Jawaharlal Nehru Technological University Hyderabad
Jawaharlal Nehru Technological University Hyderabad B.Tech II DYNAMICS OF MACHINERY Previous Question Paper (September/October - 2023 - R16)
Note: Part A is compulsory (25 Marks). In Part B, answer any one question from each unit (50 Marks).
Part A
Define D’Alembert’s principle.
Answer
D'Alembert's principle states that a system of rigid bodies in motion can be considered to be in a state of dynamic equilibrium if an inertia force is applied to each body in addition to the external forces acting on it. Mathematically, the principle is expressed as:
where ΣF represents the vector sum of all external forces acting on the body, and Fᵢ represents the inertia force, defined as the product of the mass of the body and its acceleration acting in the direction opposite to the acceleration (Fᵢ = -ma). By treating dynamic problems as equivalent to static problems, this principle allows for the application of the equations of static equilibrium to solve for unknown forces or accelerations in mechanical systems.
Explain the gyroscopic effect in aero planes.
Answer
The gyroscopic effect in aeroplanes arises due to the angular momentum of the rotating engine components (such as the propeller or turbine rotors). When an aeroplane undergoes a change in direction, the gyroscopic couple acts on the airframe, influencing its stability and maneuverability.
The magnitude of the gyroscopic couple is given by:
Where:
- I is the moment of inertia of the rotating parts.
- ω is the angular velocity of the engine/propeller.
- ωₚ is the angular velocity of precession (the rate at which the plane changes its orientation).
The effects depend on the maneuver:
- Take-off: If the propeller rotates clockwise (viewed from the rear), the gyroscopic couple during a nose-up maneuver causes the plane to yaw to the left.
- Landing: During a nose-up maneuver for landing, the gyroscopic couple acts in the opposite direction, potentially causing the plane to yaw to the right.
- Banking: When an aeroplane turns (banks), the gyroscopic couple acts to either pitch the nose up or down depending on the direction of the turn and the sense of rotation of the propeller.
These effects are critical in aircraft design, as pilots must apply corrective control inputs (such as rudder or elevator deflection) to counteract the unintended pitch or yaw moments induced by the gyroscopic action during high-speed maneuvers.
What is meant by piston effort and crank effort?
Answer
Sign in to view the complete answer paper.
What do you mean by turning moment diagram? Explain.
Answer
Sign in to view the complete answer paper.
Explain the friction circle and friction axis?
Answer
Sign in to view the complete answer paper.
What is a brake? What is the difference between brake and clutch?
Answer
Sign in to view the complete answer paper.
Describe the function of simple watt governor. What are its limitations?
Answer
Sign in to view the complete answer paper.
Why is balancing is necessary for rotors of high speed engines?
Answer
Sign in to view the complete answer paper.
What are the basic elements of vibratory system?
Answer
Sign in to view the complete answer paper.
Differentiate among the under damping, critical damping and over damping?
Answer
Sign in to view the complete answer paper.
Part B
What is the condition to design the four-wheeler to maintain the stability? Derive the expression with a neat sketch.
Answer
Sign in to view the complete answer paper.
Determine the couple T acting on the link 2 to maintain the static equilibrium of the slider crank mechanism subjected to forces as shown in Figure 1. The link lengths are AB=300mm, BC=455mm, BE=175mm.
Answer
Sign in to view the complete answer paper.
The turning moment diagram for a multi-cylinder engine has been drawn to a scale of 1 mm = 325 Nm vertically and 1 mm = 30 horizontally. The areas above and below the mean torque line are -26, +378, -256, +306, -302, +244, -380, +261 and -225 mm^2. The engine is running at a mean speed of 600 r.p.m. The total fluctuation of speed is not to exceed +1.8% of the mean speed. If the radius of flywheel is 0.7 m, find the mass of the flywheel.
Answer
Sign in to view the complete answer paper.
The crank and connecting rod of a vertical petrol engine, running at 1800 rpm are 60 mm and 270m respectively. The diameter of the piston is 100 mm and the mass of the reciprocating parts is 1.2 kg. During the expansion stoke when the crank has turned 20 deg from the top dead centre, the gas pressure is 650 kN/m^2. Determine the:
Answer
Sign in to view the complete answer paper.
Answer
Sign in to view the complete answer paper.
Answer
Sign in to view the complete answer paper.
Answer
Sign in to view the complete answer paper.
Derive the expression for uniform pressure theory and uniform wear theory with a neat sketch.
Answer
Sign in to view the complete answer paper.
The figure 2 shows a simple band brake which applied to a shaft carrying a flywheel of 300 kg mass and of radius of gyration 280 mm. The drum diameter is 220 mm and the shaft speed 240 rpm. The coefficient of friction is 0.3. Find the brake torque when a force of 100 N is applied at the lever end. Also, determine the number of turns of the flywheel and time taken by it before coming to rest.
Answer
Sign in to view the complete answer paper.
Answer
Sign in to view the complete answer paper.
Answer
Sign in to view the complete answer paper.
Answer
Sign in to view the complete answer paper.
Answer
Sign in to view the complete answer paper.
Derive an equation for the natural frequency of free transverse vibration of a shaft headed with a number of concentrated loads, by Dunkerley’s method.
Answer
Sign in to view the complete answer paper.
Three rotors A, B and C having moment of inertia of 2000, 6000 and 3500 kg m^2 respectively and carried on a uniform shaft of 0.4 m diameter. The length of the shaft between the rotors A and B is 6m and between B and C is 3.2 m. find the natural frequency of the torsional vibration. The modulus of rigidity for the shaft material is 80 GN/m^2.
Answer
Sign in to view the complete answer paper.