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Articles About Logarithmic Spiral Gears


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1 The Math of Noncircular Gearing (July/August 2000)

Noncircular gearing is not new. There are well-documented articles covering standard and high order elliptical gears, sinusoidal gears, logarithmic spiral gears, and circular gears mounted eccentrically. What these designs have in common is a pitch curve defined by a mathematical function. This article will cover noncircular gearing with free-form pitch curves, which, of course, includes all the aforementioned functions. This article also goes into the generation of teeth on the pitch curve, which is not usually covered in the technical literature. Needless to say, all this is possible only with the help of a computer.

2 Synthesis of Spiral Bevel Gears (March/April 1991)

There are different types of spiral bevel gears, based on the methods of generation of gear-tooth surfaces. A few notable ones are the Gleason's gearing, the Klingelnberg's Palloid System, and the Klingelnberg's and Oerlikon's Cyclo Palliod System. The design of each type of spiral bevel gear depends on the method of generation used. It is based on specified and detailed directions which have been worked out by the mentioned companies. However, there are some general aspects, such as the concepts of pitch cones, generating gear, and conditions of force transmissions that are common for all types of spiral bevel gears.

3 CNC Technology and the System-Independent Manufacture of Spiral Bevel Gears (September/October 1992)

CNC technology offers new opportunities for the manufacture of bevel gears. While traditionally the purchase of a specific machine at the same time determined a particular production system, CNC technology permits the processing of bevel gears using a wide variety of methods. The ideological dispute between "tapered tooth or parallel depth tooth" and "single indexing or continuous indexing" no longer leads to an irreversible fundamental decision. The systems have instead become penetrable, and with existing CNC machines, it is possible to select this or that system according to factual considerations at a later date.

4 Tooth Contact Shift in Loaded Spiral Bevel Gears (November/December 1992)

An analytical method is presented to predict the shifts of the contact ellipses on spiral bevel gear teeth under load. The contact ellipse shift is the motion of the point to its location under load. The shifts are due to the elastic motions of the gear and pinion supporting shafts and bearings. The calculations include the elastic deflections of the gear shafts and the deflections of the four shaft bearings. The method assumes that the surface curvature of each tooth is constant near the unloaded pitch point. Results from these calculations will help designers reduce transmission weight without seriously reducing transmission performance.

5 Fundamentals of Bevel Gear Hard Cutting (November/December 1990)

Some years back, most spiral bevel gear sets were produced as cut, case hardened, and lapped. The case hardening process most frequently used was and is case carburizing. Many large gears were flame hardened, nitrided, or through hardened (hardness around 300 BHN) using medium carbon alloy steels, such as 4140, to avoid higher distortions related to the carburizing and hardening process.

6 Tooth Root Stresses of Spiral Bevel Gears (May/June 1988)

Service performance and load carrying capacity of bevel gears strongly depend on the size and position of the contact pattern. To provide an optimal contact pattern even under load, the gear design has to consider the relative displacements caused by deflections or thermal expansions expected under service conditions. That means that more or less lengthwise and heightwise crowning has to be applied on the bevel gear teeth.

7 Gears for Nonparallel Shafts (September/October 1986)

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.

8 Pressure Angle Changes in the Transverse Plane for Circular Cut Spiral Bevel Gears (September/October 1986)

Recently it has been suggested that the transverse plane may be very useful in studying the kinematics and dynamics of spiral bevel gears. The transverse plane is perpendicular to the pitch and axial planes as shown in Fig. 1. Buckingham has suggested that a spiral bevel gear may be viewed as a limited form of a "stepped" straight-tooth gear as in Fig. 2. The transverse plane is customarily used in the study of straight toothed bevel gears.

9 Gear Tip Chamfer and Gear Noise; Surface Measurement of Spiral Bevel Gear Teeth (July/August 1993)

Could the tip chamfer that manufacturing people usually use on the tips of gear teeth be the cause of vibration in the gear set? The set in question is spur, of 2.25 DP, with 20 degrees pressure angle. The pinion has 14 teeth and the mating gear, 63 teeth. The pinion turns at 535 rpm maximum. Could a chamfer a little over 1/64" cause a vibration problem?

10 Transmission Errors and Bearing Contact of Spur, Helical, and Spiral Bevel Gears (July/August 1990)

An investigation of transmission errors and bearing contact of spur, helical, and spiral bevel gears was performed. Modified tooth surfaces for these gears have been proposed in order to absorb linear transmission errors caused by gear misalignment and to localize the bearing contact. Numerical examples for spur, helical, and spiral bevel gears are presented to illustrate the behavior of the modified gear surfaces with respect to misalignment and errors of assembly. The numerical results indicate that the modified surfaces will perform with a low level of transmission error in non-ideal operating environments.

11 Maximum Life Spiral Bevel Reduction Design (September/October 1993)

Optimization is applied to the design of a spiral bevel gear reduction for maximum life at a given size. A modified feasible directions search algorithm permits a wide variety of inequality constraints and exact design requirements to be met with low sensitivity to initial values. Gear tooth bending strength and minimum contact ration under load are included in the active constraints. The optimal design of the spiral bevel gear reduction includes the selection of bearing and shaft proportions in addition to gear mesh parameters. System life is maximized subject to a fixed back-cone distance of the spiral bevel gear set for a specified speed ratio, shaft angle, input torque and power. Significant parameters in the design are the spiral angle, the pressure angle, the numbers of teeth on the pinion and gear and the location and size of the four support bearings. Interpolated polynomials expand the discrete bearing properties and proportions into continuous variables for gradient optimization. After finding the continuous optimum, a designer can analyze near-optimal designs for comparison and selection. Design examples show the influence of the bearing lives on the gear parameters in the optimal configurations. For a fixed back-cone distance, optimal designs with larger shaft angles have larger service lives.

12 Development of a Face Hobbed Spiral Bevel Gearset (September/October 2015)

This article is the fourth installment in Gear Technology's series of excerpts from Dr. Hermann J. Stadtfeld's book, Gleason Bevel Gear Technology. The first three excerpts can be found in our June, July and August 2015 issues. In the previous chapter, we demonstrated the development of a face-milled spiral bevel gearset. In this section, an analogue face-hobbed bevel gearset is derived.

13 CNC Milling of Straight and Spiral Bevel Gears (January/February 2019)

Contrary to what appears to be popular belief, 5-axis CNC gear manufacturing is not limited to milling with end mill, ball mill or CoSIMT (Conical Side Milling Tool — it is the generic form of the Sandvik InvoMill and Gleason UpGear tools.) tools, where throughput is too low to prevent production at any significant level. Straight and spiral bevel gear manufacturing on 5-axis CNC machines using face mill cutters provides essentially the same throughput as conventional gear cutting machines — with added benefits.

14 Simulation of Spiral Bevel Gear Tooth Manufacturing to Aid in One-Piece Gear Shaft Design (January/February 2019)

In helicopter applications, the two-piece gear is typically joined by welding, bolts, or splines. In the case of the U.S. Army CH-47D Chinook helicopter, a decision was made to eliminate these joints through the use of integral design. Integral shaft spiral bevel gears must be designed such that the shaft does not interfere with gear tooth cutting and grinding. This paper discusses techniques to iterate in the design stage before manufacturing begins.

15 A Practical Approach for Modeling a Bevel Gear (March/April 2015)

The geometry of the bevel gear is quite complicated to describe mathematically, and much of the overall surface topology of the tooth flank is dependent on the machine settings and cutting method employed. AGMA 929-A06 — Calculation of Bevel Gear Top Land and Guidance on Cutter Edge Radius — lays out a practical approach for predicting the approximate top-land thicknesses at certain points of interest — regardless of the exact machine settings that will generate the tooth form. The points of interest that AGMA 929-A06 address consist of toe, mean, heel, and point of involute lengthwise curvature. The following method expands upon the concepts described in AGMA 929-A06 to allow the user to calculate not only the top-land thickness, but the more general case as well, i.e. — normal tooth thickness anywhere along the face and profile of the bevel gear tooth. This method does not rely on any additional machine settings; only basic geometry of the cutter, blank, and teeth are required to calculate fairly accurate tooth thicknesses. The tooth thicknesses are then transformed into a point cloud describing both the convex and concave flanks in a global, Cartesian coordinate system. These points can be utilized in any modern computer-aided design software package to assist in the generation of a 3D solid model; all pertinent tooth macrogeometry can be closely simulated using this technique. A case study will be presented evaluating the accuracy of the point cloud data compared to a physical part.

16 Setting Load Parameters for Viable Fatigue Testing of Gears in Powertrain Axles Part I: Single-Reduction Axles (August 2014)

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.

17 Meshing of a Spiral Bevel Gear Set With 3-D Finite Element Analysis (March/April 1997)

Recent advances in spiral bevel gear geometry and finite element technology make it practical to conduct a structural analysis and analytically roll the gear set through mesh. With the advent of user-specific programming linked to 3-D solid modelers and mesh generators, model generation has become greatly automated. Contact algorithms available in general purpose finite element codes eliminate the need for the use and alignment of gap elements. Once the gear set it placed in mesh, user subroutines attached to the FE code easily roll it through mesh. The method is described in detail. Preliminary result for a gear set segment showing the progression of the contact line load is given as the gears roll through mesh.

18 Design Formulas for Evaluating Contact Stress in Generalized Gear Pairs (May/June 2001)

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).

19 Reinventing Cutting Tool Production at Gleason (May 2013)

Investment in advanced new manufacturing technologies is helping to reinvent production processes for bevel gear cutters and coarse-pitch hobs at Gleason - delivering significant benefits downstream to customers seeking shorter deliveries, longer tool life and better results.

20 A Computer Solution for the Dynamic Load, Lubricant Film Thickness, and Surface Temperatures in Spiral-Bevel Gears (March/April 1986)

Spiral-bevel gears, found in many machine tools, automobile rear-axle drives, and helicopter transmissions, are important elements for transmitting power.

21 Manufacturing Method of Large-Sized Spiral Bevel Gears in Cyclo-Palloid System Using Multi-Axis Control and Multi-Tasking Machine Tool (August 2011)

In this article, the authors calculated the numerical coordinates on the tooth surfaces of spiral bevel gears and then modeled the tooth profiles using a 3-D CAD system. They then manufactured the large-sized spiral bevel gears based on a CAM process using multi-axis control and multi-tasking machine tooling. The real tooth surfaces were measured using a coordinate measuring machine and the tooth flank form errors were detected using the measured coordinates. Moreover, the gears were meshed with each other and the tooth contact patterns were investigated. As a result, the validity of this manufacturing method was confirmed.

22 The New Freedoms: Bevel Blades (September/October 2007)

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.

23 Evaluation of a Low-Noise, Formate Spiral Bevel Gear Set (January/February 2008)

Studies to evaluate low-noise Formate spiral bevel gears were performed. Experimental tests were conducted on a helicopter transmission test stand...

24 Kinematical Simulation of Face Hobbing Indexing and Tooth Surface Generation of Spiral Bevel and Hypoid Gears (January/February 2006)

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.

25 Analyzing Gear Tooth Stress as a Function of Tooth Contact Pattern Shape and Position (January/February 1985)

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.

26 Influence of Relative Displacements Between Pinion and Gear on Tooth Root Stresses of Spiral Bevel Gears (July/August 1985)

The manufacturing quality of spiral bevel gears has achieved a very high standard. Nevertheless, the understanding of the real stress conditions and the influences. of certain parameters is not satisfactory.

27 New Developments in TCA and Loaded TCA (May 2007)

How the latest techniques and software enable faster spiral bevel and hypoid design and development.

28 Spiral Bevel and Hypoid Gear Cutting Technology Update (July 2007)

Spiral bevel and hypoid gear cutting has changed significantly over the years. The machines, tools, processes and coatings have steadily advanced.

29 Gear Milling on Non-Gear Dedicated Machinery (July 2009)

Imagine the flexibility of having one machine capable of milling, turning, tapping and gear cutting with deburring included for hard and soft material. No, you’re not in gear fantasy land. The technology to manufacture gears on non gear-dedicated, mult-axis machines has existed for a few years in Europe, but has not yet ventured into mainstream manufacturing. Deckel Maho Pfronten, a member of the Gildemeister Group, took the sales plunge this year, making the technology available on most of its 2009 machines.

30 Assembling Spiral Gears: Double Taper Can Be Double Trouble (January/February 2006)

Bevel gear systems are particularly sensitive to improper assembly. Slight errors in gear positioning can turn a well-designed, quality manufactured gear set into a noisy, prone-to-failure weak link in your application.

31 New Approaches in Roll Testing Technology of Spiral Bevel and Hypoid Gear Sets (May/June 2005)

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.

32 Beveloid & Hypoloid Gears (May 2011)

Beveloids are helical gears with nonparallel shafts, with shaft angles generally between 5 degrees and 15 degrees. This is part VI in the Tribology Aspects in Angular Transmission Systems Series

33 Drive Line Analysis for Tooth Contact Optimization of High-Power Spiral Bevel Gears (June/July 2011)

In the majority of spiral bevel gears, spherical crowning is used. The contact pattern is set to the center of the active tooth flank and the extent of the crowning is determined by experience. Feedback from service, as well as from full-torque bench tests of complete gear drives, has shown that this conventional design practice leads to loaded contact patterns, which are rarely optimal in location and extent. Oversized reliefs lead to small contact area, increased stresses and noise, whereas undersized reliefs result in an overly sensitive tooth contact.

34 Hypoid Gears: Tribology Aspects in Angular Transmission Systems, Part VII (June/July 2011)

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 teeth—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.

35 Optimal Modifications of Gear Tooth Surfaces (March/April 2011)

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 finishing—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.

36 Spiral Bevel Gears: Tribology Aspects in Angular Transmission Systems, Part IV (January/February 2011)

This article is part four of an eight-part series on the tribology aspects of angular gear drives. Each article will be presented first and exclusively by Gear Technology, but the entire series will be included in Dr. Stadtfeld’s upcoming book on the subject, which is scheduled for release in 2011.

37 GPSys Critical to Spiral Bevel Gear Life (September/October 2008)

Impact Technologies considers commercial version of software package.

38 Lapping and Superfinishing Effects on Surface Finish of Hypoid Gears and Transmission Errors (September/October 2008)

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.

39 Zerol Bevel Gears: Tribology Aspects in Angular Transmission Systems, Part III (November/December 2010)

Zerol bevel gears are the special case of spiral bevel gears with a spiral angle of 0°. They are manufactured in a single-indexing face milling process with large cutter diameters, an extra deep tooth profile and tapered tooth depth.

40 Precision Forged Spiral Bevel Gears (August/September 1984)

A recent U.S. Army Tank-Automotive Command project, conducted by Battelle's Columbus Laboratories. successfully developed the methodology of CAD/CAM procedures for manufacturing dies (via EDM) for forging spiral bevel gears. Further, it demonstrated that precision forging of spiral bevel gears is a practical production technique. Although no detailed economic evaluation was made in this study, it is expected that precision forging offers an attractive alternative to the costly gear cutting operations for producing spiral bevel gears.