11_ch 07 Mechanical Design budynas_SM_ch07

11_ch 07 Mechanical Design budynas_SM_ch07 - (f Entering...

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188 Solutions Manual • Instructor’s Solution Manual to Accompany Mechanical Engineering Design Selecting the DE-Goodman criteria for a conservative first design, Eq. (7-8): d = ± 16 n π ² ³ 4( K f M a ) 2 ´ 1 / 2 S e + ³ 3( K fs T m ) 2 ´ 1 / 2 S ut µ¶ 1 / 3 d = ± 16 n π ² ³ 4(1 . 9 · 2178) 2 ´ 1 / 2 24 500 + ³ 3(2 . 8 · 2500) 2 ´ 1 / 2 68 000 µ¶ 1 / 3 d = 1 . 58 in Ans . With this diameter, the estimates for notch sensitivity and size factor were conservative, but close enough for a first iteration until deflections are checked. Check for static failure. Eq. (7-15): σ ± max = ± · 32 K f M a π d 3 ¸ 2 + 3 · 16 K fs T m π d 3 ¸ 2 1 / 2 σ ± max = ± · 32(1 . 9)(2178) π (1 . 58) 3 ¸ 2 + 3 · 16(2 . 8)(2500) π (1 . 58) 3 ¸ 2 1 / 2 = 19 . 0 kpsi n y = S y ± max = 57 / 19 . 0 = 3 . 0 Ans . (e) Now estimate other diameters to provide typical shoulder supports for the gear and bearings (p. 360). Also, estimate the gear and bearing widths.
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Unformatted text preview: (f) Entering this shaft geometry into beam analysis software (or Finite Element software), the following deflections are determined: Left bearing slope: 0.000532 rad Right bearing slope: − . 000850 rad Gear slope: − . 000545 rad Right end of shaft slope: − . 000850 rad Gear deflection: − . 00145 in Right end of shaft deflection: 0.00510 in Comparing these deflections to the recommendations in Table 7-2, everything is within typical range except the gear slope is a little high for an uncrowned gear. 8 1.56 9 11 6 1.58 0.45 1.31 1.250 2.00 1.25 0.35 7 3 4...
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