Characteristics of Strain Rings | Metal Cutting | Metallurgy

The following are the characteristics of strain rings:

i. Strain-rings provide high ratio of sensitivity to stiffness at the same time having adequate stability against buckling.

ii. A ring can be easily produced and is simple to mount.

iii. The fact that the inside is always in an opposite state of strain from the outside, allows four active arms to be effectively used in a bridge circuit.

iv. As the symmetry of a ring provides parallel paths for heat flow it can be assumed that equivalent points on opposite sides of a ring will be at same temperature. This enables drift due to temperature gradient in the vicinity of the dynamometer to be eliminated by connecting the gauge to form a complete bridge circuit.

Strain rings are generally made from aluminium because of certain advantages associ­ated with it which include; better corrosion resistance com­pared to steel, light in weight, easy machinability and excel­lent heat conductivity. A thin metal ring of radius r, thick­ness t and axial width b is shown in Fig. 25.8.

The ring is fixed at the bottom while a radial force F_r and a tangential force F_t are applied at the top. The point of load application is maintained horizontal by a suitable moment M. When only F_t is applied, the ring will deform as in Fig. 25.8. 

Thin ring elastic theory shows the strain at the inside and outside sur­faces of the ring at point A to be:

while the strain at a point B (39.6° from the vertical axis) is zero.

When only F_t is applied, the strain at A is zero while the strain at B is:

By placing strain gauges at the inside and outside surfaces of a ring at points A and B, it is possible to separate and measure F_r and F_t components of force. Only force component F_r will cause a change in resistance in the gauges at A with no change in resistance at B.

Thus, if the inside and outside gauges A mounted in the opposite arms of a Wheatstone bridge circuit we have a sensitive means for detecting changes in F_r. In a similar way the gauges at B are only sensitive to changes in F_t. As long as the strains at A and B are within elastic limit of the ring material, the strains will very linearly with the force and hence the strain rings satisfy the desired requirements of linearity.

End conditions of circular strain ring (i.e. prevention of rolling at the points of attachment) can be easily achieved by making the outside surface of the ring as octagonal. In this case points of stress concentration fall at horizontal axis and at 45° to the vertical axis. Therefore, the strain gauges in this case are mounted as shown in Fig. 25.9. The octagonal shaped rings are found to be considerably stiffer than circular ones of the same minimum section.

In this case, the expressions for strain remain same if the value of t is considered to be the thickness of the octagonal ring. The force F_r can be measured by connecting C₁ and T₁ in the Wheatstone bridge and force F_t by connecting C₂ and T₂.

It may be noted that C₂ and T₂ are mounted exactly symmetrically with respect to the ring axes for having no cross sensitivity. It has been found that sensitivity get increased by using octagonal half ring (as shown in Fig. 25.10).