C) To calculate deflection torque, the equation is as follow: Torque, T= BINA Where, T = Torque in unit Newton Meter (Nm) B = Flux density in unit Tesla (T)@wb/m2 I = Current through coil in unit Ampere (A) N = Numbers of coil A = Cross-sectional area (Length in unit Meter(m) x Diameter of coil in unit Meter (m) ) Figure 1: PMMC 2. Torque Equation for PMMC The equation for the delevoped torque of the PMMC can be obtained from the basic law of electromagnetic torque. The deflecting torque is given by, Td = NBAI Where, Td = deflecting torque in N-m B = flux density in air gap, Wb/m2 N = Number of turns of the coils A = effective area of coil m2 I = current in the moving. Fig.2: PMMC Coil Springs. One other force, known as a damping force, is required for correct operation of a deflection instrument. When no damping force is present, the pointer swings above and below its final position on the scale for some time before settling down. In the case of the PMMC instruments, the damping force uses eddy currents.
This is a variation of moving coil instruments. There are two types of moving coil instrument. One is permanent magnet moving coil instrument and another is dynamometer type instrument. We will discuss in this article about the permanent magnet moving coil instrument only.
Working Principle of Permanent Magnet Moving Coil Instrument
In this type of instrument, we allow one coil to move inside a magnetic field. Whenever we place a current carrying conductor inside a magnetic field there is a mechanical force acting on it. Depending on this principle we construct the permanent magnet moving coil instrument.
Construction of Permanent Magnet Moving Coil Instrument
As the name suggests, there must be a permanent magnet in the instrument. We allow rotating of one very lightweight coil of fine wire of many turns on a lightweight aluminium frame inside the magnetic field created by two poles of the permanent magnet. When the current flows through this coil, there will be a mechanical force acting on the coil. This is due to the interaction of the current with the magnetic field. This mechanical force acts as the deflecting force of the instrument. We use an alnico made U shaped permanent magnet for the purpose. The curved pole faces provide a cylindrical space between them as shown.
We place an iron core surrounded by a lightweight aluminium frame and pivoted at the center of the space between two pole faces. We provide the only coil of the instrument on that aluminium frame.
We attach two phosphor bronze hairsprings in the moving system. One is above the coil and other is below the coil. We connect the terminals of these two springs to two leads of the coil. These connections provide the path of the current to the coil through the springs. These springs also provide the controlling torque to the moving system. The springs are spiralled in opposite direction to neutralize temperature effects in the performance of the instrument.
We attach the pointer of the instrument to the shaft of the moving system. Due to the movement of the coil in the magnetic field the pointer rotates on the scale of the instrument.
Advantages of Permanent Magnet Moving Coil Instrument
- The instrument consumes very low power because of its light coil.
- The angle of deflection of the pointer is directly proportional to the current, hence, the scale is uniform.
- The instrument produces very high torque compared to the weight of the moving system.
- As there is no magnetization or demagnetization of iron during operation of the instrument, the instrument is free from hysteresis.
- The aluminum frame used for holding the coil provides eddy current damping. So, a permanent magnet moving coil instrument does not require any additional damping mechanism.
- As two strong magnetic poles confine the operating field of the instrument in between them. Hence, the stray magnetic field cannot much affect the performance of the instrument.
Disadvantages of Permanent Magnet Moving Coil Instrument
- Because of the sophisticated construction, this instrument costs more than a moving iron instrument.
- Because of the presence of a permanent magnet and springs in the instrument, errors in reading may arise in old instrument due to aging effects in the magnet and spring.
The PMMC instrument is shown in the below images.The moving coil is either rectangular or circular in shape. It has number of turns of fine wire. The coil is suspended so that it is free to turn about its vertical axis. The coil is placed in uniform, horizontal and radial magnetic field of a permanent magnet in the shape of a horse-shoe. The iron core is spherical if coil is circular and is cylindrical if the coil is rectangular. Due to iron core, the deflecting torque increase, increasing the sensitivity of the instrument.
The controlling torque is provided by two phosphor bronze hair springs.
The damping torque is provided by eddy current damping. It is obtained by movement of aluminum former, moving in the magnetic field of the permanent magnet.
The pointer is carried by the spindle and it moves over a graduated scale. The pointer has light weight so that it deflects rapidly. The mirror is placed below the pointer to get the accurate reading by removing the parallax. The weight of the instrument is normally counter balanced by the weights situated diametrically opposite and rapidly connected to it. The scale markings of the basic d.c PMMC instruments are usually linearly spaced as the deflecting torque and hence the pointer deflections are directly proportional to the current passing through the coil.
The top view of PMMC instrument is shown in the below image.
Advantages of PMMC
The various advantages of PMMC instruments are,
It has uniform scale.
With a powerful magnet, its torque to weight ratio is very high. So operating current of PMMC is small.
The sensitivity is high.
The eddy currents induced in the metallic former over which coil is wound, provide effective damping.
It consumes low power, of the order of 25 W to 200 mW.
It has high accuracy.
Instrument is free from hysteresis error.
Extension of instrument range is possible.
Not affected by external magnetic fields called stray magnetic fields.
Disadvantages of PMMC
The various disadvantages of PMMC instruments are ,
PMMC is Suitable for direct current measurement only.
Ageing of permanent magnet and the control springs introduces the errors.
Torque Equation Of Pmsm
The cost is high due to delicate construction and accurate machining.
The friction is due to jewel-pivot suspension.
Torque Equation Of Pmmc