Controlling Torque in Electrical Instruments — Spring & Gravity Control Methods
In electrical measuring instruments, three essential torques work together to produce accurate readings: deflecting torque, controlling torque, and damping torque. The controlling torque (also called restoring torque) is responsible for ensuring the pointer reaches a definite position corresponding to the measured quantity and returns to zero when the instrument is disconnected.
What is Controlling Torque?
Controlling torque is the torque that opposes the deflecting torque in an electrical measuring instrument. It increases as the pointer deflects from its zero position. The pointer comes to rest at a position where the controlling torque exactly equals the deflecting torque — this equilibrium determines the final reading.
Mathematically, at steady-state deflection:
Where Td is the deflecting torque and Tc is the controlling torque.
Why is Controlling Torque Necessary?
Without controlling torque, two critical problems arise:
- Indefinite deflection: The pointer would swing to the maximum position regardless of the measured quantity's magnitude, making measurement impossible.
- No zero return: Once deflected, the pointer would not return to zero when the measured quantity is removed.
The controlling torque serves two functions — it produces a definite deflection proportional to the measured quantity, and it restores the pointer to zero when the instrument is de-energized.
There are two methods of providing controlling torque:
- Spring Control Method
- Gravity Control Method
Spring Control Method
In the spring control method, two hairsprings made of phosphor bronze are attached to the spindle of the moving system. One spring is placed above and the other below the spindle. One end of each spring connects to the spindle while the other end is fixed to the instrument frame.
Fig: Arrangement of Spring Control Method showing two phosphor bronze springs wound in opposite directions.
Working Principle: When no current flows, both springs are in their natural (untwisted) state and the pointer rests at zero. When a deflecting torque is produced, the pointer rotates — one spring gets twisted while the other unwinds. The net twist produces a restoring torque that increases linearly with deflection angle.
The springs are wound in opposite directions to compensate for temperature-induced expansion or contraction. The spring material must be:
- Non-magnetic (to avoid interference with the magnetic field)
- Low specific resistance (springs also carry current to the moving coil)
- Low temperature coefficient of resistance
Since controlling torque is directly proportional to deflection angle (Tc ∝ θ), spring-controlled instruments have a uniform (linear) scale.
Design Formula for Spring Control
The controlling torque developed by a flat spiral spring is given by:
From this formula, we can see that controlling torque can be increased by using a wider, thicker, or shorter spring, or by choosing a material with higher Young's Modulus.
Advantages & Disadvantages of Spring Control
Advantages:
- Instrument can be used in any position — horizontal, vertical, or inclined
- Springs are lightweight and do not add significant weight to the moving system
- Produces a uniform (linear) scale, making readings easy and accurate
- Springs also serve as current-carrying leads to the moving coil (dual purpose)
Disadvantages:
- Temperature variations can alter spring stiffness, introducing errors
- Springs deteriorate with age (fatigue), reducing long-term accuracy
- Phosphor bronze springs are more expensive than gravity weights
Gravity Control Method
In the gravity control method, a small adjustable weight is attached to the moving system. The gravitational pull on this weight provides the controlling torque.
Fig: Gravity Control Method — weight W produces restoring torque proportional to sin θ.
Working Principle: At zero position, the control weight hangs vertically below the pivot, producing no torque. When the pointer deflects by angle θ, the weight moves from its vertical position. Gravity pulls the weight back toward vertical, creating a restoring torque.
The controlling torque in gravity control is:
Where W is the weight, l is the distance from pivot to the weight's center of gravity, and θ is the deflection angle. Since Tc ∝ sin θ (not θ), the scale is non-uniform — cramped at higher deflections.
Advantages & Disadvantages of Gravity Control
Advantages:
- Simple and inexpensive — no precision springs required
- Unaffected by temperature variations (gravity is constant)
- Does not deteriorate with time — permanent and reliable
Disadvantages:
- Produces a non-uniform (cramped) scale — difficult to read at higher deflections
- Adds weight to the moving system, increasing inertia and friction
- Instrument must be mounted vertically — cannot be used in horizontal or inclined positions
- Limited to indoor use where the instrument can be kept perfectly vertical
Comparison: Spring Control vs Gravity Control
In modern practice, spring control is preferred for most instruments due to its uniform scale and position-independence. Gravity control is used only in fixed panel-mounted instruments where cost is a primary concern.
Frequently Asked Questions
1. What is the purpose of controlling torque in measuring instruments?
Controlling torque opposes the deflecting torque to produce a definite, measurable deflection proportional to the quantity being measured. Without it, the pointer would swing to maximum regardless of the input magnitude and would not return to zero when disconnected.
2. Why is phosphor bronze used for control springs?
Phosphor bronze is non-magnetic (won't interfere with the instrument's magnetic field), has low specific resistance (can carry current to the moving coil), has a low temperature coefficient, and possesses excellent elastic properties with high fatigue resistance.
3. Why does gravity control produce a non-uniform scale?
Because the controlling torque in gravity control is proportional to sin θ (not θ). Since sin θ does not increase linearly with angle, the scale divisions become progressively cramped at higher deflections, making readings less accurate at the upper end.
4. Can a gravity-controlled instrument be used in a horizontal position?
No. Gravity control relies on the downward pull of a weight to produce restoring torque. If the instrument is placed horizontally, the weight cannot produce any torque about the spindle axis, and the controlling mechanism fails completely.
5. What is the difference between controlling torque and damping torque?
Controlling torque determines the final resting position of the pointer (where Td = Tc). Damping torque only affects how quickly the pointer reaches that position — it prevents oscillations but does not change the final reading. Controlling torque is position-dependent; damping torque is velocity-dependent.