Mechanical - Dynamics of Machines - Force Analysis

__FORCE ANALYSIS__

**1.
****Write D’Alembert’s principle. What
is the use of it? **

D'Alembert's principle
states that the inertia forces and torques, and the external forces and torques
acting on a body together result in statical equilibrium.

__Use (or) Application (or) significance:__

By
applying D’Alembert’s
principle to a dynamic analysis problem, we can reduce it into an equivalent problem of
static equilibrium.

**2.
****Distinguish between
static force and inertia force. **

·
While analyzing the mechanism, if mass of the body and inertia
force are not considered, then it is called static force.

·
The inertia force is an imaginary force, which when acts upon a
rigid body, brings it in an equilibrium position.

Inertia force = -
Acceleration force = - m. a

**3.** **What are the
conditions for a body to be in equilibrium under the action of (a) two forces,
(b) two forces and torque **

**a)
****Condition for two
forces:**

·
The forces are of the same magnitude.

· The forces act along
the same line.

· The forces are in
opposite direction.

**b)
****Condition for two
forces & Torque:**

·
The forces are equal in magnitude, parallel in direction and
opposite in sense.

·
The forces from a couple, which is equal and opposite to the
applied torque.

**4.** **What is engine
shaking force?**

The
force produces in an engine due to the mass of piston, and mass of the
connecting rod is called engine shaking force.

**5.
****Differentiate between
static & dynamic equilibrium. (or) ****What are the conditions
for a**** ****body to be in static and
dynamic equilibrium? **

Necessary and
sufficient conditions for static and dynamic equilibrium are: 1.Vector sum of
all the forces acting on a body is zero.

2. The vector sum of
all the moments of all the forces acting about any arbitrary point or axis is
zero.

First conditions are
sufficient conditions for static equilibrium together with second condition is
necessary for dynamic equilibrium.

**6.** **What is free body diagram?**

A free body diagram is a sketch of the isolated or free body
which shows all the pertinent weight force, the externally applied loads, and
the reaction from its supports &connections acting upon it by the removed
elements.

**7.** **Define piston
effort and crank effort.**

· **Piston
effort **is defined
as the net or effective force applied on the piston, along the** **line of stroke. It is also known as
effective driving force (or) net load on the gudgeon pin.

· **Crank
effort **is the net
effort (force) applied at the crank pin perpendicular to the** **crank, which gives the required
turning moment on the crankshaft.

**8.** **Define crank pin effort.**

The component of force acting along connecting rod perpendicular
to the crank is known as crank-pin effort.

**9.
****What are the requirements of an
equivalent dynamical system? (or) Write the conditions for any disturbed mass
have the same dynamical properties.**

· The mass of the rigid body must be
equal to the sum of masses of two concentrated masses.

**i.e.
m1 + m2 = m**

· The centre of gravity of the two
masses must coincide with the centre of gravity of the rigid body.

** i.e. m1l1 = m2l2**

· The sum of mass moment of inertia of
two masses about their centre of gravity is equal to the mass moment of inertia
of the rigid body.

**i.e.
l1 . l2 = (kG) ^{2}**

**10. What is the
function of a flywheel? how does it differ from that of a governor?**

· The function of flywheel is to
reduce the fluctuations of speed during a cycle above and below the mean value
for constant load from prime mover. The function of governor is to control the
mean speed over a period for output load variations.

· Flywheel works continuously from
cycle to cycle. Governor works intermittently, i.e. only when there is change
in the load.

· Flywheel has no influence on mean
speed of the prime mover. Governor has no influence over cyclic speed
fluctuations.

**11.Differentiate
between the usage of flywheel in engines and punching presses with turning
moment diagrams.**

·
In the engines, the output of the flywheel was constant and
input torque was varying during each cycle.

In case of punching press, the input of the flywheel is constant
and output torque is varying cyclically.

**12. Define coefficient
of fluctuation of energy.**

It is the ratio of
maximum fluctuation of energy to the work done per cycle.

C_{E}=Maximum
fluctuation of energy/Work done per cycle.

**13.
Why flywheels are needed in forging and pressing operations? **

In both
forging and pressing operations, fly wheels are required to control the
variations in speed during each cycle of an engine.

**14. Define unbalance and spring
surge? **

**Unbalance**: A disc cam produces unbalance
because its mass is not symmetrical with**
**the axis of rotation.

**Spring
surge**: Spring
surge means vibration of the retaining spring.

**15.Define windup. What is the remedy
for camshaft windup?**

· Twisting effect produced in the
camshaft during the raise of heavy load follower is called as windup

· Camshaft windup can be prevented to
a large extend by mounting t he flywheel as close as possible to the cam.

**TUTORIAL PROBLEMS**

**1. **The stroke of a steam engine is 600 mm and the length of connecting rod
is 1.5 m. The crank** **rotates

at 180
r.p.m. Determine: 1. velocity and acceleration of the piston when crank has
travelled through an angle of 40° from inner dead centre, and 2. the position
of the crank for zero acceleration of the piston. **[Ans. 4.2 m/s, 85.4 m/s ^{2}; 79.3° from I.D.C]**

**2. **The following data refer to a steam engine :

Diameter
of piston = 240 mm; stroke = 600 mm; length of connecting rod = 1.5 m; mass of
reciprocat-ing parts = 300 kg; speed = 125 r.p.m.

Determine
the magnitude and direction of the inertia force on the crankshaft when the
crank has turned through 30° from inner dead centre. **[Ans. 14.92 kN]**

**3. **A vertical petrol engine 150 mm diameter and 200 mm stroke has a
connecting rod 350 mm** **long. The

mass of
the piston is 1.6 kg and the engine speed is 1800 r.p.m. On the expansion
stroke with crank angle 30° from top dead centre, the gas pressure is 750 kN/m^{2}.
Determine the net thrust on the piston. **[Ans.
7535 N]**

**4. **A certain machine tool does work intermittently. The machine is fitted
with a flywheel of** **mass 200 kg and
radius of gyration of 0.4 m. It runs at a speed of 400 r.p.m. between the
operations. The machine is driven continuously by a motor and each operation
takes 8 seconds. When the machine is doing its work, the speed drops from 400
to 250 r.p.m. Find 1. minimum power of the motor, when there are 5 operations
performed per minute, and 2. energy expanded in performing each operation.

**[Ans. 4.278 kW; 51.33 kN-m]**

**5. **A constant torque 4 kW motor drives a riveting machine. A flywheel of
mass 130 kg and** **radius of gyration
0.5 m is fitted to the riveting machine. Each riveting operation takes 1 second
and requires 9000 N-m of energy. If the speed of the flywheel is 420 r.p.m.
before riveting, find: 1. the fall in speed of the flywheel after riveting; and
2. the number of rivets fitted per hour.

**[Ans. 385.15 r.p.m.; 1600]**

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