Torque Calculation for Screw Ball: TL Preload Nut

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Justin71
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Thread moved from the technical forums, so no Homework Template is shown
Reference sheet for ball screw drive load torque: formula TL = (FPB/(2πη) + μ0F0PB/(2π)) × 1/i, force formula F = FA + mg(sin θ + μ cos θ), a diagram of a table on a ball screw with direct connection, an inclined-plane diagram, and a legend of symbols including F, F0, μ0, η, PB, FA, m, μ, θ, g and i.

Hi

I don't understand what Fa mean ? This the weight or no ? And i don't understand too why in the torque TL, we have an additional part with the preload, the internal friction coeff of preload nut ... What is it ? Thanks.
 
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  • Reference sheet for ball screw drive load torque: formula TL = (FPB/(2πη) + μ0F0PB/(2π)) × 1/i, force formula F = FA + mg(sin θ + μ cos θ), a diagram of a table on a ball screw with direct connection, an inclined-plane diagram, and a legend of symbols including F, F0, μ0, η, PB, FA, m, μ, θ, g and i.
    upload_2019-1-15_14-32-13.png
    33.2 KB · Views: 2,967
It appears that Fa is force due to acceleration (F = ma).

Ball nuts are available with internal clearance for low friction, or internal preload for precision motion. Low friction ball nuts are used with low precision (lower cost) ball screws in applications that tolerate location errors of 0.005" or so. Internally preloaded ball nuts are used with precision ground ball screws (higher cost) in applications where higher precision is needed. Typical applications are machine tools where the motion is controlled to +/-0.0001".

Study some ball screw catalogs. You will find specifications for location error, backlash, allowable speed, and allowable acceleration.
 
Ok thank's a lot for your answer ! I had an other question for the acceleration (inertial force).
Axial load equation Fa = FM + Ff + Fi + Fg with key listing machining, frictional, inertial and gravitational forces in newtons, beside two diagrams of a leadscrew-driven mass: horizontal with axial load, vertical with ascent/descent.

If we machine like drilling, we have an acceleration, then a deceleration during machining. We can decompose their inertial forces with (Fi(acceleration)=m.a and Fi(deceleration)=-m.a ? Or it's an other thing ? Thank's.
 
Attachments
  • Equation Fa = FM + Ff + Fi + Fg with key listing machining, frictional, inertial and gravitational forces in newtons, plus two diagrams of a ball screw driven mass with guideway friction and axial load.
    upload_2019-1-16_9-39-8.png
    61.2 KB · Views: 527
  • Axial load equation Fa = FM + Ff + Fi + Fg with key listing machining, frictional, inertial and gravitational forces in newtons, beside two diagrams of a leadscrew-driven mass: horizontal with axial load, vertical with ascent/descent.
    upload_2019-1-16_9-44-38.png
    61.2 KB · Views: 943