1、92 FTM 11New Findings on the Loadingof Plastic Spur Gear Teethby: Jean Bessette and Henri YelleEcole Polytechnique de Montr6alAmerican Gear Manufacturers AssociationTECHNICAL PAPERNew Findings on the Loading of Plastic Spur Gear TeethJean Bessette and Henri YellePEcole Polytechnique de MontrealThe s
2、tatements and opinions contained herein are those of the author and shouldnot be construed as an officialaction or opinion of the American Gear Manufacturers Association.ABSTRACT:Plastic gearsoften breakat the tip of thetooth. To the knowledge of theauthors, there is no satisfactory explanationoftha
3、t breakage mode yet. An hypothesis put forward in this paper to explain the tooth breakage at the tip is theinterferenceon the back of the tooth. It is reported here how interferenceon the back of the tooth has been verifiedexperimentally. Then it is explained how CAD software and plastic gear calcu
4、lating software have been used tosimulate the kinematics of a gear pair to predict and to localize the interference on the back of the tooth. The resultsobtained were then used with a finite element analysis to show that the maximumtensile bending stress shifts from theroot of the tooth to a point a
5、bove the pitch circle when there is interference on the back of the tooth. The conclusion isthat the hypothesis of theback interferencecanrealisticallyexplainthe particnlarfailure ofa plastic gear tooth at the lip,but it remains to refine the calculations to find more precisely the values of the loa
6、ds that are applied on the tooth.Copyright 1992American Gear Manufacturers Association1500 King Street, Suite 201Alexandria, Virginia, 22314October, 1992ISBN: 1-55589-591-3NEW FINDINGS ON THE LOADING OF PLASTIC SPUR GEAR TEETHJean Bessette, Graduate StudentHenri Yelle, ProfessorEcole Polytechnique d
7、e Montreal, Dept. of Mechanical EngineeringP.O. Box 6079, Station “A“, Montreal (Quebec) H3C 3A7Introduction :Tooth profile and tooth proportions represents a real gear pair in mesh withoutfor plastic gears are essentially the same load. The left hand side gear is theas those used for metal gears. H
8、owever, driver gear and the direction of rotationbecause plastic materials are much less is as indicated. It is seen in figure 1rigid than metals, tooth deflection permits that the driving tooth “a“ shows a crack onthe contact between teeth to extend outside its working flank that is initiated wellt
9、he line of action, thereby spreading the above the root circle. A similar crack canload between more tooth pairs than it is be seen also on the following tooth “b“.theoretically calculated 1,2. Although Eventually, these cracks will cause aload spreading has the beneficial effect of failure of the t
10、ooth as shown in figure 2.reducing the stress on each tooth pair, it That type of failure is observed toocauses interference on the working systematically to be attributed to a randomprofiles, noise and wear. In plastic process.gears, wear acts as a regulating agent byreducing the length of contact
11、outside the Figure 3 is an outline of the engagingline of action 3. As the gears run, wear tooth pairs a-a and b-b of figure I. Theprogresses, redistributing the load among line of action, the center line and thetooth pairs; eventually, an equilibrium pitch circles of both gears have been drawnstate
12、 is reached between tooth deflection on figure 3 as well as the position of theand wear. If the load applied on each cracks on teeth “a“ and “b“; it is evidenttooth pair is not too high to cause tooth that the cracks on the tooth flanks arefailure by a crack, the gear pair will initiated above the p
13、itch circle. Oneeventually fail by wear. On the other hypothesis to explain such a failure ishand, if the load redistribution is such that the back (the non working profile) ofthat the tooth pair is too heavily the driving tooth “a“ comes in contact withstressed, the tooth will break by the the non
14、working flank of the driven toothpropagation of a crack, thermal softening, “b“. Then, the tip of tooth “a“ is bentpitting or other gear failure mode. by two opposite forces as it is shown infigure 3. One force is the normal load WnIn metal gears, tooth breakage is acting along the line of action; t
15、heassociated with the root fillet section; second, Wn, is applied on its back bybreakage at other portions of the tooth are tooth “b“. It is argued here that thiscalled random breakage 4. With plastic bending moment induces, at a section abovegears however, in many cases it is observed the pitch cir
16、cle, stresses high enough tothat the tooth breaks by a crack that break the tooth at that section. In thestarts at a point above the pitch circle following, this contact on the back of the5,6. A typical example of such a tooth will be called back interference.breakage is shown in figure 1 thatIAccor
17、ding to literature 7, back 5- the rig is put into operation for ainterference is possible in excessively few minutes and then stopped toloaded metallic q_arsj However, in the verify if there is any transfer ofcase of gears made of polymeric materials, the marking blue. This is repeatedeven without e
18、xcessive loading, much larger at several speeds to make sure thatstrains may act favourably in drawing there are no undesirable dynamicnearer non working profiles, effects that may cause the rig andthe gears to vibrate in rotation soThe objective of the study reported in that the teeth leave contact
19、 from thethis paper is to verify experimentally and working profile to make contact onanalytically that hypothesis. The the non working side,procedure followed is first to verifyexperimentally that teeth “a“ and “b“, 6- finally, the gear pair is run underfigure 3, make contact by their non working f
20、ull load for a certain time andflanks, under normal operating conditions, inspected for an eventual contact onThis part of the work is qualitative and it the non working flanks.also serves to evaluate the effect of theload, the backlash, and the tooth stiffness The results are summarized in table i.
21、(temperature). Then, a CAD (Computer A first examination shows that all theAssisted Design) software is used to tests at low load and no speed did notlocalise and quantify the positions of the cause back interference, except test N 1forces on the back of the tooth and the for which the backlash is t
22、he smaller. Itangles at which they are applied. Finally, is observed also that test N 1 reveals ausing the values previously obtained, a contact on the back of the teeth at allcoarse finite elements analysis is carried loads or speeds. Figure 4 is a photographout to verify that such a loading can ca
23、use of the gears of the test N i. The gear onthe breakage of the tooth at a section the right hand side is the driver gear thatabove the pitch circle, has been originally marked with the blue;the left hand side gear is the driven oneExperimental Verification : on which the blue has been transferred
24、byDuring a regular gear testing program, contact. That figure shows clearly a heavyseveral polyethylene and nylon gears broke contact between the two non working flanks.by crack initiation at a position above the The contact occurs all across the face atpitch circle. Although we suspected the two ra
25、dii, on each side of the pitchteeth to come in contact by their back, a circle.careful examination of the gears did notrevealed the evidence of such a contact, Using a medium backlash of 0,176 mm,probably because it was too light to leave at low load and any speed, we observed backa trace. Therefore
26、, to enhance the interference in test N 3, but not in testphenomenon, we used the simple technique of N 2 neither in test N 4. But at highthe marking blue. The marking blue was loads and speeds, gears of test N 3 madedeposited on the non working flanks of the contact in the back while those of test
27、Nteeth of the driving gear; any contact of 4 did not. A similar behaviour is observedthis side of the teeth will show as traces for the test N 5 and 6 that were made withof marking blue that is transferred to the a backlash of 0,202 mm. Figure 5 is anon working flank of the driven tooth, photograph
28、of the gear pair used for thetest N 3; in that figure, the driver gearThe experimental verification has been is on the left and the driven one on theconducted on a four square gear testing right. Compared to figure 4, the contactbench using spur gear pairs of 33 and 34 is much lighter and it does no
29、t spreadteeth having a module of 2,116 mm and a across the face width, indicating a certainpressure angle of 20; the 33 teeth gear bow in the gear teeth. As in figure 4,acted as the driving gear in all cases, back interference seems to occurs above andThe procedure used for the verification is below
30、 the pitch circle; this can be seen atthe following: the two lighter spots on one of the driventooth originally marked with blue.i- the gears are mounted on the shaftsof the testing rig, While a backlash of 0,151 mm easilyprovoked back interference, 0,176 mm or2- a small torque is applied, without 0
31、,202 mm backlash did and did not producedthe gear running, to measure the the same. But the gears we used for thosebacklash. The backlash is measured tests did have a relatively largeat four points around the gear pair, eccentricity variation. Because of that,the test run at 0,176 mm and 0,103 mm3-
32、the marking blue is then applied on backlash may, at certain points around thethe non working flank of all the gears, have quite less play between theteeth of the driving gear, teeth than measured. Unfortunately, thathas been notice after the tests; it was4- the gears are rotated by hand to then too
33、 late to perform eccentricityverify that there is no transfer of measurements. However, measurements madethe marking blue, on other similar gears showedeccentricities varying between 0,051 mmand line of action. The Youngs modulus of0,i02 mm. That means that during the plastic materials varies with t
34、emperaturetests, the backlash may has been as low as and loading rate. In the present tests,0,050 mm or as high as 0,305 mm, and in the the loading rate is constant and thereforetests at 0,151 mm backlash, it could have its effect has been neglected. As far asbeen still less. These results emphasise
35、 the temperature is concerned, its effect isthe important role the backlash plays and very difficult to evaluate; in fact, theexplain, with the variation of the temperature of a gear teeth varies mucheccentricity, the certain inconsistency of from the root to the tip and from thethe observations; fo
36、r the gear pair surface to the centerline. Also there aregeometry tested, a backlash of 0,151 mm no known reliable models that permit toseems to be a lower boundary below which calculate its distribution. Therefore,one can expect to make easily contact on because of that, we neglected its effectthe
37、back of the tooth, and we assumed the Youngs modulus to beconstant at 2.4 GPa for both gears.In conclusion of this section, one cansay that there is evidence of contact of Assuming that the teeth rotate as athe teeth on their non working side. That rigid body on the gear mesh 3, thosecontact occurs
38、at moderate loads and deformations were used to calculate, pointrepresentative values of the backlash (the by point along the line of action in thevalue recommended for plastic gears is i0 meshing zone, the new relative positionspercent of the module). Variations in the the gears would assume. The b
39、ackobservation are attributed to variations in interference is determined by the softwarethe backlash due to the eccentricity of the and visual examination. Visually, backgears that was not controlled. In any interference shows as a superposition ofcase, this emphasises the important role the teeth
40、(figures 6 and 7).that the backlash plays in the meshingcinematic of plastic gears. As mentioned in the previous section,it has been observed that the interferenceCad Simulation of the Back Tooth on the back occurs at two positions on theInterference : tooth flank, one above the pitch circle andAfte
41、r the first part of the work, it one below. In the gear mesh simulationappears quite obvious that plastic gears with tooth deformation, we also observedmay deform enough to cause interference on interference at those two positions. Thisthe back of the tooth. But, to ascertain is shown in figures 6 a
42、nd 7 for athat this interference is responsible for transmitted normal load Wn of 28 N/mm andbreakage of the tooth at a section near the a backlash of 0,126 mm. In both figures,tip, it is necessary to perform stress the driving gear is at the top and thecalculations. For this, in turn, it is rotatio
43、n is as indicated.necessary to know the magnitude of theforce to apply on the back of the tooth, In figure 6, back interference appearswhere to apply it and at which angle. The between teeth “a“ and “b“ at the tip ofobjective of this section of the work is to tooth “a“ and near the root of tooth “b“
44、,define those variables, at the beginning of the tooth palrengagement. At that position, the bendingThis part of the work has been done imposed to tooth “a“ by the normal load andwith the aid of an in house CAD software the load on its back is such that it shallthat permits to draw a gear pair in me
45、sh on generate a crack on the non working flankthe computer screen and to rotate it by of tooth “a“. But, referring to figures 1small angular increments in controllable and 3, we see that it is not the case.relative position. That software permits Therefore, we conclude that although thereto make an
46、 exact model of the gear is interference at that position, it is notcinematic knowing only the number of teeth, the critical one and it has not beenthe tooth proportions, the pressure angle studied any further.and the center distance. After havingbuilt such a model with the geometry of our Figure 7
47、shows the other positiongears, we verified that, for a perfect where interference occurs. At thisgeometry, without eccentricity neither any position, tooth “a“ is going out oftooth deformation, a backlash as small as engagement, the normal load Wn is applied0,025 mm permits to operate that gear pair
48、 at its tip and the interference, thatwithout back interference, occurs at a point below the pitch circle,applies another load called Wn as shown.To simulate a more realistic gear This type of loading corresponds to figuresoperation however, we introduced the tooth 1 and 3 and will tend to open a cr
49、ack ondeformations in the model. To do so, we the working profile of tooth “a“. Thiscalculated the plastic gear tooth position has been retained as the criticaldeformations with the aid of another one and analyzed.software 8. Starting also from the geargeometry, this second software calculates Using this CAD tool to detect thethe deformation of each tooth in mesh event of back interference below the pitchsimultaneously, at any position along the circle, we made a series of simulations inwhich we varied the load and the backlash. 2,116 mm module and 20
