Dynamics of Machinery II ME 3015 B'Tech First Year Second Semester

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Dynamics of Machinery IIME 3015B.Tech (First
Year)Second Semester
Lectured by

• Daw Thida Oo
• Lecturer
• Mechanical Engineering Department
• Yangon Technological University

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CHAPTERS

• Balancing
• Forces
• Cam Profile
• References1.Dynamics of Machinery written by U
  Kyaw Sein. 2.Theory of Machine (vol. 1) written
  by N.C Pandya C.S Shah. 3.Theory of Machines
  and Mechanism written by Joseph Edward Shigley
  John Joseph Uicker, JR

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BALANCING

• The technique of correcting or eliminating
  unwanted inertia forces and moments in rotating
  or reciprocating masses.
• The two equations to determine the amount and
  location of the correction

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Resultant Effects of Engine

• 1. S F 0 S M 0
• Complete balanced
• 2. S F 0 S M ? 0
• Unbalanced being due to a couple.
• 3. S F ? 0 S M 0
• Unbalanced being due to a single resultant force
  in the reference plane.

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Continued

• 4. S F ? 0 S M ? 0
• Unbalanced being due to a single resultant force
  which locates at a distance z from the reference
  plane and

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Balancing of Multi-cylinder In-line Engines
(Analytical Method)
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Continued

• In-line Engine Mechanism

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Continued

• The resultant inertia force,

(Secondary Force)
(Primary Force)

• For Primary force Balance,

and

• For Secondary force Balance,

and
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Continued

• The resultant moment,

(Primary Moment)
(Secondary Moment)

• For Primary Moment Balance,

and

• For Secondary Moment Balance,

and
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Example (1)

• 2 stroke, 2 cylinder, In-line Engine
• Firing interval

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Continued
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Continued
(Upwards)

• Secondary Unbalanced Force,

(CW)

• Primary Unbalanced Moment,

• Secondary Unbalanced Moment,

(CCW)
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Arrangement to balance the secondary force
(Upwards)
For balance,
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Arrangement to balance the primary moment (C.W)
For balance,
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Arrangement to balance the secondary moment
(C.C.W)
For balance,
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Balancing of multi-cylinder V-Engine
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Continued

• V-Engine Mechanism

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Continued

• The resultant vertical inertia force,

• The resultant horizontal inertia force,

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Assumptions
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Example-4

• 8-cylinder, 4-stroke,V-engine
• Firing Order 1-5-4-2-6-8-7-3
• Firing Interval 90
• V angle 90

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Continued
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Continued

• Primary Unbalanced Vertical Moment

(CW)

• Primary Unbalanced Horizontal Moment

(CCW)
Note- sinacos(a - 90)
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Continued

• Arrangement for Balancing

For Balance,
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FORCES

• To study forces acting on machine members
  Statically and Dynamically.
• To determine the magnitudes, directions and
  locations of forces.
• Assumptions.
• A member of a machine composed of all external
  forces and inertia forces is equilibrium.
• The forces acting on machines having plane motion
  are for the most part situated in parallel plane.
• The friction is disregarded.
• The system will be applied Newtons Law.

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Static Force Analysis

• Static forces exits if the system is in
  equilibrium among them, when not running.
• For equilibrium, S F 0 and S M 0.
• Two forces in equilibrium, (Two force member)

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Continued

• Three forces in equilibrium

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Continued

• To find a line of action of unknown force in
  three force member having a known force, known
  line of action of another force but not magnitude
  and known point acting the last force.

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Dynamics Force Analysis

• m total mass of body concentrated at the
  centroid, C.G, of body.
• AG absolute acceleration of the centre of mass
  of the body.
• IG mass moment of inertia.
• a angular acceleration of the body.

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Inertia Forces and DAlemberts Principle

• SF F1F2F3 , the resultant force will not be
  through the mass centre, and results the
  unbalanced force system.
• The effect of this unbalanced system is to
  produce an acceleration, AG, of the centre of
  mass of the body. SF mAG (1)
• Taking moment about centre of mass of the body
  results the unbalanced moment system. It causes
  angular acceleration, a, of the body. SM IG
  a (2)

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Continued

• (a) An unbalanced set of forces on a rigid body.
• (b) The acceleration which result from the
  unbalanced forces.

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Conitued

• From (1) and (2),
• SF (- mAG) 0 and SM (- IG a) 0
• (- mAG) is called inertia force which has the
  same line of action as the absolute acceleration
  AG but is opposite in sense.
• (- IG a) is called inertia torque which is
  opposite in sense to the angular acceleration a.
• The equations above are known as DAlemberts
  principle.

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Continued

• To describe graphically,

The distance between the forces and couple,
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Example - 1
-m3AG30.33lb
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Continued
A
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THANK YOU