Power Screws

Power Screws vs Lead Screws

• Power screws are used in lifting or lowering (pushing or pulling large axial loads)
• Lead screws refer to xyz positioning

Application: Machine Jack

There’s a lead screw which is driven which drives a gear with inner threads which drives a worm which connects to a shaft (driven manually or by a motor)

Power Screws

• A drive mechanism to convert rotary to linear motion
• Often capable of very large mechanical advantage
• Focus on establishing relationship between $T$ (input torque) and $P$ (output load) for different designs

• All the torque calculations occurs on a $d_p$ distance (screw diameter (pitch)) on the nut

Threads

• Uses the same nomenclature as the worm gear pair
• $\psi$: helix angle
• $\lambda$: lead angle
• $d$: addendum diameter
• $d_p$: pitch diameter
• $d_r$: root diameter
• $\alpha$: acme angle = $14.5°$

• The $L$ in this equation is the lead distance where $n_s$ is the start number

Force Analysis

• We abstract the problem as a mass travelling up an incline under a loading P

For Square Threads

• $\Sigma F_x=0:F-f\cos \lambda -N\sin \lambda =0$
• $f=\mu N$

For Acme Threads

In practice there is also additional friction at the collar (or the thrust bearing)

• $T_B={\mu }_{B}P\frac{D_c}{2}$
• Therefore…
  • $T_{UP}=T+T_B$
  • $T_{UP}=\frac{P}{2}\left[D_p\left(\frac{\mu +\tan \lambda }{1-\mu \tan \lambda }\right)+{\mu }_B{D}_c\right]$
  • $T_{DOWN}=\frac{P}{2}\left[D_p\left(\frac{\mu -\tan \lambda }{1+\mu \tan \lambda }\right)+{\mu }_B{D}_c\right]$

Self Locking and Back Driving

• Self locking: A condition where the screw cannot be turned by the axial force P. That is, it does not need a brake to hold the load statically
• Back-driving: A condition where the load P pushing axially on the screw will cause the screw to turn

The condition for self-locking for acme threads

• $\Sigma F_y\ne 0$
• $P=\frac{N\cos \alpha }{\cos \lambda }$
• $\Sigma F_x\ne o$
• $\mu \ge \cos \alpha \tan \lambda$ Similarly for square threads…
• $\mu \ge \tan \lambda$
• $\mu \ge {\frac{p{n}_s}{\pi D_p}}_{}$

Power Screw Efficiency

Without collar friction

• Acme: $W_{input}=2\pi T$ (input work at nut or screw)
• Acme: $W_{output}=LP$ (output work at the load P)
• For a square thread: $\eta =\frac{\tan \lambda }{\left[\frac{\mu +\tan \lambda }{1-\tan \lambda }\right]}$

Note

Depending on the lead angle, there are different efficiency curves where 45° is the optimal angle for the highest efficiency

Ball Screws

• Very smooth (low friction), thus back-drivable
• High load capacity
• Popular for linear drive mechanism