1、93FTM12The Generation of Precision Spur GearsThrough WireElectrical Discharge Machiningby: Roderick and Jack Kleiss, Kleiss Engineering andScott Hoffmann, Accu-prompt EDMAmerican Gear Manufacturers AssociationTECHNICAL PAPERThe Generation of Precision Spur Gears Through WireElectrical Discharge Mach
2、iningRoderick and Jack Kleiss, Kleiss Engineering andScott Hoffmann, Accu-prompt EDMThestatements and opinionscontained he,_in arethose oft,heauthorand should notbeconstruedas anofficial actionoropinion of the American Gear Manufacturers Association.ABSTRACT:The new generationof wire Electrical Disc
3、harge Machines (EDM) are capable of quite good generating accuracy. Wehave maximized the accuracy andrepeatabilityof this tool through fixturing,controlledcutting methods, and optimizedmathematicalalgorithms for thecuttingpath. The resultis the verifiedgenerationofprecise spurgears inpitches ranging
4、from 5 to 41 DP. The advantage of the methodis short lead timeswith accuracy approaching form ground while beingcost competitive. The method is also suitable for producing small to medium lots of very accurate spur gears in anyelectrically conductive material.Copyright 1993American Gear Manufacturer
5、sAssociation1500 King Street, Suite 201Alexandria, Virginia, 22314October, 1993ISBN: 1-55589-624-3The Generation of Precision Spur Gears ThroughWire Electrical Discharge MachiningRoderick and Jack KleissKleiss Engineering3006 Edgerton Street, Little Canada, MN 55117andScott Hoffmann, PresidentAccu-P
6、rompt EDM, Inc.100 83rd Avenue North NE, Fridley, MN 55432Introduction other forms of gear generation.In plastic gear mold-making, the wire EDM The EDM Processis often used to create the involute shape in themold cavity. This has been a point of contention Electrical Discharge Machining is based onw
7、ithin the plastic community for years, with the principal oferosionofanelectricallyconductivetraditionalists arguing that a cavity burned with a material by continuous spark discharge to itshob cut electrode is inherently more accurate than surface (1). With wire EDM, a metallic wire isa wire-burned
8、 cavity. With our own history of continuously fed through arms suspended abovesuccess using the EDM method, we decided the and below the workpiece (Fig. 1). This chargedultimate test would be to cut external spur gears in wire is then guided through the specified tool paththis fashion and use tradit
9、ional gear inspection while cutting its way through the material. Thetechniques to quantify theiraccuracy, process is relatively slow depending on wirediameter, work piece thickness, and machineOur experiment was moreover based on settings. The servo-controlled tool path is quiteneed. The plastic ge
10、ars we had designed for a gear accurate, typical for CNC type machinery. And thedriven lawn sprinkler required unique master benign environment of the EDM machinery, withgears. Lead times for form ground gears were slow feed rates, extremely low forces, very littleunacceptable. With our customers su
11、pport we friction or vibration, and controlled temperaturedeveloped a method of cutting these gears that make even finer accuracy possible. The tool pathachieved the desired shapes on time and within can either be point-to-point or via simple arcs.cost constraints for fine pitch master gears. We Adv
12、anced mathematical curves are not directlythen employed the same techniques to cut a 19 programmable by software; these must betooth 5 DP master gear in order to determine approximated with arcs and/or line movements.possible errors of scale. Profile inspection revealed Both the involute and trochoi
13、dal sections of a gearsimilar accuracy of tolerance was possible for large fall into this general category. Specifiedcoarse pitch gears as for fine pitch. In the following dimensional accuracy and repeatability of the moresections, we will present the methods we employed advanced wire EDMs are on th
14、e order of .0001to achieve this level of accuracy, the inspection data inches. Surface finishes of 16 micro-inch can befrom our work, comparisons with precision hob cut attained through careful selection of machininggears, and possible applications of this method to parameters along with multiple fi
15、nishing skim cutson low power settings.Figure 1 - Wire EDM gear cutting setupGear Cutting With Wire Difficulties with this method of generation areimmediately apparent. By focusing only on theThe wire EDM is primarily a two- involute profile, the trochoidal (or root) area is leftdimensional process,
16、 although the two wire guides arbitrary and undefined. No provision is made forcan follow independent paths allowing slight 3-D undercut even if it is required. One of themodifications. EDM software exists that claims to advantages of a hob cut gear is that any similarcreate a wire path for the spur
17、 involute. The physical gear will fit within the envelope created bysoftware requires standard gear geometry to be , the generating hob. The reason for this is that theinput along with tooth thickness, root, and outside hob removes any possible interfering material indiameters. Approximate arc segme
18、nts are then the root area that may physically interfere withfitted to the involute curve down to the root or to another gear. A majority of non-undercut standardthe base circle diameter, whichever comes first. If gears are not sensitive to this possible trochoidalthe base circle is located above th
19、e root circle, a interference since the standard whole depthstraight radial line is connected from the base provides sufficient clearance and mating teethcircle to the root diameter, and the user has the never reach below the base circle. However, asoption of specifying a fillet radius for the desig
20、ners modify gear geometry to maximizeintersection of those two features (Fig. 2). function or if undercut exists, this area becomes-_, critical through possibleinterference, or weakened?_i _ _ by excessive relief. The mathematical generationof gear teeth must provide not only conjugateaction but als
21、o designed clearance with any matinggear._-_. _:_- - Another not-so-apparent difficultywith theL-_- _-“-_ -_,-_-_=_ “ generation of approximate arcs to the involuteconcerns the nature of the involute itself. With its, _llleT L_ _ ever increasing radius of curvature from the base-Radius J “_b(user I
22、_ circle,the involuteis anything but a trivial curvespecified) J _ fitting exercise. The desirability of makingBase Root01a_eter 01ameter intersecting arcs tangent at their endpointscompounds the problem of fitting these arcs to theTypical E0M_ear Involute involute. Without careful fitting it is pos
23、sible toFigure Z2have considerable error in the approximation, especially in the critical region of the base circle.The trochoidal surface can also be intricate andrequires an equivalent attention to detail in anygenerating curve-fitting scheme.Mathematical GenerationMany texts describe the mathemat
24、icalgeneration of the involute. Buckingham (2)described both polar and Cartesian equations for Figure 4- Optimal curve fitthe involute profile. Point by point development ofthe generated trochoidal region is less welldocumented. However, Khiralla (3) and Colbourne ( and multi-valued) and because the
25、 function that(4) have both published methods to find points on represents a splined series of arc segments includesthe trochoidal curve for any involute rack. They non-linear parameters, this is not the case. Thealso describe the necessary iterative schemes to curve fitting task is difficult but no
26、tdetermine the exact involute form diameter for insurmountable. Numerous general purposeundercut gears. Solution of these equations yield optimization algorithms can be adapted to solvean array of discrete coordinate points that exactly this kind of problem (5). The use of these methodsdescribe the
27、entire surface of the gear tooth (Fig. 3). to solve curve fitting problems is not an exactscience and has sometimes been called an art.With careful selection and tuning of methods, wehave been able to generate splined arcapproximations of the involute and trochoid witharbitrarily specified maximum e
28、rror criteria(Fig. 5).15_i0-_l:evIatIon betweenSpIIned ar_s and InvnIuteFigure 5Figure 3 - Gear surface coordinatesInitial SetupCurve FittingFour external gears were made. TheThe wire EDM tool path is constrained to Diametral Pitches were 32, 36, 40, and 41.follow either straight lines or simple sin
29、gle arc Inspection equipment included a Mahr model 896segments. The involute and trochoid however are gear roll tester and a Zeiss ZMC 550 gearcurves with continuously changing radii of coordinate measurement machine for profile, lead,curvature. The designer might create a tool path and spacing chec
30、ks. The 36, 40, and 41 DP gearswith infinitesimally small linear moves to were EDMd and the 32 DP gear was cut with a 1“maximize the EDMs resolution, but the resulting dia. Grade AA precision hob in order to get a senseNC program would be excessively long and of the relative accuracy possiblewith ea
31、ch method.cumbersome. A more efficient approach would be Two of each gear were made so they could be roll-to allow the machines own software to optimize the tested against themselves to examine close meshedcutting path. A mathematically satisfying curve conjugacy. They were then inspectedfitting rou
32、tine would link approximated arcs with independently on the CMM for absolute mon tangents to the profiles (Fig. 4). The It was felt that roll testing was imperative for wire-machine tool would then follow the nearest x-y cut gears since the cutting process was purelypath to this profile At first gla
33、nce, it would appear mathematical in function. Any local aberration ina simple task to approximate the involute and the cutting or fixturing of the gear that might nottrochoidal curves, in the minimum least squares be detected by the single point of a profilometersense, with splined arcs; however, s
34、ince any arc would be more easily seen on a double flank rollsegment is mathematically non-linear tester.3Discussion of Results purpose ofplastic gear inspection. Both profile andform deviation for these gears were generallyFigures 6, 7, 8, and 9 show profilometry of improved over their hobbed count
35、erpart. Totalthe fine pitch gears as measured on the Zeiss CMM. runeut of these gears was slightly greater than forTotal profile deviation (Ff) for the EDM gears in the cut gear, but further modifications in fixturingFigures 7, 8, and 9 varied between .0001 and .0003 and machine setup should improve
36、 this feature. Atinches, while the profile form deviation consistently present, this method has not reached the samestayed within .0001 inch. The hob cut gear in accuracy as form ground masters, but they costFigure 6 maintained profile deviation between less and can be cut in a week. For certain.000
37、2 and .0003 inches, however total form applications, that can be the deciding factor. Thedeviation also varied by that amount. The EDM coarse pitch gear in this experiment benefited fromprofile traces appear more as straight lines while the lessons learned on the smaller gears. Itthe hobbed profile
38、exhibits waviness. The lead suffered no degradation in tolerances despite an 8xerror on all gears was .0001 inches maximum, and increase in size. This 5 DP gear satisfies thethe adjacent pitch deviation (fp) remained less than criteria for a Class 2 master gear, with similar cost.0002 inches for all
39、 gears. In total runout, the and production advantages over form ground gears.hobbed gear held .0002 inches, while the EDMgears variedbetween.0003and.0005inches. The involute shape is not particularlydifficult for the wire EDM. Any mathematical pathRoll tests of the gears against themselves are that
40、 can be described in arcs and/or lines can bepresented in Figure 10. A comparison trace of 32 generated with similar accuracy. Tip relief, rootDP form-ground master gears rolled against each relief, and non-involute tooth forms can beother is included as reference. Scale is identical for generated w
41、ith very little added complexity or cost.all traces at .0003 inches per large division. These The ability of cutting two separate shapes at thetraces were taken when the gears were new same time with the upper and lower cutting armswithout running them in lightly first. Later traces open other possi
42、bilities as well. We have alreadywere more uniform. Unfortunately they were not produced bevel gears using Tregoldsretained. We believe that light running-in of approximation of the equivalent spur gear formEDMd gears is desired to polish the matte surface (Fig. 12). Low helix angle gears can be acc
43、uratelyand de-burr edges, cut with only slight ove_cutof the root area at oneA Coarse Pitch Example end of the gear. Even crowning can beapproximated. In many ways, the use of thisA question remained whether EDM errors process is only limited by the users cleverness.would be magnified by scaling the
44、 generationprocess for coarse pitch gearing. We decided to _wire-cut a 5 DP 19 tooth gear and concentrate onimproving runout and optimizing the curve fit.This gear would be roughly 8x the size of thepreviously cut fine pitch gears. We generated 15arcs for this involute with a maximummathematical err
45、or of +/- 15 micro-inches. Thematerial was through-hardened 420 stainless steel.A complete profile inspection was done for eachflank of this gear. A representative sample ofresults is given in Figure 11. Total profile and formdeviation stayed within .0001 and .0002 inches,and total runout was held b
46、etween .0002 and .0003inches. Spacing and lead were both held to .0001inches. In effect we were able to improve the Figure 12- EDMd bevel geardimensional characteristics of the larger gear byimproved cutting methods and closer mathematical Further investigation needs to be done onapproximations. Thi
47、s wire-EDMd gear was the production and effect of the EDM process.ultimately used to monitor a production run of Since the generating method is new, currentthread ground spur gears, standard inspection criteria may not adequatelycover all possible production errors. SimplyConclusions specifying maxi
48、mum tooth-to-tooth and totalcomposite error would not be sufficient. It wouldThe wire EDM process is suitable for also be interesting to investigate the effect of EDMproducing accurate spur gear shapes. These early metallurgy on life, wear, pitting etc. For instance,fine pitch gears were adequate fo
49、r their intended hardening with EDM is achieved with through4hardened steels, but the cutting process underwater can produce an additional hard thin surfacelayer exceeding 70 Rockwell C. Whether this effectcan be significant for gears is unknown.Mathematically describing the total gearshape can be extended to other generation methodsas well. The latest CNC equipment can follow thesame type of path as the wire EDM. NC dresserscan directly form grind spur and helical forms.This type of generation is bound to become moreavailable as the
