Unit 1

Force analysis – Applied and Constraint Forces – Free body diagrams – Static Equilibrium conditions – two, three and four force members – Static force analysis

Inertia force and Inertia torque – D’ Alembert’s principle – principle of superposition. Dynamic Analysis in Reciprocating Engines – Gas Forces – Equivalent masses – Bearing loads – Crank shaft Torque. Turning moment diagrams – Fly wheels.

Unit 2

Balancing-Static and dynamic balancing – Balancing of rotating masses – Balancing a single cylinder Engine Balancing-Multi-cylinder Engines – Partial balancing in locomotive Engines –Balancing machines

Vibrations-single degree of freedom system- equations of motion-undamped and damped free vibration of single degree of freedom system- logarithmic decrement

Unit 3

Forced vibration of single degree of freedom system-magnification factor- rotating unbalance-support harmonic excitation- critical speed of shafts-vibration measuring instruments.Vibration of two degree of freedom systemformulation and solution of matrix eigen value problem- natural frequencies and normal modes

Gyroscope- gyroscopic couple- gyroscopic stabilization- gyroscopic effects in automobiles, airplanes and ships

Course Objectives

This course is expected to enable the student to:

• Impart knowledge on dynamic analysis and balancing of mechanisms
• Familiarize with gyroscopes and flywheels
• Familiarize with mathematical modelling and analysis of mechanical vibration systems

Course Outcomes

• CO1: Apply the principles of statics and dynamics to analyze mechanisms to determine joint forces and torques.
• CO2: Estimate the magnitude and position of balancing masses for unbalanced rotating and reciprocating parts.
• CO3: Construct turning moment diagrams for two and four stroke engines to evaluate the flywheel mass.
• CO4: Formulate the dynamic equilibrium equations of single and two degrees of freedom vibration systems and solve for the response under free and forced conditions.
• CO5: Analyze the effect of gyroscopic couple on automobiles, ships, and airplanes

CO – PO Mapping

Textbook(s)

• Shigley J E and Uicker J J, ‘Theory of Machines and Mechanisms’, Oxford University Press, 2015.

Reference(s)

• Rattan S S, ‘Theory of Machines’, Tata McGraw-Hill PublishingCompany Limited,1994.
• Ghosh A and Mallick A K, ‘Theory of Mechanisms and Machines’,Affiliated East-West,1998
• Rao SS., and FookFah Yap, ‘Mechanical vibrations’, Upper Saddle River:Prentice Hall 2011.
• L Meirovitch, ‘Elements of Vibration Analysis’, McGraw-Hill, New York, 1985
• Norton, R.L., ‘Design of Machinery ’, Tata McGraw-Hill Publishing Company Limited, 2009.

Evaluation Pattern