Download - Impact Driver Simulation
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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 of
wood, 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 the
model, 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 is
requested 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 and
light mechanical industry (Fig. 1). It has become a highly desirable tool due to its portability and
ability for continuous usage when alternating between two sets of batteries. Thanks to the
impacting 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 while
driving the screw.
The key elements of the impact driver lay in the impact unit (Fig. 2). This unit is driven by a
motor through a planetary gear and consists of a spindle with a V-grove, a steel ball, a spring
compressed 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 when
the hammer is impeded from rotation by the anvil, which feels the resistance of the screw. This
windup happens because the steel ball is trapped in the spindle V-groove and simultaneously
presses against an inverted V-shaped cavity on the inside of the hammer. The hammer rises and
gathers momentum, so it eventually clears the top of the anvil. At this point, the spring has
accumulated a large amount of elastic energy and wants to unwind. The only way for this to occur
is by causing the hammer to rotate, as it starts moving down, guided by the ball in the groove. It
will accelerate forward to maintain position with respect to the spindle, and eventually strike the
anvil again as it lowers towards the next impact position. Because of the high velocity and kinetic
energy 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 considered
to 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. driving
speed.
The purpose of simulation is to capture the effects of these design parameters and to b e able to
help predict tool efficiency. A simulation model (Fig. 4) is described in detail below. Selected
stages of the operation described in this section can be observed in a series of high-speed camera
frames in Fig. 5, together with equivalent simulation animation frames which will be discussed in
later sections.
3. Model description
The anvil and hammer are modeled with solid C3D8R bricks (Figs. 4 and 5). The spindle is
modeled with rigid elements and kept rotating at constant speed. The hammer spring is modeled
with a series of preloaded springs whose upper end rotates with the hammer but is kept restrained
vertically. The steel ball is not modeled explicitly for several reasons. The primary reason is that
this would require a prohibitive level of detail throughout the model. Preliminary 2D studies have
also suggested potential difficulties in contact stability because of the extremely small mass of this
body in comparison to hammer and anvil.
The kinematic constraints imposed between the hammer and spindle by the steel ball riding in the
V-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 equation
would have to reverse its sign in this region, which of course, is not possible. This problem was
addressed by defining two simultaneous constraint equations, which differed only by their
opposite 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 and
opposite 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 keep
the hammer lifted will actually transmit a force and cause hammer motion. This model also
permits the ball from departing the roof of the hammer V-cavity, as may physically happen (the
ball is trapped both ways in the spindle V-groove, but only one way against the hammer cavity
top). 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 current
work with other power tool simulations.
Woodscrew driving tests revealed that, after an initial rise period, the torque-rotation
characteristics vary only moderately, or remain flat with depth over most of the driving range
process. For design purposes, this study was conducted under the assumption that the threshold
torque between successive impacts remains constant, using a typical value for the average wood
screw 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 plastic
threshold 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 the
anvil 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 weak
during rise, but stronger during the decay phase. Screw/bit backlash were similarly modeled by a
combination of nonlinear dashpots and penalty type springs, (Fig. 8). Also, the elastic rebound
characteristics 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 modeled
with nonlinear dashpots that have different characteristics during rise and descent, to match
observed 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 mechanism
behaviors 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 severe
startup 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 these
mechanisms, as mentioned above, are the nonlinear dampers in the hammer spring area and the
screw 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 of
hammer and anvil. For this reason, an additional parameter was set to control hourglassing to
levels beyond the default.
Shell and solid elements in most applications undergo a limited amount of rigid body rotation. For
computational efficiency, certain second order computations are not performed by default. In
rotating bodies, where elements may be subjected to several revolutions, these effects become
important. In version 5.8 of ABAQUS/Explicit, an undocumented option had to be specified for
second 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 each
element rotation. The error is inversely proportional to the number of increments per revolution, so
it becomes less severe for small time steps. For version 6.2, the options can be found in the
pertinenet documentation.
5. Selected model results
In Fig. 5, a sequence of simulation animation frames are compared side by side with the high
speed camera images of the impact unit in operation.
Fig. 9 shows the effect of the constraint equations and nonlinear springs of the model on the
vertical hammer displacement. CE 1 represents the motion the first constraint equation imposes on
node 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 are
the two conflicting motions that each constraint equation would impose to the hammer if they
were driving it directly. But the penalty springs are in between. The penalty springs can exert a
force only upon positive relative displacement. For this reason, most of the time, equation CE1
and 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 positive
displacement 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 in
one direction. The effect of the stopper, which limits hammer vertical upward travel, is also
shown.
Fig. 11 shows typical rotational velocities for hammer and anvil before and after an impact. It can
be observed that the hammer gathers speed steadily, until reaching a maximum upon impact,
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causing a rapid decrease. At this point, the motion is transferred to the anvil, which accelerates
sharply to a peak. As is characteristic for ABAQUS/Explicit, first derivatives, such as velocities,
tend to be noisier than displacements.
Fig. 12 shows a comparison of the same hammer velocity pulse of Fig. 11 with a test
measurement. Considering the high speed sequence and short duration of events like this one, a
remarkable overall agreement can be observed, aside from some noise, which is also noticeable inthe test data.
Another comparison with test measurements is shown for a single screw torque pulse in Fig. 13.
The magnitude and duration of the pulse, which determine the amount of transmitted energy, and
thus of the amount of screw rotation, agree well between analyses and test. The local shape (rise
slope, decay slope, ring out) can also be matched closely to test by adjusting the characteristics of
the nonlinear springs and dashpots of Fig. 8.
Fig. 14 shows a series of analysis torque impulses, as seen by the screw. In this case, the
simulation reaches steady state after a few initial impacts. When each of the large torque spikes
reaches the torque threshold, screw rotation is initiated. For smaller torque spikes, the anvil-bit-
screw torsional system responds elastically only and no permanent screw rotation occurs.
Further insight into the behavior of the impact driver and the capabilities of the model is gained
from Fig. 15. It shows the rotational displacement of the three essential parts: spindle, hammer and
anvil. While the spindle moves on at constant speed (straight line), the hammer motion follows
and oscillates as it slows down and accelerates in each impact cycle. Overall, it must travel the
same amount as the spindle, since the steel ball in the cam system assembly ties the parts together.
The anvil moves much slower, making progress with each impact. The progress is directly
dependent on screw and wood characteristics and would be faster for a thin screw and softer
wood, and slower for a bigger screw or harder wood. However, it can also depend on the
efficiency of the particular design, as discussed below.
6. Modeling performance
Fig. 16 shows an example of a design study where a key design parameter was varied. The screw
angular rotation is shown versus time for three cases. It can be seen that a small elastic rebound
occurs after each impact, which rings out quickly. This is observed in practice.
The model correctly predicted the relative effect of the design changes, as verified by tests. Thus,
advanced analysis techniques were applied to help predict the product performance, in addition to
the more conventional purposes of determining stresses or vibration.
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7. Conclusions
Some simplifications were made in modeling the behavior of the power tool. The torque spike and
hammer velocity characteristics nevertheless came remarkably close to measured behavior, but it
must be made clear that driving speed prediction precision can still be improved, especially in
absolute 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 can
include interaction with the motor and may also include the tool body, for evaluation of the effects
of vibration on human response, or feel.
In the product development environment, the modeling of product performance and efficiency is
an 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 fo r the other, more
traditional objectives of stress and vibration evaluation that are also part of the development
process. This stands in contrast to conventional practice of applying an array of unrelated
individual 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 the
performance of advanced and accurate test work, this project would not have been possible. Their
help and cooperation and their funding of this effort is duly acknowledged. The technology
developed 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
Planetary
Gear
Stopper
Chuck
Spring
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Figure 3a. Hammer with invertedV-shaped cavity
Figure 3. Impact unit assembly(stopper not shown)
Figure 4. Simulation model ofimpact unit
Spindle
Hammer
V-groove
Anvil
Spring
Steel ball
V-shaped
cavity
Stopper
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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 anew 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 and
hammer 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 SHzu =
tan)(2 SHzu =
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 SHzu =
tan)(2 SHzu =
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 AnvilRotation
Threshold
*EQUATION
Relates Spring Extension with AnvilRotation
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Figure 9. Effect of constraint equations and penalty springs on hammer verticaldisplacement
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]
VerticalDisplacemen
t,[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]
VerticalDisplacemen
t,[mm]
Hammer
Zero penalty force region
0
0
0
0
0
0
Time, [s]
VerticalDisplacement,[mm]
Hit stopper
CE2
CE1
Bottoming out
Hammer
Zero penalty force region
0
0
0
0
0
0
Time, [s]
VerticalDisplacement,[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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Figure 15. Rotation of spindle, hammer and anvil
Figure 16. Screw rotation versus time for various design parameters
Spindle
Hammer
Anvil
0
2
4
6
8
10
12
14
16
18
20
0 0.02 0.04 0.06 0.08 0.1 0.12
Time, [s]
Rotation,
[ra
d]
Spindle
Hammer
Anvil
0
2
4
6
8
10
12
14
16
18
20
0 0.02 0.04 0.06 0.08 0.1 0.12
Time, [s]
Rotation,
[ra
d]
0
0.5
1
1.5
2
2.5
3
0 0.02 0.04 0.06 0.08 0.1 0.12
Time, [s]
R
otation,
[rad] Change I
Change II
Baseline
0
0.5
1
1.5
2
2.5
3
0 0.02 0.04 0.06 0.08 0.1 0.12
Time, [s]
R
otation,
[rad] Change I
Change II
Baseline