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1 Calculation of Tooth Root Load Carrying Capacity of Beveloid Gears (June 2014)

In this paper, two developed methods of tooth root load carrying capacity calculations for beveloid gears with parallel axes are presented, in part utilizing WZL software GearGenerator and ZaKo3D. One method calculates the tooth root load-carrying capacity in an FE-based approach. For the other, analytic formulas are employed to calculate the tooth root load-carrying capacity of beveloid gears. To conclude, both methods are applied to a test gear. The methods are compared both to each other and to other tests on beveloid gears with parallel axes in test bench trials.

2 Tooth Root Optimization of Powder Metal Gears - Reducing Stress from Bending and Transient Loads (June/July 2013)

This paper will provide examples of stress levels from conventional root design using a hob and stress levels using an optimized root design that is now possible with PM manufacturing. The paper will also investigate how PM can reduce stresses in the root from transient loads generated by abusive driving.

3 The Pros and Cons of Fully Ground Root Fillets (August 2014)

For maximum life in carburized and ground gearing, I have been advised that fully grinding a radius into the root gives maximum resistance against fatigue failures. Others have advised that a hobbed and unground radius root form is best. Which is best, and why?

4 The Effect of Manufaturing Microgeometry Variations on the Load Distribution Factor and on Gear Contact and Root Stresses (July 2009)

Traditionally, gear rating procedures consider manufacturing accuracy in the application of the dynamic factor, but only indirectly through the load distribution are such errors in the calculation of stresses used in the durability and gear strength equations. This paper discusses how accuracy affects the calculation of stresses and then uses both statistical design of experiments and Monte Carlo simulation techniques to quantify the effects of different manufacturing and assembly errors on root and contact stresses.

5 Influence of Hobbing Tool Generating Scallops on Root Fillet Stress Concentrations (July 2016)

While designing gear and spline teeth, the root fillet area and the corresponding maximum tensile stress are primary design considerations for the gear designer. Root fillet tensile stress may be calculated using macro-geometry values such as module, minor diameter, effective fillet radius, face width, etc.

6 The Importance of Profile Shift, Root Angle Correction and Cutter Head Tilt (January/February 2016)

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.

7 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.

8 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.

9 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.

10 Design Against Tooth Interior Fatigue Fracture (November/December 2000)

In a modern truck, the gear teeth are among the most stressed parts. Failure of a tooth will damage the transmission severely. Throughout the years, gear design experience has been gained and collected into standards such as DIN (Ref. 1) or AGMA (Ref. 2). Traditionally two types of failures are considered in gear design: tooth root bending fatigue, and contact fatigue. The demands for lighter and more silent transmissions have given birth to new failure types. One novel failure type, Tooth Interior Fatigue Fracture (TIFF), has previously been described by MackAldener and Olsson (Refs. 3 & 4) and is further explored in this paper.

11 True Bending Stress in Spur Gears (August 2007)

In this paper, an accurate FEM analysis has been done of the “true” stress at tooth root of spur gears in the function of the gear geometry. The obtained results confirm the importance of these differences.

12 Tooth Flank Corrections of Wide Face Width Helical Gears that Account for Shaft Deflections (January/February 2005)

This paper discusses the influence of tip relief, root relief, load modification, end relief and their combinations on gear stresses and transmission errors due to shaft deflections.

13 Designing Hardened & Ground Spur Gears to Operate With Minimum Noise (May/June 1994)

When designing hardened and ground spur gears to operate with minimum noise, what are the parameters to be considered? should tip and/or root relief be applied to both wheel and pinion or only to one member? When pinions are enlarged and he wheel reduced, should tip relief be applied? What are the effects on strength, wear and noise? For given ratios with enlarged pinions and reduced wheels, how can the gear set sized be checked or adjusted to ensure that the best combination has been achieved?

14 Point-Surface-Origin Macropitting Caused by Geometric Stress Concentration (January/February 2011)

Point-surface-origin (PSO) macropitting occurs at sites of geometric stress concentration (GSC) such as discontinuities in the gear tooth profile caused by micropitting, cusps at the intersection of the involute profile and the trochoidal root fillet, and at edges of prior tooth damage, such as tip-to-root interference. When the profile modifications in the form of tip relief, root relief, or both, are inadequate to compensate for deflection of the gear mesh, tip-to-root interference occurs. The interference can occur at either end of the path of contact, but the damage is usually more severe near the start-of-active-profile (SAP) of the driving gear.

15 Innovative Induction Hardening Process with Pre-heating for Improved Fatigue Performance of Gear Component (July 2014)

Contact fatigue and bending fatigue are two main failure modes of steel gears, while surface pitting and spalling are two common contact fatigue failures -- caused by alternating subsurface shear stresses from the contact load between two gear mates. And when a gear is in service under cyclic load, concentrated bending stresses exist at the root fillet -- the main driver of bending fatigue failures. Induction hardening is becoming an increasingly popular response to these problems, due to its process consistency, reduced energy consumption, clean environment and improved product quality -- but not without issues of its own (irregular residual stresses and bending fatigue). Thus a new approach is proposed here that flexibly controls the magnitude of residual stress in the regions of root fillet and tooth flank by pre-heating prior to induction hardening. Using an external spur gear made of AISI 4340 as an example, this new concept/process is demonstrated using finite element modeling and DANTE commercial software.

16 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.

17 Fatigue Aspects of Case Hardened Gears (March/April 1999)

The efficient and reliable transmission of mechanical power continues, as always, to be a central area of concern and study in mechanical engineering. The transmission of power involves the interaction of forces which are transmitted by specially developed components. These components must, in turn, withstand the complex and powerful stresses developed by the forces involved. Gear teeth transmit loads through a complex process of positive sliding, rolling and negative sliding of the contacting surfaces. This contact is responsible for both the development of bending stresses at the root of the gear teeth and the contact stresses a the contacting flanks.

18 Case Depth and Load Capacity of Case-Carburized Gears (March/April 2002)

Compared to non-heat-treated components, case-carburized gears are characterized by a modified strength profile in the case-hardened layer. The design of case-carburized gears is based on defined allowable stress numbers. These allowable stress numbers are valid only for a defined "optimum" case depth. Adequate heat treatment and optimum case depth guarantee maximum strength of tooth flank and tooth root.

19 Gear Grinding With Dish Wheels (September/October 1999)

The grinding of gears with dish wheels (Maad type grinding machines) is widely viewed as the most precise method of gear grinding because of the very short and simple kinematic links between the gear and the tool, and also because the cutting edges of the wheels represent planar surfaces. However, in this grinding method, depending on the parameters of the gears and one of the adjustments (such as the number of teeth encompassed by the grinding wheels), so-called overtravel at the tip or at the root of the teeth being ground generally occurs. When this happens, machining with only one wheel takes place. As a result, the profile error and the length of the generating path increases while productivity decreases.

20 Specifying Custom Gears (May/June 1999)

Gear design and specification are not one and the same. They are the first two steps in making a gear. The designer sits down and mathematically defines the gear tooth, working with the base pitch of the gear, the pressure angle he wants to employ, the number of teeth he wants, the lead, the tooth thickness, and the outside, form and root diameters. With these data, the designer can create a mathematical model of the gear. At this stage, he will also decide whether the gear will be made from existing cutting tools or whether new tools will be needed, what kind of materials he will use, and whether or not he will have the gear heat treated and finished.

21 Morphology of Micropitting (November/December 2012)

Understanding the morphology of micropitting is critical in determining the root cause of failure. Examples of micropitting in gears and rolling-element bearings are presented to illustrate morphological variations that can occur in practice.

22 The Halls of Ivy Tech Are Humming with Precision Tooling (October 2013)

If you've been following this space with any regularity, you know that grassroots efforts among industry and academia are springing up around the country to help win the hearts, minds and talents of young people in nudging them towards a career in manufacturing. Add another partnership to the list.

23 Tooth Flank Fracture - Basic Principles and Calculation Model for a Sub-Surface-Initiated Fatigue Failure Mode of Case-Hardened Gears (August 2015)

Cracks initiated at the surface of case-hardened gears may lead to typical life-limiting fatigue failure modes such as pitting and tooth root breakage. Furthermore, the contact load on the flank surface induces stresses in greater material depth that may lead to crack initiation below the surface if the local material strength is exceeded. Over time the sub-surface crack propagation may lead to gear failure referred to as “tooth flank fracture” (also referred to as “tooth flank breakage”). This paper explains the mechanism of this subsurface fatigue failure mode and its decisive influence factors, and presents an overview of a newly developed calculation model.

24 Premature Gear Failure (January/February 2016)

I would appreciate if you could assist with a gear failure (occurring) after just seven weeks in service, post installation. This driving gear wheel has been installed in a medium-speed engine with backlash present at four different positions; with additional backlash checked on the mating surfaces. All backlash was found within (OEM)-recommended values. Please note included photos — it seems that the crack has started at the root fillet. Any comments would be appreciated.

25 Minimal Tooth Number of Flexspline in Harmonic Gear Drive with External Wave Generator (October 2013)

Wave generators are located inside of flexsplines in most harmonic gear drive devices. Because the teeth on the wheel rim of the flexspline are distributed radially, there is a bigger stress concentration on the tooth root of the flexspline meshing with a circular spline, where a fatigue fracture is more likely to occur under the alternating force exerted by the wave generator. The authors' solution to this problem is to place the wave generator outside of the flexspline, which is a scheme named harmonic gear drive (HGD) with external wave generator (EWG).

26 Managing Shop Floor Data (September/October 2016)

There’s no substitute for a good software package in gear manufacturing. It’s a critical shop floor tool that provides practical engineering services that customers appreciate. When you’re in the business of specifying and procuring high quality gears, the software needs to meet many objectives including the consideration of all tolerances of center distance, tooth thickness and tip diameters, root diameters, fillets, etc. It’s also imperative that the software updates include the latest revisions to the gear standards being used in the industry.

27 Gear Macrogeometry (September/October 2015)

I have outsourced gear macrogeometry due to lack of resources. Now I received the output from them and one of the gears is with —0.8× module correction factor for m = 1.8 mm gear. Since bending root stress and specific slide is at par with specification, but negative correction factor —0.8× module — is quite high — how will it influence NVH behavior/transmission error? SAP and TIF are very close to 0.05 mm; how will that influence the manufacturing/cost?

28 Induction Hardening of Gears and Critical Components - Part I (September/October 2008)

Induction hardening is a heat treating technique that can be used to selectively harden portions of a gear, such as the flanks, roots and tips of teeth, providing improved hardness, wear resistance, and contact fatigue strength without affecting the metallurgy of the core and other parts of the component that don’t require change. This article provides an overview of the process and special considerations for heat treating gears. Part I covers gear materials, desired microsctructure, coil design and tooth-by-tooth induction hardening.

29 Gear Grinding Techniques Parallel Axes Gears (March/April 1985)

The fundamental purpose of gear grinding is to consistently and economically produce "hard" or "soft" gear tooth elements within the accuracy required by the gear functions. These gear elements include tooth profile, tooth spacing, lead or parallelism, axial profile, pitch line runout, surface finish, root fillet profile, and other gear geometry which contribute to the performance of a gear train.

30 Where Manufacturing and Education Mesh (January/February 2007)

But associations and grassroots organizations lack public awareness.

31 American Manufacturing - Can It Be Saved (November/December 2009)

If anyone should ever need convincing that the state of American manufacturing is in ongoing decline, consider this: the state of Michigan has the highest concentration of engineers in the country, yet also has the highest unemployment rate. But there are ripples of hope out there as grassroots and otherwise organized groups are fighting the good fight in an attempt to reverse that trend.

32 Gear Corrosion During the Manufacturing Process (September/October 2009)

No matter how well gears are designed and manufactured, gear corrosion can occur that may easily result in catastrophic failure. Since corrosion is a sporadic and rare event and often difficult to observe in the root fillet region or in finely pitched gears with normal visual inspection, it may easily go undetected. This paper presents the results of an incident that occurred in a gear manufacturing facility several years ago that resulted in pitting corrosion and intergranular attack (IGA).

33 The Skinny on Lean Manufacturing (June 2007)

While universally known as a Japanese “invention” that was popularized by Toyota, lean in fact traces its roots to the work of post-World War II American occupation forces in Japan.

34 Superfinishing Gears -- The State of the Art (November/December 2003)

Superfinishing the working surfaces of gears and their root fillet regions results in performance benefits.

35 Determining the Shaper Cut Helical Gear Fillet Profile (September/October 2006)

This article describes a root fillet form calculating method for a helical gear generated with a shaper cutter.

36 Hey Brother, Can You Spare Some Time (March/April 2010)

How you can get involved in a grassroots movement to save American manufacturing--and the American economy.

37 Effect of Web & Flange Thickness on Nonmetallic Gear Performance (November/December 1995)

Gears are manufactured with thin rims for several reasons. Steel gears are manufactured with thin rims and webs where low weight is important. Nonmetallic gears, manufactured by injection molding, are designed with thin rims as part of the general design rule to maintain uniform thickness to ensure even post-mold cooling. When a thin-rimmed gear fails, the fracture is thought the root of the gear, as shown in Fig. 1a, rather than the usual fillet failure shown in Fig. 1b.

38 Gear Tooth Profile Determination From Arbitrary Rack Geometry (November/December 1988)

This article describes a method of obtaining gear tooth profiles from the geometry of the rack (or hob) that is used to generate the gear. This method works for arbitrary rack geometries, including the case when only a numerical description of the rack is available. Examples of a simple rack, rack with protuberances and a hob with root chamfer are described. The application of this technique to the generation of boundary element meshes for gear tooth strength calculation and the generation of finite element models for the frictional contact analysis of gear pairs is also described.

39 Calculation of Optimum Tooth Flank Corrections for Helical Gears (September/October 1988)

The load carrying behavior of gears is strongly influenced by local stress concentrations in the tooth root and by Hertzian pressure peaks in the tooth flanks produced by geometric deviations associated with manufacturing, assembly and deformation processes. The dynamic effects within the mesh are essentially determined by the engagement shock, the parametric excitation and also by the deviant tooth geometry.

40 Design Implications for Shaper Cutters (July/August 1996)

A gear shaper cutter is actually a gear with relieved cutting edges and increased addendum for providing clearance in the root of the gear being cut. The maximum outside diameter of such a cutter is limited to the diameter at which the teeth become pointed. The minimum diameter occurs when the outside diameter of the cutter and the base circle are the same. Those theoretical extremes, coupled with the side clearance, which is normally 2 degrees for coarse pitch cutters an d1.5 degrees for cutters approximately 24-pitch and finer, will determine the theoretical face width of a cutter.

41 High-Temperature Testing of Stanyl Plastic Gears: A Comparison with Tensile Fatigue Data (March/April 2010)

This paper shows an experimental study on the fatigue lifetime of high-heat polyamide (Stanyl) gears running in oil at 140°C. Based on previous works (Refs. 1–2), an analysis is made correcting for tooth bending and calculating actual root stresses. A comparison with tensile bar fatigue data for the same materials at 140°C shows that a good correlation exists between gear fatigue data and tensile bar fatigue data. This insight provides a solid basis for gear designers to design plastic gears using actual material data.

42 Cool Gears (May/June 1999)

It's nice to have claim to fame. "We're probably the world's foremost authority on making gears out of ice," says Jeff Root of Virtual Engineering, Plymouth, MI.

News Items About root

1 AKGears Unveils Latest Tooth Root Fillet Optimization Software (April 14, 2015)
AKGears recently introduced the only commercially available tooth root fillet optimization software that defines the tooth root fillet pr... Read News