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Simulating an Impact Driver with ABAQUS/Explicit
Viktor Wilhelmy
Manta Corporation
1000 Ford Circle
Milford, OH 45150, USA
www.iti-oh.com
[email protected] [email protected]
Abstract: A battery powered impact driver is capable of driving
a 6 screw into a solid piece ofwood, without the need of
predrilling, in less than 10 seconds. The impact unit consists of a
gear
drive, spindle, spring, hammer and anvil, to which a tool is
connected to drive the screw or bolt.
The periodic torsional impacting action of the hammer is
achieved by a windup and releasemechanism.
The dynamic interaction between these parts is simulated using
ABAQUS/Explicit. With themodel, it is possible to predict the
kinematics of the impact mechanism, including torque spike
characteristics and driving speed. Key characteristics of the
model have been validated by tests.
Thus, analysis leads the design towards finding the most
efficient combination of cam lead angle,hammer release clearance,
inertias, and other design variables.
High-speed camera test video clips compare well with simulation
animations.
1. Introductory Remarks
The current presentation is part of consulting work performed at
Manta Corporation. The reader isrequested to understand that due to
confidentiality considerations, the extent and level of detail
ofdisclosed material must remain limited.
2. A battery powered impact driver
The battery operated impact driver is a new type of hand tool
for the construction industry andlight mechanical industry (Fig.
1). It has become a highly desirable tool due to its portability
andability for continuous usage when alternating between two sets
of batteries. Thanks to theimpacting mechanism, it can produce
torque impulses ofsufficient magnitude and duration todrive a
typical wood screw without the need of pre-drilling. Contrary to a
conventional driver, it
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does not require a high pushing force on the part of the
operator to keep the bit engaged whiledriving the screw.
The key elements of the impact driver lay in the impact unit
(Fig. 2). This unit is driven by amotor through a planetary gear
and consists of a spindle with a V-grove, a steel ball, a
springcompressed between a hammer and a disk at the top of the
spindle, an anvil and a stopper (Fig. 3).
The anvil has a chuck for attaching different drive bits.
As the planetary gear output spindle rotates at a fairly
constant speed, it winds up the spring whenthe hammer is impeded
from rotation by the anvil, which feels the resistance of the
screw. Thiswindup happens because the steel ball is trapped in the
spindle V-groove and simultaneouslypresses against an inverted
V-shaped cavity on the inside of the hammer. The hammer rises
andgathers momentum, so it eventually clears the top of the anvil.
At this point, the spring hasaccumulated a large amount of elastic
energy and wants to unwind. The only way for this to occuris by
causing the hammer to rotate, as it starts moving down, guided by
the ball in the groove. Itwill accelerate forward to maintain
position with respect to the spindle, and eventually strike
theanvil again as it lowers towards the next impact position.
Because of the high velocity and kineticenergy of the hammer upon
impact, the anvil will undergo a finite amount of rotation before
it
stops. At this point, the process is repeated and the next
impact cycle is initiated.
In the design of an impact driver, several design variable
combinations may have to be consideredto increase operation
efficiency. For example, the spring stiffness and preload,
hammer/anvilclearance, inertia and mass, V-groove cam lead angle,
etc., all affect performance, i.e. drivingspeed.
The purpose of simulation is to capture the effects of these
design parameters and to be able tohelp predict tool efficiency. A
simulation model (Fig. 4) is described in detail below.
Selectedstages of the operation described in this section can be
observed in a series of high-speed cameraframes in Fig. 5, together
with equivalent simulation animation frames which will be discussed
inlater sections.
3. Model description
The anvil and hammer are modeled with solid C3D8R bricks (Figs.
4 and 5). The spindle ismodeled with rigid elements and kept
rotating at constant speed. The hammer spring is modeledwith a
series of preloaded springs whose upper end rotates with the hammer
but is kept restrainedvertically. The steel ball is not modeled
explicitly for several reasons. The primary reason is thatthis
would require a prohibitive level of detail throughout the model.
Preliminary 2D studies havealso suggested potential difficulties in
contact stability because of the extremely small mass of thisbody
in comparison to hammer and anvil.
The kinematic constraints imposed between the hammer and spindle
by the steel ball riding in theV-groove are instead modeled with
constraint equations. This would be straight forward if the
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bottoming out of the hammer in the V-groove could be neglected.
A single constraint equationwould have to reverse its sign in this
region, which of course, is not possible. This problem wasaddressed
by defining two simultaneous constraint equations, which differed
only by theiropposite signs and by governing the vertical motion of
two separate parallel penalty springs (Fig.6). The two equations
will cause the upper node of each spring to always travel in equal
andopposite directions, in dependence of the rotation differences
between spindle and hammer.Because the penalty stiffness in
compression is zero, only the particular spring that tends to
keepthe hammer lifted will actually transmit a force and cause
hammer motion. This model alsopermits the ball from departing the
roof of the hammer V-cavity, as may physically happen (theball is
trapped both ways in the spindle V-groove, but only one way against
the hammer cavitytop). Today, connector capabilities are available
in ABAQUS/Explicit level 6 version releases.These capabilities
might be advantageous in this area, as they have proven to be in
our currentwork with other power tool simulations.
Woodscrew driving tests revealed that, after an initial rise
period, the torque-rotationcharacteristics vary only moderately, or
remain flat with depth over most of the driving rangeprocess. For
design purposes, this study was conducted under the assumption that
the thresholdtorque between successive impacts remains constant,
using a typical value for the average woodscrew driving
application. A threshold torque is that torque which is required to
initiate and
maintain rotation.
The screw is thus suited for modeling as a nonlinear spring with
elastic-plastic characteristics(Fig.7). The elastic characteristics
were estimated from screw shank dimensions and the plasticthreshold
was set to correspond to test measurement levels. In release 5.8 of
ABAQUS/Explicit,no torsional nonlinear spring was available, so a
grounded translational spring was coupled to theanvil rotation with
the *EQUATION option. In addition, a parallel nonlinear dashpot was
defined,in order to match measured torque spike rise and decay
characteristics. This dashpot is very weakduring rise, but stronger
during the decay phase. Screw/bit backlash were similarly modeled
by acombination of nonlinear dashpots and penalty type springs,
(Fig. 8). Also, the elastic reboundcharacteristics of the anvil
were controlled to match observed decay behavior using
Rayleighdamping for that part.
Friction was considered between the elastic contact surfaces of
anvil and hammer. Other energydissipating mechanisms exist, for
example, in the hammer spring assembly. These were modeledwith
nonlinear dashpots that have different characteristics during rise
and descent, to matchobserved behavior approximately. Friction
models proved more involved to apply in this area.The potential for
connector alternatives for this, as well as for all of the fairly
complex mechanismbehaviors described in the preceding paragraphs,
will be the subject of future investigations.
4. Solution stability
The model was subjected to approximate initial velocity
conditions in order to reduce severestartup response effects and to
shorten the time to steady state. Energy dissipation mechanisms
are
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present in most parts, helping solution stability and
controlling noise. Examples of thesemechanisms, as mentioned above,
are the nonlinear dampers in the hammer spring area and thescrew
model, Rayleigh damping for the anvil, as well as friction between
anvil and hammer.Severe stress pulses created by impact could
create some noise in the solid element response ofhammer and anvil.
For this reason, an additional parameter was set to control
hourglassing tolevels beyond the default.
Shell and solid elements in most applications undergo a limited
amount of rigid body rotation. Forcomputational efficiency, certain
second order computations are not performed by default. Inrotating
bodies, where elements may be subjected to several revolutions,
these effects becomeimportant. In version 5.8 of ABAQUS/Explicit,
an undocumented option had to be specified forsecond order effects
to be included, as follows:
*SECTION CONTROLS, NAME=XYZ,2ndorder=yes
If these controls are not set, accumulative model inaccuracies
will be introduced with eachelement rotation. The error is
inversely proportional to the number of increments per revolution,
soit becomes less severe for small time steps. For version 6.2, the
options can be found in thepertinenet documentation.
5. Selected model results
In Fig. 5, a sequence of simulation animation frames are
compared side by side with the highspeed camera images of the
impact unit in operation.
Fig. 9 shows the effect of the constraint equations and
nonlinear springs of the model on thevertical hammer displacement.
CE 1 represents the motion the first constraint equation imposes
onnode 1 of the first penalty spring (Fig.6). Similarly, CE 2
represents the exact opposite motion,which the second constraint
equation imposes on node 2 of the second penalty spring. These
arethe two conflicting motions that each constraint equation would
impose to the hammer if theywere driving it directly. But the
penalty springs are in between. The penalty springs can exert
aforce only upon positive relative displacement. For this reason,
most of the time, equation CE1and its associated penalty spring are
in control. Only if the displacement governed by this equation
becomes negative, the spring controlled by CE2 steers the hammer
motion, since the displacementgoverned by it becomes positive.
Thus, the hammer bottoms out and is always kept in the
positivedisplacement domain. This is also shown in more detail in
Fig. 10.
Note that the steel ball is allowed to descend away from the
inverted V-surface inside the hammercavity. The behavior is indeed
replicated computationally by the tension-only penalty
springs,which tie hammer motion with the motion imposed by the
constraint equations effectively only inone direction. The effect
of the stopper, which limits hammer vertical upward travel, is
alsoshown.
Fig. 11 shows typical rotational velocities for hammer and anvil
before and after an impact. It canbe observed that the hammer
gathers speed steadily, until reaching a maximum upon impact,
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7. Conclusions
Some simplifications were made in modeling the behavior of the
power tool. The torque spike andhammer velocity characteristics
nevertheless came remarkably close to measured behavior, but itmust
be made clear that driving speed prediction precision can still be
improved, especially inabsolute terms. In relative terms, the
simulation is very useful for predicting which design change
is expected to be the more favorable regarding performance.
The improvement of model accuracy will be the subject of future
activities. Model expansions caninclude interaction with the motor
and may also include the tool body, for evaluation of the effectsof
vibration on human response, or feel.
In the product development environment, the modeling of product
performance and efficiency isan interesting application extension
of advanced FEA analysis tools such as ABAQUS/Explicit.The benefit
is that a consistent model can be used for this purpose as it is
for the other, moretraditional objectives of stress and vibration
evaluation that are also part of the developmentprocess. This
stands in contrast to conventional practice of applying an array of
unrelatedindividual tools and is a step forward in the Analysis
Leads Design (ALD) product development
approach.
8. Acknowledgements
Without Manta Corporations client product knowledge and
expertise, in particular in theperformance of advanced and accurate
test work, this project would not have been possible. Theirhelp and
cooperation and their funding of this effort is duly acknowledged.
The technologydeveloped in this team environment is shared by all
of its members.
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Figure 1. CAD model of a battery powered impact driver
Figure 2. Impact unit and key elements
Impact unit
Battery
Motor
Anvil
Hammer
Motor Shaft
PlanetaryGear
Stopper
Chuck
Spring
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(1)Cycle start.
Hammer against anvilcauses rotating spindleto wind up the
spring
(2)Hammer rise
(3)Hammer clears anvil
Figure 5. High speed camera frames comparing various stages of
the impactmechanism operation with simulation
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(4)Hammer starts descent
and accelerates,moving to next impact
position
(5)Hammer impacts anviland initiates anvil
rotation
(6)
Anvil rotation iscompleted
Hammer reacheslowest position and a
new cycle is started
Figure 5 (Continuation). High speed camera frames comparing
various stages ofthe impact mechanism operation with simulation
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Figure 6. Penalty springs and constraint equations to
characterize spindle andhammer interaction
Figure 7. Translational elastic-plasticspring representing main
screw
characteristics
Figure 8. Additional elements tocharacterize screw behavior,
such asbacklash and torque spike rise and
decay
Uzn
= vertical displacement, node n
= hammer rotation
S
= spindle rotation
= cam lead angle
Kball
= steel ball stiffness
Kball C
ball
100 * Kball
1
2100 * K
ball
0
Kball C
ball
100 * Kball
1
2100 * K
ball
0
tan)(1 SHz
u =
tan)(2 SHz
u =
Constraint equation 1 (CE1):
Constraint equation 2 (CE2):Force
Relative displacement
Centerline
Hammer
Uzn
= vertical displacement, node n
= hammer rotation
S
= spindle rotation
= cam lead angle
Kball
= steel ball stiffness
Kball C
ball
100 * Kball
1
2100 * K
ball
0
Kball C
ball
100 * Kball
1
2100 * K
ball
0
tan)(1 SHz
u =
tan)(2 SHz
u =
Constraint equation 1 (CE1):
Constraint equation 2 (CE2):Force
Relative displacement
Centerline
Hammer
Screw Bit backlash
Springs
Dashpots
Screw Bit backlash
Springs
Dashpots
Threshold
*EQUATION
Relates Spring Extension with Anvil
Rotation
Threshold
*EQUATION
Relates Spring Extension with Anvil
Rotation
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Figure 9. Effect of constraint equations and penalty springs on
hammer vertical
displacement
Figure 10. Detail of hammer vertical displacement
CE2
See detail area below
CE1
0
0
0
0
0
0
0
0
0
0
0
0 0 0 0 0
Time, [s]
VerticalDisplacement,[mm]
Hammer
Zero penalty force region
CE2
See detail area below
CE1
0
0
0
0
0
0
0
0
0
0
0
0 0 0 0 0
Time, [s]
VerticalDisplacement,[mm]
Hammer
Zero penalty force region
0
0
0
0
0
0
Time, [s]
VerticalD
isplacement,[mm]
Hit stopper
CE2
CE1
Bottoming out
Hammer
Zero penalty force region
0
0
0
0
0
0
Time, [s]
VerticalD
isplacement,[mm]
Hit stopper
CE2
CE1
Bottoming out
Hammer
Zero penalty force region
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Figure 11. Hammer and anvil velocity before and after impact
Figure 12. Hammer rotational velocity comparison of analysis
versus test
-200
-100
0
100
200
300
400
500
600
0 0 0 0 0 0
Time, [s]
RotationalVelocity,
[rad/s]
Hammer
Anvil
-200
-100
0
100
200
300
400
500
600
0 0 0 0 0 0
Time, [s]
RotationalVelocity,
[rad/s]
Hammer
Anvil
Test
-200
-100
0
100
200
300
400
500
600
0 0 0 0 0 0 0
Time, [s]
Rotatio
nalvelocity,
[rad/s]
Analysis
Test
-200
-100
0
100
200
300
400
500
600
0 0 0 0 0 0 0
Time, [s]
Rotatio
nalvelocity,
[rad/s]
Analysis
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Figure 13. Screw torque pulse comparison of analysis versus
test
Figure 14. Screw torque signal versus time
-1
-1
0
1
1
2
2
3
3
4
4
0 0.02 0.04 0.06 0.08 0.1 0.12
Time, [s]
T
orque,
[Nm]
-1
0
1
2
3
4
0 0
Time, [s]
Torque,
[Nm
]
Test
Analysis II
Analysis I
-1
0
1
2
3
4
0 0
Time, [s]
Torque,
[Nm
]
Test
Analysis II
Analysis I
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