FRICTION AND LUBRICATION 263 
s of the screw. In each case, W being the load carried by the nut, 
- Pr tana+tangd p+yprd 
By wan et >) = Tea tan & md—pp 
_. Im practice the screw is usually rotated in the nut or the nut on the 
_ serew by a force Q acting on a wheel or lever of radius 7 attached to the 
- serew or nut, and Pd = 2Qr. 
To reverse the motion of the screw or nut 
and lower the load W the 
= a ee ee oe ee oe eee = Ar 
oa em Sal ee ee ee ee 
Bae os -- “w= = 
en Kad a- =" e- -- 
_ - ot = -" 
2 or" oO = a 
i - - a= 
+ - 
poet Zer ae <= 
= - - 
me - 
at FS 
- 
- 
- 
- 
-- -- 
wae --=- 
- 
== a 
wn oe 
- sat ae a - 
- -- ae 
- - - - oa 
ee Se A ee oe 
ae em -- 
— — => 
Fra. 400. Fia. 401. 
greater than a, P has a positive value, but when ¢ is less than a, P is 
negative, that is, it must act in the same direction for lowering as for 
raising, and if left to itself the load W will reverse the motion. 
_____In the case of a screw thread of triangular section (Fig. 402), if R, 
the normal pressure on the thread, be resolved into two 
ponents, W parallel to the axis and § perpendicular to 
__ the axis of the screw, then R=W/cos f, where £ is the 
; complement of the inclination cf the side of the section 
of the thread to the axis. Now the friction is propor- 
tional to R; hence for a triangular thread tan must be 
___ increased to » tan ¢, where n=1/cos £, and 
3 P_ tanat+ntangd _p+nprd 
| . W i-ntanatangd rd—npp Fia. 402. 
Also, since ¢ is generally a small angle, and n is less than 1} in ordinary 
cases, n tan ¢=tan n¢ nearly, then es tan (a+nq) approximately. In 
| the Whitworth thread 28=55°, and n=1'13. In the Sellers thread 
2B =60°, and n=1°15. 
