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This paper presents the geometric design of hypoid gears with involute gear teeth. An overview of face cutting techniques prevalent in hypoid gear fabrication is presented. Next, the specification of a planar involute rack is reviewed. This rack is used to define a variable diameter cutter based upon a system of cylindroidal coordinates; thus, a cursory presentation of cylindroidal coordinates is included. A mapping transforms the planar involute rack into a variable diameter cutter using the cylindroidal coordinates. Hypoid gears are based on the envelope of this cutter. A hypoid gear set is presented based on an automotive rear axle.
Hypoid gears are the paragon of gearing. To establish line contact between the pitches in hypoid gears, the kinematically correct pitch surfaces have to be determined based on the axoids. In cylindrical and bevel gears, the axoids are identical to the pitch surfaces and their diameter or cone angle can be calculated simply by using the knowledge about number of teeth and module or ratio and shaft angle. In hypoid gears, a rather complex approach is required to find the location of the teethâ€”even before any information about flank form can be considered. This article is part seven of an eight-part series on the tribology aspects of angular gear drives.
Super-reduction hypoid gears (SRH) are bevel worm gears with certain differences regarding hypoid gears. If two axes are positioned in space and the task is to transmit motion and torque between them using some kind of gears with a ratio above 5 and even higher than 50, the following cases are commonly known. Tribology Aspects in Angular Transmission Systems, Part VIII.
As is well known in involute gearing, â€śperfectâ€ť involute gears never work perfectly in the real world. Flank modifications are often made to overcome the influences of errors coming from manufacturing and assembly processes as well as deflections of the system. The same discipline applies to hypoid gears.
Our question this issue deals with high-ratio hypoid gears, and it should be noted here that this is a tricky area of gearing with a dearth of literature on the topic. That being the case, finding â€śexpertsâ€ť willing to stick their necks out and take on the subject was not a given.
Spiral bevel and hypoid gear cutting has changed significantly over the years. The machines, tools, processes and coatings have steadily advanced.
What is the relationship between angular backlash or mean normal backlash change and the axial movement of the ring gear in bevel and hypoid gears?
This paper presents a new approach in roll testing technology of spiral bevel and hypoid gear sets on a CNC roll tester applying analytical tools, such as vibration noise and single-flank testing technology.
This presentation is an expansion of a previous study (Ref.1) by the authors on lapping effects on surface finish and transmission errors. It documents the effects of the superfinishing process on hypoid gears, surface finish and transmission errors.
A very important parameter when designing a gear pair is the maximum surface contact stress that exists between two gear teeth in mesh, as it affects surface fatigue (namely, pitting and wear) along with gear mesh losses. A lot of attention has been targeted to the determination of the maximum contact stress between gear teeth in mesh, resulting in many "different" formulas. Moreover, each of those formulas is applicable to a particular class of gears (e.g., hypoid, worm, spiroid, spiral bevel, or cylindrical - spur and helical). More recently, FEM (the finite element method) has been introduced to evaluate the contact stress between gear teeth. Presented below is a single methodology for evaluating the maximum contact stress that exists between gear teeth in mesh. The approach is independent of the gear tooth geometry (involute or cycloid) and valid for any gear type (i.e., hypoid, worm, spiroid, bevel and cylindrical).
Flank breakage is common in a number of cylindrical and bevel gear applications. This paper introduces a relevant, physically based calculation method to evaluate flank breakage risk vs. pitting risk. Verification of this new method through testing is demonstrably shown.
The traditional way of controlling the quality of hypoid gears' tooth flank form is to check the tooth flank contact patterns. But it is not easy to exactly judge the tooth flank form quality by the contact pattern. In recent years, it has become possible to accurately measure the tooth flank form of hypoid gears by the point-to-point measuring method and the scanning measuring method. But the uses of measured data of the tooth flank form for hypoid gears have not yet been well developed in comparison with cylindrical involute gears. In this paper, the tooth flank form measurement of generated face-milled gears, face-hobbed gears and formulate/generated gears are reported. The authors discuss the advantages and disadvantages of scanning and point-to-point measuring of 3-D tooth flank forms of hypoid gears and introduce some examples of uses of measured data for high-quality production and performance prediction.
In addition to the face milling system, the face hobbing process has been developed and widely employed by the gear industry. However, the mechanism of the face hobbing process is not well known.
High-speed machining using carbide has been used for some decades for milling and turning operations. The intermittent character of the gear cutting process has delayed the use of carbide tools in gear manufacturing. Carbide was found at first to be too brittle for interrupted cutting actions. In the meantime, however, a number of different carbide grades were developed. The first successful studies in carbide hobbing of cylindrical gears were completed during the mid-80s, but still did not lead to a breakthrough in the use of carbide cutting tools for gear production. Since the carbide was quite expensive and the tool life was too short, a TiN-coated, high-speed steel hob was more economical than an uncoated carbide hob.
In this installment of Ask the Expert, Dr. Stadtfeld describes the best methods for measuring backlash in bevel gears.
How the latest techniques and software enable faster spiral bevel and hypoid design and development.
What is the relationship between angular backlash and mean or normal backlash, the axial movement of wheel gear, and mean or normal backlash for bevel and hypoid gears?
This presentation introduces a new procedure that - derived from exact calculations - aids in determining the parameters of the validation testing of spiral bevel and hypoid gears in single-reduction axles.
Optimizing the running behavior of bevel and hypoid gears means improving both noise behavior and load carrying capacity. Since load deflections change the relative position of pinion and ring gear, the position of the contact pattern will depend on the torque. Different contact positions require local 3-D flank form optimizations for improving a gear set.
New freedom of motion available with CNC generators make possible improving tooth contact on bevel and hypoid gears. Mechanical machines by their nature are inflexible and require a special mechanism for every desired motion. These mechanisms are generally exotic and expensive. As a result, it was not until the introduction of CNC generators that engineers started exploring motion possibilities and their effect on tooth contact.
More strength, less noise. Those are two major demands on gears, including bevel and hypoid gears.
Non-uniform gear wear changes gear topology and affects the noise performance of a hypoid gear set. The aggregate results under certain vehicle driving conditions could potentially result in unacceptable vehicle noise performance in a short period of time. This paper presents the effects of gear surface parameters on gear wear and the measurement/testing methods used to quantify the flank wear in laboratory tests.
A response to last issue's "Ask the Expert" feature on efficiency of hypoid gearing.
This article presents a summary of all factors that contribute to efficient and economical high-speed cutting of bevel and hypoid gears.
The development of a new gear strength computer program based upon the finite element method, provides a better way to calculate stresses in bevel and hypoid gear teeth. The program incorporates tooth surface geometry and axle deflection data to establish a direct relationship between fillet bending stress, subsurface shear stress, and applied gear torque. Using existing software links to other gear analysis programs allows the gear engineer to evaluate the strength performance of existing and new gear designs as a function of tooth contact pattern shape, position and axle deflection characteristics. This approach provides a better understanding of how gears react under load to subtle changes in the appearance of the no load tooth contact pattern.
The most conclusive test of bevel and hypoid gears is their operation under normal running conditions in their final mountings. Testing not only maintains quality and uniformity during manufacture, but also determines if the gears will be satisfactory for their intended applications.
In this paper a new method for the introduction of optimal modifications into gear tooth surfaces - based on the optimal corrections of the profile and diameter of the head cutter, and optimal variation of machine tool settings for pinion and gear finishingâ€”is presented. The goal of these tooth modifications is the achievement of a more favorable load distribution and reduced transmission error. The method is applied to face milled and face hobbed hypoid gears.
Transmission of power between nonparallel shafts is inherently more difficult than transmission between parallel shafts, but is justified when it saves space and results in more compact, more balanced designs. Where axial space is limited compared to radial space, angular drives are preferred despite their higher initial cost. For this reason, angular gear motors and worm gear drives are used extensively in preference to parallel shaft drives, particularly where couplings, brakes, and adjustable mountings add to the axial space problem of parallel shaft speed reducers.
Today, because of reduced cost of coatings and quicker turnaround times, the idea of all-around coating on three-face-sharpened blades is again economically viable, allowing manufacturers greater freedoms in cutting blade parameters, including three-face-sharpened and even four-face-sharpened blades.
The cutting process consists of either a roll only (only generating motion), a plunge only or a combination of plunging and rolling. The material removal and flank forming due to a pure generating motion is demonstrated in the simplified sketch in Figure 1 in four steps. In the start roll position (step 1), the cutter profile has not yet contacted the work. A rotation of the work around its axis (indicated by the rotation arrow) is coupled with a rotation of the cutter around the axis of the generating gear (indicated by the vertical arrow) and initiates a generating motion between the not-yet-existing tooth slot of the work and the cutter head (which symbolizes one tooth of the generating gear).
A reader asks about the proper setup procedures for cutting a ring and pinion set on a Gleason 116.
What are the manufacturing methods used to make bevel gears used in automotive differentials?
Face-milled hypoid pinions produced by the three-cut, Fixed Setting system - where roughing is done on one machine and finishing for the concave-OB and convex-IB tooth flanks is done on separate machines with different setups - are still in widespread use today.
Grinding of bevel and hypoid gears creates on the surface a roughness structure with lines that are parallel to the root. Imperfections of those lines often repeat on preceding teeth, leading to a magnification of the amplitudes above the tooth mesh frequency and their higher harmonics. This phenomenon is known in grinding and has led in many cylindrical gear applications to an additional finishing operation (honing). Until now, in bevel and hypoid gear grinding, a short time lapping of pinion and gear after the grinding operation, is the only possibility to change the surface structure from the strongly root line oriented roughness lines to a diffuse structure.
The configuration of flank corrections on bevel gears is subject to relatively narrow restrictions. As far as the gear set is concerned, the requirement is for the greatest possible contact zone to minimize flank compression. However, sufficient reserves in tooth depth and longitudinal direction for tooth contact displacement should be present. From the machine - and particularly from the tool - point of view, there are restrictions as to the type and magnitude of crowning that can be realized. Crowning is a circular correction. Different kinds of crowning are distinguished by their direction. Length crowning, for example, is a circular (or 2nd order) material removal, starting at a reference point and extending in tooth length or face width.
The calculation begins with the computation of the ring gear blank data. The geometrically relevant parameters are shown in Figure 1. The position of the teeth relative to the blank coordinate system of a bevel gear blank is satisfactorily defined with...
Myth No. 1: Oil Is Oil. Using the wrong oil is a common cause of gear failure. Gears require lubricants blended specifically for the application. For example, slow-speed spur gears, high-speed helical gears, hypoid gears and worm gears all require different lubricants. Application parameters, such as operating speeds, transmitted loads, temperature extremes and contamination risks, must be considered when choosing an oil. Using the right oil can improve efficiency and extend gear life.
Several articles have appeared in this publication in recent years dealing with the principles and ways in which the inspection of gears can be carried out, but these have dealt chiefly with spur, helical and bevel gearing, whereas worm gearing, while sharing certain common features, also requires an emphasis in certain areas that cause it to stand apart. For example, while worm gears transmit motion between nonparallel shafts, as do bevel and hypoid gears, they usually incorporate much higher ratios and are used in applications for which bevel would not be considered, including drives for rotary and indexing tables in machine tools, where close tolerance of positioning and backlash elimination are critical, and in situations where accuracy of pitch and profile are necessary for uniform transmission at speed, such as elevators, turbine governor drives and speed increasers, where worm gears can operate at up to 24,000 rpm.
Chapter 2, Continued In the previous sections, development of conjugate, face milled as well as face hobbed bevel gearsets - including the application of profile and length crowning - was demonstrated. It was mentioned during that demonstration that in order to optimize the common surface area, where pinion and gear flanks have meshing contact (common flank working area), a profile shift must be introduced. This concluding section of chapter 2 explains the principle of profile shift; i.e. - how it is applied to bevel and hypoid gears and then expands on profile side shift, and the frequently used root angle correction which - from its gear theoretical understanding - is a variable profile shift that changes the shift factor along the face width. The end of this section elaborates on five different possibilities to tilt the face cutter head relative to the generating gear, in order to achieve interesting effects on the bevel gear flank form. This installment concludes chapter 2 of the Bevel Gear Technology book that lays the foundation of the following chapters, some of which also will be covered in this series.
Ground bevel and hypoid gears have a designed motion error that defines parts of their NVH behavior. The surface structure is defined by the hard finishing process.
Why Prototyping with End-mills on Bevel Gear Machines? Manufacturing of spiral bevel and hypoid gears can be conducted in several ways.
News Items About hypoid
1 KISSsoft Implements Bevel and Hypoid Gear Calculations (July 26, 2018)
In the ISO Committee, the scuffing load capacity calculation for bevel and hypoid gears is currently in draft form, and has been implemen... Read News
2 Alpha Gear Launches Hypoid Gearhead (April 19, 2006)
The new HG+ series from alpha gear drives Inc. is a low-backlash hypoid gearhead that offers performance similar to a planetary gearhead.... Read News