30-11-2012, 03:07 PM
A new method for boring of non-circular holes
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Abstract
A revolving electromagnetic actuation mechanism
composed of an electromagnetic stator and an
electromagnetic rotor has been developed for boring
non-circular holes. The main component of the rotor is a
flexure-hinged based flexible body. There are four pole-pair
coils in the stator supplying actuation currents. The micro-
displacement between the stator and rotor can be
controlled by changing the currents applied in the pole-pair
coils. Through linearization of the actuation force near the
static action point, a linear relationship between the control
current and the actuation force was established, and the
synchronizing control method of the electromagnetic
actuation mechanism is presented here. With two-factor
analysis of the linearization error of the actuation force, the
influences of control current and micro-displacement to the
linearization error of the actuation force were studied. Then,
the principle for designing the basic parameters of the magnetic
actuation mechanism is put forward. The calibration of
the mechanism indicates that the relationship between the
micro-displacement of the rotor and the control current has
linear characteristics in the required micro-displacement
range. Simulation tests show that the turning radius of the
rotor changes with the control current. The proposed
mechanism can feasibly supply a controllable micro
displacement to the boring bar.
Introduction
Precision boring plays an important role in modern mechanical
manufacturing. Mechanical parts with precision bores that
have to bear severe force and/or heat would produce obvious
distortions during the working process, which will deteriorate
their performances. In order to counteract these distortions,
precision bores such as piston bin bore, cylinder
hole, spindle bore, etc., should have a non-circular hole.
Depending on the distortions caused by force and/or heat,
the non-circular hole could be an elliptic, or a horn-like surface
or a combination of both. For boring of such
non-circular holes, it is critical for the boring bar to have a
controllable radial micro-displacement. High cutting speeds
need to be used for a profitable boring process with good
surface finish. However, this would increase the difficulties
in boring the noncircular hole. To create the necessary micro-
displacement, the boring bar must be applied with direct
or indirect radial actuation force, which can be done using
actuators such as linear motor [1,2], piezoelectric [3–5], hydraulic
[6], voice-coil actuator [7–8], etc.
Modeling of the proposed mechanism
The principle of the proposed magnetic actuation mechanism
is shown in Fig. 1. Between the spindle and the boring
bar is a compound deformable body, one end of which is a
flexure-hinged elastic body and the other is an electromagnetic
rotor. Around the rotor is an 8-pole stator with eight
actuation coils. Most parts of the rotor and stator are fabricated
with Fe-Si sheets of 0.35 mm thickness to reduce eddy
flow. While current is applied to the actuation coils, an electromagnetic
actuation force would be produced between the
rotor and the stator. With the help of an encoder (not shown)
mounted on the rear end of the spindle, certain phase-angle
differences between the different actuation currents can be
guaranteed to form a synchronizing electromagnetic force
acting on the rotating boring bar.
Modeling of the electromagnetic force
Figure 2 shows the section of the rotor and stator. There are
two coils in series to form one pole-pair coil, which is actuated
by one PWM power amplifier. There are four pole-pair
coils in the Cartesian coordinate axes to produce an electromagnetic
actuation force in the X- and Y-axes. The dynamics
of each axis is considered symmetrical and uncoupled,
so a single-axis model is used for the modeling of the
magnetic force. Because magnet can only produce attractive
force rather than repelling force, the 4-pole magnet of one
axis should be arranged in back connection.
Error analysis of magnetic force modeling
Equation (3) is obtained with the preconditions of being
near the static action point and neglect of differential components
higher than the second order. With the increase of
micro-displacement, the rotor decentralizes the static action
point, and the influence of force-displacement factor reinforces
gradually. Thus, the error of the magnetic force
caused by the linearization would obviously increase.
Therefore, it is necessary for the factors that affect the error
of the magnetic force to be analyzed quantitatively. The exact
expanded formula of the magnetic force near the static
action point is as follows [14].
Conclusions
To bore a non-circular hole, it is necessary for the boring bar
to be applied with a contactless actuation force to produce a
controllable radial micro-displacement. An electromagnetic
actuation mechanism mainly composed of a flexure-hinged
elastic body, an electromagnetic rotor and an electromagnetic
stator has been developed. The striking feature of the
mechanism is that it can easily provide a contactless force
between two moving bodies at high speeds. With the linearization
of the actuation force near the equilibrium point,
the synchronizing control methods of the magnetic actuation
mechanism were acquired. With analysis of the linearization
error of the actuation force, the influences of control current
and micro-displacement to the linearization error of the actuation
force have been analyzed deeply.