HW Ch12_30 32 36 23

# HW Ch12_30 32 36 23 - PROBLEM 12-30 Statement Given A...

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p t π p d = p t 0.907 in = Normal pitch p n p t cos ψ ( 29 = p n 0.785 in = Axial pitch p x p n sin ( 29 = p x 1.571 in = 3. Use the equations in Table 11-1 with the normal diametral pitch to calculate the addendum, dedendum, and outside diameter. Addendum a 1 p nd = a 0.250 in = Dedendum b 1.25 p nd = b 0.313 in = Outside diameter D d 2 a + = D 11.470 in = 4. Use equation 12.2 to find the pressure angle in the transverse plane. φ t atan tan n ( 29 cos ( 29 = t 28.300 deg = PROBLEM 12-30 _____ Statement: A 38-tooth helical gear is cut with a 25-degree-pressure-angle hob at a helix angle of 30 deg. The hob has a standard diametral pitch of 4. The resulting teeth have standard spur-gear dimensions in the normal plane. Find the pitch diameter, addendum, dedendum, outside diamete normal, transverse, and axial pitch, and the transverse pressure angle. Given: Normal plane data: Pressure angle n 25 deg = Diametral pitch p nd 4 in 1 - = Other data: Number of teeth N 38 = Helix angle 30 deg = Solution: See Mathcad file P1230. 1. Use equation 12.1 d to calculate the transverse diametral pitch. p d p nd cos ( 29 = p d 3.464 in 1 - = 2. Use equations 12.1 to find the pitch diameter, transverse pitch, normal pitch, and axial pitch. Pitch diameter d N p d = d 10.970 in = Transverse pitch

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Pitch dia d g N g p d = d g 13.167 in = Pitch rad r g 0.5 d g = r g 6.583 in = Addendum a 1.0 p d = a 0.167 in = Center distance C N p N g + 2 p d = C 8.250 in = Length of action Z r p a + ( 29 2 r p cos φ ( 29 ( 29 2 - r g a + ( 29 2 r g cos ( 29 ( 29 2 - + C sin ( 29 - = Z 0.832 in = Transverse contact ratio m p Z p b = m p 1.690 = 2. Use equation 12.5 to find the transverse contact ratio. Face width F fwf p d = F 2.000 in = Axial contact ratio m F F p d tan ψ ( 29 π = m F 2.205 = PROBLEM 12-32 _____ Statement: A 79-tooth, 30-deg helix angle, helical gear is in mesh with a 20-tooth pinion. The p d = 6 and φ = 20 deg. Find the transverse and axial contact ratios. Given: Tooth numbers: N g 79 = N p 20 = Pressure angle 20 deg = Helix angle 30 deg = Diametral pitch p d 6 in 1 - = Assumptions: The face width factor is fwf 12 = Solution: See Mathcad file P1232. 1. Use equation 11.7 to find the transverse contact ratio. Circular pitch p c p d = p c 0.524 in = Base pitch p b p c cos ( 29 = p b 0.492 in = Pinion: Pitch dia d p N p p d = d p 3.333 in = Pitch rad r p 0.5 d p = r p 1.667 in = Gear:
Solution: See Mathcad file P1236. Pinion

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HW Ch12_30 32 36 23 - PROBLEM 12-30 Statement Given A...

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