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problems_II_3

# problems_II_3 - program_II_3_1.nb H Program II.3.1 L...

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H Program II .3 .1 L Apply @ Clear, Names @ "Global` " DD ; Off @ General::spell D ; Off @ General::spell1 D ; H input data L d = 1; H in major diameter L p = 0.2; H in pitch L µ = 0.15; M = 60; H lb in L l = 2 p; H in lead L Print @ "Lead l = ", l, " in" D ; dm = d p ê 2; Print @ "dm = ", dm, " in" D ; λ = ArcTan @ l ê H dm N @ Pi DLD ; Print @ " λ = ", λ ê Degree, " °" D ; θ = ArcTan @ µ D ; Print @ "Friction angle θ = ", θ ê Degree, " °" D ; If @ θ > λ , Print @ "the screw is sef locking" D , Print @ "the screw is not sef locking" DD ; H to the right L F = M ê H dm ê 2 Tan @ θ − λ DL ; Print @ "Force required to advance screw to the right F = ", F, " lb" D ; H to the left L F = M ê H dm ê 2 Tan @ θ + λ DL ; Print @ "Force required to advance screw to the left F = ", F, " lb" D ; Lead l = 0.4 in dm = 0.9 in λ = 8.05226 ° Friction angle θ = 8.53077 ° the screw is sef locking Force required to advance screw to the right F = 15964.8 lb Force required to advance screw to the left F = 447.742 lb program_II_3_1.nb 1

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H Program II .3 .2 L Apply @ Clear, Names @ "Global` " DD ; Off @ General::spell D ; Off @ General::spell1 D ; " −−−−−−−−−−−−−−−− " " input data " " −−−−−−−−−−−−−−−− " " H pitch L mean diameter dm @ mm D " " screw pitch p @ mm D " " coefficient of friction for thread µ " " coefficient of collar friction for thread µ c " " mean collar diameter dc @ mm D " " external load F @ kN D " data = 8 dm 30, p 4, µ −> 0.08, µ c −> 0.08, dc 40, F 6.4 < " −−−−−−−−−−−−−−−− " "solution" " −−−−−−−−−−−−−−−− " l = 2 p; H lead L Ml = 0.5 F dm H π µ dm l L ê H π dm + µ l L + 0.5 F dc µ c; Print @ "moment to lower load Ml = 0.5 F dm H π µ dm l LêH π dm + µ l L + 0.5 F dc µ c " D Print @ "Ml = ", Ml ê . data, " @ N m D = ", 10^ H 3 L Ml ê . data, " @ N m D " D sf = H π µ dm l L ; "sef locking condition: H π µ dm l L > 0 " Print @ " H π µ dm l L = ", sf ê . data D If @H sf ê . data L > 0, Print @ "the screw is sef locking" D , Print @ "the screw is not sef locking" DD Mr = 0.5 F dm H l + π µ dm L ê H π dm − µ l L + 0.5 F dc µ c; H momemnt to raise the load L e = F l ê H 2 π Mr L ; Print @ "efficiency e = F l êH 2 π Mr L = ", e ê . data D −−−−−−−−−−−−−−−− input data −−−−−−−−−−−−−−−− H pitch L mean diameter dm @ mm D screw pitch p @ mm D coefficient of friction for thread µ coefficient of collar friction for thread µ c mean collar diameter dc @ mm D external load F @ kN D 8 dm 30, p 4, µ → 0.08, µ c 0.08, dc 40, F 6.4 < program_II_3_2.nb 1
−−−−−−−−−−−−−−−− solution −−−−−−−−−−−−−−−− moment to lower load Ml = 0.5 F dm H π µ dm l LêH π dm + µ l L + 0.5 F dc µ c Ml = 9.77443 @ N m D = 0.00977443 @ N m D sef locking condition: H π µ dm l L > 0 H π µ dm l L = − 0.460178 the screw is not sef locking efficiency e = F l êH 2 π Mr L = 0.311294 program_II_3_2.nb 2

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H Program II .3 .3 L Apply @ Clear, Names @ "Global` " DD ; Off @ General::spell D ; Off @ General::spell1 D ; " −−−−−−−−−−−−−−−− " " input data " "
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