A screw jack similar to the one illustrated above raises a load of 5 kN. The screw is 24 mm double start Acme with 4 mm pitch, and the thrust bearing's mean diameter is 35 mm. Coefficients of running friction in thread and bearing are estimated to be 0.12 and 0.09 respectively.
| Mean diameter of thread | dm | = | ( d + d1)/2 = ( d +( d-p))/2 = d -p/2 = 24 -4/2 = 22 mm so rm = 11 mm |
| Lead angle ( 2-start ) | λ | = | arctan( L/πdm ) = arctan( 2x4/22π) = 6.60o |
| Take static coefficients of friction to be about a third greater than kinetic values, ie. μthread, static = 0.16, μbearing, static = 0.12. Assume that the square thread equations ( 2) are sufficiently accurate for the Acme here. | |||
| Raising, starting | φ | = | arctan μ = arctan( 0.16) = 9.09o so from ( 2) : |
| T | = | 5 ( 11 tan( 6.60o +9.09o ) +17.5x0.12) = 26 Nm | |
| Lowering, starting | T | = | 5 ( 11 tan( 6.60o -9.09o ) -17.5x0.12) = -13 Nm
ie. 13 Nm loosening |
| Raising, in motion | φ | = | arctan μ = arctan( 0.12) = 6.84o |
| so from ( 2) the load raised by 1 Nm is | W | = | 1 / ( 11 tan( 6.60o +6.84o ) +17.5x0.09) = 238 N |
| while the load raised by an ideal jack is | Wo | = | 1 / ( 11 tan( 6.60o + 0 ) +17.5x0.0 ) = 785 N |
| and so the efficiency is | η | = | W/Wo = 238/785 = 30% |
Copyright 1999-2005 Douglas Wright,
doug@mech.uwa.edu.au