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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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