leadscrew design
DESCRIPTION
Excel CalcTRANSCRIPT
document.xls
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leadscrew_design.xlsScrewthread forces
Written by Alex Slocum, last updated 1/17/03Force (no help from gravity), thrust (N) 400 BackdriveabilityLead, (mm) 2Coefficient of friction, mu 0.1Screw pitch diameter, dscrew (mm) 20Thrust bearing diameter, dthrust (mm) 25Thread angle (deg), alpha (rad) 30 0.524 EfficiencyThread root stress concentration, scf 1.5Beta 0.1Torque required at screw (N-mm) 591Torque required at thrust bearing (N-mm) 500Total torque (N-mm) 1,091Backdriveable? NOThread efficiency, et 22%Total system efficiency 12%Estimated torsional stress (N/mm^2) 0.52Tensile stress (N/mm^2) 1.57Mises equivelant stress (N/mm^2) 2.71Gearbox ratio 1Travel (mm) 50Time to travel (s) 5Motor speed (rpm, rad/s) 300 31Gearbox efficiency 90%Motor torque (N-mm) 1213Power (watts) 38Shaft StabilityTravel length L (mm, m) 1000 1root diameter dr (mm, m) 18 0.018 for leadscrews (else enter root diameter same as outer diameter)outer diameter do (mm, m) 0.020density rho (kg/m^3) 7900Modulus E (M/m^2) 2.00E+11Area A 0.0003142 based on diameterInertia I (m^4) 5.153E-09 based on root diameter
CantileveredSimply SupportedFixed-simple fixed-fixedBuckling load (N) 2546 10172 20818 40709First critical frequency (rpm) 684 1921 3001 43542nd critical frequency (rpm) 4288 7682 9724 120003rd critical frequency (rpm) 12007 17286 20285 235294th critical frequency (rpm) 23529 30727 34691 38890
linc 0.0417Shaft support K 3.142
Unsupported shaft length (m) Position/L( Critical wn (rad/sec) Travel (m)1.00 0.00 1921 201 0.0000
Enter numbers in BOLD, output in RED
p 2rcos
mode n k c k c k c k c1 1.875 2.47 3.142 9.87 3.927 20.2 4.730 39.52 4.694 6.283 7.069 7.8533 7.855 9.425 10.210 10.9964 10.996 12.566 13.352 14.137n (2n-1)/2 n (4n+1)/4 (2n+1)/2
Cantilevered Simply Supported Fixed-Simple Fixed-Fixed
24 2bucklen
EI cEIk F
L L
document.xls
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0.96 0.04 2092 219 0.04170.92 0.08 2286 239 0.08330.88 0.13 2509 263 0.12500.83 0.17 2766 290 0.16670.79 0.21 3065 321 0.20830.75 0.25 3415 358 0.25000.71 0.29 3829 401 0.29170.67 0.33 4322 453 0.33330.63 0.38 4918 515 0.37500.58 0.42 5646 591 0.41670.54 0.46 6548 686 0.45830.50 0.50 7684 805 0.50000.54 0.54 6548 686 0.54170.58 0.58 5646 591 0.58330.63 0.62 4918 515 0.62500.67 0.67 4322 453 0.66670.71 0.71 3829 401 0.70830.75 0.75 3415 358 0.75000.79 0.79 3065 321 0.79170.83 0.83 2766 290 0.83330.88 0.87 2509 263 0.87500.92 0.92 2286 239 0.91670.96 0.96 2092 219 0.95831.00 1.00 1921 201 1.0000
document.xls
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Raising torque
for leadscrews (else enter root diameter same as outer diameter)
p 2rcos
mode n k c k c k c k c1 1.875 2.47 3.142 9.87 3.927 20.2 4.730 39.52 4.694 6.283 7.069 7.8533 7.855 9.425 10.210 10.9964 10.996 12.566 13.352 14.137n (2n-1)/2 n (4n+1)/4 (2n+1)/2
Cantilevered Simply Supported Fixed-Simple Fixed-Fixed
24 2bucklen
EI cEIk F
L L
0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.001000
2000
3000
4000
5000
6000
7000
8000
Position (m)
Cri
tical
Spe
ed (
rpm
)
cos
(cos )
cos
( cos )
pitch
raise
lower
D
document.xls
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0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.001000
2000
3000
4000
5000
6000
7000
8000
Position (m)
Cri
tical
Spe
ed (
rpm
)
document.xls
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mode n k c k c k c k c1 1.875 2.47 3.142 9.87 3.927 20.2 4.730 39.52 4.694 6.283 7.069 7.8533 7.855 9.425 10.210 10.9964 10.996 12.566 13.352 14.137n (2n-1)/2 n (4n+1)/4 (2n+1)/2
Cantilevered Simply Supported Fixed-Simple Fixed-Fixed
24 2bucklen
EI cEIk F
L L
0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.001000
2000
3000
4000
5000
6000
7000
8000
Position (m)
Cri
tical
Spe
ed (
rpm
)
document.xls
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0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.001000
2000
3000
4000
5000
6000
7000
8000
Position (m)
Cri
tical
Spe
ed (
rpm
)