What is Controlling Torque?

In this lecture, we are going to learn about the controlling system used in measuring instruments. We will discuss what controlling torque is, and the essential function of the controlling system and then we will discuss the types of controlling torque. So let’s start with the definition of the controlling system.

Table of Contents

The device used for controlling the deflection of the pointer in measuring instruments over the scale is called the control device. The torque which controls the movements of the pointer is called the control torque.

Controlling System

The controlling system provides a force so that current or any other electrical quantity will produce deflection of the pointer proportional to its magnitude. The important function of this system is,

It produces a force equal and opposite to the deflecting force in order to make the deflection of the pointer at a definite magnitude. If this system is absent, then the pointer will swing beyond its final steady position for the given magnitude and deflection will become indefinite.
It brings the moving system back to zero position when the force which causes the movement of the moving system is removed. it will never come back to its zero position in the absence of a controlling system.

Controlling torque is generally provided by springs. Sometimes gravity control is also used.

Methods of Providing Controlling Torque

The controlling torque can be produced in two ways. They are,

Spring control
Gravity control

1. Gravity Control

This type of control consists of a small weight attached to the moving system whose position is adjustable. This weight produces a controlling torque due to gravity. This weight is called control weight.

Figure 1 shows the gravity control system. At the zero position of the pointer, the controlling torque is zero. This position is shown as position A of the weight in figure 2. If the system deflects, the weight position also changes, as shown in figure 2.

The system deflects through an angle $\theta$ . The control weight acts at a distance l from the center. The component $W \sin \theta$ of this weight tries to restore the pointer back to the zero position. This is nothing but the controlling torque T_c.

Thus, Controlling torque,

$\boxed{ T_C=W \sin \theta \times l }$

$= K \sin \theta$

Here, $K = W l$

= Gravity Constant

Now generally all meters are current sensing meters where Deflecting Torque,

$\boxed{T_d=K_tI}$

Where K_t = Another constant

In the equilibrium position,

$\boxed{T_d = T_c}$

$\therefore K_t I = K \sin \theta$

$\boxed{\therefore I \propto \sin \theta}$

Thus the deflection is proportional to the current i.e. quantity to be measured.

Key Point: But as it is a function of  $\sin \theta$ , the scale for the instrument using gravity control is not uniform.

Advantages of Gravity Control Mechanism:

Its performance is not time-dependent.
It is simple and cheap.
The controlling torque can be varied by adjusting the position of the control weight.
Its performance is not temperature dependent.

Disadvantages of Gravity Control Mechanism:

The scale is non-uniform causing problems to record accurate readings.
The system must be used in a vertical position only and must be properly leveled. Otherwise, it may cause serious errors in the measurement.
As delicate and proper leveling is required, in general, it is not used for indicating instruments and portable instruments.

2. Spring Control

To overcome the disadvantage of the gravity control mechanism in measuring instruments, the spring control mechanism has been introduced measuring instruments.

Two hair springs ate attached to the moving system which exerts controlling torque. To employ spring control on an instrument, the following requirements are essential.

Essential Requirements for Spring Control

The spring should be non-magnetic.
The springs should be free from mechanical stress.
The spring should have a small resistance and sufficient cross-sectional area.
It should have a low resistance temperature coefficient.

The springs are made up of non-magnetic materials like silicon bronze, hard-rolled silver or copper, platinum silver, and german silver. For most of the instruments phosphor, bronze spiral springs are provided. Flat spiral springs are used in almost all indicating instruments.

The inner end of the spring is attached to the spindle while the outer end is attached to a lever or arm which is actuated by a set of screws mounted at the front of the instruments. So zero setting can be easily done. The controlling torque provided by the instrument is directly proportional to the angular deflection of the pointer.

The controlling torque produced by the spiral spring is given by,

$\boxed{ T_c= \frac{E\; b\; t^3}{12 \;L} \;\theta}$

Where,

E = Young’s modulus of spring material in N/m²

t = thickness in meters

b = depth in meters

L = length in meters

K_s = Spring constant = $\frac{E\; b\; t^3}{12 \;L}$

$\boxed{\therefore \; T_c \propto \theta}$

Now deflecting torque is proportional to current

$\boxed{T_c \propto I}$

At equilibrium, T_d = T_c

$\boxed{I \propto \theta}$

Key Point: Thus the deflection is proportional to the current. hence the scale of the instrument using spring control is uniform.

When the current is removed, due to spring force the pointer comes back to the initial position. The spring control is very popular and is used in almost all indicating instruments.

Comparison between Spring Control and Gravity Control Mechanism

Sr. No.	Gravity Control	Spring Control
1.	Adjustable small weight is used which produces the controlling torque.	Two hairsprings are used which exert controlling torque.
2.	Controlling torque can be varied.	Controlling torque is fixed.
3.	The performance is not temperature dependent.	The performance is temperature dependent.
4.	The scale is non-uniform.	The scale is uniform.
5.	The controlling torque is proportional to $\sin \theta$	The controlling torque is proportional to $\theta$
6.	The reading can not be taken accurately.	The readings can be taken very accurately.
7.	The system must be used in a vertical position only.	The system need not be necessarily in a vertical position.
8.	Proper leveling is required as gravity control.	The leveling is not required.
9.	simple, cheap but delicate.	Simple, rigid but costlier compared to gravity control.
10.	rarely used for indicating and portable instruments.	Very popular and used in most instruments.

What is Controlling Torque? – Spring Control and Gravity Control