Research Papers

Comparative Analysis for Low-Mass and Low-Inertia Dynamic Balancing of Mechanisms

[+] Author and Article Information
V. van der Wijk

University of Twente, Faculty of Engineering Technology,  Volkert van derWijk, P.O. Box 217, 7500 AE, Enschede, Netherlands

B. Demeulenaere

Atlas Copco Airpower NV,Bram Demeulenaere, Boomsesteenweg 957, B-2610, Wilrijk, Belgium

C. Gosselin

Laval University, Department of Mechanical Engineering,  Clément Gosselin,Pavillon Adrien-Pouliot, 1065 Avenue de la médecine, Québec, Québec G1V 0A6, Canada

J. L. Herder

University of Twente, Faculty of Engineering Technology,  Just L. Herder, P.O.Box 217, 7500 AE, Enschede, Netherlands

J. Mechanisms Robotics 4(3), 031008 (Jun 08, 2012) (8 pages) doi:10.1115/1.4006744 History: Received November 12, 2011; Revised April 25, 2012; Published June 07, 2012; Online June 08, 2012

Dynamic balance is an important feature of high speed mechanisms and robotics that need to minimize vibrations of the base. The main disadvantage of dynamic balancing, however, is that it is accompanied with a considerable increase in mass and inertia. Aiming at low-mass and low-inertia dynamic balancing, in this article the relative importance of the balance parameters of common balancing principles is analyzed and the balancing principles are compared. To do this, the evaluation of a balanced rotatable link is found to be representative for a large group of balanced mechanisms. Therefore, a rotatable link is balanced with duplicate mechanisms (DM), with a countermass (CM) and a separate counter-rotation (SCR), and with a counter-rotary countermass (CRCM). The equations for the total mass and the inertia are derived and compared analytically while the balancing principles are compared numerically. The results show that the DM-balanced link is the best compromise for low mass and low inertia but requires a considerable space. For the CRCM-balanced link and the SCR-balanced link that are more compact, there is a trade-off between mass and inertia for which the CRCM-balanced link is the better of the two.

Copyright © 2012 by American Society of Mechanical Engineers
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Figure 1

A double pendulum balanced with CRCM, shown in (a) [6], can be regarded for detailed analysis of the parameters as two individually balanced single links as shown in (b)

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Figure 2

DM-balanced link with axial and mirror duplicates of the initial link l, drawn to scale

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Figure 3

Balanced rotatable link with a countermass and a separate counter-rotation

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Figure 4

CRCM-balanced rotatable link by using: (a) gears with chain [23], (b) external gears [16], and (c) internal gears [24]

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Figure 5

Design chart for the CRCM-balanced link showing the dependency of I *, l *, and k on countermass m*

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Figure 6

Relation of the transmission ratio k with respect to the masses m* and mcr* for the SCR-balanced link showing similar behavior as compared to Fig. 5

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Figure 7

SCR-balanced link drawn to scale with k = −4

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Figure 8

CRCM-balanced link drawn to scale with k = −4

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Figure 9

Relation between the total mass and the inertia of the CRCM-, SCR-, and DM-balanced links. For the CRCM-balanced link, the curve is below the curves of the SCR-balanced link. The DM-balanced link has the lowest value.

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Figure 10

The reduced inertia with respect to the transmission ratio for CRCM- and SCR-balanced links. A break-even point exists and is at the lowest k for mSCR*=mSCR,min(Iθred)*.

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Figure 13

Mass–inertia values for a low inertia being twice as important than a low total mass (with wM  = 1 and wθ  = 2)

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Figure 11

Characteristic mass–inertia curves (wM  = wθ  = 1). The value is the lowest for the DM-balanced link. The values of the SCR-balanced link are, for all mcr*, higher than those of the CRCM-balanced link.

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Figure 12

Mass–inertia values for a low total mass being twice as important than a low inertia (with wM  = 2 and wθ  = 1)

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Figure 14

Curves for the characteristic mass–inertia factor (wM  = wθ  = 1) for ρt /15. The minimum mass–inertia value for the CRCM-balanced link is lower than that of both DM- and SCR-balanced links.

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Figure 15

By reducing the product ρt (here ρt/15), the transmission ratio the transmission ratio for which the minimum break-even point for the inertia exists also reduces



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