Instrumentation Portion 1 PDF

ME301 Metrology and Instrumentation Dr Mervin Joe Thomas Assistant Professor Department of Mechanical Engineering National Institute of Technology Karnataka, Surathkal Dr Mervin Joe Thomas, Dept. of Mechanical Engg., NITK Surathkal...

ME301 Metrology and Instrumentation Dr Mervin Joe Thomas Assistant Professor Department of Mechanical Engineering National Institute of Technology Karnataka, Surathkal Dr Mervin Joe Thomas, Dept. of Mechanical Engg., NITK Surathkal 2  What is Instrumentation? The human senses cannot provide exact quantitative information about the knowledge of events occurring in our environments. The stringent requirements of precise and accurate measurements in the technological fields have led to the development of mechanical aids called instruments. Dr Mervin Joe Thomas, Dept. of Mechanical Engg., NITK Surathkal 3  What is a sensor? A sensor consists of a transducer whose function is to convert one form of energy into electrical form of energy. A sensor is a sensing element of a measurement system that converts the input quantity being measured into an output signal which is related to the quantity. Dr Mervin Joe Thomas, Dept. of Mechanical Engg., NITK Surathkal 4  Sensor – Introduction A device that provides a usable output in response to a specified measurement. Sensor is a device that detects and responds to some input from the physical environment Input could be light, heat, motion, moisture, force, pressure, displacement, etc. It produces a proportional output signal (electrical, mechanical, magnetic, etc.). Human beings are equipped with 5 different types of sensors. Eyes detect light energy, ears detect acoustic energy, a tongue and a nose detect certain chemicals, and skin detects pressures and temperatures. The eyes, ears, tongue, nose, and skin receive these signals and then send messages to the brain which outputs a response. For example, when you touch a hot plate, your brain tells you it is hot, not your skin. Dr Mervin Joe Thomas, Dept. of Mechanical Engg., NITK Surathkal 5  What are the Purposes of Sensors? To monitor processes and operations – To Control processes and operations – Dr Mervin Joe Thomas, Dept. of Mechanical Engg., NITK Surathkal 6  What are the Purposes of Sensors? (contd..) To carry out analysis – Dr Mervin Joe Thomas, Dept. of Mechanical Engg., NITK Surathkal 7  Sensors – Types Sensors can be classified into various groups according to factors such as measurand, application fields, conversion principle, and thermodynamic considerations A. Displacement, position and B. Velocity and motion C. Force D. Temperature proximity sensors Incremental encoder Strain gauge Bimetallic strips Potentiometer Tachogenerator loadcell Resistance Strain-gauged element Pyroelectric sensors temperature detectors Capacitive element E. Fluid pressure Thermistors Differential transformers Diaphragm pressure gauge Thermo-diodes and Eddy current proximity sensors Capsules, bellows, pressure tubes transistors Inductive proximity switch Piezoelectric sensors Thermocouples Optical encoders F. Liquid flow Light sensors G. Liquid level Pneumatic sensors Orifice plate Photodiodes Floats Proximity switches(magnetic) Turbine meter Photoresistors Differential pressure Hall effect sensors Dr Mervin Joe Thomas, Dept. of Mechanical Engg., NITK Surathkal 8 Static Characteristics of Instruments By static characteristics, we mean attributes associated with static measurements or measurements of quantities that are constant or vary slowly with time. For example, the measurement of emf (electromotive force) of a cell or the resistance of a resistor at constant temperature are both static measurements. Dr Mervin Joe Thomas, Dept. of Mechanical Engg., NITK Surathkal 9 Accuracy Accuracy determines the closeness of an instrument reading to the true value of the measurand No instrument gives an exact value of what is being measured, there is always some uncertainty in the measured values. This uncertainty express in terms of accuracy and error. The difference between measured value (𝑉𝑚 ) and true value (𝑉𝑡 ) of the quantity is expressed as instrument error. Dr Mervin Joe Thomas, Dept. of Mechanical Engg., NITK Surathkal 10 Precision Precision is another term which is often used in the same connotation as accuracy. But in reality, precision is different from accuracy. Precision is, therefore, related to the repeatability of the instrument reading and is a characteristic of the instrument itself. Dr Mervin Joe Thomas, Dept. of Mechanical Engg., NITK Surathkal 11 Sensitivity Sensitivity is defined as the absolute ratio of the increment of the output signal (or response) to that of the input signal (or measurand). 𝑞𝑜 𝑎𝑛𝑑 𝑞𝑖 𝑎𝑟𝑒 𝑜𝑢𝑡𝑝𝑢𝑡 𝑎𝑛𝑑 𝑖𝑛𝑝𝑢𝑡 𝑞𝑢𝑎𝑛𝑡𝑖𝑡𝑖𝑒𝑠 𝑟𝑒𝑠𝑝𝑒𝑐𝑡𝑖𝑣𝑒𝑙𝑦 Dr Mervin Joe Thomas, Dept. of Mechanical Engg., NITK Surathkal 12  Undesirable characteristics in Measuring Instruments – Static Characteristics Drift denotes the change in the indicated reading of an instrument over time when the value of the measurand remains constant. If there is no drift, the reproducibility is 100%. Several causes contribute to the drift. Stray electromagnetic fields and mechanical vibrations are some of the causes. Hysteresis – Not all the energy put into a system while loading is recoverable upon unloading. For example, a spring balance may show one set of readings when the weight is increased in steps and another set of readings when the weight is decreased in steps. The loading and unloading curves do not coincide because of the consumption of some energy by the internal friction of the solid, and also because of the external sliding friction between components of the instrument. Dr Mervin Joe Thomas, Dept. of Mechanical Engg., NITK Surathkal 13 Undesirable characteristics in Measuring Instruments – Dynamic Characteristics Threshold – Suppose an instrument is in its zero position, i.e. there is no input to it. If now an input is gradually applied to it, the instrument will require some minimum value of input before it shows any output Dr Mervin Joe Thomas, Dept. of Mechanical Engg., NITK Surathkal 14 Undesirable characteristics in Measuring Instruments Resolution – Even above threshold input, an instrument needs a minimum increment in input to produce perceptible output. This minimum necessary increment is called the resolution of the instrument. Dr Mervin Joe Thomas, Dept. of Mechanical Engg., NITK Surathkal 15  Undesirable characteristics in Measuring Instruments – Dynamic Characteristics Creep – A measurement system may take some time to adjust fully to a change in the applied input, and the creep of a transducer is usually defined as the change of output with time following a step increase in the input from one value to another. Many instrument manufacturers specify the creep as the maximum change of output over a specified time after increasing the input from zero to the rated maximum input. Dr Mervin Joe Thomas, Dept. of Mechanical Engg., NITK Surathkal 16 Dynamic Characteristics Speed of response and measuring lag: In a measuring instrument, the speed of response (or) responsiveness is defined as the rapidity with which an instrument responds to a change in the value of the quantity being measured. Measuring lag refers to the delay in the response of an instrument to a change in the input signal. The lag is caused by conditions such as inertia, or resistance. Dr Mervin Joe Thomas, Dept. of Mechanical Engg., NITK Surathkal 17  Dynamic Characteristics (contd..) Fidelity It is defined as the degree to which a measuring instrument is capable of faithfully reproducing the changes in input, without any dynamic error. It refers to the ability of the system to reproduce the output in the same form as the input. If the input is a sine wave then for 100% fidelity the output should also be a sine wave. Dr Mervin Joe Thomas, Dept. of Mechanical Engg., NITK Surathkal 18 Dynamic Characteristics (contd..) Overshoot The overshoot is defined as the maximum amount by which the pointer moves beyond the steady state. Dr Mervin Joe Thomas, Dept. of Mechanical Engg., NITK Surathkal 19  Standard test inputs: The dynamic performance of both the measuring and control systems is determined by applying some known and predetermined input signal to its primary sensing element and then studying the behaviour of the output signals. The most common standard inputs used for dynamic analysis i. Step functions ii. Linear (or) ramp functions iii. Sinusoidal (or) sine wave functions Dr Mervin Joe Thomas, Dept. of Mechanical Engg., NITK Surathkal 20 Step Function Taking Laplace transform, we get, Dr Mervin Joe Thomas, Dept. of Mechanical Engg., NITK Surathkal 21 In engineering, simulation, and design are the crucial stages in the physical realization of any invention because one cannot afford the trial-and- error method on a complex engineering project. To facilitate the design and simulation we must go through various mathematical equations. Every time it is not feasible to solve them in the time domain, especially the differential equations. To make this simple we convert these complex time- domain equations into the frequency domain where they will be simply solvable algebraic functions. Dr Mervin Joe Thomas, Dept. of Mechanical Engg., NITK Surathkal 22 Ramp or Linear Function Taking Laplace transform, we get, Dr Mervin Joe Thomas, Dept. of Mechanical Engg., NITK Surathkal 23 Sinusoidal (or) sine wave function Here the input has a cycle variation, the input varies sinusoidal with a constant amplitude mathematically it may be represented as where A is the amplitude and 𝜔 is the frequency in rad/s A general measurement system can be mathematically described by the following differential equation = Dr Mervin Joe Thomas, Dept. of Mechanical Engg., NITK Surathkal 24  = Dr Mervin Joe Thomas, Dept. of Mechanical Engg., NITK Surathkal 25 Zero Order Systems A system whose output is directly proportional to the input, irrespective of how input varies, without any distortion or time lag The mathematical representation of zero order system is when the power of n is set to zero in the general equation – Examples – Mechanical levers, amplifier, potentiometer (gives output voltage proportional displacement of slider) Dr Mervin Joe Thomas, Dept. of Mechanical Engg., NITK Surathkal 26 First Order System It is a system whose dynamic behaviour is described by a first-order differential equation. Example: Thermometer, build-up of pressure in bellows Dr Mervin Joe Thomas, Dept. of Mechanical Engg., NITK Surathkal 27  First Order System (Time Domain) Dr Mervin Joe Thomas, Dept. of Mechanical Engg., NITK Surathkal 28  Taking Laplace Transform, 𝜏𝑠𝜃0 𝑠 + 𝜃0 𝑠 = 𝐾𝜃𝑖 𝑠 First Order System Therefore, the transfer function is given by, 𝜃0 𝐾 (Frequency = 𝜃𝑖 1 + 𝜏𝑠 Domain) Note: The time constant is a measure of how fast the system responds. The smaller the time constant, the more responsive is the system. 𝜏 also called “dead time” or “dynamic lag” Dr Mervin Joe Thomas, Dept. of Mechanical Engg., NITK Surathkal 29 Standard form of first-order transfer functions Dr Mervin Joe Thomas, Dept. of Mechanical Engg., NITK Surathkal 30  Example on first order systems – Mercury Thermometer Basic assumptions: 1. All the resistance to heat transfer resides in the film surrounding the bulb (conduction resistance 𝑇𝑚 is neglected). = 𝑀𝑒𝑟𝑐𝑢𝑟𝑦 𝑇𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒 𝑇𝑓 = 𝐹𝑙𝑢𝑖𝑑 𝑇𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒 2. All the thermal capacity is in the mercury. 3. The mercury assumes a uniform temperature throughout. 4. The glass wall containing the mercury does not expand or contract during the transient response. 5. Constant properties. Dr Mervin Joe Thomas, Dept. of Mechanical Engg., NITK Surathkal 31  Mercury Thermometer 𝑋 = 𝐹𝑙𝑢𝑖𝑑 𝑇𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒 𝑌 = 𝑀𝑒𝑟𝑐𝑢𝑟𝑦 𝑇𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒 Dr Mervin Joe Thomas, Dept. of Mechanical Engg., NITK Surathkal 32 Dynamic Response of First Order Instruments For first-order systems, the transfer function is given as, Dr Mervin Joe Thomas, Dept. of Mechanical Engg., NITK Surathkal 37 Dynamic Response of First-Order Instruments – Step Input Taking Inverse Laplace Transform, Input 𝒒𝒊 (𝒕) Step Response of first-order instrument 38 Measurement error and Steady-state Error – Step Response Dr Mervin Joe Thomas, Dept. of Mechanical Engg., NITK Surathkal 39 Dr Mervin Joe Thomas, Dept. of Mechanical Engg., NITK Surathkal 40 Solution Dr Mervin Joe Thomas, Dept. of Mechanical Engg., NITK Surathkal 41 Dynamic Response of First-Order Instruments – Ramp Input Dr Mervin Joe Thomas, Dept. of Mechanical Engg., NITK Surathkal 42 Measurement error and Steady-state Error – Ramp Response Dr Mervin Joe Thomas, Dept. of Mechanical Engg., NITK Surathkal 43 Second Order System 44  Second Order Examples of Second Order systems System Spring mass system employed for acceleration and force measurements (contd..) Piezoelectric pickups Galvanometers Pen control in x-y plotter mechanisms Dr Mervin Joe Thomas, Dept. of Mechanical Engg., NITK Surathkal 45 Spring-Mass-Damper System – Weighing Balance Dr Mervin Joe Thomas, Dept. of Mechanical Engg., NITK Surathkal 46 Dynamic equation of Weighing Balance Dr Mervin Joe Thomas, Dept. of Mechanical Engg., NITK Surathkal 47  Overdamped, Critically Damped and Underdamped Therefore, the roots of the denominator are - Dr Mervin Joe Thomas, Dept. of Mechanical Engg., NITK Surathkal 48 Overdamped System with Step Response Dr Mervin Joe Thomas, Dept. of Mechanical Engg., NITK Surathkal 49 Overdamped System with Step Response (contd..) Dr Mervin Joe Thomas, Dept. of Mechanical Engg., NITK Surathkal 50 Second Order system with Step Response (contd..) Dr Mervin Joe Thomas, Dept. of Mechanical Engg., NITK Surathkal 51 Second Order system with Step Response (contd..) Dr Mervin Joe Thomas, Dept. of Mechanical Engg., NITK Surathkal 52