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Convoloid® Gearing Technology Introductory Tutorial

REV 16 • 7/19/2018

1 USE OF THIS TUTORIAL .................................................................................... 3

2 THE GENESIS OF CONVOLOID GEARING TECHNOLOGY ................................ 3

3 SIMILARITIES TO INVOLUTE GEARING ............................................................ 4

3.1 WORLD’S MACHINE TOOL COMPLEMENT .................................................................................... 4 3.2 PROCESSING AND SEQUENCING .................................................................................................. 4 3.3 MANUFACTURING PROCESS TIMES .............................................................................................. 4 3.4 INSPECTION PRACTICE ................................................................................................................ 5 3.5 CONJUGACY ............................................................................................................................... 5 3.6 CONVOLOID GEARING ARRANGEMENTS ...................................................................................... 5

4 DIFFERENCES COMPARED TO INVOLUTE GEARING ....................................... 6

4.1 CENTER DISTANCE CHANGES ...................................................................................................... 6 4.2 THE CONVOLOID GEAR TOOTH FORM ......................................................................................... 6 4.3 CONVOLOID TOOTH PROFILE SPECIFICATION ............................................................................... 7 4.4 TRANSITION ZONE ..................................................................................................................... 8 4.5 RACK OFFSETS ........................................................................................................................... 8 4.6 NO UNDERCUT .......................................................................................................................... 8 4.7 SHAVING OF CONVOLOID GEARS ................................................................................................. 9

5 CONVOLOID GEARING DETAILED DESIGN CONCEPTS ................................... 9

5.1 ADDENDUM ............................................................................................................................... 9 5.2 DEDENDUM ............................................................................................................................... 9 5.3 ROOT CONFIGURATION .............................................................................................................. 9 5.4 TRANSITION ZONE .................................................................................................................. 10 5.5 PITCH DIAMETERS ................................................................................................................... 10 5.6 CONTACT RATIOS .................................................................................................................... 10 5.7 CROWNING ............................................................................................................................ 10 5.8 CONVOLOID GEAR PAIR RATING .............................................................................................. 11


5.9 BEARING CONSIDERATIONS AND BEARING FORCES ................................................................... 12 5.10 RETROFITTING ......................................................................................................................... 12 5.11 BACKLASH ............................................................................................................................... 12 5.12 HELIX ANGLES ......................................................................................................................... 13 5.13 CONVOLOID PAIR DESIGN BIASING ........................................................................................... 13 5.14 SPEED INCREASING OR DECREASING DRIVES .............................................................................. 13 5.15 INCREASED SHOCK RESISTANCE ................................................................................................ 13 5.16 LOW BACKLASH DESIGNS ......................................................................................................... 14 5.17 LONGER LIFE DESIGNS ............................................................................................................. 14

6 MANUFACTURING CONVOLOID GEARING ................................................... 14

6.1 SEQUENCING .......................................................................................................................... 14 6.2 PROCESSING ........................................................................................................................... 15 6.3 HOBBING ............................................................................................................................... 15 6.4 SHAPING ................................................................................................................................ 16 6.5 GEAR TOOTH GRINDING .......................................................................................................... 16 6.6 INSPECTION ............................................................................................................................ 16 6.7 INSPECTION CHARTS. ............................................................................................................... 17

7 PREPARATION FOR THE USE OF CONVOLOID GEARING ............................. 19

7.1 PREPARATION ......................................................................................................................... 19 7.2 LONGER LIFE .......................................................................................................................... 19 7.3 REDUCED VOLUME AND WEIGHT ............................................................................................. 20 7.4 GEAR SYSTEM PART REDUCTION .............................................................................................. 20 7.5 CONSTRAINED INVOLUTE SYSTEM ............................................................................................ 21

8 TESTING AND DEPLOYING CONVOLOID GEARING ...................................... 22

8.1 PREREQUISITES ....................................................................................................................... 22 8.2 RETROFITTING ........................................................................................................................ 22 8.3 ROBUST TEST PROCEDURES ..................................................................................................... 23 8.4 ECONOMICS ........................................................................................................................... 23

9 DEVELOPMENTAL FLOW CHART .................................................................... 23

10 GETTING SERIOUS ABOUT CONVOLOID GEARING TECHNOLOGY ............. 24


1 Use of this Tutorial

This tutorial is intended to provide the designer, process engineer, and manufacturer with many aspects of Convoloid™ Gearing Technology. The descriptions, postulates, and opinions expressed in this Tutorial are those in effect at the current state of the Technology and will be constantly updated and improved as new information and data is either generated or developed. Gear Innovations accept no liability whatsoever either contingent or otherwise as a result of the use of this Tutorial and its teachings. Since application of this technology varies widely, it is solely the responsibility of the buyer of the gearing employing the technology and the seller to not only work out the accepted standards governing business transactions between these parties but also the design and execution of acceptance test protocols to ensure satisfactory operation and field use.

2 The Genesis of Convoloid Gearing Technology

The involute curve, in use for gearing systems since 1754, is a geometric shape meeting several of the highly desirable characteristics for carrying load and torque in an efficient gearing system. Its form can be described as the locus of points described by unwrapping a string from a barrel (the “barrel” being the base circle) with the points defined at the end of the string. Gear mating surfaces are convex/convex in nature and the relative curvature between the mating gear surfaces changes substantially as the gear pair rolls through mesh.

Convoloid gear tooth forms are also described by a locus of points. These points, however, are described differently, conform to a rigorous protocol that maximizes the load carrying capacity of a pair of gears, requires convex/concave or conformal mesh characteristics, and optimizes relative curvatures. The result is a major increase in load carrying capacity of gear systems of the order of 30% to 60% and higher compared to an equivalent involute design where center distance, gear face width, ratio, and materials and heat treatments are equal for both gear systems.


3 Similarities to Involute Gearing

3.1 World’s Machine Tool Complement

It would be economically untenable to create a new gear tooth form without its being compatible with the world’s gear manufacturing industry with respect to its capital asset infrastructure, that is, the machine tools and associated equipment in present use. Since Convoloid gear pairs are designed using a point by point calculation optimizing three primary characteristics affecting gear operation and stress reduction, these forms are totally compatible with the digital gear manufacturing capabilities which presently exist. Along with the operation of these machine tools is the ease with which its associated gear tooling packages are designed and manufactured. Hobs, shaper cutters, and other gear tools can be designed and manufactured using the standard accepted formulas in use today to design rack forms and other important features which lead to highly efficient and accurate manufacture of Convoloid gears.

3.2 Processing and Sequencing

Manufacturing processes and their sequencing of Convoloid gears are generally the same as in use for involute gears. Gear blanking, hobbing, shaping ,various types of gear tooth grinding, and other processes for production of Convoloid gears operate in the same manner as involutes. For example, a standard high performance involute gear may be sequenced as follows:

� Blanking � Pre-grind hobbing � Carburizing and hardening � Gear tooth grinding

A competing Convoloid gear would be sequenced in the same manner.

3.3 Manufacturing Process Times

Manufacturing process times are also very similar to involute process times. For example, hobbing an involute gear takes about the same cycle time as hobbing a Convoloid gear allowing for pitch, materials, outside diameter and face width. The hob forms themselves are different. Hob materials, speeds and feeds, fixturing, and coolant selections are generally the same for Convoloids as for involutes. There are, however, differences in the way sizes, ie, tooth thicknesses, are held. These methods are different from involute practice, although not difficult. See section 4 for details.


3.4 Inspection Practice

Existing modern CNC inspection machinery and equipment for involute gearing is quite sufficient for inspecting Convoloids. Since Convoloid gears have no base circle as in an involute ( see Section 4.1 for detail) and since the pressure angles of Convoloid pairs vary throughout the meshing cycle, the X –Y coordinate files used to specify Convoloid forms can be supplemented with i, j, k or u, v, w vector coordinates to compensate for the probe touching points on the Convoloid profiles providing compensation for probes of various diameters. The accuracy standards for Convoloid gears follow exactly that used for the involute world. AGMA, JIS, DIN, and ISO are all applicable to Convoloid gears when pitch diameter size, module and other qualification parameters are used. The use of span measurements for tooth thickness control are also used for Convoloid gears just as with involutes.

3.5 Conjugacy

In order to ensure constant relative angular motion between a pair of gears – involute or Convoloid – it is essential that the pair conform to the Law of Gearing and the Euler Savary equation for conjugacy. Conformance to this norm for gearing helps to ensure good load carrying capacity, reasonable noise control, and long gear life. Involutes are by design conjugate and Convoloids by absolute definition as a precondition are conjugate. With regard to center distance changes and effects of this changeable parameter on conjugacy, involutes do have considerable latitude as to center distance changes and the maintenance of conjugacy. Convoloids also have considerable flexibility with respect to center distance changes without detrimental effects on conjugacy and in most cases on stress characteristics. Design center distance tolerances become an important input parameter to the design of Convoloid pairs to ensure conjugacy throughout the planned performance envelope.

3.6 Convoloid Gearing Arrangements

At this writing Convoloid gear pair designs include parallel axis spurs, helicals, double helicals, planetaries, and other epicyclics. With regard to planetaries and other epicyclics, the conventions applicable to involute planetaries and epicyclics are to be followed with Convoloid versions of these configurations. Two of these conventions are:

� The relationship of tooth numbers in the ring, pinion, and number of evenly spaced planets.

� The 30% derating practice of planet gears due to the reverse bending characteristics of this gear member as practiced in involutes.


4 Differences Compared to Involute Gearing

4.1 Center Distance Changes Although Convoloid gear pairs might appear to be like previous conformal gearing designs with particular sensitivity to center distance this is not the case with Convoloids. Gear Innovations has analyzed this issue in depth and has actual experience with a 108 KW 2 stage wind turbine gearbox where Convoloids were retrofitted into the involute housing. Convoloid pairs operate well when center distance tolerances are held to up- to- date tolerance bands on modern machinery. LEARN MORE

4.2 The Convoloid Gear Tooth form

The Convoloid tooth form has some similarities with involute tooth forms but the convex addendum, concave dedendum and transition zone are crafted using Gear Innovations protocols and are quite different from involutes. Although there is conjugate contact from the lowest point of contact (LPC) to the tooth tip, the Convoloid designs have carefully designed root structures for maximum beam strength and do utilize tip relief characteristics not unlike involutes. Tip relief is calculated in approximately the same manner as that for involutes with some important changes in coefficients to allow for the high beam strength afforded by the Convoloid concave dedendum form.

Convoloid Tooth Form Features


4.3 Convoloid Tooth Profile Specification

The specification of Convoloid tooth flanks is different than that of involutes. Although variations on this convention are possible the coordinate system is primarily used as below.

The Convoloid design protocol calculates the coordinate points of a Convoloid tooth at up to several hundred places from root to tip depending on several factors including the designer’s objectives. Root configuration is designed separately and carefully integrated with the Convoloid dedendum to comply with the intended manufacturing processes for the gear, that is, finish hobbing or pre-grind hobbing in anticipation of subsequent tooth grinding. The coordinate files of Convoloid gears and pinions being different most often require a rack design for each member, that is, for example, a pinion hob and a different gear hob. Below is a partial printout of a typical coordinate file.

Coordinate File Convention


4.4 Transition Zone

The area of tooth surface engagement around the pitch diameter of Convoloid gears is the transition zone. It is in this area that the convex addendum meets the concave dedendum. Carrying loads through this change in curvature direction, doing it at lowest possible stress, and yet providing adequate conjugacy with known center distance changes is an important requirement for Convoloid pairs. Center distance variation is a critical parameter to be used in the design of Convoloid pairs. Not only changes in the machining of the basic operating center distance of a Convoloid pair are to be considered, but also changes due to the flexing of gear support shafts, and changes due to the effects of temperature extremes on dissimilar materials of ,say, aluminum housings and steel gears and shafts. These changes produce operating center distance extremes and must be taken into account when designing Convoloid pairs.

4.5 Rack Offsets

Convoloid gear pairs do not have the same rack offset design features of involutes. Involute practice alters the position of the gear and pinion involute curves most often to accommodate speed decreasing pairs and speed increasing pairs in coordination with the desirable characteristics in the arcs of approach and recess. Convoloid pairs do not use rack offsets and are designed in the same matter whether a speed decreasing or speed increasing pair is desired.

4.6 No Undercut

Convoloid gear tooth forms are designed by simultaneously solving three major characteristics that influence gear system power density. There is no base circle for Convoloid gears and consequently there is no potential for tooth contact below a base circle and possible undercutting. The concave dedendum of Convoloid forms promotes good tooth beam strength especially when combined with careful gear root designs. One advantage of this Convoloid characteristic is that smaller numbers of teeth in pinions are practicable compared with involutes and thus the potential exists for higher single stage gear ratios than their involute baselines. It is possible and practical in some cases to design and rate a Convoloid single stage pair to replace an involute two stage design while rating at the same or lower stress levels for the Convoloid pair. This potential exists for all multi-stage gear trains, that is, a three stage involute design can be redesigned to a two stage Convoloid design. etc.


4.7 Shaving of Convoloid gears

Shaving of Convoloid gears is not recommended. A shaving operation depends on the intimate contact with and controlled radial forcing of the shaving cutter into the workpiece. Although satisfactory for involutes the study of these effects on the accuracy and size control of Convoloid pairs has not been determined.

5 Convoloid Gearing Detailed Design Concepts

5.1 Addendum

The addendum of a Convoloid gear is defined as that portion of the tooth profile from the outside diameter or tip diameter down to the addendum transition point (ATP). It is convex in nature and is conjugate to the concave dedendum of the mating Convoloid gear. The addendum can include a tip relief portion which is defined in much the same way as an involute tip relief. Due to the inherent beam strength of concave Convoloid dedendums, tooth bending in the addendum is generally not as great as involutes under similar load intensity conditions. Actual testing has resulted in initial factors for tip relief to be different from that of involutes especially the value of the coefficient used for its calculation.

5.2 Dedendum

The dedendum of a Convoloid gear is that portion of the tooth profile from the dedendum transition point (DTP) down to the lowest point of contact (LPC) and is concave in nature. It is conjugate to the convex addendum of the mating gear.

5.3 Root Configuration

As with involutes the root configuration of Convoloid gears is carefully crafted to meet one or more of the following criteria:

� Maximum bending strength � Smooth transition from the lowest point of contact in the dedendum into the root

area. � Smooth finish grinding tooth surface into an assumed ungrounded root area.

Obviously this feature is not applicable if the root is to be finished ground along with the active profile.


5.4 Transition Zone

The transition zone of a Convoloid gear extends from the ADP down through the pitch diameter to the DTP. The value of the radial distance from the ADP to the DTP may change depending on several factors among which is the design center distance variation. Contact through the transition zone is conjugate and the geometric shape of the pinion’s transition zone and gear’s transition zone will depend on several factors.

5.5 Pitch Diameters

Convoloid gears are designed around the operating pitch diameters needed to achieve the design gear ratio and are therefore calculated from the center distance and tooth numbers in the same manner as involute operating pitch diameters. Tooth size and all other values are based on this foundation.

5.6 Contact Ratios

Contact ratios of Convoloid gears are calculated in much the same way as involutes. However, the absence of a base circle makes the calculations somewhat more involved. Values of face contact ratio are calculated using the common expression as follows:

FCR= (F* sin b) / (mn *π)

F= face width in mm, β= helix angle and mn = normal module

Studies of face contact ratios and their effects on load intensity and power density capabilities of Convoloid gearing have shown that maximum loads per unit of face width are obtained when the face contact ratio is set to an integer plus a small amount for edge break or crowning. As an example, values of 1.10, 2.07, etc. are used. Setting face contact ratio in the “mid-ranges”, that is, for example, 1.6, 2.4, etc. actually reduces the load carrying capacity per unit face at a given stress limit. Profile contact ratios are also calculated with the methods common to involutes. Typical profile contact ratios of Convoloid pairs are in the 1.2 to 1.5 range. It is due to this fact that effective Convoloid gear pairs can be either helicals or spurs.

5.7 Crowning

For all the reasons a design engineer may want to crown a pair of involute gears, those same reasons apply to Convoloid pairs. At the present state of technology development, however, there are a few recommended changes in design approach and method for crowning Convoloid pairs. First, it has been found that the involute helical tooth twist correction protocols offered by the gear grinding community for threaded wheel and form tooth grinding do not work for Convoloids. This correction procedure is intended to apply to “barrel crowning” where the face extremities of the involute gear are ground a slight bit deeper than at the face centerline. This procedure is not recommended for Convoloids


since the wheel infeed at the face extremities tends to mitigate the conjugacy of the Convoloid mesh in those areas. The preferred method of crowning Convoloids is the “radial edge break”. Here the wheel is not fed into a deeper root diameter at the gear face extremities but the workpiece is advanced or retarded into the wheel to affect a slight but gradual thickening of the tooth space for both flanks. Short of this software option being offered by the gear tooth grinding community the infeed method can be used. It is further recommended that only the larger member of the pair (usually the gear) be the only member crowned and that the pinion be tooth ground with no crown. The total amount of this type of crown should approximate that of similarly designed set of involute gear pairs. For example, if a pair of involutes is designed to have .0003 inches crown on the pinion and .0004 inches on the gear the Convoloid pair should be crowned in the range of .0007 inches and the pinion cut or ground with no crown. The effects of twist for ground tooth helical Convoloids is inversely proportional to the diameter of the gear being crowned. For this reason the larger of the Convoloid pair should be the member crowned. The expertise of the gear grinding community, however, can develop TPG (topographical profile grinding) permitting the effective crafting of profiles to adequately accommodate gear tooth load spectrums, gear configurations and interfacing component effects.

5.8 Convoloid Gear Pair Rating

Involute contact stresses change according to the changes in relative curvatures (convex/convex) as the involute teeth roll through mesh. AGMA standards for rating contact stress stipulate a “stress number” which through years of experience have established allowable stress numbers and related those numbers to satisfactory test and field performance for the materials and heat treatment of the particular gear pair. The relative curvatures of Convoloid pairs (convex/concave) exhibit substantially constant relative contact stress throughout the meshing cycle. The AGMA stress number and the actual calculation of Convoloid pair Hertzian stress, calculated classically, are directly compared for comparison to a baseline involute. Applied equally on this baseline comparison for both the involute and Convoloid pairs are all the appropriate derating factors used by AGMA standards. In this way an “apples to apples” comparison is achieved. Such calculations have been used to design involute versus Convoloid test programs with actual results confirming this rating practice. With regard to bending stress, the concave dedendum of the Convoloid tooth form enhances the basic bending strength of this tooth profile. Notwithstanding this fact care must be taken in the crafting of robust root configurations. Most of the standard accepted root configurations of involutes can be applied to Convoloids such as full fillet, flat root with corner radii, etc. Stress concentration factors in the range of 1.5 have shown through testing and FEA to be satisfactory. All normal design caveats for involute root stress configurations apply to Convoloids as well.


5.9 Bearing Considerations and Bearing Forces

Bearing selection for supporting Convoloid gear pairs as to type and capacity closely follows that used for involutes. The tangential and axial forces are calculated in the same manner as for involutes using input gear torque and pitch radius and the helix angle. Since the operating pressure angle changes as Convoloid gears go through mesh, the separating forces needed to complete the analysis also changes. It has been calculated that using an operating pressure angle for Convoloid pairs at 26.5° will provide conservative separating force values with which to calculate resulting bearing forces and thence the proper selection of type and size of bearing.

5.10 Retrofitting

Convoloid design and rating protocols make retrofitting straightforward. The important factors to establish for the involute pair to be retrofitted are:

� The center distance and its tolerance � The number of pinion teeth and gear teeth � Whether an exact ratio match is desired and if not what percentage of tolerance on

the desired ratio is acceptable. Note that exact ratio matches although easily doable probably do not create the most optimized Convoloid pair

� Effective face width for allowable contact and bending stresses � Materials and heat treatment � Any special performance upgrades that may be desired in the retrofitted pair such

as better shock resistance, longer life etc. (See section 5.13, Biasing of Convoloid pairs)

5.11 Backlash

The standard Convoloid design protocol defaults pair backlash at 0.048 times the normal module. This amount can be changed to suit the design requirements of the gear pair. This figure becomes part of the design of the rack of the gear to be manufactured and is designed and made into a generating tool such as a hob, shaper cutter, or threaded wheel for grinding such that when size (generally root diameter) is reached the proper backlash is established in the workpiece. (See Section 6 , Manufacture of Convoloid Gearing.)


5.12 Helix Angles

The selection of helix angles for Convoloid gear pairs follows the same practice as for involutes. Gear axial thrust values and face contact ratios help to determine the range of helix angle that should be used in a Convoloid pair given supporting bearing capacities. Convoloid pairs usually use face contact ratios of an integer plus a small bit of overlap to allow for edge breaks, chamfers etc. Examples are 1.10, 2.05, etc. It been found that the load carrying capability per unit of face width is maximized at these integers and that values of face contact ratio in between these values do not add capacity in proportion to the increase in face width.

5.13 Convoloid Pair Design Biasing

For like or approximate ratio combinations at a common center distance comparing both involute and Convoloid, a heavier (larger) module will most probably be used for the Convoloid pair. The reason is that at this matching center distance, face width, ratio, and materials and heat treatment, the contact stresses in the Convoloid pair are so much lower than those of the involute pair, increasing the input torque up to the contact stress limit of the Convoloid pair will require a considerably heavier pitch (larger module) to achieve appropriate bending stresses and a “balanced” design. Just as with involute designs Convoloid gear pairs can be designed to enhance special performance requirements including:

� Speed increasing or speed decreasing combinations � Increased shock resistance � Low backlash designs � Longer life designs.

5.14 Speed Increasing or Decreasing Drives

A conventionally designed Convoloid pair is designed for balance between contact stress and bending stress among other important features. If the designer wishes to use Convoloid pairs in a speed increasing device with the gear driving a smaller pinion and wants to reduce the absolute and/ or specific sliding characteristic of the pair, going to a finer or smaller module with more total numbers of teeth in the pair helps the sliding phenomenon.

5.15 Increased Shock Resistance

To achieve improved shock resistance in a Convoloid pair, the module selected should be increased and the total number of teeth in the pair decreased to obtain lower bending stresses and added shock resistance.


5.16 Low Backlash Designs

The standard Convoloid designed pair defaults to a backlash value per gear of about 0.048 times the normal module. This factor can be changed to lower values to decrease overall pair backlash. As said previously this value has a pronounced effect on the design of rack tools with which the pinion and gear of the pair are being manufactured. It is with this factor that the backlash of each member is controlled. Backlash can be increased, however, with a tool so designed but the procedure is different than that for involutes. There should be no infeed to get additional thinning of the teeth since infeeding would detract from the crafted conjugacy conditions of the mesh. Side cutting by some method is preferred. (See section M, Manufacture of Convoloid gears).

5.17 Longer Life Designs

To achieve longer life designs by lowering contact stresses, finer or smaller modules are recommended. The higher number of teeth in the pair the more profile contact ratio is obtained as well as increasing face contact ratio. (See section H above for recommendations regarding face contact ratio).

6 Manufacturing Convoloid Gearing

6.1 Sequencing

The general processes and sequencing used in the manufacture of involute gearing is followed mostly if not exactly by the processes and sequencing of Convoloid gearing. There are three basic reasons for this validity.

a) The Convoloid form is calculated using special protocols which optimize the most important kinematic and geometric characteristics of gearing to provide the highest possible power density in a gear set. The result is an X-Y plot of the Convoloid form at anywhere between 100 and 300 points from tip diameter to root diameter. This Convoloid practice merely specifies the pinion and gear tooth form in a different framework than involutes generally are specified. It is certainly possible to specify an involute curve in the same way Convoloid forms are specified but that has not been general practice. The Convoloid form protocols are generally different than involutes but not more difficult.

b) Our computer world creates a much more flexible and comprehensive treatment of gear design, stressing, and manufacture. From a Convoloid X-Y coordinate file, standard mathematical relationships of that file to define basic rack, grinding wheel forms, shaper cutters, and many other commonly used gear manufacturing tools are used. With CNC machinery the creation of those tools are also straightforward.


c) The facts stipulated in (1) and (2) above verify that Convoloid gears can be and are made using the exact same sequences and processes in use for involutes. For example, the manufacture of an involute pinion which is carburized, hardened, and tooth ground would be processed as follows.

� Blanking � Pre-grind hobbing or shaping � Carburizing and hardening � Grinding teeth

A Convoloid pinion would be done in the same manner.

6.2 Processing

Processes common to both involutes and Convoloids are but are not limited to:

� Hobbing � Shaping � Scudding � Form grinding � Threaded wheel grinding

Currently the only process not used for Convoloids but used for involutes is gear tooth shaving.

6.3 Hobbing

There are two differences in the procedure for hobbing Convoloids compared to that of involutes. Convoloid hobs are designed such that gear root clearances, root structure, grind stock allowances, and tip relief are all characteristic of the hob form being used. Hob speeds and feeds are generally the same as those used for involutes consistent with the hob material and coating being used, and the size of the teeth (module) being cut. The two differences are:

� Providing the hob form has been verified as accurate to the specification required, the root diameter of the gear being hobbed is the primary size feature that must be held. If that parameter is held to practical tolerance limits then the balance of the Convoloid form will be correct.

� The second difference is in achieving additional tooth thinning or added backlash for gears being used as hobbed. To achieve additional tooth thinning for Convoloids the involute method of advancing the hob into the workpiece is not to be used. Advancing the Convoloid hob into the workpiece can adversely affect the conjugacy features of the Convoloid form with its mate, or if pre-grind hobbing is being used, this procedure can change the depths of grind stock following a case hardening and grinding operation. The proper way to thin Convoloid teeth in a hobbing operation


is to move the hob spindle axis axially an amount desired for the increase in backlash or tooth thinning without disturbing the established workpiece/ hob spatial and rotational relationship. This hob spindle axial movement can be accomplished in either direction.

6.4 Shaping

The same criteria apply to shaping Convoloid gears as hobbing except that for tooth thinning, the shaper cutter must be moved radially measured at the pitch diameter of the shaper cutter an amount equal to the desired increase in backlash.

6.5 Gear Tooth Grinding

There are two types of gear tooth grinding that require special processing compared to conventional involute gear grinding.

� Threaded wheel grinding. Here the procedure for achieving desired tooth thickness is similar to that of hobbing per Section 6.3 above with one caveat: It is imperative to consult the threaded wheel manufacturer regarding axial movement of the threaded wheel, which should be equal to the amount of tooth thinning desired. If twist-free grinding has been designed into the threaded wheel, the wheel manufacturer should be consulted regarding axial movements so you do not disturb special geometric relationships that generate the appropriate Convoloid twist-free form.

� Form wheel grinding. To achieve desired tooth thickness the basic rack form of the Convoloid gear being ground is dressed into the wheel. To reduce tooth thickness the wheel should not be moved axially to achieve the desired thinning nor should the wheel be plunged into the work. Either of these “corrections” will compromise the desired Convoloid form being ground. The only procedural move to reduce tooth thickness is to rotate the work spindle on the work axis rotationally an amount equal to the desired decrease in tooth thickness measured at the pitch diameter. To maintain reasonable balance in the design case depth amount after grinding, equal amounts of stock should be removed from each flank of the gear tooth.

6.6 Inspection

All of the involute criteria for qualification of the accuracy of tooth form apply to Convoloid gears. The standards of AGMA, ISO, DIN, JIS etc. can be effectively applied to categorize the accuracy of Convoloid forms. At this writing qualification of Convoloids using involute


standards is sufficient to qualify Convoloids for field service applicable to that of involutes of equal quality level.

6.7 Inspection charts.

The only difference between an involute chart and the Convoloid accuracy chart is the construction of the electronic master, that is, the straight vertical line with superimposed descriptive Convoloid radial features in the same way as involutes.

Note in this profile chart the horizontal lines indicating the radial location and value of the primary profile features of the Convoloid form called out at the extreme right of the chart.


7 Preparation for the Use of Convoloid Gearing

7.1 Preparation

There are obviously many factors to be considered when making the decision to use Convoloid Gearing Technology. Convoloid gearing should be evaluated when one or more of the objectives below are evident:

� Longer life is desired from involute gearing

� More compactness is desired in involute gearing pairs

� Dramatic reductions in weight and size of a present geared system are needed

� A 2-gear system is needed to replace a 4 gear involute system with the same ratio (up to 10 to 1 per stage) using existing materials, heat treatment and processing techniques

� Significant increase in power capacity is needed from an existing “constrained” involute system with respect to one of or all of materials, heat treatments, center distance, face width, housing size, and ratio

The first step is to outline the basic objectives of a change to Convoloid gearing, its assumed success, and resulting projected economic and performance advantages. Gear Innovations CCE’s can assist with this task and many others during any development. Next, a detailed stress analysis of the Convoloid pair should be compared against the existing stress analysis of its competing involute pair if there is one. If not, the Convoloid gearing stresses should be considered on their own merit and the resulting geometry analyzed for cost-effectiveness, performance, and economics. Once the optimized Convoloid gearing pair has been designed, rigorous testing should be completed. Here it would be a major advantage if there exists robust test protocols for the existing involute gear pair or system that reliably predicts successful field use. The Convoloid gearing pair can be put through those same protocols and results directly compared with the involute performance. Test Convoloid gearing can be manufactured by gear Innovations Trusted Manufacturing Partners with assistance from Gear Innovations Certified Convoloid Engineers (CCE’s) or Gear Innovations directly. Rigorous testing must be completed and even Alpha and Beta production runs manufactured and successfully proven before actual production is considered.

7.2 Longer Life

Since under the same input torques and speeds assuming all other variables are essentially equal, Convoloid pairs exhibit much lower Hertz contact stresses while adequately supporting very capable bending stresses. As a result, under equal power inputs, Convoloid gears should last much longer than the involute baseline under consideration. As an


example the Gear Research Institute at Penn State University tested involute baseline pairs against Convoloid pairs. Data common to both the involute and the Convoloid pairs was as follows: (Termed hereafter as an “equivalent involute”)

� Center distance � Ratio � All materials and heat treatments � Face widths � Input toque and speed � Lubrication

At the conclusion of the comprehensive testing program the result was that at a 95% confidence level the involute pair life was calculated at 240,000 cycles where the Convoloid pair life was 2,500,000 cycles. The lower contact stress in the Convoloid pairs took this gear pair life well out the S/N curve before failures occurred.

7.3 Reduced Volume and Weight

The reader is encouraged to visit involutegearcomparison.com. Here not only are examples provided which directly compare the weight and size of Convoloid designs versus a competing involute design but this site allows you to input your own involute data to assess Convoloid’s performance and economic advantages.

7.4 Gear System Part Reduction

Here substitution of a four gear, two-stage involute gear system with a two gear single stage Convoloid design is analyzed. There are two important characteristics of Convoloid gears compared with involutes that enhance Convoloid’s capability to be design efficient with respect to the geometry of pinions with small numbers of teeth. This fact in turn enhances the ability of Convoloids to reduce 4 gear involute systems to 2 gear Convoloid systems while operating at equal or lower stress levels exhibited by the involute baseline design.

The first is that with Convoloid Technology there is no base circle. Convoloid forms are crafted by the software to meet specific convex/concave gearing postulates to produce excellent gear power transmission. Below the involute base circle there is no involute curve and, in addition, the possibility of undercut exists which can severely limit pinion bending strength.

The second is that the Convoloid dedendums are concave and are carefully crafted in the root area. These 2 factors add to the bending strength of Convoloid pinions with small numbers of teeth.


A recent test of Convoloid against an “equivalent involute” (see 7.1 above) has preliminarily proven this supposition. The involute failed in bending at 34e6 cycles and the Convoloid was pristine at 37e6 cycles.

The following specific analysis is theoretical and has not been tested.

Involute data Convoloid Data

Power Rating 310KW 310KW

Center Distance 210 mm 150 mm

Ratio 9.72 to 1 (4 gears) 9.72 to 1 (2 gears)

Tooth Bending Stresses all within allowable limits

Contact Stress 1340 Mpa (LS) 1261 Mpa

Total Gear Volume 1909 mm^3 1523 mm^3 20.3% LESS VOLUME

Total Gear Weight 13.34 Kg 11.3 Kg 22.3% LESS WEIGHT

7.5 Constrained Involute System

Gear Innovations has analyzed a highly constrained involute design for a ball mill drive. Here two motors of 11,100 kW each driving a ~15,000 mm (26 foot) diameter gear. The constraints are as follows and cannot be changed without large expenditures of time and money.

� Gear material and heat treatment. Cast steel gears of this size have been optimized at about 35 HRC. Casting, processing, and heat treatment are the economic and performance drivers with this component.

� Center distance. Existing mills have the center distance built into the housing support structure. One can imagine the complexity and cost of changing this parameter.

� Face width. Face width is limited to the existing value for reasons indicated under the center distance limitations listed above.

� Pinion materials. The existing design has maximized the power capacity of this component.

� Ratio. A ratio change is out of the question since motor location and output speeds have been optimized to comply with the idealized output speed of the ball mill itself.


Objectives for the ball mill design. The objective is to maximize the power capacity of the gearing within the constraints above. Involute designs have already fulfilled this objective by using two 10 Mw motor pinions driving a single output gear. Using AGMA 2101 D4 rating standards, the allowable input torque per motor was 1,396,000 Nm. Convoloid gearing would raise the allowable torque to 2,390,000 Nm without violating the contact stress or bending stress values of the involute design, overall gear ratio, the materials and heat treatments of the existing design, and the face width constraint. (Gear Innovations defines allowable torque as that torque that does not violate established stress maximums for contact and/ or bending.) For this particular example, center distance was 5984.8 mm and output gear outside diameter was 11,174mm (~36 feet).

8 Testing and Deploying Convoloid Gearing

8.1 Prerequisites

It is preferable that the following prerequisites exist as a good start on utilizing Convoloid gearing:

� Existing and robust involute baseline test procedures. � Thorough economic evaluation on future profitability of the user. � Comprehensive performance evaluation.

8.2 Retrofitting

When considering a retrofit or new design of Convoloid gearing pairs the basic objectives of the change to Convoloid pairs must be defined. For retrofitting it simple mathematics is used to match center distance, ratio, gear face width, and material and heat treatment and obtain significant performance advantages. Good practice demands thorough study of bearing capacities, shaft and shaft and keyway strengths, and other important analyses. For maximum power density certain parameters with respect to a retrofit or new design should not have to be necessarily constrained to their involute equivalents. Ratio changes especially higher single pass ratios in gear face width’s do not have to be matched to the involute baseline design. Every advantage of Convoloid Gearing Technology should be applied in these cases.


8.3 Robust Test Procedures

It is a major advantage for the potential user of Convoloid pairs to have established a robust involute testing procedure such that successful completion of these protocols portends a high degree of confidence that the gearing so tested will perform satisfactorily in the field. Putting test Convoloid gears through these same procedures with successful results should greatly increase the confidence that field performance for the new gearing will be acceptable.

8.4 Economics

To make the economic case for any change to Convoloid gearing, a thorough study of the market into which not only the production cost implications are studied, but also the intangible advantages of increased market share, potential gains resulting in economies of scale, the resulting increase in the users goodwill perception by the market as a progressive purveyor of advanced technology, and the watershed affects accruing to significantly higher power densities and other relevant factors.

9 Developmental Flow Chart

Talk to our team. Compare your current involute gears with our free gear comparison app. Learn what’s possible!

Learn more with our Convoloid Gearing Technology tutorials. Work with a Certified Convoloid Engineer (CCE). Train your engineers.

Engage a Trusted Manufacturing Partner (TMP). Or, we can train your in-house manufacturing team.

Learn more about Convoloid test programs.


10 Getting Serious About Convoloid Gearing Technology The intellectual property (IP) content of Convoloid Gearing Technology is contained in three parts:

� Trade name. � Design and manufacturing know-how. � Internationally filed patents, existing patent portfolio, and new patent applications

in process.

Due to the sensitive nature of information provided and developed by both Gear Innovations and a prospective client surrounding Convoloid gearing use, confidentiality is a major consideration. Should a prospective client wish to test Convoloid gearing as a preamble to production quantities, the following general steps are recommended to design, build, test and then produce Convoloid gearing pairs in production quantities.

1. Contact Gear Innovations expressing interest in testing. At this point a mutually acceptable NDA will be signed (example can be provided).

2. Gear Innovations, through its Certified Convoloid Engineer (CCE) network, will work with the client to assist in designing Convoloid pairs to meet or exceed the client’s defined performance requirements.

3. Once the finalized design and stress analysis has been completed to the satisfaction of the client, it is strongly recommended that the client analyze the tangible and intangible effects of embedding Convoloid Gearing Technology into their product line or product lines with an objective of determining acceptable returns on investment (ROI).

4. If the analysis is favorable and testing is the next logical step, a Cooperative Development Agreement (CDA) should be consummated ( term sheet can be provided).

5. Gear Innovations can assist client in setting test protocols and test objectives. Gear Innovations can also assist in sourcing the test gearing if the client does not wish to manufacture the test Convoloid pairs in house.

6. If tests are successful and client wishes to proceed to production, a Technology Use Agreement is completed (term sheet can be provided).

convoloid gearing technology ... - gear innovations

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