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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).
Explaining the mechanics and forces involved in the irreversibility of a steering worm and nut system.

Identifier  ExFiles\Box 67\4\  scan0327
Date  13th July 1927
  
48430
Hs{Lord Ernest Hives - Chair}/Tsn/LG13.7.27.

IRREVERSIBILITY OF STEERING
WORM AND NUT.

The nut and worm can be represented respectively
by a weight and an inclined plane.

In case (1) to be considered, the worm will be
considered as driving the nut i.e., the plane will be lifting
the weight. This is 'Parking'.

Imagine a force P. between
the two, ⊥ to the surface
of the plane, and of un-
known magnitude.

The only
two external forces are :-

Fn = force on nut and is the force resisting motion.

Fw = force on plane. This is force on worm,
considered as acting at Pitch Radius.

[DIAGRAM]
Labels on diagram:
- P
- NUT
- WORM
- μP
- θ
- P
- Fw
- Fn
- Direction of motion of worm (plane).
[/DIAGRAM]

Equating forces in vertical plane :

Fn + μPsinθ = P cosθ

Fn = P cosθ - μPsinθ

Similarly in horizontal plane :

Fw = P sinθ + μPcosθ

Fw/FN = (sinθ + μcosθ) / (cosθ - μsinθ)

Calling Y "∠ of friction"

μ = tan Y = sinY/cosY

contd :-
  
  


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