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Our research group has been engaged in the study of gear noise for some nine years and has succeeded in cutting the noise from an average level to some 81-83 dB to 76-78 dB by both experimental and theoretical research. Experimental research centered on the investigation into the relation between the gear error and noise. Theoretical research centered on the geometry and kinematics of the meshing process of gears with geometric error. A phenomenon called "out-of-bound meshing of gears" was discovered and mathematically proven, and an in-depth analysis of the change-over process from the meshing of one pair of teeth to the next is followed, which leads to the conclusion we are using to solve the gear noise problem. The authors also suggest some optimized profiles to ensure silent transmission, and a new definition of profile error is suggested.
Base helix error - the resultant of lead and profile errors is the measured deviation from the theoretical line of contact (Fig. 1). It can be measured in the same way that lead error on a spur gear is measured, namely, by setting a height gage to height H based on the radial distance r to a specified line of contact (Fig. 2), rotating the gear so as to bring a tooth into contact with the indicator on the height gage, and then moving the height gage along two or more normals to the plane of action. The theoretical line of contact on helical gear must be parallel to the surface plate, which is attained by mounting the gear on a sine bar (Fig. 3).
Much information has been written on gear inspection, analytical. functional. semiautomatic and automatic. In most cases, the charts, (if you are lucky enough to have recording equipment) have been explained.
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.
The authors have developed a rack-type rolling process in which a rack tool is used to roll gear teeth. The results and analysis show that the proposed method reduces errors.
An analysis of possibilities for the selection of tool geometry parameters was made in order to reduce tooth profile errors during the grinding of gears by different methods. The selection of parameters was based on the analysis of he grid diagram of a gear and a rack. Some formulas and graphs are presented for the selection of the pressure angle, module and addendum of the rack-tool. The results from the grinding experimental gears confirm the theoretical analysis.
In the last section, we discussed gear inspection; the types of errors found by single and double flank composite and analytical tests; involute geometry; the involute cam and the causes and symptoms of profile errors. In this section, we go into tooth alignment and line of contact issues including lead, helix angles, pitch, pitchline runout, testing and errors in pitch and alignment.
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.
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.
This paper will demonstrate that, unlike commonly used low-contact-ratio spur gears, high-contact-ratio spur gears can provide higher power-to-weight ratio, and can also achieve smoother running with lower transmission error (TE) variations.
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.
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?
This article describes a root fillet form calculating method for a helical gear generated with a shaper cutter.
The concept of "transmission error" is relatively new and stems from research work in the late 1950s by Gregory, Harris and Munro,(1) together with the need to check the accuracy of gear cutting machines. The corresponding commercial "single flank" testing equipment became available in the 1960s, but it was not until about ten years ago that it became generally used, and only recently has it been possible to test reliably at full load and full speed.
The presence of significant errors in the two-flank roll test (a work gear rolled in tight mesh against a master gear) is well-known, but generally overlooked.
Everyone makes mistakes. Nobody's perfect. We've all heard those or similar words, and if you happen to be in charge of your company's quality efforts, you've probably heard them more than most people.
Minimizing gear losses caused by churning, windage and mesh friction is important if plant operating costs and environmental impact are to be minimized. This paper concentrates on mesh friction losses and associated scuffing risk. It describes the preliminary results from using a validated, 3-D Finite Element Analysis (FEA) and Tooth Contact Analysis (TCA) program to optimize cylindrical gears for low friction losses without compromising transmission error (TE), noise and power density. Some case studies and generic procedures for minimizing losses are presented. Future development and further validation work is discussed.
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.
Presumably, everyone who would be interested in this subject is already somewhat familiar with testing of gears by traditional means. Three types of gear inspection are in common use: 1) measurement of gear elements and relationships, 2) tooth contact pattern checks and 3) rolling composite checks. Single Flank testing falls into this last category, as does the more familiar Double Flank test.
Anyone involved in the design, manufacture and use of gears is concerned with three general characteristics relative to their application: noise, accuracy, and strength or surface durability. In the article, we will be dealing with probably the most aggravating of the group, gear noise.
Gear noise can be a source of intense annoyance. It is often the primary source of annoyance even when it is not the loudest noise component. This is because of the way it is perceived. Gear noise is a collection of pure tones which the human ear can detect even when they are 10dB lower than the overall noise level. Another reason for our sensitivity to transmission noise is that we associate it with impending mechanical failure.
Joe Arvin comments on his recent trip to Scandinavia and how U.S. defense dollars are being spent overseas. J.D. Smith responds to an article on gear noise from the previous issue.
A pair of spur gears generally has an effective lead error which is caused, not only by manufacturing and assembling errors, but also by the deformations of shafts, bearings and housings due to the transmitted load. The longitudinal load distribution on a contact line of the teeth of the gears is not uniform because of the effective lead error.
Vehicle gear noise testing is a complex and often misunderstood subject. Gear noise is really a system problem.(1) most gearing used for power transmission is enclosed in a housing and, therefore, little or no audible sound is actually heard from the gear pair.(2) The vibrations created by the gears are amplified by resonances of structural elements. This amplification occurs when the speed of the gear set is such that the meshing frequency or a multiply of it is equal to a natural frequency of the system in which the gears are mounted.
There are problems in dimensional measurement that should be simple to solve with standard measuring procedures, but aren't. In such cases, using accepted practices may result in errors of hundreds of microns without any warning that something is wrong.
In some gear dynamic models, the effect of tooth flexibility is ignored when the model determines which pairs of teeth are in contact. Deflection of loaded teeth is not introduced until the equations of motion are solved. This means the zone of tooth contact and average tooth meshing stiffness are underestimated, and the individual tooth load is overstated, especially for heavily loaded gears. This article compares the static transmission error and dynamic load of heavily loaded, low-contact-ratio spur gears when the effect of tooth flexibility has been considered and when it has been ignored. Neglecting the effect yields an underestimate of resonance speeds and an overestimate of the dynamic load.
The two-flank roll test measures kickout (tooth-to-tooth composite error) and tooth thickness. In this article, it will be shown that measured values vary with the number of teeth on the master gear.
The purpose of this article is to clarify some terms and methods used in measuring the size of gears. There is also an explanation given of the error induced and how to correct for it in certain cases when the measurement is made using pins instead of balls.
The data discussed in this article was taken from an upright vacuum cleaner. This was a prototype cleaner that was self-propelled by a geared transmission. It was the first time that the manufacturer had used a geared transmission in this application.
How should we consider random helix angle errors fHÎ˛ and housing machining errors when calculating KHÎ˛? What is a reasonable approach?
Gear-loaded tooth contact analysis is an important tool for the design and analysis of gear performance within transmission and driveline systems. Methods for the calculation of tooth contact conditions have been discussed in the literature for many years. It's possible the method you've been using is underestimating transmission error in helical gears. Here's why.
In the design process of transmissions, one major criterion is the resulting noise emission of the powertrain due to gear excitation. Within the past years, much investigation has shown that the noise emission can be attributed to quasi-static transmission error. Therefore, the transmission error can be used for a tooth contact analysis in the design process, as well as a characteristic value for quality assurance by experimental inspections.
This article presents an analysis of asymmetric tooth gears considering the effective contact ratio that is also affected by bending and contact tooth deflections. The goal is to find an optimal solution for high performance gear drives, which would combine high load capacity and efficiency, as well as low transmission error (which affects gear noise and vibration).
Question: I am a gear engineer for a motor manufacturer in China. I am writing about noise generated from cross-helical gear assembly error. I want to learn the relationship between the misalignment (center distance change and cross-angle shift) and transmission error. It is better under the loading and theory conditions. What is the trend of cross-helical gear development (use ZI worm and involute helical gear, point contact)?
The gear tooth fillet is an area of maximum bending stress concentration. However, its profile is typically less specified in the gear drawing and hardly controlled during gear inspection in comparison with the gear tooth flanks. This paper presents a fillet profile optimization technique for gears with symmetric and asymmetric teeth based on FEA and a random search method. It allows achieving substantial bending stress reduction in comparison with traditionally designed gears. This bending stress reduction can be traded for higher load capacity, longer lifetime, lower noise and vibration and cost reduction.
Glancing back now, The Falk Corp. looks to have had a straight path toward power transmission when it opened in 1892.
This article shows the newest developments to reduce overall cycle time in grinding wind power gears, including the use of both profile grinding and threaded wheel grinding.
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.
In many gear transmissions, tooth load on one flank is significantly higher and is applied for longer periods of time than on the opposite one; an asymmetric tooth shape should reflect this functional difference. The advantages of these gears allow us to improve the performance of the primary drive tooth flanks at the expense of the opposite coast flanks, which are unloaded or lightly loaded during a relatively short work period by drive flank contact and bending stress reduction. This article is about the microgeometry optimization of the spur asymmetric gearsâ€™ tooth flank profile based on the tooth bending and contact deflections.
Transmission error (TE) is recognized as one of the most important causes of gear acoustic emissions...
A programmable algorithm is developed to separate out the effect of eccentricity (radial runout) from elemental gear inspection date, namely, profile and lead data. This algorithm can be coded in gear inspection software to detect the existence, the magnitude and the orientation of the eccentricity without making a separate runout check. A real example shows this algorithm produces good results.
A graphical procedure for selecting optimum combinations of profile and lead modifications.
Modern gearboxes are characterized by high torque load demands, low running noise and compact design. In order to fulfill these demands, profile and lead modifications are being applied more often than in the past. This paper will focus on how to produce profile and lead modifications by using the two most common grinding processesâ€”threaded wheel and profile grinding. In addition, more difficult modificationsâ€”such as defined flank twist or topological flank correctionsâ€”will also be described in this paper.
The use of dimensionless factors to describe gear tooth geometry seems to have a strong appeal to gear engineers. The stress factors I and J, for instance, are well established in AGMA literature. The use of the rack shift coefficient "x" to describe nonstandard gear proportions is common in Europe, but is not as commonly used in the United States. When it is encountered in the European literature or in the operating manuals for imported machine tools, it can be a source of confusion to the American engineer.
The NASA Lewis Research Center investigated the effect of tooth profile on the acoustic behavior of spur gears through experimental techniques. The tests were conducted by Cleveland State University (CSU) in NASA Lewis' spur gear testing apparatus. Acoustic intensity (AI) measurements of the apparatus were obtained using a Robotic Acoustic Intensity Measurement System (RAIMS). This system was developed by CSU for NASA to evaluate the usefulness of a highly automated acoustic intensity measurement tool in the reverberant environment of gear transmission test cells.
The newer profile-shifted (long and short addendum) gears are often used as small size reduction gears for automobiles or motorcycles. The authors have investigated the damage to each cutting edge when small size mass-produced gears with shifted profiles are used at high speeds.
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.
On many occasions a reasonably approximate, but not exact, representation of an involute tooth profile is required. Applications include making drawings, especially at enlarged scale, and laser or EDM cutting of gears, molds, and dies used to produce gears. When numerical control (NC) techniques are to be used, a simple way to model an involute can make the NC programming task much easier.
Question: I have just become involved with the inspection of gears in a production operation and wonder why the procedure specifies that four involute checks must be made on each side of the tooth of the gear being produced, where one tooth is checked and charted in each quadrant of the gear. Why is this done? These particular gears are checked in the pre-shaved, finish-shaved, and the after-heat-treat condition, so a lot of profile checking must be done.
A major source of helicopter cabin noise (which has been measured at over 100 decibels sound pressure level) is the gear box. Reduction of this noise is a NASA and U.S. Army goal.
It isn't for everyone, but... Within the installed base of modern CNC gear profile grinding machines (approximately 542 machines worldwide), grinding from the solid isn't frequent, but a growing number of gear profile grinder users are applying it successfully using CBN-plated wheels.
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.
This paper initially defines bias errorâ€”the â€śtwisted tooth phenomenon.â€ť Using illustrations, we explain that bias error is a by-product of applying conventional, radial crowning methods to produced crowned leads on helical gears. The methods considered are gears that are finished, shaped, shaved, form and generated ground. The paper explains why bias error occurs in these methods and offers techniques used to limit/eliminate bias error. Sometimes, there may be a possibility to apply two methods to eliminate bias error. In those cases, the pros/cons of these methods will be reviewed.
Three experts tackle the question of profile shift in this issue's edition of "Ask the Expert."
Vibration and noise from wind turbines can be significantly influenced - and therefore reduced - by selecting suitable gearing modifications. New options provided by manufacturers of machine tools and grinding machines, and especially state-of-the-art machines and controls, provide combined gearing modifications - or topological gearing corrections - that can now be reliably machined. Theoretical investigations of topological modifications are discussed here with the actual machining and their possible use.
Measurement institutions of seven different countries â€” China, Germany, Japan, Thailand, Ukraine, United Kingdom and the U.S. â€” 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.
The name Gleason is practically synonymous with gear manufacturing. Since the company was founded in 1865, the technology of gear manufacturing has been its focus, its core and its competitive advantage.
Introduction The standard profile form in cylindrical gears is an involute. Involutes are generated with a trapezoidal rack â€” the basis for easy and production-stable manufacturing (Fig. 1).
Helical gear teeth are affected by cratering wear â€” particularly in the regions of low oil film thicknesses, high flank pressures and high sliding speeds. The greatest wear occurs on the pinion â€” in the area of negative specific sliding. Here the tooth tip radius of the driven gear makes contact with the flank of the driving gear with maximum sliding speed and pressure.
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.
The deformation of the gear teeth due to load conditions may cause premature tooth meshing. This irregular tooth contact causes increased stress on the tooth flank. These adverse effects can be avoided by using defined flank modifications, designed by means of FE-based tooth contact analysis.
In order to improve load-carrying capacity and noise behavior, gears usually have profile and lead modifications. Furthermore, in gears where a specified tooth-flank load application direction (for drive and coast flanks) is a design enhancement, or even compulsory, the asymmetric tooth profile is a further solution. Nowadays, many gears need to be hard finished. Continuous generating grinding offers a very high process efficiency, but is this process able to grind all modifications, especially asymmetric gears? Yes, it is!
A reader asks: We are currently revising our gear standards and tolerances, and a few problems with the new standard AGMA 2002-C16 have arisen. Firstly, the way to calculate the tooth thickness tolerance seems to need a "manufacturing profile shift coefficient" that isn't specified in the standard; neither is another standard referred to for this coefficient. This tolerance on tooth thickness is needed later to calculate the span width as well as the pin diameter. Furthermore, there seems to be no tolerancing on the major and minor diameters of a gear.
In order to grind gears burn-free and as productively as possible, a better understanding of the process is required.
This paper presents a new approach to repair industrial gears by showing a case study where pressure angle modification is also considered, differently from the past repairing procedures that dealt only with the modification of the profile shift coefficient. A computer program has been developed to automatically determine the repair alternatives under two goals: minimize the stock removal or maximize gear tooth strength.