This document provides an overview of how engineering mechanics relates to electrical engineering. It discusses how concepts from Newtonian physics and classical mechanics, such as forces, motion, and strength of materials, are applicable to electrical systems and machinery. Examples covered include stresses on motor shafts and poles, vibration analysis, transmission line design, and mechanical forces generated by magnetic fields. The document aims to illustrate how an understanding of engineering mechanics can facilitate work in various electrical domains like electrical machinery, power systems, rail transport, and communication engineering.

1. Engineering Mechanics for
Electrical Engineering
Prepared by -
Manish Kumar

2. Electrical Engineering is a branch of engineering which deals with the
applications of electricity and the study of electricity itself. Subjects dealing
with electrical engineering are Engineering Mathematics especially
Calculus, Physics (Newtonian Physics) and all the subjects that deals with
the involvement and applications of electricity. Newtonian physics deals
with classical mechanics especially forces.

3. Engineering mechanics is very similar to Newtonian physics. The main
subjects of this course are forces and motion of an object, whether the said
object or particle is a rigid or deformable. When an object is said to be a
rigid body, this means that an object can withstand a very high value of force
without bending or breaking it while a deformable body is already self –
explanatory.

5. Engineering Mechanics Syllabus
Module 1: Introduction to vectors and tensors and co-ordinate systems
Module 2: Three-dimensional Rotation
Module 3: Kinematics of Rigid Body
Module 4: Kinetics of Rigid Bodies
Module 5: Free Body Diagram
Module 6: General Motion
Module 7: Bending Moment
Module 8: Torsional Motion
Module 9: Friction

6. APPLICATIONS OF MECHANICS TO
ELECTRICAL ENGINEERING

7. A. Electrical Machinery
(a) Shafts subjected to a combination of torsion and flexure.
Fig. 1 Torsional failure in the shaft. This
is often found when a vertical facing
motor has a load set on top with improper
mounting. (https://gesrepair.com/what-caused-my-motor-shaft-to-
break/)

8. A. Electrical Machinery
(b) Critical speeds and whirling of shafts.
Fig. 2 Critical or whirling or whipping
speed is the speed at which the shaft tends
to vibrate violently in transverse direction.
(https://www.youtube.com/watch?v=JF99svLShUY)

9. A. Electrical Machinery
(c) Unbalanced magnetic pull (UMP) as an additional load on the shaft.
Fig. 3 Cross-section of electrical machine with eccentric
rotor. The net electromagnetic force can be significant
in the direction of the shortest air gap between the rotor
and stator axes , also called ‘Unbalanced Magnetic Pull’
(UMP), tries to increase the eccentricity magnitude and
may cause serious damage to the electrical machine.
(http://lib.tkk.fi/Diss/2007/isbn9789512290062/isbn9789512290062.pdf)

10. A. Electrical Machinery
(d) Mechanical stresses in revolving field poles, dovetails, etc.
Fig. 4 The (a) rotor and (b) the illustration of
corresponding key parts. The rotor of motor-generator has
to start and stop for several times on a single day. Under
the highest applied load, the dovetails are “weak link” of
the rotor. The magnet yoke and pole made of steel sheets
are subjected to fatigue loading and fatigue crack
propagation, and those can lead to the final fracture.
(Liangliang Nie et al., “Fatigue life prediction of motor-generator rotor for pumped-storage plant”,
Engineering Failure Analysis 79 (2017) 8–24)

11. A. Electrical Machinery
(e) Strength of revolving disks, solid and with holes.
Fig. 5 Faraday disk. (https://pwg.gsfc.nasa.gov/Education/dynamos.htm)

12. A. Electrical Machinery
(f) Torque, speed, power, and energy in various units.
Fig. 6

13. A. Electrical Machinery
(g) Retardation tests on electrical machines; gradual conversion of stored energy into
losses; the law of retardation.
• Retardation test is also called as running down test. This is the very efficient way to
find out stray losses in dc shunt motors. In this test, we get total stray losses nothing
but the combination of mechanical (friction & windage) and iron losses of the
machine.

14. A. Electrical Machinery
(h) Expressions for the moment of momentum and stored energy of rotation, in
terms of angular velocity and of moment of inertia; the question of units. Changes in
momentum and in energy as a result of a given external impulse.

15. A. Electrical Machinery
(i) Centrifugal governors of hydroelectric units and their theory.
• The parameters of hydraulic turbine governor directly affect the dynamic
characteristics of the hydraulic unit, thus affecting the regulation capacity and the
power quality of power grid.
• The governor of conventional hydropower unit is mainly PID governor with three
adjustable parameters, which are difficult to set up. We need to optimize the
hydraulic turbine governor.

16. A. Electrical Machinery
(j) Hunting of synchronous machines; reduction of a machine to a pendulum;
equivalent inertia, restoring force, and damping.
Fig. 7 KTX-I, South Korean high speed train with 3-
phase synchronous motor. The word hunting is used
because after the sudden application of load the rotor has
to search or ‘hunt’ for its new equilibrium position.
(https://en.wikipedia.org/wiki/KTX-I)

17. A. Electrical Machinery
(k) Noise and vibration of machinery; effect on surrounding structures.
Fig. 8 The existence of abnormal mechanical noises or
vibrations when an electric motor is running can be a sign
of internal damage. (https://www.powertransmissionworld.com/is-your-electric-motor-
trying-to-tell-you-something/)

18. A. Electrical Machinery
(l) Natural frequencies and harmonics of vibrating bodies.

19. A. Electrical Machinery
(m) Mechanics of lubricating oils and of bearings.
Fig. 9 The lubricating oils reduce maintenance cost and
extends the life of motors.

20. A. Electrical Machinery
(n) Motion of air and other gases used for cooling.
Fig. 10 Cooling is essential for long transformer life.
Transformers are either self cooled through natural oil
convection and fan cooled (on photo: Cooling unit of 10kV high voltage
transformer; by jan elemans via flickr)

21. B. Transmission Lines
(a) The curve form of a conductor in a span; a catenary replaced approximately by a
parabola.
Fig. 11 Sag or dip in overhead transmission lines.
While erecting an overhead line, it is very
important that conductors are under safe
tension.(https://electricalengineerresources.com/2018/01/02/complete-sag-
tension-relationship-in-transmission-and-distribution-lines-concepts/)

22. B. Transmission Lines
(b) Supports on equal and unequal heights; effect of temperature.
Fig. 12 Sag calculation when support are at
unequal level.(http://www.electricalunits.com/sag-calculation-overhead-line/)

23. B. Transmission Lines
(c) Stresses in an aerial conductor due to its weight, sleet, and wind.

24. B. Transmission Lines
(d) Secondary stresses in special conductors, such as steel-core aluminum cables, duplex
conductors, hollow core conductors, hemp-core conductors, etc.
Fig. 13 Steel-core aluminum cables.

25. B. Transmission Lines
(e) Stresses in a messenger cable supporting an electrical cable at intervals; double and
single catenary construction; tie-off on curves.
Fig. 14 Catenary system.
(https://www.researchgate.net/publication/282217813_
Contact_Force_Control_in_Multibody_PantographCaten
ary_Systems/figures?lo=1)

26. B. Transmission Lines
(f) Stresses in steel towers, concrete poles, and wood poles, with and without wind.

27. B. Transmission Lines
(g) Unbalanced pull when one or more of the conductors are absent.
• If the 3 phase wires are supplying a balanced load (i.e. a load which pulls an equal
amount of current from each phase), nothing will happen - everything will look the
same: phase currents, voltages, and power. If the load is unbalanced, or if there is a
fault, then things are not so simple.

28. B. Transmission Lines
(h) Stresses in the foundations for towers.
Fig. 15 Types of transmission
tower foundations: (a) inverted-
T or footing, (b) pile, (c) mat,
and (d) single pole. (D. Kyung, J. Lee /
Soils and Foundations 55 (2015) 575–587)

29. B. Transmission Lines
(i) Stresses in crossarms, insulator pins, etc.
Fig. 16 Crossarm, insulator pins

30. C. Electric Railways
(a) Train resistance, its elements and their variation with the velocity; acceleration and
speed—time curves. Braking.

31. C. Electric Railways
(b) Energy input on acceleration. Energy storage in the parts moving on a straight line
and in the revolving parts, such as the wheels and the motors. A pendulum as an
acceleration meter.

32. C. Electric Railways
(c) Electric locomotives; suspended and non-suspended weights, link motions,
connecting rods; their unbalanced forces and stresses; influence of the position of the
center of gravity in nosing.

33. D. Mechanical Forces due to Magnetic Fields
(a) The magnitude of these forces is most conveniently derived on the principle of
virtual displacements, and this principle can be best explained on a system of material
points or on an elastic girder under load, so as not to complicate the treatment by
electromagnetic quantities.
Fig. 17 Torque on a Current Loop: Mechanical forces
appear wherever magnetic fields act on electric currents.
The work done by all electric motors is the result of
these forces.

34. D. Mechanical Forces due to Magnetic Fields
(b) Busbars through which alternating currents are flowing behave like uniformly
loaded beams and also vibrate at the synchronous frequency or a multiple thereof.
Fig. 18 Copper busbar in an LT Panel. In electric power
distribution, a busbar is a metallic strip used for local
high current power distribution. (https://en.wikipedia.org/wiki/Busbar)

35. E. Electromechanical Applications
(a) Belting, rope, gears, silent chains, etc.; properties of springs.

36. E. Electromechanical Applications
(b) Energy storage in large adjustable-speed driving motors used in steel mills and with
mine hoists.

37. E. Electromechanical Applications
(c) Starting and stopping of elevators and cranes.
Fig. 19 An elevator.

38. F. Communication Engineering
(a) Laws of vibration of diaphragms in telephone transmitters and receivers,
automobile horns, etc. Nodes and harmonics; vibrational impedance.
Fig. 20 Convert audio signal into electrical
signal and vice-versa.

39. F. Communication Engineering
(b) Acoustics of buildings, resonating chambers, horns, etc.

40. F. Communication Engineering
(c) Properties of sound waves.

41. F. Communication Engineering
(d) Speech analysis.

42. G. Galvanometers and Oscillographs
(a) Study of the motion of the coil in a ballistic galvanometer, as an example of a
damped pendulum. Effect of the moment of inertia, torsion constant of the
suspension, air friction, eddy currents, etc.

43. G. Galvanometers and Oscillographs
(b) Laws of vibrating strings, resonance.

44. H. Waves and Oscillations
(a) An understanding of electromagnetic waves and oscillations is much facilitated by a
previous study of mechanical waves and oscillations.
Fig. 21 Electromagnetic
waves and mechanical
waves.

45. H. Waves and Oscillations
(b) The following topics would help in particular: theory of the pendulum, resolution
of an irregular periodic motion into harmonics; resonance and near-resonance; wave-
motion in solids and gases; velocity phase and pressure phase; water waves in pipes and
in open cabals; different kinds of reflection.

46. I. Vector Analysis
(a) Vector analysis plays an increasingly important part in electrical engineering. Its
principles can be best learned in mechanics; first, because it is wonderfully effective
there, and secondly, because the student deals with more tangible applications than
with electric vectors. The following topics are of particular interest, as leading to
corresponding electrical subjects:
Differentiation of vectors in deriving components of acceleration of a material point
moving along a curved path; Gradient and potential, in application to gravitation;
Concept of divergence, explained in application to hydrodynamics; Curl explained in
application to translation and rotation of a rigid body and to vortex formation in a
liquid.

47. I. Vector Analysis
(b) General equations of hydrodynamics of a perfect liquid, in the language of vector
analysis, introducing velocity potential, conjugate functions, and mapping of lines of
flow in two-dimensional problems.

48. J. Theory of Elasticity
(a) The general method of treatment used in the theory of elasticity is useful in the
study of electrostatic and magnetic fields, preparing the student's mind both from a
physical and formal mathematical points of view.

49. K. General Laws of Motion
(a) Modern electronics is built essentially upon classical laws of motion of material
points and rigid bodies, these laws being modified by the quantum hypothesis.

50. K. General Laws of Motion
(b) The following topics are useful in understanding modern works on the structure of matter:
• Laws of motion of planets around the sun, because of their application to the structure of the atom.
• General laws of motion under the influence of attractive or repelling centers.
• Flight of a projectile subjected to various forces; application to moving ions and their deflection by
electric and magnetic forces.
• The gyroscope and its precession; this finds an application in the theory of atomic spectra.
• A'Alembert's principle and analytical expression of constraints. Fundamentals of the calculus of
variations and the principle of least action.
• Lagrangian equations of motion and the Hamiltonian canonical form of equations; theory of
astronomical perturbations and its modification in the theory of a complex atom.

51. L. Statistical Mechanics
(a) In ionized gases and liquids, we have to consider a large number of discreet
particles endowed with different velocities. They are dealt with according to the
principles of the so-called statistical mechanics, which is a rapidly growing science,
auxiliary to atomic physics. The best introduction into the subject is the classical kinetic
(or dynamical) theory of gases, with its considerations of distribution of velocities of
particles, probabilities of various kinds of collisions, elastic and inelastic, viscosity,
Brownian movements, motion of a sphere in a medium consisting of bombarding
particles, etc.

52. L. Statistical Mechanics
(b) A useful topic is also that of partition of energy among various degrees of freedom
of a mechanical system. This later leads to the principle of equipartition and to its
failure in certain cases, thus preparing the student's mind to the quantum theory (or
jumpwise changes in energy), with its applications to the problems of conduction,
radiation, specific heats, etc.

53. Other Applications
• Roof antennas are sometimes held up by three guy - wires.
• The robot, drones that we see uses EEE and also mechanics.
Fig. 22 A guy-wire, guy-line, or guy-rope,
also a guy, is a tensioned cable designed to
add stability to a free-standing structure.

54. • So in conclusion, all electrical technology, in order to be put to any
practical use, will need a mechanical design to implement it. The electric
motor is a prime example. So is the electric light bulb. So is the computer.
• Whether you directly use dynamics depends on exactly what you end up
doing. If you’re designing electric motors, or the control system for a
drone, it would be directly relevant. If you’re designing signal processing
algorithms, it won’t be.

55. Thank You