3_ch 15 Mechanical Design budynas_SM_ch15

# 3_ch 15 Mechanical Design budynas_SM_ch15 - The velocity...

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Chapter 15 381 The pinion controls wear: H = 11 . 0hp Ans. The power rating of the mesh, considering the power ratings found in Prob. 15-1, is H = min(16 . 4, 14 . 8, 11 . 0, 12 . 6) = 11 . 0hp Ans . 15-3 AGMA 2003-B97 does not fully address cast iron gears, however, approximate compar- isons can be useful. This problem is similar to Prob. 15-1, but not identical. We will orga- nize the method. A follow-up could consist of completing Probs. 15-1 and 15-2 with identical pinions, and cast iron gears. Given: Uncrowned, straight teeth, P d = 6 teeth/in, N P = 30 teeth, N G = 60 teeth, ASTM 30 cast iron, material Grade 1, shaft angle 90°, F = 1 . 25, n P = 900 rev/min, φ n = 20 , one gear straddle-mounted, K o = 1, J P = 0 . 268, J G = 0 . 228, S F = 2, S H = 2 . Mesh d P = 30 / 6 = 5 . 000 in d G = 60 / 6 = 10 . 000 in v t = π (5)(900 / 12) = 1178 ft/min Set N L = 10 7 cycles for the pinion. For R = 0 . 99, Table 15-7: s at = 4500 psi Table 15-5: s ac = 50 000 psi Eq. (15-4): s w t = s at K L S F K T K R = 4500(1) 2(1)(1) = 2250 psi
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Unformatted text preview: The velocity factor K v represents stress augmentation due to mislocation of tooth proﬁles along the pitch surface and the resulting “falling” of teeth into engagement. Equation (5-67) shows that the induced bending moment in a cantilever (tooth) varies directly with √ E of the tooth material. If only the material varies (cast iron vs. steel) in the same geometry, I is the same. From the Lewis equation of Section 14-1, σ = M I / c = K v W t P FY We expect the ratio σ CI /σ steel to be σ CI σ steel = ( K v ) CI ( K v ) steel = ± E CI E steel In the case of ASTM class 30, from Table A-24( a ) ( E CI ) a v = (13 + 16 . 2) / 2 = 14 . 7 kpsi Then ( K v ) CI = ² 14 . 7 30 ( K v ) steel = . 7( K v ) steel...
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