DETERMINATION OF EFFECTIVE MASS IN IMPACT TESTING
Cathie L. Kessler, Ismail El Maach, Jean-Philippe Dionne, Aris Makris
Med-Eng Systems Inc., Ottawa, Ontario, Canada
E-mail: [email protected] Web: www.med-eng.com
INTRODUCTION
The concept of effective mass (meff) is
useful for determining impact force using an
accelerometer on the impactor, based on
Newton’s law (F=ma) [Bir, 2000]. Effective
mass is not always the actual mass of an
impacting object, as in the case of a blunt
impact simulator [Dionne et. al, 2002]. This
impact simulator has a pneumatically-driven
cam, which swings a baseball bat in an arc at
various energy levels. Since some of the
weight of the baseball bat is taken at the
fulcrum, meff<mactual, but there is also a
rotational inertia component that must be
considered.
With the intent of determining meff of a
particular baseball bat, initial tests were
performed using a blunt impactor and the
assumption that meff=F/a (using the peak
values from the force and acceleration
signals, respectively). It became apparent
that the value of meff was strongly dependent
on the material being hit, thus identifying
the need for more fundamental type testing.
METHODS
In the drop tower tests, the drop object had a
steel cylindrical impacting surface (8.0 cm x
2.2 cm) with an accelerometer (PCB
Piezotronics 353B18) attached. The total
drop mass of 5.0 kg was dropped on a
platform supported by three force
transducers (PCB Piezotronics 208C05) (see
Figure 1). The platform was covered with
various protective layers, as discussed
below. The acceleration signal and the three
force signals were acquired at 10 000 Hz
using a PC-based data acquisition system.
The signals were filtered in accordance with
the SAE J-211 CFC 1000 standard. The
three force signals were summed, and ‘force
signal’ henceforth refers to this sum.
Protective
material
Impactor
Force platform
Figure 1: Test apparatus
For comparison, three different materials
were impacted with the same drop weight:
HL34 foam (2 layers of 12.7 mm), standard
Dow Styrofoam insulation (25.4 mm), and
HD80 foam (25.4 mm). For each set of
tests, the protective layer consisted of a
76 mm x 102 mm piece of material covered
by a centred 64 mm x 89 mm piece of 1 mm
lexan sheet. Five drops were made on each
material from a drop height of 80 cm, and
five more were made on each material from
a drop height of 40 cm. For each drop, both
the foam and the lexan sheet were replaced.
-20
0
t1
-2000
0
0.005
t2
0.01
0.015
Time (s)
0.02
-30
0.025
Figure 2: Example of a set of force and
acceleration signals, showing the integration
limits for determining impulse and velocity
RESULTS AND DISCUSSION
Results from the testing are presented in
Table 1 and in Figure 3. For each set of test
conditions (drop height, protective material),
Table 1 shows the average meff as calculated
with the above methods, including standard
deviation among the five trials. In Figure 3,
the averages are plotted to compare
calculation methods.
In general, the values for meff were lower
than the actual mass of the drop object, due
to the fact that some energy was absorbed by
the protective foam layers. This indicates
that using an instrumented impactor may not
be a suitable method of measuring forces
transmitted through protective layers of
energy-absorbing materials. Since the test
The results also indicate that using impulse
and velocity rather than peak force and
acceleration gives a much more consistent
value of effective mass, which is closer to
the nominal value of 5.0 kg.
meff =F/a
meff =I/V
6.0
5.0
4.0
3.0
2.0
1.0
0.0
80 1cm drop2 height 3
HD80 foam
-10
2000
meff=I/V
(±SD)
4.7 (0.4) kg
4.6 (0.3) kg
4.4 (0.2) kg
4.3 (0.2) kg
4.5 (0.3) kg
4.8 (0.3) kg
Dow foam
0
4000
40 cm
HL34
Dow
HD80
HL34
Dow
HD80
HL34 foam
10
80 cm
meff=F/a
(±SD)
5.2 (0.1) kg
4.5 (0.2) kg
3.6 (0.4) kg
3.7 (0.2) kg
2.7 (0.5) kg
3.1 (0.3) kg
HD80 foam
Acceleration (m/s^2)
eff
Drop Foam
Height
Dow foam
m
6000
20
Table 1: Tabulated results of testing, with
average values and standard deviations from
five trials in each configuration (actual
mass: 5.0 kg)
HL34 foam
8000
t
∫ t12 Fdt
=
t
∫ t12 adt
sample composition my affect the
measurement, this should only be used when
there is no alternate method available.
Effective Mass (kg)
10000
Force (kN)
The effective mass was determined using
two different methods. In the first, the peak
value of the force signal and the peak value
of the acceleration signal were used in
meff=F/a. For the second, the peak value of
the force signal was found, and the signal
was searched backward and forward from
the peak to the points at which it became
zero. The force signal was integrated
between these points to get impulse (I), the
acceleration signal was integrated between
the same two time indices to get velocity
(V), and these were used in meff=I/V (see
Figure 2).
5 height6
404 cm drop
Figure 3: Comparison of average values of
meff for various drop heights and protective
materials as calculated by the two different
methods (actual mass: 5.0 kg)
REFERENCES
1. Bir, C.A. (2000). The Evaluation of
Blunt Ballistic Impacts of the Thorax,
Ph.D. Thesis, Wayne State University,
Detroit, Michigan
2. Dionne, J.P. et al. (2002). Proceedings
of European Society of Biomechanics,
Wroclaw, Poland