directgeardesignforspurandhelicalinvolutegears-外文文献(编辑修改稿)

directgeardesignforspurandhelicalinvolutegears-外文文献(编辑修改稿)内容摘要：

essure angle is a gear meshparameter and it cannot be defined for one separate gear. (1)(2)(2a)(3)(4)(4a)(5)(5a)(5b)(5c)Figure 2—The involute tooth parameters’ definition.Figure 3—The involute mesh parameters’ definition.(6)(7)(8)(9)(10)Page 30 35 8/1/02 12:53 PM Page 32The center distance isaw= db1 • (1 + u)/(2 • cos(αw)) db1= aw• (2 • cos(αw))/(1 + u) The contact ratio (for spur gears and for helicalgears in the transverse section) isεα= z1• (tan(αa1) + u • tan(αa2) – (1 + u) • tan(αw))/(2 • π). The profile angle in the bottom contact pointmust be larger than or equal to zero to avoid involute undercut:for the pinionαp1= atan((1 + u) • tan(αw) – u • tan(αa2)) ≥ 0, for the gearαp2= atan((1 + u) • tan(αw)/u – tan(αa1)/u) ≥ 0. The axial contact ratio for helical gears isεβ = z1•φ1/(2•π) where φ (in radians) is the angular shift betweenthe opposite transverse sections in the helicalmesh (see Fig. 4), and φ = (2 • bw) • tan(βb)/db, where bwis the width of the helical mesh and βbisthe helix angle on the base circle.The fillet profile must provide a gear mesh withsufficient radial clearance to avoid tipfillet interference. The fillet also must provide necessary toothbending fatigue resistance and mesh stiffness. Thedirect gear design approach allows selection of anyfillet profile (parabola, ellipsis, cubic spline, etc.)that would best satisfy those conditions. This profileis not necessarily the trochoid formed by the rack orshaper generating process. Tool geometry definition is the next step indirect gear design. This will depend on the actualmanufacturing method. For plastic and metal gearmolding, gear extrusion, and powder metal gearprocessing, the entire gear geometry—includingcorrection for shrinkage—will be directly appliedto the tool cavity. For cutting tools (hobs, shapercutters), the reverse generating approach “gearforms tool” can be applied. In this case, the tooling pitch and profile (pressure) angle are selectedto provide the best cutting conditions. Area of Existence of Involute GearsFigure 5 shows an area of existence for a pinionand gear with certain numbers of teeth z1, z2, andproportional top land thicknesses ma1, ma2(Ref. 2).Unlike the zone shown in Figure 1, the area of existence in Figure 5 contains all possible gear binations and is not limited to restrictions imposed by agenerating rack. This area can be shown in proportional base tooth thicknesses mb1– mb2coordinatesor other parameters describing the angular distancebetween two involute flanks of the pinion and gearteeth, like αa1– αa2or ν1– ν2. A sample of the areaFigure 4—The angular shift of the transverse sections for a helical gear.Figure 5—The area of existence for the gear pairz1= 14, z2= 28.Figure 6—Involute gear meshes: 6a, at point A of Figure 5 (αwmax= 176。 , εα=)。 6b, at point B of Figure 5 (αw= 176。 , εαmax= )。 6c, at point C ofFigure 5 (αwmax= 176。 , εα= )。 6d, at point D of Figure 5 (αw= 176。 , εαmax= ). 32 SEPTEMBER/OCTOBER 2020 • GEAR TECHNOLOGY • • (11)(11a)(12)(13)(14)(15)(16)Page 30 35 8/1/02 12:53 PM Page 33of existence for a pair of gears z1= 14, z2= 28, ma1= ma2= is shown in Figure 5. The area of existence includes a number of isograms reflecting constant values of different gear parameters, such asoperating pressure angles αw, contact ratios εα, etc.The area of existence of spur gears (thick line 1) islimited by isogram εα= , and undercut isogramsαp1= 0H11034, αp2= 0H11034. Helical gears can have a transverse contact ratio less than because the axialcontact ratio can provide proper mesh. The area ofexistence of helical gears is therefore much greater.Each point on the area of existence reflects a pair ofgears with dimensionless properties that can fit a particular application. These properties are pressureangles, contact ratios, pitting resistance geometryfactor I, specific sliding ratio, etc. The absolute area of existence includes spur gearbinations with any values of proportional topland thicknesses between ma1= ma2= 0 to ma1= mb1and ma2= mb2(phantom line 2). This area is substantially larger than the area with given values ofproportional top land thicknesses. The zone for astandard generating rack with 20H11034 pressure angle (asshown in Fig. 1) is only a fractional part of the available area of existence as shown by hidden line 3 inFigure 5. An application of a traditional gear generating approach for gear pairs outside the zone outlined by hidden line 3 requires selection of a generating rack with different parameters. The generationof some gear binations (top left and bottom rightcorners of the area of existence shown in Fig. 5) willrequire different generating racks for the pinion andfor the gear.Analysis of the area of existence shows howmany gear solutions could be left out of consideration if a traditional approach based on a predetermined set of rack dimensions is applied. For example, spur gears with a h。