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The first edition of the international calculation method for micropitting—ISO TR 15144–1:2010—was just published last December. It is the first and only official, international calculation method established for dealing with micropitting. Years ago, AGMA published a method for the calculation of oil film thickness containing some comments about micropitting, and the German FVA published a calculation method based on intensive research results. The FVA and the AGMA methods are close to the ISO TR, but the calculation of micropitting safety factors is new.
In the past gear manufacturers have had to rely on hob manufacturers' inspection of individual elements of a hob, such as lead, involute, spacing, and runout. These did not always guarantee correct gears, as contained elements may cause a hob to produce gears beyond tolerance limits.
Examining the history of software in mechanical engineering
Tooth contact under load is an important verification of the real contact conditions of a gear pair and an important add-on to the strength calculation according to standards such as ISO, AGMA or DIN. The contact analysis simulates the meshing of the two flanks over the complete meshing cycle and is therefore able to consider individual modifications on the flank at each meshing position.
An accurate and fast calculation method is developed to determine the value of a trigonometric function if the value of another trigonometric function is given. Some examples of conversion procedures for well-known functions in gear geometry are presented, with data for accuracy and computing time. For the development of such procedures the complete text of a computer program is included.
Gear design has long been a "black art." The gear shop's modern alchemists often have to solve problems with a combination of knowledge, experience and luck. In many cases, trial and error are the only effective way to design gears. While years of experience have produced standard gearsets that work well for most situations, today's requirements for quieter, more accurate and more durable gears often force manufacturers to look for alternative designs.
Dear Editor: In Mr. Yefim Kotlyar's article "Reverse Engineering" in the July/August issue, I found an error in the formula used to calculate the ACL = Actual lead from the ASL = Assumed lead.
Whether gear engineers have to replace an old gear which is worn out, find out what a gear's geometry is after heat treatment distortion, or just find out parameters of gears made by a competitor, sometimes they are challenged with a need to determine the geometry of unknown gears. Depending on the degree of accuracy required, a variety of techniques are available for determining the accuracy of an unknown gear. If a high degree of precision is important, a gear inspection device has to be used to verify the results. Frequently, several trial-and-error attempts are made before the results reach the degree of precision required.
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.
The proper design or selection of gear cutting tools requires thorough and detailed attention from the tool designer. In addition to experience, intuition and practical knowledge, a good understanding of profile calculations is very important.
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.
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.
The face load factor is one of the most important items for a gear strength calculation. Current standards propose formulae for face load factor, but they are not always appropriate. AGMA 927 proposes a simpler and quicker algorithm that doesn't require a contact analysis calculation. This paper explains how this algorithm can be applied for gear rating procedures.
Crown gearings are not a new type of gear system. On the contrary, they have been in use since very early times for various tasks. Their earliest form is that of the driving sprocket, found in ancient Roman watermills or Dutch windmills. The first principles of gear geometry and simple methods of production (shaper cutting) were developed in the 1940s. In the 1950s, however, crown gears' importance declined. Their tasks were, for example, taken over by bevel gears, which were easier to manufacture and could transmit greater power. Current subject literature accordingly contains very little information on crown gears, directed mainly to pointing out their limitations (Ref. 1).
This article illustrates a structural analysis of asymmetrical teeth. This study was carried out because of the impossibility of applying traditional calculations to procedures involved in the specific case. In particular, software for the automatic generation of meshes was devised because existing software does not produce results suitable for the new geometrical model required. Having carried out the structural calculations, a comparative study of the stress fields of symmetrical and asymmetrical teeth was carried out. The structural advantages of the latter type of teeth emerged.
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.
Profile corrections on gears are a commonly used method to reduce transmission error, contact shock, and scoring risk. There are different types of profile corrections. It is a known fact that the type of profile correction used will have a strong influence on the resulting transmission error. The degree of this influence may be determined by calculating tooth loading during mesh. The current method for this calculation is very complicated and time consuming; however, a new approach has been developed that could reduce the calculation time.
If you make hardened gears and have not seen any micropitting, then you haven’t looked closely enough. Micropitting is one of the modes of failure that has more recently become of concern to gear designers and manufacturers. Micropitting in itself is not necessarily a problem, but it can lead to noise and sometimes other more serious forms of failure. Predicting when this will occur is the challenge facing designers.
For high-quality carburized, case hardened gears, close case carbon control is essential. While tight carbon control is possible, vies on what optimum carbon level to target can be wider than the tolerance.
Calculation of gear tooth flexibility is of interest for at least two reasons: (a) It controls, at least in part, the vibratory properties of a transmission system hence, fatigue resistance and noise: (b) it controls load sharing in multiple tooth contact.
On gear drives running with pitch line velocities below 0.5 m/s so called slow speed wear is often observed. To solve some problems, extensive laboratory test work was started 10 years ago. A total of circ. 300,000 h running time on FZG back-to-back test rigs have been run in this speed range.
This article includes a brief summary of the characteristics of involute asymmetric teeth and the problems connected with the related bending tests.
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.
The power of high speed gears for use in the petrochemical industry and power stations is always increasing. Today gears with ratings of up to 70,000kW are already in service. For such gears, the failure mode of scoring can become the limiting constraint. The validity of an analytical method to predict scoring resistance is, therefore, becoming increasingly important.
This is the third article in a series exploring the new ISO 6336 gear rating standard and its methods of calculation. The opinions expressed herein are htose of the author as an individual. They do not represent the opinions of any organization of which he is a member.
One of the best ways to learn the ISO 6336 gear rating system is to recalculate the capacity of a few existing designs and to compare the ISO 6336 calculated capacity to your experience with those designs and to other rating methods. For these articles, I'll assume that you have a copy of ISO 6336, you have chosen a design for which you have manufacturing drawings and an existing gear capacity calculation according to AGMA 2001 or another method. I'll also assume that you have converted dimensions, loads, etc. into the SI system of measurement.
The present article contains a preliminary description of studies carried out by the authors with a view toward developing asymmetrical gear teeth. Then a comparison between numerous symmetrical and asymmetrical tooth stress fields under the same modular conditions follows. This leads to the formulation of a rule for similar modules governing variations of stress fields, depending on the pressure angle of the nonactive side. Finally a procedure allowing for calculations for percentage reductions of asymmetrical tooth modules with respect to corresponding symmetrical teeth, maximum ideal stress being equal, is proposed. Then the consequent reductions in size and weight of asymmetrical teeth are assessed.
This is the fourth and final article in a series exploring the new ISO 6336 gear rating standard and its methods of calculation. The opinions expressed herein are those of the author as an individual. They do not represent the opinions of any organization of which he is a member.
An experimental and theoretical analysis of worm gear sets with contact patterns of differing sizes, position and flank type for new approaches to calculation of pitting resistance.
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.
Part I of this paper, which appeared in the January/February issue of Gear Technology, described the theory behind double-flank composite inspection. It detailed the apparatus used, the various measurements that can be achieved using it, the calculations involved and their interpretation. The concluding Part II presents a discussion of the practical application of double-flank composite inspection -- especially for large-volume operations. It also addresses statistical techniques that can be used in conjunction with double-flank composite inspection, as well as an in-depth analysis of gage R&R for this technique.
Part I of this paper describes the theory behind double-flank composite inspection, detailing the apparatus used, the various measurements that can be achieved using it, the calculations involved and their interpretation. Part II, which will appear in the next issue, includes a discussion of the practical application of double-flank composite inspection, especially for large-volume operations. Part II covers statistical techniques that can be used in conjunction with double-flank composite inspection, as well as an in-depth analysis of gage R&R for this technique.
Early in the practice of involute gearing, virtually all gears were made with the teeth in a standard relationship to the reference pitch circle. This has the advantages that any two gears of the same pitch, helix angle and pressure angle can operate together, and that geometry calculations are relatively simple. It was soon realized, though, that there are greater advantages to be gained by modifying the relationship of the teeth to the reference pitch circle. The modifications are called profile shift.
Two-shaft planetary gear drives are power-branching transmissions, which lead the power from input to output shaft on several parallel ways. A part of the power is transferred loss-free as clutch power. That results in high efficiency and high power density. Those advantages can be used optimally only if an even distribution of load on the individual branches of power is ensured. Static over-constraint, manufacturing deviations and the internal dynamics of those transmission gears obstruct the load balance. With the help of complex simulation programs, it is possible today to predict the dynamic behavior of such gears. The results of those investigations consolidate the approximation equations for the calculation of the load factors...
The availability of technical software has grown rapidly in the last few years because of the proliferation of personal computers. It is rare to find an organization doing technical work that does not have some type of computer. For gear designers and manufacturers, proper use of the computer can mean the difference between meeting the competition or falling behind in today's business world. The right answers the first time are essential if cost-effective design and fabrication are to be realized. The computer is capable of optimizing a design by methods that are too laborious to undertake using hard calculations. As speeds continue to climb and more power per pound is required from gear systems, it no longer is possible to design "on the safe side" by using larger service factors. At high rotational speeds a larger gear set may well have less capacity because of dynamic effects. The gear engineer of today must consider the entire gear box or even the entire rotating system as his or her domain.
Since we are a high volume shop, we were particularly interested in Mr. Kotlyar's article describing the effects of hob length on production efficiency which appeared in the Sept/Oct issue of Gear Technology. Unfortunately, some readers many be unnecessarily deterred from applying the analysis to their own situations by the formidabilty of the mathematical calculations. I am making the following small suggestion concerning the evaluation of the constant terms.
The connection between transmission error, noise and vibration during operation has long been established. Calculation methods have been developed to describe the influence so that it is possible to evaluate the relative effect of applying a specific modification at the design stage. These calculations enable the designer to minimize the excitation from the gear pair engagement at a specific load. This paper explains the theory behind transmission error and the reasoning behind the method of applying the modifications through mapping surface profiles and determining load sharing.
In this paper, the potential for geometrical cutting simulations—via penetration calculation to analyze and predict tool wear as well as to prolong tool life—is shown by means of gear finish hobbing. Typical profile angle deviations that occur with increasing tool wear are discussed. Finally, an approach is presented here to attain improved profile accuracy over the whole tool life of the finishing hob.
This paper presents a unique approach and methodology to define the limits of selection for gear parameters. The area within those limits is called the “area of existence of involute gears” (Ref. 1). This paper presents the definition and construction of areas of existence of both external and internal gears. The isograms of the constant operating pressure angles, contact ratios and the maximum mesh efficiency (minimum sliding) isograms, as well as the interference isograms and other parameters are defined. An area of existence allows the location of gear pairs with certain characteristics. Its practical purpose is to define the gear pair parameters that satisfy specific performance requirements before detailed design and calculations. An area of existence of gears with asymmetric teeth is also considered.
Designing and manufacturing gears requires the skills of a mathematician, the knowledge of an engineer and the experience of a precision machinist. For good measure, you might even include the are of a magician, because the formulas and calculations involved in gear manufacturing are so obscure and the processes so little known that only members of an elite cadre of professionals can perform them.
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.
The design of any gearing system is a difficult, multifaceted process. When the system includes bevel gearing, the process is further complicated by the complex nature of the bevel gears themselves. In most cases, the design is based on an evaluation of the ratio required for the gear set, the overall envelope geometry, and the calculation of bending and contact stresses for the gear set to determine its load capacity. There are, however, a great many other parameters which must be addressed if the resultant gear system is to be truly optimum. A considerable body of data related to the optimal design of bevel gears has been developed by the aerospace gear design community in general and by the helicopter community in particular. This article provides a summary of just a few design guidelines based on these data in an effort to provide some guidance in the design of bevel gearing so that maximum capacity may be obtained. The following factors, which may not normally be considered in the usual design practice, are presented and discussed in outline form: Integrated gear/shaft/bearing systems Effects of rim thickness on gear tooth stresses Resonant response
Micropitting, pitting and wear are typical gear failure modes that can occur on the flanks of slowly operated and highly stressed internal gears. However, the calculation methods for the flank load-carrying capacity have mainly been established on the basis of experimental investigations of external gears. This paper describes the design and functionality of the newly developed test rigs for internal gears and shows basic results of the theoretical studies. It furthermore presents basic examples of experimental test results.
The finished gear engineer, the man who is prepared for all emergencies, must first of all know the basic design principles. Next he must be well versed in all sorts of calculations which come under the heading of "involute trigonometry."
Influences of Load Distribution and Tooth Flank Modifications as Considered in a New, DIN/ISO-Compatible Calculation Method
ISO 6336 Calculation of Load Capacity of Spur and Helical Gears was published in 1997 after 50 years of effort by an international committee of experts whose work spanned three generations of gear technology development. It was a difficult compromise between the existing national standards to get a single standard published which will be the basis for future work. Many of the compromises added complication to the 1987 edition of DIN 3990, which was the basic document.
I received a letter from Mr. G. W. Richmond, Sullivan Machinery Company, N.H., in which in addition to correcting mistyping, he made several suggestions concerning my article "General Equations for Gear Cutting Tool Calculations."
News Items About calculation
1 KISSsoft Releases Bearing Calculation Module (August 5, 2011)
For the bearing calculation in KISSsoft, a new module is available (module WB4). This module permits the calculation of a single bea... Read News
2 Software Update Includes Calculation Method for Scuffing (June 18, 2010)
In the release 04/2010, the calculation of flash and integral temperature according to ISO/TR 13989-1 and 13989-2 is available. With... Read News
3 KISSsoft Offers Bolt Calculation with FE Results (August 16, 2012)
In KISSsoft, the calculation of bolts in accordance with VDI 2230 is implemented as specified in Sheet 2 (SPK module). The draft version ... Read News
4 KISSsoft Offers Calculation of Cold-Wear (December 2, 2013)
Low-speed wear or cold-wear is a phenomenon that occurs with slow rotating and heavily loaded gears. In the process, the EHD lubricant fi... Read News
5 KISSsoft Releases Calculation for Shearing Strength for Plastic Worm Wheels (February 17, 2011)
For crossed axis helical gear designs where a worm meshes with a cylindrical worm wheel made of plasti... Read News
6 KISSsoft Implements Marine Calculations (March 13, 2013)
Det Norske Veritas provides with the standard No. 41.2 "Calculation of gear rating for marine transmission" a widespread gear ... Read News
7 KISSsoft Offers Gearbox Variant Calculations (September 1, 2011)
With KISSsys, gearbox variants can now be calculated very efficiently (module KS1). In contrast to the GPK-models, where within the fixed... Read News
8 KISSsoft Offers Standards in the Shaft Strength Calculation (February 27, 2014)
For an analytical strength assessement, in the first instance the currently valid standard has to be applied. Therefore, an essential tas... Read News