Impact Driver Simulation

8/7/2019 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


0

0

0

0

0

0

Time, [s]

VerticalDisplacement,[mm]

Hit stopper

CE2

CE1

Bottoming out

Hammer


0

0

0

0

0

0

Time, [s]

VerticalDisplacement,[mm]

Hit stopper

CE2

CE1

Bottoming out

Hammer



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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

Documents

Impact Driver Simulation