Velocity measurements

measurement of linear and angular velocities including tachometers, transducers

1. VELOCITY MEASUREMENTS AKHIL KRISHNAN G 1

2. MEASUREMENT OF LINEAR VELOCITY Velocity is the first derivative of displacement. Linear velocity is defined as the rate of change of the position vector with time at an instant in time . 2

3. The methods used for measurement of linear velocity utilize the following type of transducers . Electro-magnetic transducers. Seismic transducers . Linear velocity transducer. Digital transducers. Transducers using Doppler effect. Velocity measurement using displacement and acceleration sensors Moving magnet type Moving Coil Type 3

4. 1.ELECTROMAGNETIC TRANSDUCERS The most commonly used transducer for measurement of linear velocities . This transducer utilizes the voltage produced in a coil on account of change in flux linkages resulting from change in reluctance. They are classified into two types A)Moving magnet type B)Moving coil type 4

5. A)MOVING MAGNET TYPE TRANSDUCER The sensing element is a rod type permanent magnet that is rigidly coupled to the device whose velocity is being measured . There is a coil surrounding the permanent magnet. The motion of the magnet induces a voltage in the coil and the amplitude of the voltage is directly proportional to the velocity. The polarity of the output voltage determines the direction of motion 5

6. For a coil placed in magnetic field the voltage generated is: e 0= BAN v = K v K=BAN= a constant B=flux density ; Wb /m 2 , A= area of coil; m 2 N= Number of turns of coil, v =relative velocity of magnet with respect to coil 6

7. ADVANTAGES The maintenance requirements of these transducers are negligible , because there are no mechanical surfaces or contacts. The output voltage is linearly proportional to velocity. DISADVANTAGES The performance of these transducers is adversely affected by stray magnetic fields. These fields can cause noise. The frequency response is usually limited and is stated. These transducers are not very useful for measurement of vibrations because their calibration deteriorates as contact with steel tools etc. leads to progressive demagnetization. 7

8. B)MOVING COIL TYPE VELOCITY TRANSDUCER It operates essentially through the action of a coil moving in a magnetic field. A voltage is generated in the coil which is proportional to the velocity of the coil. 8

9. The coil is mounted on a pivoted arm. There is a mass attached at the end of the arm. The velocity to be measured is applied to the arm and therefore the coil moves in the field of permanent magnet. A voltage is generated on account of motion of the coil in the magnetic field. The output voltage is proportional to the velocity. ADVANTAGES This is a more satisfactory arrangement as the system now forms a closed magnetic circuit with a constant air gap, and the whole device is contained in an antimagnetic case which reduces the effects of stray magnetic fields. 9

10. 2.SEISMIC TYPE VELOCITY TRANSDUCER A permanent magnet is supported between two springs and fitted with low friction bearing rings. It act as a seismic mass. The frame is rigidly attached to the object whose velocity is being measured. The object is vibrating at a frequency in excess of the low natural frequency of the transducer. The self resonant frequencies of seismic mass are typically 10 Hz to 15 Hz. If the operation at frequencies above 20 Hz occurs the mass is relatively stationary, and the case and coil moving in the magnetic field has a large voltage induced in it which is proportional to the velocity . 10

11. The seismic transducer have a good frequency response. Both moving coil and seismic transducers have the disadvantage that connections must be made on the moving part. 11

12. 3.LINEAR VELOCITY TRANSDUCER ( LVT ) A linear velocity transducer ( LVT ) is an inductive device which utilizes the link between electricity and magnetism as found by H. A. Lorentz, if a magnetic field moves near an electrical wire, current flows through the wire . 12

13. An LVT consists of a rod called the core (a permanent magnet), and two electrical coils The core slides inside a hollow cylindrical tube called a bobbin and A DC voltage is generated when the core moves . Since the two coils are wrapped with opposite polarity , and since the magnet also has two poles (north and south), the south pole induces a voltage primarily in coil 1, and the north pole primarily in core 2 . It turns out that the net voltage is proportional to the speed of the core . Although the range is limited, LVTs are used in some types of machinery , like milling machines. 13

14. 4.DIGITAL TRANSDUCERS Velocity is the rate of change of displacement with respect to time. If a number of evenly spaced marks are placed on the moving object ant the number of these marks is n, passing at a given time t s, the velocity is v= nd /t d =distance between the marks The marks can be made photo electrically or there may be protrusions which are detected by inductive or capacitative techniques. 14

15. 5.TRANSDUCERS USING DOPPLER EFFECT The doppler effect is an effective and accurate method of measuring linear velocity. If a narrow radio beam or ultrasonic beam is aimed at an object, the beam will be reflected back to the source. However ,if the object is moving ,the frequency of the signals received back differs from that of the transmitted signal. 15

16. A radar-Doppler velocimeter Radio waves of wavelength λ are transmitted (incident waves) towards a moving object . The object moves with velocity V at angle θ relative to the radar unit, as sketched 16

17. The radio waves reflect off the moving object, and are sensed by a radio wave detector (receiver), that is also mounted on the radar unit . The detector measures the frequency of the reflected radar beam, and the unit compares the frequency of the transmitted and reflected beams . Doppler radar units are used by police to measure the speed of automobiles, and they are also used in professional sports to measure the speed of baseballs, etc . Laser light can be used in place of radio waves. Then, the device is called a laser Doppler velocimeter 17

18. 6.VELOCITY MEASUREMENT USING DISPLACEMENT AND ACCELERATION SENSORS Displacement sensors velocity is the time derivative of displacement V ( t ) ₌ dx ( t ) / dt. W e could calculate velocity by taking the time derivative of displacement measurements from a displacement sensor(potentiometer , LVDT, laser displacement meter, etc .) This technique is often used for measuring the velocity of very fast-moving objects like bullets. Disadvantage: the process of differentiation of a signal amplifies the noise in the system. 18

19. Acceleration sensors velocity is the time integral of acceleration. V ( t) = V ₀ + ∫ a (t) dt Unlike differentiation, the process of integration decreases the noise in the system. Thus, velocity measurement by integration of acceleration data is generally a wise choice. 19

20. MEASUREMENT OF ANGULAR VELOCITY The measurement of angular velocity may be made with a tachometer. The tachometer may be defined as: An instrument used for measure of angular velocity , as of shaft , either by registering the total number of revolutions during the period of contact, or by indicating directly the number of revolutions per minute. An instrument which either continuously indicates the value of rotary speed or continuously displays a reading of average speed over rapidly operated short intervals of time. 20

21. The tachometers are classified as: Mechanical tachometers Electrical tachometers 21

22. 1.MECHANICAL TACHOMETERS Hand speed tachometers. It has a spindle which can be attached to this to be measured. The spindle is connected to mechanical counters which display the count. This indicator has an inbuilt stop watch and a mechanical counter with automatic disconnect. The hand speed indicators can be used to speeds of 20,000 to 30,000 rpm with an accuracy of 1 %. 22

23. Disadvantages of Mechanical Tachometers. Mechanical tachometers impose a load on the shafts to which they are connected and hence absorb power. So they cannot be used for applications involving small powers since the attachment of tachometer to the shaft will decrease the speed. Therefore mechanical tachometers are only useful for heavy machinery. On account of inertia of mechanical parts, the mechanical tachometers are not able to follow the variations in the speed. Therefore they indicate only the average speed over a particular interval of time. They cannot be used in applications where instantaneous indication of speed is desired. The mechanical tachometers normally use an arrangement wherein a counter is used for counting the number of events and a stop watch for measurement of time. The speed is calculated from the reading of two. This involves large errors especially when the stop watch is operated manually . 23

24. 2.ELECTRICAL TACHOMETERS D.C. Tachometer Generators They consist of a small armature which is coupled to the machine whose speed is to be measured. This armature revolves in a field of permanent magnet. The emf generated is proportional to the product of flux and speed. Since the flux of the permanent magnet is constant, the voltage generated is proportional to speed. The polarity of output voltage indicates the direction of rotation. This emf is measured with the help of a moving coil voltmeter having a uniform scale and calibrated directly in terms of speed. 24

25. A series resistance is used in the circuit for the purpose of limiting the current from the generator in the event of a short circuit on the output side. 25

26. Advantages The direction of rotation is directly indicated by the polarity of the output voltage. The output voltage is typically 10mv/rpm and can be measured with conventional type d.c. voltmeters. Disadvantages Brushes of small tachometer generators often produce maintenance problems, as their contact resistance may vary and produce appreciable error. Thus the commutator and the brushes require periodic maintenance. The input resistance of meter should be very high as compared with output resistance of generator. This is required to limit the armature current to small value. If the armature current is large, the field of the permanent magnet is distorted giving rise to non-linearity 26

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