IEC 62969-3:2018

IEC 62969-3 ®
Edition 1.0 2018-05
INTERNATIONAL
STANDARD
NORME
INTERNATIONALE
colour
inside
Semiconductor devices – Semiconductor interface for automotive vehicles –
Part 3: Shock driven piezoelectric energy harvesting for automotive vehicle
sensors
Dispositifs à semiconducteurs – Interface à semiconducteurs pour les véhicules
automobiles –
Partie 3: Récupération de l’énergie piézoélectrique produite par les chocs pour
les capteurs de véhicules automobiles

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IEC 62969-3 ®
Edition 1.0 2018-05
INTERNATIONAL
STANDARD
NORME
INTERNATIONALE
colour
inside
Semiconductor devices – Semiconductor interface for automotive vehicles –

Part 3: Shock driven piezoelectric energy harvesting for automotive vehicle

sensors
Dispositifs à semiconducteurs – Interface à semiconducteurs pour les véhicules

automobiles –
Partie 3: Récupération de l’énergie piézoélectrique produite par les chocs pour

les capteurs de véhicules automobiles

INTERNATIONAL
ELECTROTECHNICAL
COMMISSION
COMMISSION
ELECTROTECHNIQUE
INTERNATIONALE
ICS 31.080.99 ISBN 978-2-8322-5685-5

– 2 – IEC 62969-3:2018 © IEC 2018
CONTENTS
FOREWORD . 4
INTRODUCTION . 6
1 Scope . 7
2 Normative references . 7
3 Terms and definitions . 7
3.1 General terms . 8
3.2 Piezoelectric transducer . 9
3.3 Characteristic parameters . 10
4 Essential ratings and characteristic parameters . 11
4.1 Identification and type . 11
4.2 Limiting values and operating conditions . 11
4.3 Additional information . 12
5 Test method . 12
5.1 General . 12
5.2 Electrical characteristics . 13
5.2.1 Test procedure . 13
5.2.2 Capacitance . 14
5.2.3 Natural frequency . 14
5.2.4 Damping ratio . 15
5.2.5 Output voltage . 15
5.2.6 Output current . 16
5.2.7 Output power . 16
5.2.8 Optimal load impedance . 17
5.2.9 Maximum output power . 17
5.3 Mechanical characteristics . 18
5.3.1 Test procedure . 18
5.3.2 Temperature range . 19
5.3.3 Shock magnitude . 20
5.3.4 Temperature and humidity testing . 20
5.3.5 Mechanical reliability (shock) testing . 20
Annex A (informative) Mechanical shock pulses . 21
Annex B (informative) Electromechanical coupling . 23
B.1 Compliance and coupling coefficient relation. 23
B.2 Young’s modulus and coupling coefficient relation . 23
Bibliography . 24

Figure 1 – Shock driven energy harvester using cantilever with piezoelectric film . 8
Figure 2 – Conceptual diagram of shock driven piezoelectric energy harvester . 9
Figure 3 – Equivalent circuit of shock driven piezoelectric energy harvester . 10
Figure 4 – Measurement procedure of shock driven piezoelectric energy harvester . 13
Figure 5 – Test setup for the electrical characteristics of shock driven piezoelectric
energy harvester . 14
Figure 6 – Output waveform and its frequency component of a shock driven
piezoelectric energy harvester . 15
Figure 7 – Output voltages of shock excited piezoelectric energy harvester at various
external loads . 16

Figure 8 – Output currents of shock driven piezoelectric energy harvester at various
output voltages . 16
Figure 9 – Output power of shock driven piezoelectric energy harvester at various
external loads . 17
Figure 10 – Output power and voltage of shock driven piezoelectric energy harvester at
various shock amplitudes . 18
Figure 11 – Block diagram of a test setup for evaluating the reliability of shock driven
piezoelectric energy harvester . 19
Figure A.1 – Comparison of general shock patterns and shock pattern from automobile . 21
Figure A.2 – Impact (or shock) recorded by an electronic impact recorder . 22

Table 1 – Specification parameters for shock driven piezoelectric energy harvesters . 11

– 4 – IEC 62969-3:2018 © IEC 2018
INTERNATIONAL ELECTROTECHNICAL COMMISSION
____________
SEMICONDUCTOR DEVICES –
SEMICONDUCTOR INTERFACE FOR AUTOMOTIVE VEHICLES –

Part 3: Shock driven piezoelectric energy harvesting
for automotive vehicle sensors

FOREWORD
1) The International Electrotechnical Commission (IEC) is a worldwide organization for standardization comprising
all national electrotechnical committees (IEC National Committees). The object of IEC is to promote
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patent rights. IEC shall not be held responsible for identifying any or all such patent rights.
International Standard IEC 62969-3 has been prepared by IEC technical committee 47:
Semiconductor devices.
The text of this International Standard is based on the following documents:
FDIS Report on voting
47/2461/FDIS 47/2480/RVD
Full information on the voting for the approval of this International Standard can be found in
the report on voting indicated in the above table.
This document has been drafted in accordance with the ISO/IEC Directives, Part 2.

A list of all parts in the IEC 62969 series, published under the general title Semiconductor
devices – Semiconductor interface for automotive vehicles, can be found on the IEC website.
The committee has decided that the contents of this document will remain unchanged until the
stability date indicated on the IEC website under "http://webstore.iec.ch" in the data related to
the specific document. At this date, the document will be
• reconfirmed,
• withdrawn,
• replaced by a revised edition, or
• amended.
IMPORTANT – The 'colour inside' logo on the cover page of this publication indicates
that it contains colours which are considered to be useful for the correct
understanding of its contents. Users should therefore print this document using a
colour printer.
– 6 – IEC 62969-3:2018 © IEC 2018
INTRODUCTION
The IEC 62969 series is composed of four parts as follow:
• IEC 62969-1, Semiconductor devices – Semiconductor interface for automotive vehicles –
Part 1: General requirements of power interface for automotive vehicle sensors
• IEC 62969-2, Semiconductor devices – Semiconductor interface for automotive vehicles –
Part 2: Efficiency evaluation methods of wireless power transmission using resonance for
automotive vehicle sensors
• IEC 62969-3, Semiconductor devices – Semiconductor interface for automotive vehicles –
Part 3: Shock driven piezoelectric energy harvesting for automotive vehicle sensors
• IEC 62969-4 , Semiconductor devices – Semiconductor interface for automotive vehicles
– Part 4: Evaluation method of data interface for automotive vehicle sensors
The IEC 62969 series covers power and data interfaces for sensors in automotive vehicles.
The first part covers general requirements of test conditions such as temperature, humidity,
vibration, etc for automotive sensor power interface. This part also includes various electrical
performances of power interface such as voltage drop from power source to automotive
sensors, noises, voltage level, etc. The second part covers “Efficiency evaluation methods of
wireless power transmission using resonance for automotive vehicle sensors “. The third part
covers “Shock driven piezoelectric energy harvesting for automotive vehicle sensors”. The
fourth part covers “Evaluation methods of data interface for automotive vehicle sensors”.

___________
To be published
SEMICONDUCTOR DEVICES –
SEMICONDUCTOR INTERFACE FOR AUTOMOTIVE VEHICLES –

Part 3: Shock driven piezoelectric energy harvesting
for automotive vehicle sensors

1 Scope
This part of IEC 62969 describes terms, definitions, symbols, configurations, and test
methods that can be used to evaluate and determine the performance characteristics of
mechanical shock driven piezoelectric energy harvesting devices for automotive vehicle
sensor applications.
This document is also applicable to energy harvesting devices for motorbikes, automobiles,
buses, trucks and their respective engineering subsystems applications without any limitations
of device technology and size.
2 Normative references
The following documents are referred to in the text in such a way that some or all of their
content constitutes requirements of this document. For dated references, only the edition
cited applies. For undated references, the latest edition of the referenced document (including
any amendments) applies.
IEC 60749-5, Semiconductor devices – Mechanical and climatic test methods – Part 5:
Steady-state temperature humidity bias life test
IEC 60749-10, Semiconductor devices – Mechanical and climatic test methods – Part 10:
Mechanical shock
IEC 60749-12, Semiconductor devices – Mechanical and climatic test methods – Part 12:
Vibration, variable frequency
IEC 62830-1, Semiconductor devices – Semiconductor devices for energy harvesting and
generation – Part 1: Vibration based piezoelectric energy harvesting
3 Terms and definitions
For the purposes of this document, the terms and definitions given in IEC 62830-1 and the
following apply.
ISO and IEC maintain terminological databases for use in standardization at the following
addresses:
• IEC Electropedia: available at http://www.electropedia.org/
• ISO Online browsing platform: available at http://www.iso.org/obp

– 8 – IEC 62969-3:2018 © IEC 2018
3.1 General terms
3.1.1
shock
sudden acceleration or deceleration resulting in transient physical excitation; characterized by
the peak acceleration, the duration, and the shape of the shock pulse (rectangular, half-sine,
sawtooth, etc.)
Note 1 to entry: The fundamental frequency of the automotive vehicle shock is varied from 0,5 Hz to 20 Hz.
Note 2 to entry: Mechanical shock pulses are sinusoidal, rectangular, half-sine, sawtooth, etc. waves. Detailed
explanation of mechanical shock pulses with an analysis of shock amplitude and duration/frequency of automobile
and conventional shaker have been included in Annex A (informative).
3.1.2
shock driven energy harvester
generator that responds to the applied mechanical shock, transforms shock into vibration
(mechanical oscillation), and converts the vibration to the electricity
Note 1 to entry: The generated power depends on the characteristics of applied shock and, mechanical and
electrical characteristics of the generator itself.
Note 2 to entry: Shock energy harvester to convert shock to electricity by using piezoelectric transducers is
comprised of inertial mass, spring, and piezoelectric transducer as shown in Figure 1. The piezoelectric transducer
contains two electrodes and a piezoelectric film. Vibration is induced in response to the applied shock that
introduces a reciprocating motion to the mass. The spring which suspends the mass is bended and the bending of
spring introduces tensile and compression of piezoelectric film. The top and bottom electrodes of piezoelectric film
harvest generated charges from the piezoelectric effect.
Note 3 to entry: Shock driven energy harvester is represented as shown in Figure 2. It is configured by mass,
spring, damping, and piezoelectric transducer. The piezoelectric transducer is generally viewed as damping.
Electrodes
Piezoelectric film
Output
R
Spring
Mass
Fixed base
Shock
IEC
Key
Configuration of energy harvester Components to operate a energy harvester
Mass Inertial mass to induce mechanical Shock Transient physical excitation supplied
oscillation responding to applied shock to vibrate the mass of energy
harvester
Spring To couple the induced vibration to the R External load
mass by suspending it
Piezoelectric Body layer of piezoelectric transducer for
film energy harvester
Figure 1 – Shock driven energy harvester using cantilever
with piezoelectric film
Spring
Piezoelectric
transducer
Mass
Damping
Shock
IEC
Key
Configuration of energy harvester Components to operate an energy harvester
Damping Reduction of the acceleration of Piezoelectric Power generator via piezoelectric
oscillation of mass transducer effect
Figure 2 – Conceptual diagram of shock driven piezoelectric
energy harvester
3.2 Piezoelectric transducer
3.2.1
piezoelectric effect
phenomenon in which a mechanical deformation produces an electric polarization of
piezoelectric material, and conversely an electric polarization produces a mechanical
deformation
[SOURCE: IEC 60050-121:1998, 121-12-86, modified]
3.2.2
piezoelectric charge constant
d
ij
polarization generated per unit of mechanical stress applied to a piezoelectric material
Note 1 to entry: The first subscript to d indicates the direction of polarization generated in the material when the
electric field, is zero or, alternatively, is the direction of the applied field strength. The second subscript is the
direction of the applied stress or the induced strain, respectively. d : induced strain in direction Z-axis per unit
electric field applied in direction Z-axis. d : induced strain in direction X-axis per unit electric field applied in
direction Z-axis.
3.2.3
electromechanical coupling coefficient
k
value to describe the conversion rate of electrical energy to mechanical form or vice versa
Note 1 to entry: The coefficient is a combination of elastic, dielectric and piezoelectric constants which appears
naturally in the expression of piezoelectric transducer as following
d
k= (1)
1/2
(sε)
– 10 – IEC 62969-3:2018 © IEC 2018
where
d is the piezoelectric charge constant
s is elastic compliance (inverse of Young's modulus) at constant electric field
ε is permittivity of the piezoelectric material at constant stress
Note 2 to entry: The relationship of electromechanical coupling coefficient with compliance and Young’s modulus
have been elaborated in Annex B (informative).
3.3 Characteristic parameters
3.3.1
equivalent circuit
arrangement of ideal circuit elements that has circuit parameters, electrically equivalent to
those of a shock driven piezoelectric energy harvester
Note 1 to entry: Shock driven piezoelectric energy harvester can be divided into mechanical and electrical parts
as shown in Figure 3. The mechanical part consists of series elements m, k , b , and transformer (coupling
sp m
element between mechanical and electrical parts)- where m, k , and b represent the effective mass, spring
sp m
constant of spring, damping, respectively; and piezoelectric effect to convert mechanically induced strain to
electrical charge density with coupling coefficient k. The electrical part is comprised of parallel connected C , R,
p
and transformer- where C and R represent the capacitance between two electrodes of piezoelectric transducer and
p
external load.
k b
m sp m
k
C
p
A(t) R
Mechanical part Electrical part
IEC
Key
Mechanical part Electrical part
m effective mass C capacitance of piezoelectric
p
transducer
k spring constant R external load
sp
b damping coefficient
m
A(t) induced vibration in response to the
applied shock
Figure 3 – Equivalent circuit of shock driven
piezoelectric energy harvester
[SOURCE: IEC 60050-521:2002, 521-05-35, modified]
3.3.2
natural frequency
ω
n
free vibration frequency of the mass-spring-damping system of the energy harvester to
generate largest output power
k
sp
ω = (2)
n
m
3.3.3
damped natural frequency
ω
d
frequency of free vibration of the mass-spring-damping system of the energy harvester
incorporating damping in response to the shock excitation
ω =ω 1−ζ (3)
d n
where ζ is the damping ratio determined by logarithmic decrement of output voltage waveform,
normalized from electrical and mechanical damping.
3.3.4
shock excitation amplitude
acceleration amplitude of the random applied shock to the energy harvester for maximum
duration as measured on the enclosure over which the energy harvester will not sustain
permanent damage though not necessarily functioning within the specified tolerances
4 Essential ratings and characteristic parameters
4.1 Identification and type
The shock driven energy harvester shall be clearly and durably marked in the order given
below:
a) year and week (or month) of manufacture;
b) manufacture’s name or trade mark;
c) terminal identification (optional);
d) serial number;
e) factory identification code (optional).
4.2 Limiting values and operating conditions
The characteristic parameters should be listed as shown in Table 1. The manufacturer shall
clearly announce the operating conditions and their limitation for energy harvesting. Limiting
value is the maximum induced vibration to ensure the operation of vibration energy harvester
for power generation without any damage.
Table 1 – Specification parameters for shock driven
piezoelectric energy harvesters
Measuring
Parameter Symbol Min. Max. Unit
conditions
Insert name of
characteristic
parameters
– 12 – IEC 62969-3:2018 © IEC 2018
4.3 Additional information
Some additional information should be given such as equivalent circuits (natural frequency,
internal impedance, output voltage and power, etc.), handling precautions, physical
information (outline dimension, terminals, accessories, installation guide, etc.), package
information, PCB interface and mounting information, and other information, etc.
5 Test method
5.1 General
Basically, general test procedures for shock driven energy harvester are performed as shown
in Figure 4. After the energy harvester is being mounted on a test fixture, it is measured by
using voltage, current, and LCR meters. Since the input impedances of these meters are
usually 10 MΩ, miniaturized or micro sized energy harvesters should not be characterized
accurately due to their large internal impedance. For measuring and characterizing these
devices accurately, the ultra-high-impedance meters should be used.
Before connecting the energy harvester to the test fixture, meter, cable, and vibration exciter
shall be calibrated. After calibration, connect test cable with mounted energy harvester test
fixture on shaker table (shock exciter). The reading of output voltage or current on display of
the meters is carefully taken with applied shock which is measured by the accelerometer.
NOTE Shock driven energy harvester can be measured as shown in Figure 4. After mounting the energy
harvester onto a shaker table, electrical characteristic are measured by using a meter or equivalent equipment. If
the measurements are satisfactory, reliability test for temperature range with thermal cycling and mechanical
failure with various shock and vibration, is performed for commercially use.

Start
Output voltage
Natural frequency
Output power
Damping ratio
Electrical characterization
Optimal load
Capacitance
Maximum output power
Temperature range
Shock excitation Mechanical characterization
Mean-time-to-failure
End
IEC
Key
Procedure Reference subclause Procedure Reference subclause
Start  Optimal load 5.2.8
Electrical characterization Maximum output power 5.2.9
Natural frequency 3.3.2 and 5.2.3 Mechanical characterization
Damping ratio 3.3.3 and 5.2.4 Temperature range 5.3.2
Capacitance 5.2.2 Shock excitation 3.3.4 and 5.3.1
Output voltage 5.2.5 Mean-time-to-failure 5.3.3
Output power 5.2.7
Figure 4 – Measurement procedure of shock driven
piezoelectric energy harvester
5.2 Electrical characteristics
5.2.1 Test procedure
Figure 5 shows a test setup of the electrical characteristic of a shock driven piezoelectric
energy harvester. To measure the electrical characteristics of a shock driven piezoelectric
energy harvester, the device shall be attached on a shaker table as shown in Figure 5. When
a particular type of shock with specified acceleration amplitude is applied to the device, an
output voltage or current across an external load is measured.
The following test procedure is performed:
a) A specified shock is induced to the energy harvester.
b) The voltage or current across the external load which is connected to the terminals of the
energy harvester is measured using a voltage or current meter.
c) The voltage and current are measured with various acceleration amplitude of shock by
adjusting the amplifying ratio of power amplifier.
d) The maximum voltage and current are derived from various external loads to find the
optimal load.
– 14 – IEC 62969-3:2018 © IEC 2018
A
Vibration controller
DUT
V
Terminals
Electrodynam
ic Shaker External load
Power amplifier
IEC
Key
Component and meters to monitor Equipment and supplies
DUT: device A piece of energy harvester Vibration To produce and supply an initial
under test controller drive signal (specified type of shock)
to the power amplifier
Voltage meter (V) To detect a voltage across the Power To supply a specified level of
external load amplifier electrical power to the shock exciter
Ampere meter (A) To detect a current through the Electrodynamic To supply a specified level and type
external load Shaker of mechanical shock to a piece of
DUT
External load (R)
Figure 5 – Test setup for the electrical characteristics
of shock driven piezoelectric energy harvester
5.2.2 Capacitance
It is a capacitance measured between two terminals of energy harvesting device. A calibration
of a LCR meter shall be made in order to eliminate systematic errors occurred in the LCR
meter, cable, and connectors. When the device is connected to the LCR meter, its
capacitance will be displayed.
5.2.3 Natural frequency
It is the frequency, normally expressed in Hz, of the energy harvester at which its output
voltage/power is obtained. Figure 6 shows the typical output voltage waveform of a sock
excited energy harvester and its frequency component obtained by Fast Fourier Transform
(FFT).
Voltage
FFT
0 2
–5
–10
0 0,02 0,04 0,06 0,08 0,1 50 100 150 200 250 300 350 400 450
Time (s) Frequency (Hz)
IEC IEC
a) b)
Figure 6 – Output waveform and its frequency component
of a shock driven piezoelectric energy harvester
5.2.4 Damping ratio
It is a measure of how the output decays with time after a single shock impulse is applied to
the energy harvester. It is a dimensionless quantity that is calculated from the logarithmic
decrement of the output voltage response by using the following formula:
1  a
 
ζ= ln (4)
 
2π a
 2
where a and a are the two consecutive peak amplitudes of the voltage waveform.
1 2
5.2.5 Output voltage
It is the peak-peak/rms voltage for specified duration measured across the terminals of energy
harvester with a specified external load in response to applied shock. Figure 7 shows the
graphical shape of measured output voltage versus external resistive load connected to the
terminal of energy harvester. The open circuit voltage is the measured peak-peak/rms voltage
for specified duration when there is no external load connected to the terminal of energy
harvester at a specific shock excitation.
Output voltage (V)
Amplitude (a.u.)
– 16 – IEC 62969-3:2018 © IEC 2018
1,5
0,5
0 1 2 3 4 5 6 7 8 9 10
External load (KΩ)
IEC
Figure 7 – Output voltages of shock excited piezoelectric
energy harvester at various external loads
5.2.6 Output current
It is the current measured through the specified external load connected to the terminal of
vibration energy harvester at the specified shock excitation. Figure 8 shows the graphical
shape of measured current versus output voltage of energy harvester. The short circuit
current from the terminal of the energy harvester is the measured current when the voltage
across the energy harvester is zero.
0,9
0,8
0,7
0,6
0,5
0,4
0,3
0,2
0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6 1,8 2
Output voltage (V)
IEC
Figure 8 – Output currents of shock driven piezoelectric
energy harvester at various output voltages
5.2.7 Output power
Output power (peak/average) is calculated from the measured output voltage and current for
specified duration of energy harvester with external load.
Output current (µA) Output voltage (V)

(5)
P= IV[W]
Figure 9 shows the graphical shape of measured output power (peak/average) versus external
load of energy harvester.
0,5
0,4
0,3
0,2
0,1
0 1 2 3 4 5 6 7 8 9 10
External load (KΩ)
IEC
Figure 9 – Output power of shock driven piezoelectric energy
harvester at various external loads
5.2.8 Optimal load impedance
Optimal load impedance is the specified value of the external load transferred the largest
electrical energy from energy harvester.
5.2.9 Maximum output power
It is a maximum value of output power (peak/average) measured from energy harvester at a
specified applied shock amplitude for specified duration. The applied shock amplitude is
defined in 5.3.3. Figure 10 shows the graphical shape of measured output power
(peak/average) and voltage (peak-peak/rms) for specified duration versus various applied
shock amplitudes.
Output power (µW)
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3 3
Voltage
2,5 2,5
Power
2 2
1,5 1,5
1 1
0,5 0,5
0 0
0 0,1 0,2 0,3 0,4 0,5
Input vibration (g)
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Figure 10 – Output power and voltage of shock driven piezoelectric
energy harvester at various shock amplitudes
5.3 Mechanical characteristics
5.3.1 Test procedure
Figure 11 shows a test setup of the reliability of a shock driven piezoelectric energy harvester.
The harvesting device shall be repeatedly operated until the failure of device. When a specific
type of shock excitation is applied to the device, output voltage or current is measured
through an external load connected to the device.
To test the reliability, the following test procedure is performed:
a) A shock impulse is induced to the energy harvester.
b) The output voltage or current of energy harvester is measured by the meter.
c) The test is continuously performed for a few months.
Output voltage (V)
Output power (µW)
Temperature
controller
A
Vibration controller
DUT
V
Electrodyna
mic Shaker
Temperature controlled
Power amplifier
environmental chamber
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Key
Component and meters to monitor Equipment and supplies
DUT: device under test A piece of energy Vibration controller To produce and supply an initial
harvester drive signal (specified type of
shock) to the power amplifier
Voltage meter (V) To detect a voltage Power amplifier To supply a specified level of
across the external load electrical power to the shock
exciter
Ampere meter (A) To detect a current Electrodynamic shaker To supply a specified level and
through the external load type of mechanical shock to a
piece of DUT
Temperature controlled To keep a specified temperature
environment chamber value of a piece of DUT
Figure 11 – Block diagram of a test setup for evaluating the reliability
of shock driven piezoelectric energy harvester
5.3.2 Temperature range
The objective of this test is to evaluate its reliability by low/high temperature cycling test. The
temperature range should be specified from the applications. First, the test is performed at the
temperature cycling test chamber, and second, by placing the finished energy harvester in an
oven. The performance characteristics are monitored by a meter.

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5.3.3 Shock magnitude
The objective of this test is to evaluate its reliability by high input acceleration for specified
duration. The operating range should be specified from the application. First, the test is
performed as repetitive test of shock excitation with various acceleration and duration.
Second, by placing the finished energy harvester on the shock exciter. The performance
characteristics are monitored by a meter.
IEC 60749-12 applies.
5.3.4 Temperature and humidity testing
IEC 60749-5 applies.
5.3.5 Mechanical reliability (shock) testing
IEC 60749-10 applies.
Annex A
(informative)
Mechanical shock pulses
Mechanical shock pulses are sinusoidal, rectangular, half-sine, sawtooth, etc. waves. The
damage potential of a shock pulse depends upon its peak amplitude, duration and waveform.
The peak amplitude is measured in units of “g” where g = 9,8m/s . The waveform is described
in three ways, namely frequency, duration, and velocity change (ΔV). Frequency describes
the time as compared to cycles per second and the unit of measurement is Hertz (Hz).
Duration describes the time as compared to seconds and the usual unit of measure is
milliseconds (ms). Velocity change (ΔV) is the area under the acceleration time graph of the
shock. It directly relates to the energy contained in the shock. The higher the velocity changes
the higher the energy content.
Subfigure A.1 a) shows a shock wave or an impact wave in time domain. The wave is a sine
curve with acceleration in g (g = 9,8m/s ) along the y-axis and time in ms along the x-axis.
The magnitude of shock pulse varies depending on the origin of shock in automobile and one
general shock pattern is shown in Subfigure A.1 b). This kind of shock can be reproducible
using conventional electrodynamic shaker.
An analysis of shock amplitude and duration/frequency of conventional shaker is shown in
Figure A.2. The following conditions when simultaneously reach damage a transformer of
electrodynamic shaker: (a) the peak acceleration exceeds the critical acceleration, and (b) the
duration of the peak half sine curve exceeds the critical shock duration, or the frequency is
lower than the critical frequency.

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a) General shock patterns b) Shock pattern from automobile

Figure A.1 – Comparison of general shock patterns and shock pattern from automobile

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Figure A.2 – Impact (or shock) recorded by an electronic impact recorder

Annex B
(informative)
Electromechanical coupling
B.1 Compliance and coupling coefficient relation
The relation between elastic compliance and piezoelectric coupling coefficient is the following:
D E 2
s = s (1− k )
where
D
s is the compliance at constant dielectric field D (open circuit);
E
s is the compliance at constant field strength E (short circuit);
k is the piezoelectric coupling coefficient.
B.2 Young’s modulus and coupling coefficient relation
The relation between Young’s modulus and the piezoelectric coupling coefficient is the
following:
2 E
1 (1− k ) Y
D
=  or  Y =
D E 2
Y Y (1− k )
where
D
Y is the Young's modulus at open circuit;

E
Y is the Young's modulus at short circuit.
The piezoelectric material has two different Young's moduli, depending on the electrical
boundary conditions (short circuit or open circuit). Since k is always less than 1.0, the open
D E
circuit
...