JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech III MECHANICAL MEASUREMENTS AND CONTROL SYSTEMS Previous Question Paper (October - 2020 - R16)

A generalized measurement system consists of several functional stages that transform a physical quantity into a readable output. The block diagram represents the flow of information through these stages:

Input Quantity → Primary Sensing Element → Variable Conversion Element → Variable Manipulation Element → Data Transmission Element → Data Presentation/Recording Element

1. Primary Sensing Element: This stage is in direct contact with the physical quantity being measured. It converts the physical input into a usable electrical or mechanical signal. Example: A Bourdon tube in a pressure gauge converts pressure into mechanical displacement.
2. Variable Conversion Element: This element converts the signal from the sensing element into a more suitable form, typically an electrical signal, without changing the information content. Example: A strain gauge converts mechanical displacement into a change in electrical resistance.
3. Variable Manipulation Element: This stage manipulates the signal to make it suitable for the next stage, often involving amplification, filtering, or linearization. Example: An operational amplifier increases the voltage level of a low-power signal from a thermocouple.
4. Data Transmission Element: This stage is required when the measurement system components are physically separated. It transmits the signal from one location to another without distortion. Example: Telemetry systems or shielded cables used to send sensor data to a control room.
5. Data Presentation/Recording Element: The final stage provides the information to the observer or a control system. It may be an analog indicator, a digital display, or a data logger. Example: A digital multimeter display or a chart recorder showing temperature variations over time.

These stages work in series to ensure that the measured physical variable is accurately detected, processed, and displayed for analysis or control purposes.

Transducers are devices that convert physical quantities into electrical signals. Capacitive and inductive transducers are widely used for measuring displacement, pressure, and force.

Capacitive Transducers: These operate on the principle of variable capacitance. A capacitor consists of two parallel plates separated by a dielectric. The capacitance C is given by the formula:

where ε₀ is the permittivity of free space, εᵣ is the relative permittivity, A is the area of overlap, and d is the distance between plates. Capacitance can be varied by changing the distance (d), the overlap area (A), or the dielectric constant (εᵣ). In a typical displacement sensor, the movement of a diaphragm or a probe changes the gap 'd', resulting in a measurable change in capacitance, which is then converted into an electrical signal using a bridge circuit or an oscillator circuit.

Inductive Transducers: These operate on the principle of electromagnetic induction or change in reluctance. They are categorized into self-generating and passive types. A common type is the Variable Reluctance Transducer, where the inductance L is given by:

where N is the number of turns, μ is the permeability, A is the cross-sectional area, and l is the length of the magnetic path. By moving a ferromagnetic core within a coil, the reluctance of the magnetic circuit changes, which in turn changes the inductance of the coil. This change in inductance is measured using an AC bridge circuit (like an LVDT - Linear Variable Differential Transformer). In an LVDT, a primary winding is energized by an AC source, and two secondary windings connected in series opposition produce an output voltage proportional to the displacement of the magnetic core.