鼓形齿轮一章 内容更新crown gear chapter（可编辑）

鼓形齿轮一章 内容更新crown gear chapter（可编辑） 鼓形齿轮一章 内容更新crown gear chapter CROWNED MOLDED PLASTICS GEARS A NEW SOLUTION TO AN OLD PROBLEM Copyright July 22,2004 by ABA-PGT, Inc CONTENTSPage 1 INTRODUCTION Page 1 MISALIGNMENT of GEAR TEETH Page 2 PROBLEMS CAUSED by MISALIGNMENT Page 3, 4 SOURCES of MISALIGNMENT Page 5 BENEFITS of CROWNING Page 5 CROWNING of MACHINED GEARS Page 5 CROWNING of MOLDED PLASTICS GEARS Page 6, 7 DESIGN of CROWNED GEARS Page 8 SIZE and PITCH LIMITATIONS Page 8 CROWN INSPECTION Page 9 INSPECTION DATA ? MACHINED STEEL AUTOMOTIVE GEAR Page 10 INSPECTION DATA ? PLASTICS GEAR MOLDED at ABA-PGTEDITOR’S NOTE: Many of the sketches, especially those depicting misalignments, are exaggerated to clarify a point PAGE 1 INTRODUCTIONThe ol d problem is the common condition of misaligned mating parallel-axis spur and helical gear tooth s urfaces, as described below. The solution, new to molded plastic gears but old in machined gear practice, is the modification of gear flanks by making them full thickness at mid-face-width and tapering them to each edge. See figure 1. This modification, extending over the full height of the gear tooth, is referred to as crowning. The result is a crowned tooth or gear, not to be confused with o ther references in gear terminology Fig 1MISALIGNMENT of GEAR TEETH Instead of the ideally parallel gear rotation axes, the axes may be intersecting in the same plane, or skew in different planes, or a combination of both. See figure 2 for illustrations relating to spur gearsFig 2PAGE 2PROBLEMS CAUSED by MISALIGNMENT The major problem associated with gear tooth misalignment is the concentration of contact to a narrow strip at one end of the gear face width. The load transmitted through this narrow width gains support from adjacent material on only one side of the contact area, resulting in high bending stressesSee figure 3. These high stresses may lead to the start of a crack which progresses across the face width until a major portion of the tooth breaks. Also, the concentrated area of contact may initiate rapid tooth surface wear with the wear detritus further accelerating surface failure In the case of helical gears, the localized area of contact due to misalignment reduces the helical continuity of contact. This reduction effectively eliminates the ‘smoothing’ action in motion transmission expected from helical gearsFig 3 PAGE 3 SOURCES of MISALIGNMENT Molded plastic gears are commonly used with molded plastic housings, often of a fiber reinforced material. This process, with its often unpredictable distortions, makes it difficult to achieve and maintain a high degree of accuracy in gear alignment features. The same may be true in die-cast metal housings, even if less so with secondary machined bearing openings. All these housings are subject to further distortions under changes in temperature or the passage of time. See figures 4a 4bFig 4a Fig 4b Also, molded plastic gears are most likely to be supported in sleeve bearings with relatively large clearances in contrast to the small clearances in ball bearings. If the journal and bearing diameters are produced by molding, with their sizes controlled by typical tolerances, the resulting clearances may permit significant misalignment. As shown in figure 5, the misalignment results from the combination of the clearance and the axially offset and opposing forces, such as those on compound gears Fig 5 PAGE 4 In some plastic gear assemblies, the gears are supported by small diameter metal shafts, either fixed to the gear and rotating, or fixed to the housing and non-rotating. With either simple or cantilevered types of supports, there are further opportunities for gear misalignment. This results when there are forces large enough to deflect the shafts and when the gears are positioned on the high slope portion of the shaft deflection curve, as shown in figures 6a and 6b. With slender molded plastic shafts in place of metal, the deflections may be even greater. Cantilevered support may also be accompanied by a compliant structure, as shown in figure 6c, where it is shown without accompanying shaft deflection Fig 6a Fig 6b Fig 6c One type of gear assembly is particularly sensitive to misalignment due to deflections under load The planet gear in planetary gear arrangements is often supported by a cantilevered shaft, which may be of limited diameter to reduce bearing friction losses. The web portion of the planet carrier, connecting the planet shafts, may be of reduced thickness to save space. The combined deflection of these features under load, pictured in figure 7 contributes to gear mesh misalignmentFig 7 Then the gears themselves may have tapered faces, figure 8a, which will misalign and/or tapered bor es which will allow movement under loadDistortion in the web creates wobble of the gear tee th to both sides of center, figure 8b Fig 8a Fig 8b PAGE 5 BENEFITS of CROWNING The use of crowned gears can improve the adverse conditions imposed by tooth misalignmentContact will be shifted away from the end of the tooth to some central location along the tooth flank. Instead of contact on a nearly sharp edge, over a narrow width at best, contact will take place along a gradually curved surface over a greater width. Support to the applied tooth load will come from this greater contact width and also from adjoining material on both sides of the contact center. Wear at the broader contact area will progress more slowly. If helical, more of the helical gear action will be maintained, often preserving the helical gear noise reduction. Refer back to figure 3 There may be a further, if indirect, benefit of crowning. The application of crowning will permit a greater tolerance of misalignment in the product assembly. This relief may often be converted into manufacturing cost reduction CROWNING of MACHINED GEARS There is a long standing practice of crowning machined steel gears. The modification of metal tooth surfaces is generally accomplished by secondary operations Crowned gears have been used in a great variety of gear transmissions, including automotiveThere is a need even when the transmission housing is of rigid metal construction with accurately machined features for mounting ball bearings with negligible clearances. In applications associated with molded plastic gears, the need is greater CROWNING of MOLDED PLASTICS GEARS The recent introduction of crowned molded plastic gears has required significantdevelopment in new tooling and processing methods. The new tooling includes the construction of the mold cavity with varying cross-section, smallest at the ends and largest at the center of the face width The new processing covers the ejection of the molded gear while preserving the modified tooth surfaces. This requires the optimum control of the ejection timing so as to take advantage of the initial shrinkage and the limited elasticity of the still hot plastic material. This researched process is readily available for spur gears and some helical gears. Except for a moderate increase in the cost of tool construction, there is no significant increase in molded gear costPAGE 6 DESIGN of CROWNED GEARS Crown is commonly specified by the height of the circular arc spanning the width of the gear tooth in a direction perpendicular to the tooth surface, see figure 9Fig 9A simple equation may be used to determine the height of crown needed: 2 F h ------ C 3 where: h height of the crown as a circular arc normal to the tooth surface,Crequired to maintain contact in the central third of the face width, see figure 9F face width spanned by the crown? angle of misalignment, in radians As an example, for shaft support misalignment of .005 inches over a length of 1.25 inches, giving a value to the angle, ?, of .0051.25 .004 radians. For a face width, F .375 inches, therequired height of crown, h 2 x .375 .0043 .0010 inches C A tolerance, ?olh , should be applied as an addition to the design value of crown height. A Cproposed tolerance may be calculated from the equation:Tolh .0002 + .20 x h inchesC C For the above example, the tolerance would be: Tolh .0002 + .20 x .0010 .0004 inches C PAGE 7 The full required crown is generally applied to only one of the two mating gears, preferably to the gear which will provide the greater shrinkage clearance to assist in the ejection of the molded part If the two gears are from materials with similar shrink rates, this would be the larger gear. If the required crown height is too large to be accommodated in the molding of a single gear, it may be divided as needed between the two mating gears The preferred zone of contact is the central one third of the face width. See figure 10Fig 10PAGE 8SIZE and PITCH LIMITATIONS If the gears have very narrow face widths, there is no significant benefit from adding crowning. A tentative lower limit on face width in inches is 2.5 divided by the diametral pitch in millimeters, 2.5 times the module. There is no upper limit, with the larger face width most likely to require greater crowningAs to gear diameter, there is again no upper limit. The lower limit is based on the shrink rate of the gear material and other factors which will influence the ease of molded part ejection. For higher shrinkage material such as un-reinforced acetal or nylon, one-half inch 12.7 mm pitch diameter is a tentative lower limit. This lower limit is likely to be revised as experience is expandedThe pitch or module of the gear has to be considered before specifying crowning. There is no upper limit on how coarse the pitch. When it comes to how fine the pitch, restrictions apply that relate to the methods of mold cavity processing and, in some cases, to the fillet design of the gear tooth. A tentative limit is the diametral pitch of 32 or the module of .80. This limit, too, is likely to be revised with greater experienceThese limits are based on experience with spur gears. They may be applied to helical gears with helix angles up to, say, 30 degrees. However, other issues relating to tool processing and part ejection may, with further experience, introduce tighter limitsCROWN INSPECTION Inspection of the crown, for shape and height, is generally made on elemental gear inspection equipment, such as supplied by the M & M Company. The measuring probe follows the gear surface at the inspection diameter from one face to the other. On spur gears, its path is a straight line. On helical gears, the gear is rotated as specified by the gear design and the path of the probe relative to the rotating gear is a helix. This is typically applied to four equally, or nearly equally, spaced teethThe results of this inspection are in the form of magnified plots of the measured surfaces. The shape of the crown is apparent in each of these plots and the height may be read from the enlarged scale. In addition, the height values are typically supplied in printed form. See figures Figure 11 represents measurements made on machined steel automotive gears. The printed values show crown heights of approximately .0003 inches .007 mmFigure 12 represents measurements made on a plastics gear molded at ABA-PGTThe values range from .0014 to .0017 inches, which handily met the original tolerance specification of .0015 +/- .0005 inches PAGE 9 Figure 11 Inspected crown on a machined steel automotive gear