From the Rolls-Royce experimental archive: a quarter of a million communications from Rolls-Royce, 1906 to 1960's. Documents from the Sir Henry Royce Memorial Foundation (SHRMF).
Calculation of forces in a worm and nut system for 'joggling' and 'parking' conditions.
| Identifier | ExFiles\Box 67\4\ scan0333 | |
| Date | 13th July 1927 guessed | |
| contd :- -3- Case 11. Nut is now driving worm i.e. condition is that known as 'joggling'. Forces in vertical plane: Fn = P cosθ + μP sinθ Fw = P sinθ - μP cosθ Fw / Fn = (sinθ - μcosθ) / (cosθ + μsinθ) [DIAGRAM START] A diagram shows a free body analysis of a nut on an inclined worm thread. Labels on the diagram include: - NUT (the block) - WORM (the inclined plane) - P (force upwards, perpendicular to the plane) - Fm (force downwards, parallel to the plane) - μP (force upwards, parallel to the plane) - P (force downwards, vertical) - μP (force downwards, parallel to the plane) - Fw (force horizontally to the left) - An arrow pointing right labeled "(Direction of motion of worm (plane))" [DIAGRAM END] = (sinθcosγ - sinγcosθ) / (cosθcosγ + sinγsinθ) = sin(θ - γ) / cos(θ - γ) = tan(θ - γ) η now = (2πr Fw) / Fn = Fw / (Fn tanθ) = tan(θ - γ) / tanθ With const. γ, η increases with θ, hence, with given lead of worm, advantage of small pitch diameter for parking. In experiments carried out with .940 worm (θ = 12° 5'), and load of 3250 lbs. (1) Force at 20" radius to raise ≅ 38 lbs. (2) Force to resist drop same radius = 11 lbs. (1) Corresponds to 'parking'; in this case, T = Fw r = Fn r tan(θ + γ) ∴ tan(θ + γ) = (38 X 20) / (.7 X 3250) = 760 / 2275 = .334. (.7 = r = Pitch radius) contd :- | ||