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- 1 CHAPTER 1 INTRODUCTION TO SHOCK TESTING MACHINE Table of Contents
- 2 Basic Definitions
- 2.1 Concept of shock
- 2.2 Definition of shock........................................................................................................
- 2.3 How is it measured?
- 2.4 Time Histories
- 2.5 Shock Response Spectrum..........................................................................................
- 2.6 Specification of Shock Test
- 3 Classification of mechanical Shocks
- 4 Principle of Shock Testing:
- 4.1 Energy method
- 4.2 Force and Distance domain.
- 4.3 Force and Time domain:
- 5 Methods of Shock Testing
- 6 Shock Testing Machines
- 6.1 SHOCK-MACHINE CHARACTERISTICS ........................................................................
- 6.1.1 DAMAGE POTENTIAL ........................................................................................
- 6.1.2 SHOCK RESPONSE SPECTRA..........................................................................
- 6.1.3 SPECIFYING A SHOCK TEST ............................................................................
- 6.2 CHARACTERISTIC TYPES OF SHOCKS ........................................................................
- 6.3 KINEMATICS OF SIMPLE SHOCKS ...............................................................................
- 6.3.1 ANALYSIS IN TIME DOMAIN ..............................................................................
- 6.3.2 HALF-SINE PULSE ............................................................................................. vi
- 6.4 SIMPLE SHOCK PULSE MACHINES ..............................................................................
- 6.4.1 Drop Tables .........................................................................................................
- Figure 1: Classical Shock Pulse
- Figure 2: Shock Response Spectrum (SRS) Plot
- Figure 3: Sawtooth Shock
- Figure 4: Triangle Shock
- Figure 5: Pyroshock Shock Time & Response Spectrum
- Figure 6: Seismic Shock Time History
- Figure 7: Air blast
- Figure 8: Types Of Shocks ........................................................................................................
- Figure 9: Types Of Shocks ........................................................................................................
- Figure 10: Velocity change of a half-sine...................................................................................
- Figure 12: Drop-table arrangement ...........................................................................................
1 CHAPTER 1 INTRODUCTION TO SHOCK TESTING MACHINE
Aircraft, spacecraft, other aerospace structures and all structures in general endure shocks
in one form or another throughout their lifetime. These shocks can result from mechanical
or natural phenomena causing the excitation. Many things cause shocks in aircraft: catapult
take-offs, carrier landings, weapons release, rough transportation and air turbulence to
name a few. For these aircraft to survive these harsh events, they need to undergo rigorous
testing before flight to ensure the safety of the flight crew and their airplane.
2 Basic Definitions
2.1 Concept of shock Shock is defined as a non-periodic excitation of a system characterized by sudden and severe
relative displacements in the system. Early shock tests called for classical pulses such as half-
sine, and these tests could be accomplished via drop methods. Presently, many shock tests
require complex, oscillatory pulses that require other methods such as pyrotechnic, impact or
shaker induced environments.
2.2 Definition of shock A shock is defined by a transmission of kinetic energy into a system in a short event interval relative to the system’s natural period. A steady-state response is not achieved. 2.3 How is it measured? Shock is commonly measured via time histories or shock response spectrum (SRS). 2.4 Time Histories Time histories measure the amplitude and time duration of shock event. They are
commonly used for measurement of classical shock pulses (Figure 1), but also are used for
transient events as well. Typically, their amplitude is measured in g’s and time in seconds,
but one can also measure velocity, displacement, force, pressure, stress or torque.
Figure 1: Classical Shock Pulse
2.5 Shock Response Spectrum A Shock Response Spectrum (SRS) is a plot of the maximum response of a single degree of
freedom (SDOF) system, as a function of its natural frequencies, in response to an applied
shock input (Figure 2). SRS plots may be expressed in terms of acceleration, velocity or
displacement, but commonly are acceleration based. However, a SRS does not uniquely
define the shock input, since two different shock pulses can have the same maximum peak
response. The maximum of the peaks is only a single point in the time of the response
Figure 2: Shock Response Spectrum (SRS) Plot
Figure 3: Sawtooth Shock
Another classical shock is the triangle shock (Figure 4). It is similar to a sawtooth; however
the drop is not quite as severe. The triangle shock is infrequently used in shock testing.
Figure 4: Triangle Shock
b) Spectrum Shock
A shock response spectrum defined by frequency and acceleration level pairs and uses the SRS
for measurement. (Figure 2)
c)Pyroshock
Pyroshock is characterized by a high acceleration, short duration shock pulse. This shock
oscillates somewhat symmetrically around a zero baseline value, and typically decays in a very
short time of less than 20 milli-seconds. Pyro-shocks are measured using the SRS (Figure 5).
d) Seismic Shock
Seismic shock (Figure 6) is characterized by low acceleration, high displacement, and long time
duration.
Figure 6: Seismic Shock Time History
Figure 5 : Pyroshock Shock Time & Response Spectrum
mgh = 1/2 mv^2 where: m = mass h = drop height g = acceleration of gravity v = velocity at impact The impact velocity is independent of mass. Solving the conservation of energy equation above and neglecting drag forces caused by air resistance, velocity is calculated from:
v =
4.2 Force and Distance domain.
Using the work energy principle, the next step for the test engineer is to estimate the expected force. The net work done during an impact is equal to the average force of impact multiplied by the distance traveled during impact. Wnet=1/2 mvfinal^2 - 1/2 mvinitial^2 In a drop test application, Wnet = 1/2 mv final^2 , since the initial velocity ( v initial) is equal to zero. Assuming one could easily measure the impact distance, the average impact force F is calculated as follows:
where d = distance traveled after impact. The test engineer must estimate the distance traveled after impact to select an impact force sensor with the proper measuring range. Whether or not there is a perfectly elastic collision can affect the distance estimation and the resulting force calculation. (For the purpose of this article, a perfectly elastic collision means a perfect rebound after impact.) To explain this, suppose a steel ball bearing is dropped from a certain height onto a foam pad. Since it penetrates the material, the material is absorbing the energy, and the impact force is minimized and is not a perfectly elastic collision. On the other hand, if the same steel ball is dropped on to a steel plate, it may rebound back to the same height to which it was originally dropped and absorbs very little energy. The impact force is very large, and a near-perfect elastic collision has taken place. [2].
4.3 Force and Time domain:
Another approach to determine the expected impact force is to estimate the pulse width of the expected force-time curve. Here we can employ Newton’s 2nd law of motion, F = ma. This acceleration term depends on the pulse width of the force-time curve and must take on an estimated value based on various material types similar to the way impact distance was estimated. Impact acceleration may be calculated from the change in velocity during the pulse width time[3]. or
The highest peak impact forces occur when there is a steel-on steel impact. If we assume a perfect rebound, which approximates steel-on-steel impacts, the initial and final velocities are equal in magnitude but opposite in direction and are additive. The resulting peak acceleration may be calculated from:
It is important not to confuse acceleration due to free-fall gravity g used in the impact velocity calculation with the impact acceleration. The impact force is then calculated from Newton’s 2nd law equation: F = ma
5 Methods of Shock Testing
A shock testing machine (frequently called a shock machine ) is a mechanical device that applies a mechanical shock to equipment under test. The nature of the shock is determined from an analysis of the field environment. Tests by means of shock machines usually are preferable to tests under actual field conditions for four principal reasons:
1. The nature of the shock is under good control, and the shock can be repeated with reasonable exactness. This permits a comparative evaluation of the equipment under test and allows exact performance specifications to be written. 2. The intensity and nature of shock motions can be produced that represent an average condition for which protection is practical, whereas a field test may involve only a specific condition that is contained in this average. 3. The shock machine can be housed at a convenient location with suitable facilities available for monitoring the test. 4. The shock machine is relatively inexpensive to operate, so it is practical to perform a great number of developmental tests on components and subassemblies in a manner not otherwise practical. Shock testing is commonly performed via the following methods. Each method imparts the kinetic energy to the system in a different manner. - Drop - Impact - Shaker - Pyro shock - Hopkinson Bar In drop testing ΔV≠0 (change in velocity) and Δd≠0 (change in displacement), while others
maintain zero overall change in velocity and displacement
a) Drop Shock method
During drop shock the test item is moving towards an impact surface. It is usually free-fall or an assisted (pulled by a bungee-cord) fall. There is a massive target surface and a shock programmer (target surface) that determines the pulse shape, peak acceleration and duration. The drop height and assist method determine the impact velocity. Typically, there is very little energy outside the pulse bandwidth. Drop shock is performed by general- purpose machines. They are capable of large ΔV (changes in velocity) and large Δd (changes in displacement). A drop shock machine is typically used for producing simple (Classical) pulses shapes.
b) Impact Testing
- The shock machine is relatively inexpensive to operate, so it is practical to perform a great number of developmental tests on components and subassemblies in a manner not otherwise practical.
6.1 SHOCK-MACHINE CHARACTERISTICS
6.1.1 DAMAGE POTENTIAL
The damage potential of a shock motion is dependent upon the nature of an equipment subjected to the shock, as well as upon the nature and intensity of the shock motion To obtain a comparative measure of the damage potential of a shock motion, it is customary to determine the effect of the motion on simple mechanical systems. This is done by determining the maximum responses of a series of single degree of freedom systems to the shock motion and considering the magnitude of the response of each of these systems as indicative of the damage potential of the shock motion.
6.1.2 SHOCK RESPONSE SPECTRA
The responses are plotted as a function of these natural frequencies. A curve representing these responses is called a shock response spectrum, or response spectrum. Its magnitude at any given frequency is a quantitative measure of the damage potential of a particular shock motion to a single degree-of-freedom system with that natural frequency. This concept of the shock response spectrum originally was applied only to undamped single degree-of freedom systems, but the concept has been extended to include systems in which any specified amount of damping exists
6.1.2.1 TYPES OF SHOCK RESPONSES SPECTRA
The response of a simple system can be expressed in terms of the relative displacement, velocity, or acceleration of the system. It is customary to define velocity and acceleration responses as 2π f and (2π f )^2 times the maximum relative displacement response, where f is frequency expressed in hertz. The corresponding response curves are called displacement, velocity, or acceleration shock response spectra. Of the three motion parameters (displacement, velocity, and acceleration) describing a shock spectrum, velocity is the parameter of greatest interest from the viewpoint of damage potential. This is because the maximum stresses in a structure subjected to a dynamic load typically are due to the responses of the normal modes of the structure, that is, the responses at natural frequencies. At any given natural frequency, stress is proportional to the modal (relative) response velocity.[4]. Specifically,
Where ςmax = maximum modal stress in the structure νmax = maximum modal velocity of the structural response E = Young’s modulus of the structural material ρ = mass density of the structural material C = constant of proportionality dependent upon the geometry of the structure (often assumed for complex equipment to be 4 < C < 8)^2
6.1.3 SPECIFYING A SHOCK TEST Two methods of specification are employed in defining a shock test:
- a specification of the shock motions (or response spectra) to which the item under test is subjected
- a specification of the shock machine, the method of mounting the test item, and the procedure for operating the machine. [6].
6.2 CHARACTERISTIC TYPES OF SHOCKS
The shock machines described below are grouped according to the types of shocks they produce. When a machine can be classified under several headings, it is placed in the one for which it is primarily intended. One characteristic shared by all shock machines is that the motions they produce are sudden and likely to create significant inertial forces in the item under test. The types of shock shown in Fig 8. are classified as ( A ) through ( D ), simple shock pulses, whose shapes can be expressed in a practical mathematical form; ( E ), single complex shock; and ( F ), a multiple shock. In contrast to a simple shock pulse specification, the motions illustrated in Fig 8. ( E ) and ( F ) often are the result of a shock test in which the shock testing machine, the method of mounting, and machine operations were specified.
(A) Velocity shock, or step velocity change.
(B) Simple half-sine acceleration shock pulse.
(C) Rectangular force pulse.
(D) Saw-tooth acceleration pulse.
(E) Single complex shock.
(F) Multiple shock.
Figure 9: Types Of Shocks
6.3 KINEMATICS OF SIMPLE SHOCKS
The shock test is generally specified by an acceleration varying with time. This acceleration profile can be obtained with various velocity and displacement profiles depending on the initial velocity of the table supporting the specimen, leading theoretically to various types of shock programmers. All shock test facilities are, in other respects, limited in regard to
Figure 8 : Types Of Shocks
)
At the moment t= of the end of the shock, velocity is equal to:
)
i.e., since
The body subjected to this shock thus undergoes a velocity change
This is the area delimited by the curve the time axis
between 0 and.
The displacement is calculated by a second integration; we will take the initial conditions to be t=0, x=0 as is practically always the case in these problems. This yields
)
To further the study of this movement it is
preferable to specify the test conditions. Two cases arise;
the velocity is able to be:
- either zero before the beginning of the shock: the object subjected to the shock, initially at rest, acquires, under the effect of the impulse, a velocity equal to
- or arbitrarily non-zero: the specimen has a velocity which varies during the shock duration from a value to a value for t = it is then said that there is impact.
Figure 10 : Velocity change of a half-sine
6.3.2.2 IMPACT MODE
The initial velocity is arbitrary and zero here. The body subjected to the shock arrives
on the target with the velocity , touches the target (which has a programmer intended to
shape the acceleration according to a half-sine) between time t=0 and t =. At time at
t = the end of the shock, the velocity can be either zero (no rebound); or arbitrary,
different from zero. It is said there is rebound with velocity. We assume that the
movement is carried out along only one axis, the velocity having a different direction from the velocity of impact. The velocity change is equal, in absolute terms, to
The most general case is where is arbitrary.
With ( = coefficient of restitution) The velocity change equal to
makes it possible to calculate
i.e., in algebraic value, and by definition
Velocity thus written as:
)
i.e since
can only be determined by measurement.
6.4.1 Drop Tables A great variety of drop testers are used to obtain acceleration pulses having magnitudes ranging from 80,000 g down to a few g. The machines each include a carriage (or table) on which the item under test is mounted; the carriage can be hoisted up to some required height and dropped onto an anvil. Guides are provided to keep the carriage properly oriented. When large velocity changes are required, the carriage may be accelerated downward by a means other than gravity. Frequently, parts of the carriage, associated with its lifting and guiding mechanism, are flexibly mounted to the rigid part of the carriage structure that receives the impact. This is to isolate the main carriage structure from its flexible appendages so as to retain the simple pulse structure of the stopping acceleration.
References
[1]. Nave, R., “Hyper Physics, Mechanics,” National Science Teachers Association, 2001. [2]. Metz, R., “Automotive Component Durability Testing using Quartz Piezoelectric Force Sensors,” Automotive Testing Expo, 2005. [3]. Tustin, No. 9., Random Vibration & Shock Testing , Equipment Reliability Institute,
[4]. Gaberson, H. A., and R. H. Chalmers: Shock and Vibration Bull., 40(2):31 (1969). [5]. Piersol, A.G.: J. IEST, 44(1):23 (2001). [6]. “Specification for the Design, Construction, and Operation of Class HI (High Impact) Shock Testing Machine for Lightweight Equipment,” American National Standards Institute Document ANSI S2.15-1973.
