Measurements & Measuring Instruments - AIE 141 Lecture Notes PDF

Measurements & Measuring Instruments - AIE 141 Ch.#2-1: Indicating Instruments Dr. Hany S. E. Mansour Electrical Engineering Department, Faculty of Engineering, Suez Canal University Email:...

Measurements & Measuring Instruments - AIE 141 Ch.#2-1: Indicating Instruments Dr. Hany S. E. Mansour Electrical Engineering Department, Faculty of Engineering, Suez Canal University Email: [email protected] Phone: 010 243 27 200 Dr. Hany S. E. Mansour Measurements & Measuring Instruments Lec. #4 Ch.2_1 Classification of Electrical Measuring Instrument ❖Indicating Instruments: Classification Directly indicate the value of electrical Indicating quantity with the help of pointer. Instruments Examples: Analog Ammeters, Analog Integrating Voltmeters. Instruments Recording Instruments Dr. Hany S. E. Mansour Measurements & Measuring Instruments Lec. #4 Ch.2_1 2 Classification of Electrical Measuring Instrument ❖Integrating Instruments: Classification Measure the total quantity of electrical Indicating energy over a specified period of time. Instruments Give the summation of electrical quantity Integrating being supplied for the given time only. Instruments Examples: Household Energy meter, Recording Ampere hour meter. Instruments Dr. Hany S. E. Mansour Measurements & Measuring Instruments Lec. #4 Ch.2_1 3 Classification of Electrical Measuring Instrument ❖Recording Instruments: Classification Give a continuous record of variations of Indicating the electrical quantity to be measured. Instruments Example: Recording voltameters which Integrating is used to record the generated voltage. Instruments Recording Instruments Dr. Hany S. E. Mansour Measurements & Measuring Instruments Lec. #4 Ch.2_1 4 Essential Features of Indicating Instruments ❖Deflecting (Operating) Torque: Deflecting Torque The torque needed to obtain the deflection. Torques It is proportional to the magnitude of Controlling Torque electrical quantity being measured. Inertia Torque Damping Torque Dr. Hany S. E. Mansour Measurements & Measuring Instruments Lec. #4 Ch.2_1 5 Essential Features of Indicating Instruments ❖Controlling (Restoring/Balancing) Torque: Deflecting Torque Controls the movement of the pointer. Torques Opposes the deflecting torque and increases Controlling Torque with the deflection of the moving system. Brings pointer to zero position when the Inertia Torque deflecting torque is removed. Damping Torque Dr. Hany S. E. Mansour Measurements & Measuring Instruments Lec. #4 Ch.2_1 6 Essential Features of Indicating Instruments Controlling Torque Spring Control Gravity Control 𝑇𝑐 = 𝐶𝑠 × 𝜃 𝑇𝑐 = 𝑘 × sin(𝜃) Dr. Hany S. E. Mansour Measurements & Measuring Instruments Lec. #4 Ch.2_1 7 Example For a given ammeter, the deflecting torque is in proportional with the square of the current. A current of 2 A produces a deflection angle of 90°. What is the required current to produce a deflection angle 45°? Assume that the instrument has: i) Spring control ii) Gravity control Dr. Hany S. E. Mansour Measurements & Measuring Instruments Lec. #4 Ch.2_1 8 Example For a given ammeter, the deflecting torque is in proportional with the square of the current. A current of 2 A produces a deflection angle of 90°. What is the required current to produce a deflection angle 45°? Assume that the instrument has: i) Spring control ii) Gravity control Solution 𝑇𝑑 ∝ 𝐼2 For spring control: 𝑇𝑑 ∝ 𝜃 For gravity control: 𝑇𝑑 ∝ sin(𝜃) 𝑇1 𝐼12 𝜃1 22 90 𝑇1 𝐼12 sin(𝜃1 ) 22 sin(90) = 2= 2 = 45 = 2= 2 = sin(45) 𝑇2 𝐼2 𝜃2 𝐼2 𝑇2 𝐼2 sin(𝜃2 ) 𝐼2 𝐼2 = 1.4142 𝐴 𝐼2 = 1.682 𝐴 Dr. Hany S. E. Mansour Measurements & Measuring Instruments Lec. #4 Ch.2_1 9 Essential Features of Indicating Instruments ❖ Inertia Torque: Deflecting Torque The moving parts of instrument have a mass and the Torques movement depends on the inertia of this mass “J”. Controlling Torque The inertia produces an inertia torque that counteracts Inertia Torque the pointer movement during the transient period only, Damping Torque while it will be zero at steady state conditions. It depends on angular acceleration of the pointer. Dr. Hany S. E. Mansour Measurements & Measuring Instruments Lec. #4 Ch.2_1 10 Essential Features of Indicating Instruments Damping Torque: Because of inertia, the pointer oscillates around its final deflected position for some time before coming to rest. Damping force acts as a brake to prevent these oscillations and brings the pointer to it’s final deflected position quickly. The damping torque should be of such a magnitude that the pointer quickly comes to its final steady position, without overshooting. Dr. Hany S. E. Mansour Measurements & Measuring Instruments Lec. #4 Ch.2_1 11 Essential Features of Indicating Instruments ❖ Damping Torque: If the instrument is underdamped, the moving system will oscillate about the final steady position with a decreasing amplitude and will take some time before it comes to rest. When the moving system moves rapidly but smoothly to its final steady position, the instrument is said to be critically damped or deadbeat. In an overdamped instrument, the moving system moves slowly to its final steady position in a lethargic fashion. Dr. Hany S. E. Mansour Measurements & Measuring Instruments Lec. #4 Ch.2_1 12 Essential Features of Indicating Instruments Air Friction Damping Damping Fluid Friction Torque Damping Eddy Current Damping Dr. Hany S. E. Mansour Measurements & Measuring Instruments Lec. #4 Ch.2_1 13 Essential Features of Indicating Instruments ❖Air Friction Damping: It consists of a light aluminum piston that is attached to the moving system. This piston moves in a fixed air chamber which is closed at one end. The clearance between piston and chamber walls is uniform throughout and is very small. When there are oscillations, the piston moves into and out of an air chamber. Dr. Hany S. E. Mansour Measurements & Measuring Instruments Lec. #4 Ch.2_1 14 Essential Features of Indicating Instruments ❖Air Friction Damping: When the piston moves into the chamber, the air inside is compressed and the pressure of air thus built up, opposes the motion of the piston and hence of the whole of the moving system. When the piston moves out of the air chamber, pressure in closed space falls, and the pressure on the open side of the piston is greater than on the other side. Thus there is again an opposition to the motion. Dr. Hany S. E. Mansour Measurements & Measuring Instruments Lec. #4 Ch.2_1 15 Essential Features of Indicating Instruments ❖Fluid Friction Damping: This method is similar to air friction damping, only air is replaced by working fluid. The friction between the disc and fluid is used for opposing motion. Damping force due to fluid is greater than that of air due to more viscosity. The frictional force between oil and the vane is used to produce the damping torque, which opposes the oscillating behavior of the pointer. Dr. Hany S. E. Mansour Measurements & Measuring Instruments Lec. #4 Ch.2_1 16 Essential Features of Indicating Instruments ❖ Fluid Friction Damping: The advantages of this method are : 1) Due to more viscosity of fluid, more damping is provided. 2) The oil can also be used for insulation purposes 3) Due to the upthrust of oil, the load on the bearings is reduced, thus reducing the frictional errors. The disadvantages of this method are : 1) This can be only used for the instruments which are in vertical position. 2) Due to oil leakage, the instruments can not be kept clean. Dr. Hany S. E. Mansour Measurements & Measuring Instruments Lec. #4 Ch.2_1 17 Essential Features of Indicating Instruments ❖Eddy Current Damping: This is also known as electromagnetic damping. When a conductor moves in a magnetic field an emf is induced in it and if a closed path is provided, a current (known as eddy current) flows. This current interacts with the magnetic field to produce an electromagnetic torque that opposes the motion. Dr. Hany S. E. Mansour Measurements & Measuring Instruments Lec. #4 Ch.2_1 18 Essential Features of Indicating Instruments ❖ Eddy Current Damping: This torque is proportional to the strength of the magnetic field and the current produced. The current is proportional to emf which, in turn, is proportional to velocity of the conductor. Thus, if the strength of the magnetic field is constant (if it is produced by a permanent magnet), the torque is proportional to the velocity of the conductor. Dr. Hany S. E. Mansour Measurements & Measuring Instruments Lec. #4 Ch.2_1 19 Essential Features of Indicating Instruments The total torque equation is given by: Deflecting Torque 𝑇𝑑 = 𝑇𝑐 + 𝑇𝐽 + 𝑇𝐷 Torques Controlling Torque At steady state: Inertia Torque 𝑇𝑑 = 𝑇𝑐 Damping Torque Dr. Hany S. E. Mansour Measurements & Measuring Instruments Lec. #4 Ch.2_1 20