What is Controlling Torque?
Controlling torque refers to the force applied to a measuring instrument's pointer to control its movement across the scale. This force is necessary in order to ensure that the pointer remains stable and accurate, and that it does not move too quickly or too slowly.
A control device generates and applies the control torque to the pointer. This device may be a spring, a weight, or an electromagnet, depending on the design of the instrument. The control device is typically located in the base of the instrument, and it is connected to the pointer by a shaft or other mechanical linkage.
The control torque must be carefully calibrated to match the pointer's weight and the scale's sensitivity. If the control torque is too high, the pointer will move too quickly and the readings will be less accurate. If the control torque is too low, the pointer will move too slowly and the readings will be less precise.
The Function of Controlling Torque:
- The function of the controlling system is to produce a force that is equal and opposite to the deflecting force in order to ensure that the pointer on a measuring instrument moves to a specific position on the scale. This is necessary to ensure that the pointer remains stable and accurate. Without a controlling system, the pointer would continue to move past its final position, resulting in an indefinite deflection and inaccurate readings.
- The controlling system also brings the moving system back to its zero position when the force that caused the movement is removed. This is important to ensure that the instrument is ready for the next measurement and that the readings are accurate. Without a controlling system, the moving system would not return to its zero position, and subsequent measurements would be affected.
Controlling torque is generally provided by springs. The spring exerts a force on the pointer, which is proportional to the deflection of the pointer from its zero position. This force helps to balance out the deflecting force and return the pointer to its zero position.
Sometimes, gravity control is also used as a controlling system. In this case, a weight or counterbalance is attached to the pointer, which produces a force that opposes the force of gravity and helps to return the pointer to its zero position.
Methods of Providing Controlling Torque:
- Gravity control
- Spring control
1. Gravity Control:
Gravity control is a type of control system that uses a small weight attached to the moving system to produce a controlling torque due to gravity. The weight, known as the control weight, is positioned in such a way that it can be adjusted to produce the appropriate amount of controlling torque.
In a gravity control system, the control weight is positioned at the zero position of the pointer when the system is at rest. This is the position where the controlling torque is zero and is shown as position B of the weight in the figure.
If the system deflects, the position of the control weight also changes, as shown in the figure. The system deflects through an angle θ. The control weight acts at a distance l from the center. The component Wsinθ of this weight tries to restore the pointer back to the zero position. This is the controlling torque Tc. The equation that represents this relationship is:
∴ Tc = Wsinθ x l = Ksin θ
where K = W l = gravity constant.
Now generally all meters are current sensing meters where the deflecting torque Td = Kt I where Kt is another constant. In equilibrium position, Td = Tc and thus we have
∴ Kt I = Ksinθ
∴ I α sinθ
Thus the deflection is proportional to current i.e. quantity to be measured. But as it is a function of sinθ , the scale for the instrument using gravity control is not uniform. The readings are not linear and the scale is not evenly spaced. Therefore, instruments that use gravity control are not as accurate as those that use other types of control systems.
Advantages of Gravity Control:
- One of the advantages of gravity control is that its performance is not time dependent. This means that the controlling torque produced by the control weight remains consistent over time, regardless of how long the instrument has been in use. This helps to ensure the accuracy and precision of the instrument's readings over time.
- Another advantage is that gravity control is simple and cheap. The control weight is a small, inexpensive component that can be easily added to a measuring instrument. This makes it an attractive option for instruments that need to be produced at a low cost.
- The controlling torque can be varied by adjusting the position of the control weight. This allows the instrument to be fine-tuned to match the specific requirements of the measurement. This can be useful for instruments that measure a wide range of quantities or for instruments that need to be used in different environments.
- The performance of gravity control is not temperature dependent. This means that the controlling torque produced by the control weight remains consistent regardless of the ambient temperature. This helps to ensure the accuracy and precision of the instrument's readings, even in environments where the temperature may fluctuate.
Disadvantages of Gravity Control:
- One of the main disadvantages of gravity control is that the scale is non-uniform, which means that the readings are not evenly spaced. This can make it more difficult to take accurate readings, especially if the instrument is measuring a wide range of quantities.
- Another disadvantage is that the system must be used in a vertical position only, and it must be properly levelled. This means that the instrument must be placed on a flat surface and adjusted so that it is perfectly level. If it is not properly levelled, it can cause serious errors in the measurement.
- Due to delicate and proper levelling required, gravity control is not commonly used for indicating instruments and portable instruments. Indicating instruments are those that have a pointer and a scale and are used to display a measurement. Portable instruments are those that can be easily carried and used in different locations. Because of the sensitivity required to level and adjust the instrument, it is not practical for these types of instruments.
2. Spring Control:
Spring control is a type of control system that uses two hair springs attached to the moving system to exert a controlling torque. The spring control is widely used in measuring instruments to control the movement of the pointer.
To use spring control in an instrument, certain requirements must be met. These include:
- The spring should be non-magnetic so it doesn't get affected by magnetic fields.
- The spring should be free from mechanical stress, meaning it should not be stretched or compressed in any way.
- The spring should have a small resistance and sufficient cross-sectional area to produce the correct amount of controlling torque.
- It should have low resistance temperature coefficient, which means that the spring's resistance should not change significantly with changes in temperature.
- The springs are usually made of non-magnetic materials like silicon bronze, hard-rolled silver copper, platinum silver, and German silver. For most instruments, phosphor bronze spiral springs are used. Flat spiral springs are used in almost all indicating instruments.
In the spring control system, the inner end of the spring is attached to the spindle, while the outer end is attached to a lever or arm that is actuated by a set of screws mounted at the front of the instrument. This allows for easy zero setting of the instrument. The controlling torque provided by the instrument is directly proportional to the angular deflection of the pointer.
The controlling torque produced by spiral springs is given by,
∴ Tc = Ebt3θ / 12L = Ks θ
where Tc is the controlling torque,Eb is the modulus of elasticity of the spring material,
t is the thickness of the spring,
θ is the angular deflection of the pointer, and
L is the length of the spring.
This equation shows that the controlling torque is directly proportional to the modulus of elasticity of the spring material (Eb), the cube of the thickness of the spring (t^3), the angular deflection of the pointer (θ), and inversely proportional to the length of the spring (L).
It means that when modulus of elasticity, thickness and deflection of the pointer increases, the controlling torque will also increase and when the length of the spring increases the controlling torque will decrease.
This equation is used to calculate the controlling torque of the spring control system and ensure that it produces the correct amount of torque for the instrument to function properly.
It's important to note that the controlling torque is directly related to the spring's properties and the angular deflection of the pointer, but it is also affected by other factors such as the length of the spring and the modulus of elasticity of the spring material. Thus, the spring control system is designed to provide the correct amount of torque for the specific instrument and application.
The deflecting torque in an instrument is proportional to the current being measured,
∴Td α I
This means that as the current increases, the deflecting torque also increases.
In the spring control system, the controlling torque (Tc) is also proportional to the angular deflection of the pointer (θ). When the instrument is in equilibrium, the deflecting torque (Td) is equal to the controlling torque (Tc).
This means that
∴ Td = Tc
Therefore, when the current is removed, the pointer comes back to its initial position due to the spring force. This is because the spring force helps to balance out the deflecting force and return the pointer to its zero position.
The spring control is very popular and is used in almost all indicating instruments. This is because it provides a uniform scale for the instrument, meaning that the readings are evenly spaced. This makes it easy to take accurate readings, especially if the instrument is measuring a wide range of quantities. Additionally, the spring control system ensures that the pointer returns to its initial position when the current is removed, making it ready for the next measurement.
Advantages of Spring Control:
- A uniform scale is present since the current flowing is proportional to deflections. This means that the readings are evenly spaced and easy to take accurate readings, especially if the instrument is measuring a wide range of quantities.
- High accuracy can be obtained with spring control. The spring control system ensures that the pointer returns to its zero position, and the scale of the instrument is uniform, making it easy to take accurate readings.
- This method of providing controlling torque is simple. The spring control system uses two small springs to exert a force that is proportional to the angular deflection of the pointer, which helps to balance out the deflecting force caused by the current being measured.
- The system can be used in any position. Unlike gravity control, the instrument can be placed in any position and still function correctly.
- Spring control is most preferable and is commonly used in many systems. Due to its advantages, spring control is widely used in almost all indicating instruments, making it a widely accepted and preferred method for controlling the movement of the pointer on a measuring instrument.
Disadvantages of Spring Control:
- The spring control torque depends upon temperature changes. As the temperature changes, the spring's properties also change which can affect the controlling torque produced by the spring. This can make the instrument less reliable in environments where the temperature fluctuates.
- The spring control system requires a high cost. The spring control system uses high-quality and precise springs which can be expensive, making it a more costly option when compared to other control systems.
- Controlling torque cannot be varied. In spring control system, the controlling torque is directly proportional to the angular deflection of the pointer, and it cannot be varied after the instrument is set up. This means that the instrument cannot be fine-tuned to match the specific requirements of the measurement.
Comparison between Spring Control and Gravity Control:
| Features | Spring Control | Gravity Control |
|---|---|---|
| Method of producing controlling torque | Using two hair springs | Using a small weight |
| Variability of controlling torque | Can be varied | Fixed |
| Temperature dependence | Not affected | Affected |
| Scale uniformity | Uniform | Non-uniform |
| Controlling torque proportionality | Proportional to angular deflection | Proportional to sine of angular deflection |
| Reading accuracy | High | Low |
| Position and leveling requirements | Can be used in any position, no leveling required | Must be used in vertical position, proper leveling required |
| Cost | More complex and costly | Simple and cheap |
| Temperature sensitivity | Sensitive | Not sensitive |
| Popularity in indicating instruments | Widely used | Rarely used |