surfaces Using Geometric Algebra

As is well known, analysis of two surfaces in mesh plays a fundamental role in gear theory. In the past, special coordinate systems, vector algebra, or screw theory was used to analyze the kinematics of meshing. The approach here instead relies on geometric algebra, an extension of conventional vector algebra. The elegance of geometric algebra for theoretical developments is demonstrated by examining the so-called “equation of meshing,” which requires that the relative velocity of two bodies at a point of contact be perpendicular to the common surface normal vector. With surprisingly little effort, several alternative forms of the equation of meshing are generated and, subsequently, interpreted geometrically. Via straightforward algebraic manipulations, the results of screw theory and vector algebra are unified. Due to the simplicity with which complex geometric concepts are expressed and manipulated, the effort required to grasp the general three-dimensional meshing of surfaces is minimized.

Dynamic Analysis of Sliding Friction in a Gear Pair

Chief objective of this article is to evaluate the role of sliding friction in gear dynamics, and more specifically the effect of the periodic variations in mesh stiffness, load distribution and friction torque during a mesh cycle. A non-unity speed ratio spur gear is considered. Only the torsional degree of freedom of the gear pair, with ideal Coulomb friction law, is analyzed. Previous studies by Vaishya and Singh [1–3] make idealized assumptions about temporal (or spatial) variation of mesh stiffness and load sharing in order to obtain more tractable analytical solutions. In our formulation, an accurate Finite Element/Contact Mechanics analysis code [4] is run in the static mode to compute the mesh stiffness and load distribution at every time instant of the mesh. The computed parametric variation of stiffness is then incorporated into our dynamic formulation that includes frictional torques. Next, we use appropriate numerical techniques to solve for the dynamic response in time domain. This study, though preliminary in nature, examines the effects of pinion speed, coefficient of friction and mean input torque. This, along with work in progress, should yield further insights into the role of friction sources in gear vibro-acoustics.

The Influence of Additive Chemistry on Gear Micropitting

Gear micropitting has been a highly visible issue in selected applications in recent years, most notably in large wind turbine transmissions. Various industry groups have addressed the problem from their own area of expertise. This has included evaluation of the gear design characteristics, surface finishing, the use of special coatings, and lubrication. A common approach to improve the lubrication has been first to increase the viscosity and create thicker films, which, in turn, reduce the amount of surface asperity interaction. Another approach from the lubricant side has been to alter the additive chemistry to effect a change in the wear properties of the system. This paper discusses the potential effects observed for different antiwear and EP chemistry on the micropitting of cylindrical gears. Tests were conducted in an FZG test rig which has been used by the industry as a guide to general gear performance. Fluids were examined in a series of experimental designs which served as the iterative process leading toward an optimized additive system. The results show that the EP, or antiscuff agent, was the most effective component at reducing the level of micropitting.

New Investigation on the Geometry of the Contact in Gear Generation

Based on a recently developed geometric approach to the theory of gearing that does not make use of any reference systems [1], this paper presents some useful relations between the geometric properties of the enveloping surface and those of its envelope. Treating vectors as such, that is without expressing their components in any reference systems, it is possible to obtain compact expressions for the coefficients of the first and second fundamental forms of the envelope surface. These coefficients show to be central in the determination of the contact matrix between mating surfaces. Moreover, since this approach is coordinate free, it is valid regardless of the reference frame actually employed to perform calculations and allows a, hopefully, clearer understanding of the roles played by the intrinsic geometric properties of the enveloping surface, the relative position of the gear axes and the gear ratio.

High-Reduction, High-Torque Gear Reducer Design Emphasizes Compactness

The design of high-torque, high-reduction gear reducers often requires the use of multi-stage gearing, planetary gear systems, or both. Because these systems contain many independent parts, they often become bulky. When these systems will be used in downhole oilfield equipment, compactness can become a crucial factor. Moreover, downhole oilfield equipment generally requires that areas of the system be reserved to provide some fluid flow-path around the equipment. A unique gear reducer was designed to accommodate this need for compactness. The new reducer system consists of only four gears, two of which are built as a single part. All four gears are positioned roughly concentrically within a donut-like space, and the open center accommodates fluid flow. Unlike other gear reducer systems, this system employs not only a ratio (divisional) method, but also a unique subtraction method. Consequently, a reduction of more than 2000:1 is possible. With this radical design, conventional gear teeth cannot be used if good meshing is desired. Subsequently, a special gear tooth shape was designed to provide surface contact between the teeth. With this special shape, full contact of more than 30% of the teeth can be achieved, compared to one or two teeth in standard designs. Thus, the new system also improves load-transmitting capacity. In this paper, the design of the new gear reducer is discussed in detail. A specific application in which high-pressure, sand-laden slurry is pumped through the center of this gear reducer is also discussed.

Optimal Tooth Modifications in Hypoid Gears

A method for the determination of optimal tooth modifications in hypoid gears based on improved load distribution and reduced transmission errors is presented. The modifications are introduced into the pinion tooth surface by using a cutter with bicircular profile and by changing the cutter diameter. In the optimization of tool parameters the influence of shaft misalignments of the mating members is included. As the result of these modifications a point contact of the meshed teeth surfaces appears instead of line contact; the hypoid gear pair becomes mismatched. By using the method presented in [1] the influence of tooth modifications introduced on tooth contact and transmission errors is investigated. Based on the results that was obtained the radii and position of circular tool profile arcs and the cutter diameter for pinion teeth generation were optimized. By applying the optimal tool parameters, the maximum tooth contact pressure is reduced by 16.22% and the angular position error of the driven gear by 178.72%, in regard to the hypoid gear pair with a pinion manufactured by a cutter of straight-sided profile and of diameter determined by the commonly used methods.