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Articles About Free Form Pitch Curves


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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 Size and Material Influence on the Tooth Root, Pitting, Scuffing and Wear Load-Carrying Capacity of Fine-Module Gears (September 2011)

In this study, limiting values for the load-carrying-capacity of fine-module gears within the module range 0.3–1.0 mm were determined and evaluated by comprehensive, experimental investigations that employed technical, manufacturing and material influence parameters.

3 Economics of CNC Gear Gashing vs. Large D.P. Hobbing (August/September 1984)

Gear gashing is a gear machining process, very much like gear milling, utilizing the principle of cutting one or more tooth (or tooth space) at a time. The term "GASHING" today applies to the roughing, or roughing and finishing, of coarse diametral pitch gears and sprockets. Manufacturing these large coarse gears by conventional methods of rough and finish hobbing can lead to very long machining cycles and uneconomical machine utilization.

4 Base Pitch Tables (September/October 1992)

There is one dimension common to both members of a pair of properly mating spur gears - the base pitch (BP). This base pitch is equal to the circular pitch of the gear on the base circle (see Fig. 1). For a helical gear, the base pitch can be described in either the transverse or normal plane, and is called the transverse base pitch (TBP) or normal base pitch (NBP), respectively. For parallel axis helical gears, both the TBP and NBP must be the same on both mating gears. For skew axis helical gears, only the NBP must be common.

5 An Emphasis on Accuracy (June/July 2011)

Meeting the many challenges of large gear inspection.

6 Wind Turbine Pitch and Yaw Drive Manufacturers Draw Breath as Market Slows (January/February 2010)

The global wind energy market has seen average growth rates of 28 percent over the last 10 years, according to the Global Wind Energy Council (GWEC), creating major challenges for the component supply industry. GWEC also forecasts an average growth rate of 22 percent for the next five years, which if realized, will continue to put pressure on suppliers of turbine components.

7 Extending the Benefits of Elemental Gear Inspection (July 2009)

It may not be widely recognized that most of the inspection data supplied by inspection equipment, following the practices of AGMA Standard 2015 and similar standards, are not of elemental accuracy deviations but of some form of composite deviations. This paper demonstrates the validity of this “composite” label by first defining the nature of a true elemental deviation and then, by referring to earlier literature, demonstrating how the common inspection practices for involute, lead (on helical gears), pitch, and, in some cases, total accumulated pitch, constitute composite measurements.

8 Measuring Pitch Diameter (September/October 2005)

Wait a minute, we don't measure pitch diameter. We're sometimes asked to measure it by customers, though, especially ones with older drawings.

9 Coarse Pitch Gears (May/June 1993)

This article discusses briefly some common manufacturing problems relating to coarse pitch gears and their suggested solutions. Most of the discussion will be limited to a low-quality production environment using universal machine tools.

10 The Effect of Straight-Sided Hob Teeth (November/December 2010)

It is well known that hobs with straight-sided teeth do not cut true involutes. In this paper, the difference between the straight side of a hob tooth and the axial profile of an involute worm is evaluated. It is shown that the difference increases as the diametral pitch increases, to the extent that for fine-pitch gearing, the difference is insignificant.

11 A Huge Success (September/October 1995)

Sivyer Steel Corporation, Bettendorf, IA, an ISO-9002-certified casting specialist, is familiar with tackling tough jobs. The company has built an international reputation as a supplier of high-integrity castings, especially those which require engineering and/or full machining. Its not unusual for Sivyer's customers, especially those in the mining, recycling, power generation, valve and nuclear fields, to ask the foundry to produce a one-of-a-kind casting - often something revolutionary - but AnClyde Engineered Products' request was a special challenge, even for Sivyer.

12 Small-Module Gear Design (November/December 2014)

Gears with a diametral pitch 20 and greater, or a module 1.25 millimeters and lower, are called fine-pitch or low-module gears. The design of these gears has its own specifics.

13 Increased Tooth Bending Strength and Pitting Load Capacity of Fine-Module Gears (September/October 2016)

The common calculation methods according to DIN 3990 and ISO 6336 are based on a comparison of occurring stress and allowable stress. The influence of gear size on the load-carrying capacity is considered with the size factors YX (tooth root bending) and ZX (pitting), but there are further influences, which should be considered. In the following, major influences of gear size on the load factors as well as on the permissible tooth root bending and contact stress will be discussed.

14 Calculated Gear Life Values (May 2018)

I have a query (regarding) calculated gear life values. I would like to understand for what % of gear failures the calculated life is valid? Is it 1-in-100 (1% failure, 99% reliability) or 1-in-one-thousand (0.1% failure)?

15 First International Involute Gear Comparison (August 2014)

Measurement institutions of seven different countries — China, Germany, Japan, Thailand, Ukraine, United Kingdom and the U.S. — participated in the implementation of the first international comparison of involute gear measurement standards. The German metrology institute Physikalisch-Technische Bundesanstalt (PTB) was chosen as the pilot laboratory as well as the organizer. Three typical involute gear measurement standards provided by the PTB were deployed for this comparison: a profile, a helix and a pitch measurement standard. In the final analysis, of the results obtained from all participants, the weighted mean was evaluated as reference value for all 28 measured parameters. However, besides the measurement standards, the measured parameters, and, most importantly, some of the comparison results from all participants are anonymously presented. Furthermore, mishandling of the measurement standards as occurred during the comparison will be illustrated.

16 My Gear Is Bigger than Your Gear (March/April 2013)

Industry battles it out for World's Largest Gear title.

17 Measuring Profile and Base Pitch Error with a Micrometer (September/October 2002)

In this article, equations for finding profile and base pitch errors with a micrometer are derived. Limitations of micrometers with disc anvils are described. The design of a micrometer with suitable anvils is outlined.

18 Gear Material Selection and Construction for Large Gears (January/February 2013)

A road map is presented listing critical considerations and optimal use of materials and methods in the construction of large gears.

19 Large Pinions for Open Gears - The Increase of Single Mesh Load (January/February 2013)

This paper introduces mandatory improvements in design, manufacturing and inspection - from material elaboration to final machining - with special focus on today's large and powerful gearing.

20 Big Gears - High Standards, High Profits (January/February 2009)

Natural resources—minerals, coal, oil, agricultural products, etc.—are the blessings that Mother Earth confers upon the nations of the world. But it takes unnaturally large gears to extract them.

21 Optimal Flank Forms for Large Bevel Gears (November/December 2016)

At first sight the appearance of 5-axis milling for bevel gears opens new possibilities in flank form design. Since in comparison to existing machining methods applying cutter heads no kinematic restrictions exist for 5-axis milling technology, any flank form can be machined. Nevertheless the basic requirements for bevel gears did not change. Specifications and functional requirements like load carrying capacity and running behavior are still increasing demands for design and manufacturing. This paper describes the demands for gear design and gives an overview about different design principles in the context of the surrounding periphery of the gear set.

22 Engineering Constants (July/August 1986)

Below are listed a variety of commonly used constants arranged numerically to permit ease of reference. Wherever an asterisk (*) is shown, the constant is exact as given, it being generally a mathematical constant or one fixed by definition. In cases where the first constant listed is followed by another in parenthesis, the first is the round number generally used, while the second is the more exact value.

23 Engineering Constants (May/June 1987)

Rules and Formula for worm gears, bevel gears and strength of gear teeth.

24 Finishing of Gears by Ausforming (November/December 1987)

Almost all machines or mechanical systems contain precision contact elements such as bearings, cams, rears, shafts, splines and rollers. These components have two important common requirements: first, they must possess sufficient mechanical properties, such as, high hardness, fatigue strength and wear resistance to maximize their performance and life; second, they must be finished to close dimensional tolerances to minimize noise, vibration and fatigue loading.

25 A Wheel Selection Technique for Form Gear Grinding (May/June 1986)

Until recently, form gear grinding was conducted almost exclusively with dressable, conventional abrasive grinding wheels. In recent years, preformed, plated Cubic Boron Nitride (CBN) wheels have been introduced to this operation and a considerable amount of literature has been published that claim that conventional grinding wheels will be completely replaced in the future. The superior machining properties of the CBN wheel are not disputed in this paper.

26 CNC Controlled CBN Form Grinding (May/June 1984)

Borazon is a superabrasive material originally developed by General Electric in 1969. It is a high performance material for machining of high alloy ferrous and super alloy materials. Borazon CBN - Cubic Born Nitride - is manufactured with a high temperature, high pressure process similar to that utilized with man-made diamond. Borazon is, next to diamond, the hardest abrasive known; it is more than twice as hard as aluminum oxide. It has an extremely high thermal strength compared to diamond. It is also much less chemically reactive with iron, cobalt or nickel alloys.

27 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...

28 Manufacturing Net-Shaped, Cold-Formed Gears (May 2008)

A net-shaped metal forming process has been developed for manufacturing quality, durable, high-yield and cost-efficient gears for high-volume production.

29 Gear Finishing by Shaving, Rolling and Honing, Part II (May/June 1992)

Part I of this series focused on gear shaving, while Part II focuses on gear finishing by rolling and honing.

30 Hard Gear Finishing (March/April 1988)

Hard Gear Finishing (HGF), a relatively new technology, represents an advance in gear process engineering. The use of Computer Numerical Controlled (CNC) equipment ensures a high precision synchronous relationship between the tool spindle and the work spindle as well as other motions, thereby eliminating the need for gear trains. A hard gear finishing machine eliminates problems encountered in two conventional methods - gear shaving, which cannot completely correct gear errors in gear teeth, and gear rolling, which lacks the ability to remove stock and also drives the workpiece without a geared relationship to the master rolling gear. Such a machine provides greater accuracy, reducing the need for conventional gear crowning, which results in gears of greater face width than necessary.

31 Industry Forum (July/August 1988)

Letters to the editor on a variety of subjects, including couplings, gear planers and ausforming.

32 Net-Shape Forged Gears - The State of the Art (January/February 2002)

Traditionally, high-quality gears are cut to shape from forged blanks. Great accuracy can be obtained through shaving and grinding of tooth forms, enhancing the power capacity, life and quietness of geared power transmissions. In the 1950s, a process was developed for forging gears with teeth that requires little or no metal to be removed to achieve final geometry. The initial process development was undertaken in Germany for the manufacture of bevel gears for automobile differentials and was stimulated by the lack of available gear cutting equipment at that time. Later attention has turned to the forging of spur and helical gears, which are more difficult to form due to the radial disposition of their teeth compared with bevel gears. The main driver of these developments, in common with most component manufacturing, is cost. Forming gears rather than cutting them results in increased yield from raw material and also can increase productivity. Forging gears is therefore of greater advantage for large batch quantities, such as required by the automotive industry.

33 Worm Gears - Ask the Expert (October 2013)

How does one determine the center of a worm and a worm wheel? Also, what are the differences between the common worm tooth forms?

34 Practical Gear Characteristics: Process Characteristics of the Most Popular Cutting Methods (March/April 2016)

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).

35 Mechanical Behavior and Microstructure of Ausrolled Surfaces in Gear Steels (March/April 1995)

Ausforming, the plastic deformation of heat treatment steels in their metastable, austentic condition, was shown several decades ago to lead to quenched and tempered steels that were harder, tougher and more durable under fatigue-type loading than conventionally heat-treated steels. To circumvent the large forces required to ausform entire components such as gears, cams and bearings, the ausforming process imparts added mechanical strength and durability only to those contact surfaces that are critically loaded. The ausrolling process, as utilized for finishing the loaded surfaces of machine elements, imparts high quality surface texture and geometry control. The near-net-shape geometry and surface topography of the machine elements must be controlled to be compatible with the network dimensional finish and the rolling die design requirements (Ref. 1).

36 Generation of Helical Gears with New Surface Topology by Application of CNC Machines (January/February 1994)

Analysis of helical involute gears by tooth contact analysis shows that such gears are very sensitive to angular misalignment leading to edge contact and the potential for high vibration. A new topology of tooth surfaces of helical gears that enables a favorable bearing contact and a reduced level of vibration is described. Methods for grinding helical gears with the new topology are proposed. A TCA program simulating the meshing and contact of helical gears with the new topology has been developed. Numerical examples that illustrate the proposed ideas are discussed.

37 Hard Finishing By Conventional Generating and Form Grinding (March/April 1991)

The quality of a gear and its performance is determined by the following five parameters, which should be specified for each gear: Pitch diameter, involute form, lead accuracy, spacing accuracy, and true axis of rotation. The first four parameters can be measured or charted and have to be within tolerance with respect to the fifth. Pitch diameter, involute, lead, and spacing of a gear can have master gear quality when measured or charted on a testing machine, but the gear might perform badly if the true axis of rotation after installation is no longer the same one used when testing the gear.

38 Grinding of Spur and Helical Gears (July/August 1992)

Grinding is a technique of finish-machining, utilizing an abrasive wheel. The rotating abrasive wheel, which id generally of special shape or form, when made to bear against a cylindrical shaped workpiece, under a set of specific geometrical relationships, will produce a precision spur or helical gear. In most instances the workpiece will already have gear teeth cut on it by a primary process, such as hobbing or shaping. There are essentially two techniques for grinding gears: form and generation. The basic principles of these techniques, with their advantages and disadvantages, are presented in this section.

39 Improving Gear Manufacturing Quality With Surface Texture Measurement (March/April 1993)

The working surfaces of gear teeth are often the result of several machining operations. The surface texture imparted by the manufacturing process affects many of the gear's functional characteristics. To ensure proper operation of the final assembly, a gear's surface texture characteristics, such as waviness and roughness, can be evaluated with modern metrology instruments.

40 Performance and Machining of Advanced Engineering Steels in Power Transmission Applications - Continued Developments (May 2017)

It is becoming increasingly apparent that material properties can and will play a greater role than before in addressing the challenges most transmission manufacturers are facing today. Making use of materials' intrinsic fatigue properties provides a new design tool to support the market changes taking place.