1、91 FTM 14vThe Effect of Thermal Shrink and Expansionon Plastic Gear Geometryby: Roderick E. Kleiss, Plastic Gear Consultant,vAmerican Gear Manufacturers AssociationTECHNICAL PAPERThe Effect of Thermal Shrink and Expansion on Plastic Gear GeometryRoderick E. Kleiss, Plastic Gear ConsultantTheStatemen
2、ts andopinions contained hereinarethoseof theauthorandshouldnotbe construedasan official actionoropinion of the American Gear ManufacturersAssociation.ABSTRACT:A significant characteristic of plastic gears when meshed with steel gearscan be the differences in thermal expansionbetween the two materia
3、ls. If a particular gearmesh is expected tooperate satisfactorily over a wide thermal range, thevariations in mesh geometry due to temperaturemust be taken into account. Quiteoften gears of differing expansionsare put into a housing with yet another thermal expansion rate. All of these variable para
4、meters can pose vexingproblems tothe plasticsgeardesigner. Thispaperwill presenta straightforwardway to considerthe shrinkageof plastic Agears both in molding and in operation.Copyright 1991American Gear Manufacturers Association1500 King Street, Suite 201Alexandria, Virginia, 22314October, 1991ISBN
5、: 1-55589-611-1THE EFFECT OF THERMAL SHRINKAND EXPANSION ON PLASTICGEAR GEOMETRYRoderick E. Kleiss, Plastic Gear Consultant3006 Edgerton StreetLittle Canada, MN 55117i. Introduction gears can be properly designed orinspected. This paper will examine thebehavior and governing equations forOne of the
6、fundamental differences this type of application. In summary,between plastic and metal gears is their the reader will be able to calculate thei_ differing rates of thermal expansion. An actual gear geometry of the mold thatunfilled engineering plastic such as produces the finished part as well asnyl
7、on or acetal will have four to five determine the change that will occur intimes the thermal expansion coefficient the finished part due to operating atof steel. If the gear mesh is expected elevated temperatures.to operate at elevated temperatures, thedesigner must account for this expansion 2. The
8、 Nature of Plastic Shrinkor risk interference at hightemperatures or low contact ratio at low A basic understanding oftemperatures. Historically, this is thermoplastic shrink of the part duringachieved by altering backlash and root the cooling cycle of the molding processclearance of the mating pair
9、 to will be of help in understanding itsaccommodate expansion, thermal expansion when operated atelevated temperatures. In plasticsSuch an approach is perfectly terminology the term “shrink (s) refersacceptable for gears with similar to the ratio of the expected reductionexpansion rates. However, if
10、 a plastic of the plastic part dimension as thegear with a relatively high thermal part solidifies in the mold and cools toexpansion is in mesh with a steel gear room temperature to the original moldat an elevated temperature, the method dimensions.(1) The first question mustwill cause improper mesh
11、ing action. The concern the nature of thermal shrink.higher thermal expansion rate of the Much is written about the anisotropicplastic gear will cause its basic gear behavior of engineering thermoplastics.geometry to change much more In the molding process material shrinkdramatically than the steel
12、gear. This will vary with cross sectional area,change in geometry due to thermal cooling rate, fiber orientation, moldingexpansion is very similar to thermal temperatures and pressures, and othershrinkage during the cooling cycle in variables. With the software toolsthe mold. And the result will be
13、gears available to the molder, models can beoperating with dissimilar base pitches, constructed to predict the process whichwill best fill the mold cavity andThe effect of thermal shrink and result in a properly molded part. Butexpansion on plastic gear geometry must these models do not as yet addre
14、ss thebe thoroughly understood before such very small but critical area of theinvolute. The co_on practice at presentis to assume isotropic radial shrinkage c- orlg_notfrom the axis of the gear. A simple Ditch _o -straight sided cogged wheel can be used shrunken -_to describe this isotropic shrinkag
15、e, base di_ /_or iglna_? shrunken _ base d_a.Figures 2 and 3 show that everydimension of the gear is shrunkenuniformly. The only thing that remainsunchanged is the nu_er of teethFiQure i With isotropic shrinkage, only anglerelationships remain unchanged. SinceIsotropic shrinkage assumes that the dia
16、metral pitch of the gear isdefined to be We nu_er of teeththe rate of shrinkage will be the samebetween any two points on the surface of divided by the pitch diameter, thethe object. In figure 1 the origin is diametral pitch of the cavity would be _the axis of the cogged wheel and theshrinkage is id
17、entical from any point on Pn = N*(l-s)/Dpthe surface to that origin. The shrunkenshape has a large displacement of its where s is the shrink rate inoutside diameter to the origin and a inches/inch. For isotropic shrinkage thecorrespondingly small displacement diametral pitch of the mold would varyac
18、ross the face of the cogged tooth, inversely with the plastic shrink rate.Isotropic shrinkage for an involute geartooth from a mold cavity is identical in The same would hold true for theisotropic the_al expansion of Wenature, molded gear in service. In fact, thebasic gear parameters listed in table
19、 1oriQin_ _ /- 0riQino would vary as noted between molded gearpltch di_, I /base _i0 and mold cavity. Note that the moldedgear is defined fund_entally and thel_ cavity is expanded by the shrink rate._ty)Gear CavityNo. of teeth N NDiametral pitch Pn Pn*(l-s)Pitch Die. Dp Dp/(l-s)9eor) circular pitch
20、pc pc/(l-s) Base pitch pb pb/(l-s) q _,_ “)_ Circ. Tth thk tn tn/(l-s)pressure angle phi phi “ Base diameter Db Db/(l-s)/_“ “ _i“ _ Lead L L/(l-s)_ / _!_! .? Table 1The pressure angle in Table 1shrunken _3 _ _ shrunken remains constant. This is due to thep_tch di_ b_se _i_ fact that the pitch diamet
21、er wasselected as the quantity to expand byF;gt_r e _ the shrink factor. If the pitch diameterwere held constant, one would have to Exampleincrease the cosine of the pressureangle by the shrink rate to generate the Consider the example of a 32cavity geometry. This is due to the fact tooth, 16 DP sta
22、ndard carbon steel gearthat pitch diameter and pressure angle intended to mate with a 64 tooth nylonare not attributes of the gear itself 6/6 gear at an operating temperature ofbut functions of the generating rack 200F. If the carbon steel gear had beenrequired to produce the gear. By cut with a sta
23、ndard 16 DP hob and itsaltering either the pressure angle or coefficient of thermal expansion werethe pitch diameter, the generating rack 6.7E-6 in/in/F, then the governingis properly expanded to produce the geometry based on the metal gear atexpanded shape. 200F would beMetal Pinion Nylon3. Mesh an
24、alysis of thermally expanded GeargearsNumber of teeth 32 64For the present state of the art, 20 deg Pitch diao 2.00174 4.00348plastic gears operating at elevated Diametral Pitch 15.9861 15.9861temperatures are assumed to expandisotropically in exactly the same manner Pressure Angle 20 20as they are
25、assumed to shrink from the circ. tooth .09826 .09826mold. For an unfilled plastic gear thisexpansion rate may well be four to five thk (in.)times the expansion of a steel gear it Outside dia.(in.) 2.12685 4.12859is intended to mesh with. This presents Root Dia.(in.) 1.84536 3.84571the designer with
26、a problem that he maynot have encountered with any other gear If the nylon gear has a thermalmaterial. In order to design a pair of expansion coefficient of 50xE-6 in/in/Fgears that mesh correctly, the designer then its base pitch would have grown bymust produce three distinct gear .00119 inch from
27、ambient conditionsgeometries - mold cavity, molded gear at while the metal gear with an expansionroom temperature, and molded gear at rate of 6.7xE-6 in/in/F will expandoperating temperature. He must also only .00016 inches in base pitch. Ininsure that at least adequate meshing order to make the pla
28、stic gear that_- occurs at any expected transitory would expand to the above geometry ittemperature, is required to increase its diametralpitch while decreasing its toothThe traditional method of thickness and its radial features.describing a gear by the rack. that would However, by converting its o
29、peratinggenerate it becomes a clumsy device with geometry into the base pitch parametersthermally expanding plastics. A more of Table i, one can adjust everystraightforward approach is to define variable dimension by the samethe gear in terms of its basic physical expansion factor, and adjust moldge
30、ometry and expand or contract this dimensions for expected shrinkage atgeometry by the appropriate shrink or the same time. In the above example, ifexpansion factors. There are nine basic the nylon shrink (s) were .017 in/in,variables needed to describe the actual then Table 3 describes the proper b
31、asicgeometry of a gear tooth (3). gear geometry of the mold cavity, theambient gear as molded, and the gear atI. number of teeth its operating temperature2. Base circle diameter Gear as3. Base circular tooth thickness Gear at Molded Mold4. Lead and hand of helix5. Outside circle diameter 200F _70F)
32、Cavity6. True start of involute form diameter Coefficient 1 0.9936 .9936*7. True end of involute form diameter 1.01729(due to tip rounding) Number of teeth 64 64 648. Root circle diameter Base circle dia. 3.76204 3.73796 3.801519. Face width Base circ. pitch 0.18467 0.18349 0.18666Base circ. 0.14841
33、 0.14746 0.14997Each of these attributes is tth thkdirectly affected by shrink except for Outside circle 4.12859 4.10217 4.17190the number of teeth and the hand of the dia.helix which remain constant. The pitch Root circle dia. 3.84571 3.82110 3.88606diameter at which the gear meshes with (for refer
34、ence:its mate should be calculated from the Diametral Pitch 15.9861 16.0891 15.8155physical geometry at the expected Standard Pitch 4.00348 3.97786 4.04665)operating temperature. This approach dia.removes the confusion of inverselyproportional diametral pitches or other Table 3confusing terminology.
35、Formulas for converting to basecircledimensionsare as follows: rDb = Dp*cos(phi)TTb = (TTg/Dg + tan(phi) -phi) * DbThis author treats the mold cavityas if it were an external gear, eventhough the cavity itself is internal.Treating it as an external gear allowsan immediate correlation between thecavi
36、ty and the plastic gear that itproduces.SummaryThe methods described above willaccurately describe molded partgeometry for isotropic shrinkage andthermal expansion. For properlydesigned unfilled plastics, isotropicshrinkage is a good approximation. Butexperimental investigation needs to bedone on mo
37、lded part geometry in non-ambient environments. Materialproperties as well are much affected bytemperature and duration of load, andstandard published data on plasticmaterial properties do not relate tothe very short term cyclical loadingthat most plastic gears encounter.REFERENCES(i) Designing With Plastics, HoechstCelanese Corp.(2) Irving Laskin, Unpublished papersand letters on plastic geargeometry(3) C. Kent Reece, An Approach to theDesign of Spur and Helical Gears,SAE Technical Paper #881293
