Page 113 - Tribology in Machine Design

Friction, lubrication and wear in lower kinematic pairs 99

and Q be the resultant reactions on the moving element at B and A
respectively. These will act at an angle </> with the normal to the guide
surface in such a manner as to oppose the motion. If 0 is large, P and Q will
intersect at a point C' to the left off and jamming will occur. Alternatively,
if (j> is small, as when the surfaces are well lubricated or have intrinsically
low-friction properties, C' will lie to the right of F so that the force F will
have an anticlockwise moment about C' and the saddle will move freely.
The limiting case occurs when P and Q intersect at C on the line of action of
F, in which case

and

Hence, to ensure immunity from jamming/must not exceed the value given
by eqn (4.5). By increasing the ratio x:y, i.e. By making y small, the
maximum permissible value of/greatly exceeds any value likely to be
attained in practice.

Numerical example
A rectangular sluice gate, 3 m high and 2.4 m wide, can slide up and down
between vertical guides. Its vertical movement is controlled by a screw
which, together with the weight of the gate, exerts a downward force of
4000 N in the centre-line of the sluice. When it is nearly closed, the gate
encounters an obstacle at a point 460 mm from one end of the lower edge. If
the coefficient of friction between the edges of the gate and the guides is
/= 0.25, calculate the thrust tending to crush the obstacle. The gate is shown
Figure 4.4 in Fig. 4.4.

Solution
A. Analytical solution

Using the notion of Fig. 4.4, P and Q are the constraining reactions at B and
A. R is the resistance due to the obstacle and F the downward force in the
centre-line of the sluice.
Taking the moment about A,

Resolving vertically

Resolving horizontally