226-Lect 12 - 1 W eek 12 MECH226 1 Balancing Chapter 12...

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Unformatted text preview: 1 W eek 12 MECH226 1 Balancing Chapter 12 Norton Additional reading in chapters 13 and 14 for engine balancing Phil Commins W eek 12 MECH226 2 Balancing • We have considered forces applied to links in motion • What about link 1? • Link 1 was only used to restrain the mechanism and has never entered the calculations. 1 1 W eek 12 MECH226 3 Balance • Any link that is pure rotation can, theoretically, be balanced • Usually all mechanisms are designed to be balanced. When are they not? • Both static and dynamic balancing is usually required. • Balancing is achieved by placing masses at a desired location W eek 12 MECH226 4 Balance • Variations in the external loads or the loads due to inertia forces are resisted by the grounding forces. • Balancing for external loads – Use energy storage devices, such as flywheel to moderate the resulting affect • Balancing for inertia loads 2 W eek 12 MECH226 5 Balance • The magnitude of the inertia forces and torques reflect the balance of the mechanism. • Often called “shaking forces” • Usually undesirable and causes fatigue failure • May excite natural mechanical frequencies causing further damage. W eek 12 MECH226 6 Balance • Balancing of rotors • Balancing of reciprocating mechanisms • Balancing the general four bar linkage • Balancing an inverted pendulum??? W eek 12 MECH226 7 Rotors • In most cases, balancing requires a static and dynamic analysis. • Basic requirement is the same as any system in equilibrium Sum of Forces = zero Sum of Moments = zero • In this case, it is the inertia forces and torques/moments to be in equilibrium. W eek 12 MECH226 8 Rotors • 3 cases will be analysed Unbalanced masses in a single transverse plane Unbalanced masses in a single axial plane General case – masses in various axial and transverse planes 3 W eek 12 MECH226 9 Examples • Aeroplane propeller • Single gear or pulley • Bicycle tyre • Car tyre – reasonably thick compared to radius. Suited for a dynamic balance W eek 12 MECH226 10 Rotors – single transverse plane The inertia force resulting from an eccentric mass at constant angular velocity is • F o = - ma cg = m R ω 2 directed away from the axis Where m is the mass, R is the radial distance of point mass from axis of rotation and ω is the speed. It may be balanced by placing a balance mass directly opposite, have the same “mR” term. W eek 12 MECH226 11 Single transverse plane- m 1 R 1 ω 2- m 2 R 2 ω 2- m b R b ω 2 = 0 The shaft speed is a common factor and can be factored out....
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This note was uploaded on 10/27/2009 for the course MECH 226 taught by Professor Weihuali during the Three '09 term at University of Wollongong, Australia.

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226-Lect 12 - 1 W eek 12 MECH226 1 Balancing Chapter 12...

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