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

The dynamic performance characteristics of a measuring instrument describe its behavior when the input signal varies with time. These characteristics are essential for understanding how an instrument responds to transient or time-varying inputs before reaching a steady state. The primary dynamic characteristics include:

• Speed of Response: This is the rapidity with which an instrument responds to changes in the measured quantity. It indicates how quickly the output reaches a stable value after a change in input.
• Dynamic Error: This is the difference between the true value of the quantity changing with time and the value indicated by the instrument, assuming no static error. It arises due to the inability of the instrument to track rapid input changes.
• Fidelity: This represents the ability of the system to reproduce the input signal in its true form without any distortion. A high-fidelity instrument accurately follows the time-varying input.
• Lag: This refers to the delay in the response of an instrument to a change in the measured variable. It is categorized into retardation lag (where the response begins immediately but takes time to reach the final value) and time delay (where the response does not begin until a specific time has elapsed after the input change).
• Settling Time: The time taken by the instrument output to reach and remain within a specified percentage (usually 2% or 5%) of its final steady-state value following a step input.
• Frequency Response: This describes how the amplitude ratio and phase shift of the output vary with the frequency of a sinusoidal input. It is critical for determining the bandwidth of the instrument.
• Damping Ratio: A measure of how oscillations in the output decay over time. It determines whether the system is underdamped (oscillatory), overdamped (sluggish), or critically damped (fastest response without oscillation).

A piezoelectric transducer operates on the principle of the piezoelectric effect, where certain crystalline materials, such as quartz, Rochelle salt, or barium titanate, generate an electric charge proportional to the mechanical stress applied to them. When used to measure displacement, the transducer is typically configured such that the displacement to be measured exerts a force on the piezoelectric crystal.

The working principle can be broken down into the following steps:

1. When a mechanical displacement is applied, it is converted into a force through a mechanical linkage or a spring-mass system.
2. This force causes physical deformation of the piezoelectric crystal, resulting in the displacement of internal positive and negative charges.
3. The separation of these charges creates a potential difference across the crystal faces, which is directly proportional to the applied force and, consequently, the original displacement.
4. The generated charge Q is given by the relation Q = d × F, where d is the piezoelectric charge constant and F is the applied force.
5. Since the crystal has inherent capacitance C, the resulting voltage V is expressed as V = Q / C.

Because piezoelectric sensors have very high output impedance, the signal is typically fed into a charge amplifier or a high-impedance voltage amplifier to prevent signal attenuation and to convert the charge into a measurable voltage signal. These instruments are primarily used for dynamic displacement measurements due to their excellent frequency response, though they are not suitable for static measurements as the charge leaks away over time.