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Semi-active reaction force compensation for a linear motor motion stage

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Abstract

Acceleration and deceleration of a mover excite unwanted vibration to the system base, causing a significant reduction of life and productivity to manufacturing equipment. The system base vibration of a linear motor motion stage can be reduced with a passive reaction force compensation (RFC) mechanism. However, the passive RFC mechanism cannot provide the capability to adjust its stiffness and damping coefficient in real-time. Therefore, resonance may occur if the frequency of the passive RFC mechanism accidentally matches with the frequency components of applied motion profile. This paper presents a semi-active RFC method for a linear motor motion stage using an additional fixed coil. The semi-active RFC mechanism can adjust damping coefficient by changing the resistor load or switching the period of the additional fixed coil. The semi-active RFC mechanism also does not require an additional amplifier or control axis. Mathematical analysis of the semi-active RFC is presented to demonstrate the adjustable damping capability by changing the load resistor. Finally, the effectiveness of the proposed semi-active RFC mechanism is verified via simulations and experiments.

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Abbreviations

a-b-c :

a-b-c three phase coordinate

a M :

acceleration of the mover

c coil :

damping coefficient of fixed coil

c MT :

damping of magnet track

F coil :

Lorentz force of the fixed coil

F t :

thrust force of the mover

F tran :

transmitted force via fixed coil

I a,b,c :

three phase currents in a-b-c frame of fixed coil

I ab,bc,ca :

currents in resistor loads

I d,q :

currents in d-q frame

I q peak :

peak current of fixed coil in q axis

K emf :

electromotive force gain

K f :

force constant of fixed coil

k MT :

stiffness of magnet track

L coil :

inductance of fixed coil

L d,q :

inductance of fixed coil in d-q frame

L q load :

inductance of fixed coil in q axis

m MT :

mass of the magnet track

m M :

mass of the mover

p :

number of pole pairs

R load :

load resistance

R q load :

resistor of load in q axis

R coil :

resistance of fixed coil

R q coil :

resistor of coil in q axis

V a emf :

electromotive force of fixed coil in q-axis

x M :

position of mover

\({\dot x_M}\) :

velocity of mover

x MT :

position of magnet track

\({\dot x_{MT}}\) :

velocity of magnet track

τ :

magnet track pole pitch

ψ :

flux linkage of magnet track

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Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Graduate School, Soongsil University, 369 Sangdo-ro, Dongjak-gu, Seoul, 34056, South Korea

    Duc Canh Nguyen

  2. Department of Mechanical Engineering, Soongsil University, 369 Sangdo-ro, Dongjak-gu, Seoul, 34056, South Korea

    Hyeong-Joon Ahn

Authors
  1. Duc Canh Nguyen
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  2. Hyeong-Joon Ahn
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Correspondence to Hyeong-Joon Ahn.

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Nguyen, D.C., Ahn, HJ. Semi-active reaction force compensation for a linear motor motion stage. Int. J. Precis. Eng. Manuf. 17, 857–862 (2016). https://doi.org/10.1007/s12541-016-0104-y

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  • DOI: https://doi.org/10.1007/s12541-016-0104-y

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