^ecUnical ^lot& 150

GENERAL CHARACTERISTICS OF

LINEAR STRAIN GAGE ACCELEROMETERS

USED IN TELEMETRY

P. S. LEDERER

U. S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS
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NATIONAL BUREAU OF STANDARDS

technical ^Ylote

150

JUNE 1962

GENERAL CHARACTERISTICS OF

LINEAR STRAIN GAGE ACCELEROMETERS

USED IN TELEMETRY

P. S. Lederer

NBS Technical Notes are designed to supplement the Bureau's regular publications program. They provide a means formaRng available scientific data that are of transient or limiied interest. Technical Notes may be

listed or referred to in the open literature.

For sale by the Superintendent of Documents, U.S. Government Printing Office Washington 25, D.C. - Price 40 cents

Contents

page

1. Introduction 1

2. Description of Strain Gage Accelerometers 2

3. Theory of the Ideal Seismic Pickup 3

3-1. Figure of Merit, Natural Frequency, Range 4

4. Design Principles for Unbonded Strain Gage Accelerometers 5 4-1. Seismic Mass Determination 5 4-2. Electrical Sensitivity 8

4-3. Bridge Resistance 9

4-4. Design Considerations 9

4-4-1. Higher Gage-Factor Wire 10

4-4-2. Smaller Displacement 11

4-4-3. Higher Excitation Voltage 11

5. Design Principles for Bonded Strain Gage Accelerometers 15

5-1. Range, Natural Frequency and Sensitivity 15

5-2. Electrical Sensitivity 19

5~3« Bridge Resistance 19

5-4. Design Considerations 19

5-4-1. Semiconductor Strain Gages 22

5-4-2. Low Modulus Beam Material 22

5-4-3. Higher Excitation Voltage 22

5-5« Characteristics of Bonded Strain Gages 23

6. Frequency Response of Strain Gage Accelerometers 24

7. Performance Characteristics 28

7-1. Accuracy and Fidelity 28

7-2. Repeatability 30

7-2-1. Short Term Repeatability 30

7-2-2. Long Term Repeatability 31

7-3- Linearity 31

7-4. Hysteresis 32

7-5. Resolution 33

7-6. Response to Transverse Excitation 33

7-6-1. Transverse Response to Steady State Accelerations 33

7-6-2. Transverse Response to Vibrational Accelerations 35

7-7. Temperature Effects 36

7-7-1. Slowly Changing Ambient Temperatures 36

7-7-1-1- Zero Shift 36

7-7-1-2. Sensitivity Change 37

7-7-1-3. Effects on Dynamic Characteristics 39

7-7-2. Thermal Transients 40

7-8. Tolerance to Environmental Extremes 4l

7-8-1. Steady Acceleration Overload 4l

7-8-2. Vibration and Shock Along the Sensitive Axis 42

7-8-3. Acoustic (Airborne) Noise 43

7-8-4. Extremes of Ambient Temperatures 43

7-8-4-1. Effects on Unbonded Strain Gages 43

7-8-4-2. Effects on Bonded Strain Gages 44

7-8-4-3. Effects on Cantilever Beam (Spring) Materials 46

7-8-4-4. Damping 46

7-8-5. Ambient Press-u^ Variations 47

7-8-6. Effects of Nuclear Radiation 48

7-8-7. Other Environmental Conditions 48

-iii-
Abstract

This paper presents a summary of pertinent

information, theoretical and experimental, on the

design characteristics, performance capabilities and

limitations of strain gage accelerometers used in

telemetry. Properties and characteristics of unbonded

and bonded types of strain gage accelerometers are

discussed.

-IV-
GENERAL CHARACTERISTICS OF LINEAR STRAIN GAGE

ACCELEROMETERS USED IN TELEMETRY

P. S. LEDERER

1. INTRODUCTION

Linear acceleration is one of the important parameters measured in

the flight testing of airplanes, missiles and space vehicles, and transmitted to the ground receiving station by means of telemetry.

Two general types of instruments are used to measure accelerations.

Vibration and shock pickups are seismic instruments which, while generally not having any response to steady acceleration, are capable of sensing accelerations over very wide amplitude and frequency ranges. They

are used primarily for the measurement of vibrations and shock due to

environmental conditions

Spring-mass accelerometers, which respond to steady accelerations

as well .as changing or transient accelerations, are generally used when

measurements are to be made of steady accelerations or a faithful record

of the total acceleration-time history is required. These instruments

are used for attitude and flight path determination, as well as flight

control. They may also be used to measure vibrations and shock, but

within narrower amplitude and frequency ranges than vibration pickups.

The basic element of a spring mass accelerometer is a seismic mass

suspended on a spring which is attached to the case of the instrument.

The motion of the case can be indicated by the relative motion of the

seismic mass with respect to the case.

This paper describes one class of spring-mass accelerometers, those

using resistance strain gages to sense the relative motion of the seismic
mass. There are two types: -unbonded strain gage accelerometers and

bonded strain gage accelerometers.

While an effort was made to cover readily available literature on the

subject, no exhaustive literature survey was attempted. The experimental

results cited are derived largely from tests performed on strain gage

accelerometers in the Mechanical Instruments Section of the National

Bureau of Standards as part of a program dealing with the development of

improved evaluation techniques for telemetering transducers.

2. DESCRIPTION OF STRAIN GAGE ACCELEROMETERS

In the case of an unbonded strain gage accelerometer, the strain

wires supply almost the entire spring force in the spring mass system and

auxiliary springs serve only to restrict the mass to motion along the sensitive axis $ the resistance of the strain wires is a function of the displacement of the mass with respect to the case. Under certain conditions,

this is proportional to the acceleration to which the case is subjected.

Therefore, the output of the strain gage is a measure of the applied

acceleration.

A bonded strain gage accelerometer generally consists of a mass

attached to the end of one or more cantilever beams mounted in the instrument case. Strain gages are attached to the surface of the beam so as to

measure the deflection of the mass in terms of the strain along the beam

surface. As above, under certain conditions, the deflection of the mass

is proportional to the applied acceleration, and therefore, the output of

the strain gages is a measure of the acceleration. In both types, viscous

damping is provided to increase the frequency range over which accurate

measurements may be taken and to damp out transient oscillations due to

high frequency excitation.
3. THEORY OF THE IDEAL SEISMIC PICKUP

The relationship between x, the relative motion between the seismic

mass and the case, and the motion of the case y, for an ideal seismic

pickup with lumped constants is

x + 4imfnx + 4jt 2 fn

2 x = -y (l)

where y = displacement of case, inches

x = relative displacement between mass and case, inches

n = pr- the damping ratio

^c

fn = — VI — the natural frequency of the pickup

2rt f m

cycles per second.

m = seismic mass, pounds second squared per inch,

k = spring constant, pounds per inch.

C = equivalent viscous damping constant pounds per inch

per second.

Cc = 2 « km, critical damping constant, pounds per inch

per second. (See Reference 1, 11.)

For sinusoidal motions of the case at frequency f and peak displacement y , the instantaneous case displacement y is given by

y = y sin 2*ft (2)

The steady state solution of equation (l) for the relative displacement between mass and case becomes

f 2 x = yQ n — sin \ &tft - tan"

/

t 2 r~

-I

-^^w
If, — ^ 0.6 and n^O.65, (most accelerometers are designed to

fn

have these characteristics), then

x <& y fn

2 sin 2sTft (*0

The acceleration of the case is equal to

y = -y

^2fn

2 sin 2ltft (5)

therefore, substituting in (k)

tt x ^ - —_£— (See Reference l) (6)

4«2fn2

As long as the accelerometer is used at frequencies below 60$ of its

natural frequency and is damped near 65$ of critical, the relative displacement between the seismic mass and the case is equal to the acceleration amplitude divided by the square of the natural frequency to a good

approximation. Since the peak acceleration amplitude is generally expressed in "G" units (multiples of the acceleration due to gravity, 386

inches/sec2 equation (6) can be written as

x peak b. 9.77 JL. (7)

fr, 2

G = peak acceleration, G-units

This is the basic relationship used in the design of strain gage accelerometers .

3-1 • Figure of Merit, Natural Frequency, Range .

Although there are some applications, where it is necessary to

sense low frequency accelerations in the presence of high frequency vibrations, and where an accelerometer with a low natural frequency may be

used, which would then be comparatively insensitive to the high frequency vibrations, for a general purpose accelerometer of given range it is

k
desirable to have as high a natural frequency as possible with a given

range of acceleration, output, etc. The higher the natural frequency,

the wider the frequency range of sinusoidal accelerations sensed and the

more faithful the measurement of nonsinusoidal accelerations consisting

of many frequency components.

Thus the ratio of the natural frequency to the range of the accelerometer constitutes a figure of merit, which, a.n other things being

equal, it is desirable to have as large as possible. Equation (7) shows

that a high figure of merit requires a low sensitivity, in terms of displacement per unit acceleration, so that the practical limitation or

figure of merit is the effective resolution of the accelerometer . Moreover, it is seen from this equation that the figure of merit is better

expressed in terms of the square of the natural frequency.

The figure of merit, M , of an accelerometer represents an important design criterion and is given by

M - ¥ - ^k w

k. DESIGN PRINCIPLES FOR UNBONDED STRAIN GAGE ACCELERCMETERS

4-1. Seismic Mass Determination .

In the case of unbonded strain gage accelerometers , most of the

spring force is supplied by the strain wires, themselves. Cantilever

flexure plates, which contribute a very small amount of spring force,

are used to restrict the mass to rectilinear motion. In the design of

such an accelerometer, the incremental value of strain produced in the

wires when the mass responds to the full scale value of acceleration is

5
generally limited to the maximum of 0.0015 inch per inch of gage length.

iDuring assembly, sufficient initial tension is applied to the strain

sensitive resistance wires to keep them under some residual tension when

the mass is in either extreme position. Travel of the mass is limited

mechanically to protect the wires from overloads. '-See Figure 1.

It is desirable to have the vibrating mass in the accelerometer as

small as possible to minimize the volume and weight of the instrument

and to require that as little energy as possible need be taken from the

system whose acceleration or vibration is to be measured.

The basic design equation for unbonded strain gage accelerometers

describes the seismic mass in terms of the other design parameters. The

equation is derived by considering the mass -spring system to have been

set into free sinusoidal oscillation at its natural frequency by an initial displacement (damping is neglected). During each oscillation, the

kinetic energy of the moving mass is transferred into potential energy

of spring displacement and recovered again. Since no loss of energy

occurs due to damping, the maximum kinetic energy of the mass during

each cycle must equal the maximum potential energy stored in the spring

during this cycle. The spring force contributed by the flexure plates

is usually quite small compared to that due to the strain wires and is

therefore neglected in the following derivation. The maximum kinetic

energy of the mass is given by:

Tmax » | m V^ (9)

since the motion is sinusoidal, the maximum velocity is

vmax * 2*fn Xmax (10)

therefore
Tmax "I 111 ^2fn

2

*lax (ll)

and from this, in consistent units

m = T- i^fc (12)

Substituting equation (7) in equation (12) yields

m 386 fn2

m * Tmax ~p— Q

xP o °r 2^ (9.77) G^

fn2

m - .208 Tmax -=-

(13)

The maximum potential energy stored in the strain wire in terms of

the spring constant k and the design strain £ and the total length of

strain wire S is given by:

w - I

s ke2

(14)

The spring constant k is a function of the elastic modulus of the strain

wire Y and its cross-sectional area A, that is,

k « YA

or in terms of the wire diameter

k - I

*Yd2

(15)

therefore

_ 1 ^ 0^^2-2

ma* H * SYd * < l6 >

since F^q^ = Tmax> substituting (l6) in (13) results in

fn2

where

m m 8.07 x 10" 2 £

2 SYd2 — (17)

G

2

m = mass, lb.

£ = design strain, inches/inch

S » total length of strain wire, inches

7
Y = modulus of elasticity of strain wire, lb/in2

d » diameter of strain wire, inches

fn

w natural frequency, cps

G = maximum range of accelerometer, from zero, in "G" units

(See references 2 and 11).

In the case of unbonded strain gage accelerometers with the maximum design strain of 0.0015 inches per inch, equation (l6) becomes

m = 18.2 x 10"8 SYd2 £^ (18)

G

2

This is the second important design criterion. The actual design must

represent a compromise since, as pointed out above, m is desired to be

f 2

small , but the figure of merit, and therefore the term —^

to be large.

G

2

k-2. Electrical Sensitivity.

The electrical output of a linear strain gage accelerometer is

based on the following considerations. The electrical pickoff generally

consists of a bridge with four active arms. The output of such a bridge

is V - E AS ( 19 )

^*i- = fractional change in resistance of each of the four

R

active arms of bridge.

The gage factor of the strain wire, Kg given by

Ks- %/tz A*ye (20) R

which, on substituting in (l8), becomes

V = E Ksfc (21)

where

E = bridge excitation voltage, volts

8
Kg = gage factor of strain wire

£ =3 design strain, inches/inch

The sensitivity, Q, of the accelerometer is therefore

Q = 1 = 1000 Ks B (22)

where Q » sensitivity, millivolts per volt excitation for full

range acceleration.

4-3. Bridge Resistance .

The resistance of a bridge with four equal active arms is equal to

the resistance of one of the arms. It can be computed from

R = 2.08 x 10'8 p-^- ohms (23)

d

2

S w total length of wire in bridge, inches

d = diameter of wire, inches

p =s resistivity, ohms per circular milfoot

Commonly used bridge resistances are 120 ohms, 180 ohms, 350 ohms

and about 3000 ohms.

4-4. Design Considerations .

If one considers an unbonded strain gage accelerometer with a gage

length of one inch (a common value for a commercial instrument) and if

the mass is furthermore considered to act directly on the strain wires

and strain them to the full scale value of ±0.0015 inches the resulting

*n2 figure of merit for this instrument would be M = —pr~ ~ 6530.

Or The most commonly used materials for the strain wires in such

accelerometers are "Constantan" ("advance"), an alloy of copper and

nickel with a gage factor of about 2.0, and "alloy 479 "> an alloy of

platinum and tungsten, with gage factor near 4.0. The sensitivity of

9
the accelerometers (Equation 22) would then be about 3.0 MV/V and about

6.0 MV/V, respectively, for full range output.

Table 1 contains the characteristics of a number of commercial unbonded strain gage accelerometers obtained from the manufacturers literature. From this it can be seen that sensitivities fall into two ranges:

I.89 to 2.33 MV/V, and 3.89 to 4.58 MV/V, corresponding roughly to the

computed sensitivities. It is also apparent that the computed figures

of merit in the table are near that shown above (—77- = 6530) for a postulated strain of 0.0015 only in three cases. It appears then that in

these cases the seismic mass acts directly on the strain wires, and in

straining them 0.0015 inches/inch, actually moves .0015 inch (for a one

inch gage length). In the other cases, leverage exists between the mass

and the strain wires so that, for M *C6530 the mass moves a greater distance than that due only to the stretching of the strain wires; conversely for M^653O> ^ne mass moves a shorter distance.

The design requirements for the majority.of accelerometers, that is,

high natural frequency and high sensitivity, are contradictory. The

large displacement of the seismic mass required to generate a large value of strain, and thereby a high output voltage, will also reduce the

natural frequency. However there are several means of, at least partially, circumventing the difficulty.

k-k-1. Higher Gage-Iactor Wire .

The use of strain wire of higher gage factor will result in higher

sensitivity and therefore higher output voltage at the same electrical

excitation and strain. Currently, "alloy 479" with a gage factor of

10
about 4.0 represents the limit in reproducible stable, temperature inseno sitive strain gage wire materials. (Commonly used constantan has a gage

factor of about 2.0). Recently developed semiconductor strain gages of

very high gage factors will be covered in the section on "bonded strain

gage accelerometers".

4-4-2. Smaller Displacement .

Smaller displacement of the seismic mass can result in the same

strain in the wires if leverage is used. This requires a larger mass

(see equation 18) and limitations here are imposed by the mass which is

desired to be small to minimize instrument weight and therefore energy

taken from the system whose acceleration is to be measured. Space and

stiffness requirements limit the leverage to a factor of about five.

4-4-3. Higher Excitation Voltage .

The output voltage can be raised by increasing the excitation voltage. The limitation here is imposed by the allowable heat dissipation

of the strain wires. With insufficient dissipation, the temperature of

the strain wires may rise until the wires sag (causing nonlinear output)

or actually melt. The allowable heat dissipation of the wires depends

on the heat transfer characteristics of the medium surrounding the wires.

Table 1 indicates allowable excitation voltages up to 12 volts for a

number of instruments known to be filled with damping oil which is a

good heat conductor. The power dissipated in these instruments may

therefore reach 0.4 watts. The table also shows the allowable excitation for another group of accelerometers to be only 5 volts (power dissipated: 0.07 watts); in these instruments, the strain gages are in air,

11
which is a poor heat conductor.

It does not appear practical to get higher output voltages by just

increasing the maximum strain: for one thing, the natural frequency

would be decreased by the required increased deflection; for another,

the present design strains may approach the proportional limit for the

wires. This is true because the design strain referred to throughout

this section, 0.0015 inches/inch is really an incremental strain. The

mass of the standard bi-directional accelerometer, capable of movement

in two directions, will thereby reduce the strain in one part of the

strain gage bridge as it increases the strain in the other. In order

to avoid wire sag (and output nonlinearity) when the strain is reduced,

the wires must be under initial tension. Additional tension must be

added to allow for wire expansion caused by the current through it and

that due to differential expansion of the components in the accelerometer

caused by environmental temperature changes. When all these are taken

into account, the final maximum strain in the wire may well reach three

times the incremental design strain.

A relatively new design approach ° shown schematically in Pig. 2

seems to get around this problem. It is the "zero length" strain gage

which derives its name from the fact that the points at which the strain

sensitive wire are attached to the fixed and movable members are longitudinally superimposed by mounting the wire in a V-shaped configuration.

One end of the wire is attached to a fixed member of the instrument

structure, the other to the moving one (seismic mass). The midpoint of

the wire is connected to the instrument structure through a sliding con12
tact at the end of a long spring with a low spring rate so that the tension it exerts remains essentially constant for small changes in its

length even with extension of the wire due to heating.

The sum of the tensions in the two sections of the wire is constant

and equal to the tension exerted by the spring. When the movable member is displaced from its normal position an amount b, the point of

attachment of the spring will move along the wire by an amount — . This

will result in an increase in the length of one half of the wire by an

amount — and a decrease in length of — of the other half of the wire.

2 2

Since the strain wire is kept under relatively constant tension by the

spring, despite the movement, a change in length results in a corresponding change in resistance of each section of the wire. If the two

sections of the wire are connected as part of a bridge circuit, the resultant resistance changes produce an output proportional to the displacement of the movable member. Most "zero length" strain gage devices employ two such configurations in a four arm bridge. This design produces

relative immunity from overloading and permits higher excitation voltages since wire sag with heating is counteracted by the spring.

Finally, one accelerometer in the table shows a very high figure

of merit as well as high sensitivity. This instrument employs "gas

damping". A piston or diaphragm attached to the seismic mass serves to

close a small chamber equipped with a restriction. Movement of the

seismic mass moves the piston or diaphragm and thereby forces gas to

flow through the restriction which dissipates the energy of motion and

furnishes damping to the system. In addition to gas flow, there is also

13
compression and expansion of the gas in the chamber. The pneumatic

spring created and the existing spring of the strain "wires in conjunction "with the seismic mass will determine the dynamic characteristics of

the accelerometer. An understanding may he gained of the properties of

such a system-1 by considering the two extreme cases. If no restriction

exists to the flow of gas to and from the chamber there will be no damping. Movement of the seismic mass will not change the pressure of the

gas in the chamber. This eliminates pneumatic spring action. The accelerometer would behave somewhat like an undamped single degree of freedom system with a relatively low natural frequency.

If the restriction is such that no gas can flow through it, the

pressure of the gas in the chamber will change with seismic mass motion

and resist the motion. The net effect is a stiffer spring which results

in a much higher natural frequency than above. Since practically no

energy is dissipated (no flow) the system again appears undamped.

It seems feasible then "by proper choice of the parameters of the

restriction to achieve a system with a relatively wide and flat frequency response. Furthermore since damping depends on the viscosity of

the gas and since the viscosity of a gas is much less temperature dependent than that of a liquid, the frequency response of a gas damped instrument is less effected by changes in ambient temperature.

Such a system is, however, nonlinear. As the amplitude of motion

increases, at constant frequency, the quantity of gas which can flow

through the restriction does not increase proportionately and the pneumatic spring becomes stiffer. This results in a proportionately decreased electrical output.

Ik
The values of natural frequency listed for these accelerometers can

be computed for the basic system without gas damping. This was done

so as to arrive at a figure of merit which permits comparison with the

other accelerometers. The values obtained indicate that apparently

leverage is also employed between the seismic mass and the strain wires

to reduce the required displacement of the mass by a factor of about

four.

5. DESIGN PRINCIPLES FOR BONDED STRAIN GAGE ACCELEROMETERS

5-1. Range, Natural Frequency and Sensitivity .

Bonded strain gage accelerometers basically consist of a weight

mounted on a uniform cantilever beam leaf spring with the strain gages

bonded to the spring. Practical instruments frequently use two cantilever beams joined by a common weight and mounted in such a manner that

strains produced by transverse accelerations acting along the axis of

the beams are cancelled out. In the design of a bonded strain gage accelerometer, the value of strain acting on the strain gage for the full

scale value of acceleration is generally limited to about 0.001 inches/

inch (1000 micro-inches per inch). This is done so as not to overstress

the cantilever beam and also to prevent fatigue failure of the strain

gage. (The latter may occur at the junction of gage wires and lead

wires at high strain levels).

The theory of simple structures applied to an ideal (weightless)

cantilever beam with a weight W at Its free end shows that the maximum

unit fibre stress at a distance Z from the fixed end of the beam due to

gravity is

Q* = W (L-2) h (A)

15
where W(L-Z) is the bending moment at the distances Z from the fixed end

of the beam

O* = unit fibre stress, pounds per square inch

h »s height of beam, inches

Z =» distance from fixed end of beam, inches

I a moment of inertia of beam, inches

W =s weight, pounds

L = length of beam, inches

If an acceleration of "G" times the force of gravity acts on the

weight W, the resulting fibre stress at Z will be _ x wg(l-z) h

(25)

21

If this fibre stress is within the proportional limit of the beam's

material, the corresponding strain in the outermost fibres will be

a

m q m WG (L-Z) h

(26)

Y 2IY

where Y » modulus of elasticity of beam material

£ w strain, inches per inch at Z

The deflection of the free end of the beam under the action of the

force of gravity is

u - WL3

( } 3IY '

where u = deflection of end of beam, inches.

The natural frequency of a spring mass system in the gravitational

field can be expressed by

16
where a » acceleration due to gravity, inches per second per

second.

Therefore, the natural frequency of this cantilever beam system can

be expressed as

at V wl5

Squaring and rearranging the above relation, the following equation

is obtained

IY

^2L5fn

2

W 3a

From equation (26) it follows that

(30)

u mg (l-z) h /„%

W 2£ U;

at one "G" this becomes

IY _ (L-Z) h

W 2£

Equating the equations (30) and (32), the following is obtained:

(32)

£ = 55- ( L

;Z

) h

(See Reference 10) (33)

8«2 L5fn

2

This describes the fibre strain in inches per inch for this cantilever beam accelerometer due to the force of gravity (or for one "G") in

terms of beam dimensions and natural frequency. The fibre strain will

be directly proportional to the acceleration in "G" units.

The relations developed above apply equally well to systems with

two cantilever beams joined by a common weight. This is true since one

cantilever beam of width b is equivalent in all respects to two cantilevers (joined) of width _, with all other dimensions unchanged.

17
By rearranging the above relation and substituting same numerical

values, a figure of merit can be obtained for a bonded strain gage accelerometer just as was done for unbonded strain gage accelerometers

M m £n£ m G

3a(L-Z)h ^

^

2L3

<fmax

where £ max » strain due to full scale acceleration in "G" units.

In most bonded strain gage accelerometers, the strain gage is

mounted very close to the fixed end of the beam. This makes the distance

Z (strain gage centered on Z) small compared to L. Therefore,

^ & ^ - ^ (35)

1? I? L

2

The maximum value of full scale fibre strain is generally taken to

be 0.001 inches/inch. On substituting these values, the figure of merit

of the bonded strain gage accelerameter becomes

M - £b! „ 1.47 x 10k 4 (36)

G L

2

The weight required at the end of the beam is given by

(37) W = 3aIY

4* 2L3f 2n

For a rectangular cross section beam of width b, height h the weight

becomes

W - aYbn3

(38)

For such a rectangular cross section beam, the fiber strain is

£ = £2&£l (59)

Ybh2

Thus the strain produced (everything else remaining constant) is inver18
sely proportional to the square of the beaa. height h. Since the figure

of merit is directly proportional to beam height h, the design of a

bonded strain gage accelerometer must be a compromise between a high

figure of merit and high sensitivity.

5-2. Electrical Sensitivity .

The sensitivity for a bonded strain gage accelerometer with a

bridge with four equal active arms is also given in millivolts per volt

excitation for full range output by equation (2l), i.e., Q = 1000 Kg £

5-3« Bridge Resistance .

The resistance of a bridge with equal active arms is equal to the

resistance of one of the arms. Commercial bonded strain gages can be

obtained in a variety of resistance values. The most commonly used ones

are: 120 ohms, 350 ohms, 500 ohms and 1000 ohms.

5-4. Design Considerations .

The two most commonly used materials for wires in a bonded strain

gage are "constantan" (as used in unbonded strain gage instruments) with

a gage factor of about 2.0, and "iso-elastic", an alloy of iron, nickel,

and chromium, with a gage factor of about 3«3« Although "iso-elastic"

has a higher gage factor than "constantan" and has an improved fatigue

Q

life, it has a much higher temperature coefficient of resistance.

Instead of wire, bonded strain gages are often constructed of

metallic foils or films. Commonly used materials for these are:

"constantan", and "nichrome V", an alloy of nickel and chromium, with a

gage factor of about 2.k. Foil gages show a slightly higher gage factor

than wire gages made of the same material and dissipate heat better,

19
thereby permitting operation with higher excitation voltages. Although

most of these gages will measure strains up to 0.005 inches/inch satisfactorily, fatigue life is greatly improved by limiting the maximum

strain to 0.002 inches/inch and frequently to 0.001 inches/inch.

At the design strain of 0.001 inches/inch, the sensitivities of

accelerometers with strain gages made of the above materials would be

expected to range from about 2.0 MV/V to 3.3 MV/V for full range output.

Bonded strain gages are available which utilize the piezo resistive

properties of semiconductor materials, like germanium and silicon.

These semiconductor strain gages have very high gage factors, ranging

from about 70 to 250. However, the gage factor is quite temperature

dependent, so that if an instrument is to operate over an appreciable

temperature range, some form of compensation must be employed,, The maximum strain level for these semiconductor gages is about 0.003 inches/

inch. Table 2a lists the characteristics as obtained from the manufacturers literature of a number of commercial bonded strain gage accelerometers.

For the wire or foil gage type, sensitivities correspond to those

of the unbonded strain gage accelerometers. Figures of merit are much

lower. As an example, an unbonded strain gage accelerometer with a

range of ±2 G's has a natural frequency of 100 cps; its bonded counterpart has a natural frequency of 25 cps.

This difference in figure of merit is easily understandable when one

f 2

considers that the figure of merit (—^-) is the reciprocal of the full

G

scale displacement of the seismic weight. Whereas, in the unbonded

20
strain gage accelerometer, the strain in the wires is produced directly

by the displacement of the seismic weight, in the bonded strain gage

instrument this strain is produced through the medium of a cantilever

beam. A considerable deflection of the free end of the beam (displacement of the seismic weight) is necessary to produce the required strain

in the fibers of the beam where strain gages are attached. It can be

shown that the ratio of the deflection of the end of the beam to the

strain produced in outermost fibers of the beam at the fixed end is

u _ 2L_

£

~ 3h

For the bonded strain gage accelerometer described above, this ratio was

computed to be ^>k. For the same amount of strain produced by acceleration then, the weight in the "bonded" accelerometer has to be displaced

about ~$k times as far as that in the "unbonded" instrument assuming unity

gage length. This should result in a natural frequency for the "bonded"

instrument roughly one sixth of that of the "unbonded" one. Manufacturing tolerances may account for discrepancies between measured and computed values.

In Table 2b, the characteristics of the two accelerometers using

semiconductor strain gages show the expected high sensitivity combined

with the high figure of merit normally associated with unbonded strain

gage accelerometers. While the manufacturer of these two instruments

markets semiconductor strain gages for bonded use, the sensitivity and

figure of merit listed do not seem consistent with the design characteristics imposed by the use of the seismic mass mounted on a beam to which

the strain gages are bonded.

21
5-4-1. Semiconductor Strain Gages .

One possible way of achieving high sensitivity with a relatively

high natural frequency is by the use of the new semiconductor strain

gages in place of wire wound strain gages.

5-4-2. Low Modulus Beam Material .

Another one is by the use of a beam material with a low modulus of

elasticity. Copper alloys like phosphor, bronze or beryllium copper

possess a modulus of elasticity of half that of steel. The improvement

is not spectacular. However halving the modulus and with unchanged deflection of the seismic mass, the maximum strain, and therefore the sensitivity, increase by about 25$.

5-4-3. Higher Excitation Voltage .

The output voltage can be raised by increasing the excitation voltage. As before the limiting factor is allowable heat dissipation, but

bonded strain gages being mounted on a heat sink (the beam) can dissipate more power. Allowable levels (from the table) are from 0.53 "to 0.75

watts, more than for unbonded strain gages.

Very often, the weight of an "unbonded" accelerometer is considerably less than that of its "bonded" counterpart (due to smaller mass re- quired by the former to produce the same strain, and therefore output,

for the same value of acceleration). This may be a very important consideration where it is required to measure the motion of some object by

means of an accelerometer. If this object is itself the mass of a seismic system, the natural frequency of that system will be

In 2« f m

22
If, now, an accelerameter of mass Mg were mounted on the object and if

Me were, say 0.2m, the natural frequency of the seismic system would he

reduced to

t * )( m + 0.2m n

5-5. Characteristics of Bonded Strain Gages .

Despite the fact that bonded strain gages have been used for a number of years, much of the information about their characteristics is inconsistent and unreliable. This is not due to any lack of effort or

skill on the part of investigators, but rather due to the fact that

strain gages, even of the same type, differ in characteristics when

mounted. This, in turn, is due to such factors as composition of the

mounting surface, preparation of that surface, type of bonding cement

used, temperature of cement, curing time, pressure exerted on gage during curing, strain cycling of surface with mounted gage, temperature cycling of same, skill of the person who does the bonding, and other factors. A few general conclusions are presented based on refs. 13 and lk.

Apparently most bonded strain gages will show creep, which is attributed to the bonding cement used as well as to discontinuities in the

wires at the end of loops and at the points of attachment of the lead

wires. While creep usually shows up most after a static load had been

applied for a period of time, some creep may result even from short time

loading. One way of reducing this effect is by strain cycling the member to which the strain gage is mounted. This must be done judiciously

because one of the other general characteristics of bonded strain gages

appears to be their proneness to fatigue failure. On the basis of some

23
tests performed at a strain of ±0.001 inch/inch, it appeared that some types of gages failed after about 16,000 cycles, while others were still

good after 1,000,000 cycles. The conclusions drawn from these tests

were as follows: Strain gages with a bakelite grid carrier have a longer

life under dynamic conditions than paper backed gages. A number of the

fatigue failures appeared at the junction between gage wires and lead

wires. Gages with dual lead construction appear to have a longer life.

Finally grid wire made of Iso-Elastic appear to last longer than those

of copper-nickel alloys. Iso-Elastic, as mentioned previously, while

possessing a higher gage factor than the copper-nickel alloy (constantan)

has a larger temperature coefficient. In the matter of fatigue life,

etched foil strain gages appear to hold some promise. The use of bonded strain gages at other than ambient room temperatures introduces other

complications which will be discussed later on.

6. FREQUENCY RESPONSE OF STRAIN GAGE ACCELEROMETERS

In order for a general purpose accelerometer to measure applied accelerations faithfully over a wide frequency range, it should have a

flat frequency response from steady state accelerations (D.C. ) to the

highest frequency component of the acceleration to be measured. In addition, the instrument should possess a phase shift characteristic linear

with frequency? Such a phase shift characteristic, will result in a

time delay of the recorded signals, but will cause no distortion by unequal relative shifts of different frequency components.

Most strain gage accelerometers are designed to be linear singledegree-of- freedom systems and experimental evidence indicates that their

2k
"behavior generally approximates that of such systems.

The frequency response characteristic of a one degree-of-freedam

seismic accelerometer with a damping ratio of 0.707 gradually decreases

as the frequency increases, dropping 5$ "below the steady state response

when the frequency reaches 0.57 of the natural frequency. For this same

damping ratio, the phase shift characteristic is linear within about ±2°,

from its steady state value of 0° to 90° a"t the natural frequency.

For a damping ratio of 0.59> the frequency response characteristic

first gradually rises with increasing frequency reaching a peak value 5$

above the steady state response at a frequency of 0.55 of the natural

frequency. After that, the response drops, until it is 5$ below the

steady state response at O.87 of the natural frequency. The phase shift

characteristic in this case is no longer linear, but deviates from linearity by as much as 6°

For practical purposes this nonlinear phase response may be disregarded in comparison to the frequency response of the amplitude since

this amplitude varies from the steady state response in all cases before

the phase differs more than a few degrees from the linear.

The time lag between acceleration input to the instrument and its

output is obtained from its phase characteristic. In the case of O.707

of critical damping, the time lag is about 0.25 of the natural period of

the instrument. A linear phase shift characteristic assures the correct

reproduction of complex wave shapes of acceleration since all frequency

components are shifted in phase proportionately, thus preserving the

character of the wave shape.

There is no general criterion for the faithfulness of reproduction

25
of a complex wave shape, since there is an infinite number of such possible shapes. Theoretical work at NBSindicates that for input wave

shapes which are either triangular or sinusoidal pulses, for an accuracy

of reproduction of about 5$ of the peak acceleration, the accelerometer

should have a damping ratio of about O.k to 0.7 of critical, and a natural period of less than about one-third of the duration of the acceleration pulse. For a square pulse, it appears that a similar accuracy may

be attained for a damping ratio of 0.7 and a natural period of less than

one-third that of the input pulse.

It is apparent from the two cases given above that if the damping

ratio in a given accelerometer changed from 0.707 to 0.59> at a frequency of about O.56 of the natural frequency, the instrument response would

increase about 10$. The change in response would he proportionately less

at lower frequencies, for example, about 3$ at 0.30 of the natural frequency. By restricting the frequency range of accelerations measured to

a region far below the natural frequency of the instrument, the fidelity

of the response can be made relatively independent of the damping ratio.

As mentioned earlier, there are cases where an instrument with a

low natural frequency is used so as not to respond to extraneous high

frequency accelerations. In such case, measurements would often be

carried out close to the natural frequency of the instrument and the

accuracy of these measurements would be highly dependent on the value of

the damping ratio.

Commercial accelerometers generally employ a viscous liquid to supply the damping. For a one degree-of-freedom system with pure viscous

damping supplied by a liquid of the silicone family, it can be shown

26
that the damping ratio is directly proportional to the kinematic viscosity of the fluid over a wide range of viscosities. Thus, any change in

viscosity of the damping fluid would affect the accuracy of dynamic

measurements, particularly at frequencies approaching the natural frequency of the accelerometer. Changes in temperature of the damping

fluid have a radical effect on its viscosity (this will be discussed

more fully later on). For this reason specifying a damping ratio without specifying the fluid temperature at which it applies is rather meaningless.

Theoretically, in the case of pure viscous damping, the addition of

damping fluid to an undamped single degree of freedom system should not

affect the natural frequency of the system. Actually, however, some of

the added fluid will he pushed back and forth by the movement of the

seismic mass as it responds to accelerations. This will have the affect

of increasing the seismic mass, thereby lowering the natural frequency

of the instrument^" For a manufacturer it is often much easier to determine the natural frequency of an accelerometer before it is filled with

damping fluid. If the instrument is not rechecked after filling, considerable errors may result due to the inertia of the fluid if the originally determined value of natural frequency is used as the one applying to the damped instrument. In addition, some loss in sensitivity may

result due to the buoyancy of the damping fluid which reduces the active

unbalanced mass of the seismic element.

If in the design of a liquid damped accelerometer, the spacing between the moving mass and some element of the case is made very narrow

to provide shear damping, certain complications may arise. Unless an

27
additional large return path is provided for the moving fluid, its effective inertia will be increased as a function of the square of the velocity of the fluid in the narrow gap. If a high viscosity damping fluid

(with an appreciable modulus of elasticity in shear) is used in this case,

shear movement of the mass will also cause elastic deformation of the

fluid in addition to viscous flow. This effectively adds another spring

to the seismic system, resulting in a system response in the form of a

fourth order differential equation (corresponding to a two degree-offreedom system)r This may be the explanation for response curves obtained from some unbonded strain gage accelerometers which appeared to be

those of two degree-of- freedom systems.

Although it is generally assumed that the fluid damping is linear,

this is true only if no turbulence or bubbles exist. When very low viscosity damping fluids are used, turbulence may arise, manifesting itself

as output nonlinearities in the high frequency and large amplitude regions of applied accelerations.

"Gas damping" which has recently come into use for strain gage

accelerometers is discussed previously.

7. PERFORMANCE CHARACTERISTICS

7-1. Accuracy and Fidelity.

There are many properties which influence the quality of the measurements performed by an instrument, particularly a telemetering instrument. Among them are instrument characteristics like linearity, hysteresis, repeatability, temperature effects, acceleration and vibration effects, and others. In view of the many factors involved, it is meaning28
less to give one figure of accuracy as an indication of the quality of

the measurements possible without going into elaborate detail on all the

conditions under which this figure applies. It is preferable to list as many of the instrument characteristics, as is possible and to let the

user decide the overall accuracy of his measurements. This appears to

be the present practice of many manufacturers of telemetering instruments

with these measuring properties listed under a general heading entitled

"Accuracy".

The properties listed above are "steady state characteristics" obtained from steady state calibrations with fairly well established methods with the aid of reliable working standards. Since most measurements

in telemetering are made of time varying physical quantities, the dynamic characteristics of the instrument will have an Important effect on

the quality of the measurements. Such dynamic characteristics as frequency response, phase response, dynamic linearity, damping factor, distortion, variation of hysteresis with frequency, and others can neither

be determined as readily and precisely as the "steady state characteristics", nor are the methods and working standards for their determination

as well established or reliable. In view of these uncertainties it is

desirable that the use of the term "accuracy" be confined to the description of the quality of steady state measurements. The term "fidelity"

is suggested to describe the quality of dynamic measurements. The accuracy can be no better than the maximum error likely to be encountered

in a careful static calibration under stated environmental conditions

and is usually expressed either as a percentage of the instrument range

or in acceleration units.

29
7-2. Repeatability.

Repeatability is the maximum difference between corresponding points

of acceleration obtained by repeated uni- directional static calibrations

and is expressed in acceleration units or as a percentage of the instrument range.

Actually, two types of repeatability exist : short term repeatability and long term repeatability, also called drift. "Short term" generally refers to a period of time of the order of minutes to a day over

which the test is performed. "Long term" repeatability tests generally

extend over from days to months.

7-2-1. Short Term Repeatability .

This may be a function of many factors, such as backlash, imperfect

elasticity of elastic members, coldworking of elastic members, energy

absorption of instrument from the quantity to be measured and minor variations in the local environment.

Tests to determine short term repeatability are performed with

steady state input at other than zero, preferably near full scale.

Short term variations of the output with zero input are seldom encountered and when they appear to occur are generally due to stray pickup or

other faults of the output sensing equipment or possibly, in the case of

strain gage pickup, a noisy excitation voltage supply. In tests, two

bonded strain gage accelerometers (±10 G's range) showed repeatability

over a period of less than a day within ±0.7$ of range. Two unbonded

strain gage accelerometers (±10 G's) showed repeatabilities within ±0.4$

and ±0.8$ of range over an eight hour period. Two others (±50 G's) tes30
ted had repeatability of 0.28$ of range over a few minutes, while another accelerometer with a range of ±1.5 G's, had repeatability of 0.2$

of range over a period of eight hours.

7-2-2. Long Term Repeatability .

Long term repeatability, sometimes referred to as drift, results

from gradual changes in the property of materials, dimensions, and chemical changes, as well as from changes induced by varied environmental

conditions and use.

To determine long term repeatability, repeated measurements are

made of the instrument's output, with zero input as well as some value

of input near full scale over a long period of time. From these data,

values of long term repeatability may be given in terms of zero shift

as well as sensitivity change (for linear pickup). Two 10 "G" bonded

strain gage accelerometers were tested at 1G and long term repeatability

was found to be within 0.35$ and 1.4$ of range over a period of four

months. These same two 10 "G" accelerometers repeated within ±0.7> 0.8$

of the range at ±1G over periods between nine and eleven months.

In the case of the two ±50G unbonded strain gage accelerometers,

zero shifts over a period of 2 months were about 1.2$ of full scale and

about 0.3$ of full scale. During the same period of time, the sensitivity of the first instrument increased about 0.5$, that of the second

about 0.9$. A 1.5G accelerometer showed a shift of 1.0$ over a period

of sixty days. Bonded and unbonded strain gage accelerometers appear to

show repeatabilities of the same order of magnitude.

31
7-3. Linearity (of the electrical output with respect to acceleration

input .

)

Linearity is described as the maximum excursion of any point from

the best straight line of the plot of any careful static calibration

performed under stated environmental conditions. The manner in which

the best straight line is determined must be stated. Linearity is also

expressed either in acceleration units or in percent of the range.

The linearity of both types of strain gage accelerometers should be

quite good, since deflections involved are small and if properly designed,

strain gages operate well within the elastic limit.

Experimentally, it is not easy to determine linearity precisely.

Limitations are imposed by the experimental accuracy of the calibration

and the repeatability of the instrument under test. The value of linearity assigned to the instrument cannot be any better than the repeatability. The scatter of experimental data will limit the determination of

linearity, so that frequently, the conclusion drawn is that linearity is

no worse than the scatter. Test results showed values of linearity (expressed as maximum deviations from mathematically determined straight

line through all calibration points) to range from 0.6$ to 1.0$ of the

range for bonded, and from 0.3$ to 1.4$ of the range for unbonded strain

gage accelerometers.

1-k. Hysteresis .

Hysteresis may be defined as the summation of all effects, other

than backlash, wherein the output assumes different values for the same

value of input when that input is applied in an increasing or decreasing

direction.

As in the case of linearity, as long as the instrument operates

32
well within the elastic limits of springs and strain gages, the hysteresis should he quite small. As above, the short term repeatability of

the instrument under test as well as the accuracy of the calibration

will limit the precise determination of hysteresis. Manufacturers literature frequently combines hysteresis and linearity by stating "nonlinearity and hysteresis not more than -$ of full scale". Experimental

results show that hysteresis values are of the order of 0.3$ to 0.4$ of

the range for bonded accelerometers and 1.0$ to 3-1$ of the range for

unbonded strain gage accelerometers.

7-5* Resolution .

The output of a strain gage, whether bonded or unbonded is a smooth

function of applied strain. For this reason the resolution of a strain

gage accelerometer, the ability to detect small changes in input level,

will generally be that imposed by the associated equipment.

7-6. Response to Transverse Excitation .

The transverse response of an accelerometer represents the output

when acceleration is applied to the instrument in a direction perpendicular to the sensitive axis of the instrument. Generally, the (steady

state) transverse response (also called "cross coupling" or "cross talk")

is expressed as the ratio of the sensitivity of the instrument to accelerations perpendicular to the sensitive axis to the sensitivity to accelerations along the sensitive axis.

7-6-1. Transverse Response to Steady State Accelerations .

Much of this transverse response is due to manufacturing tolerances

and misalignments during assembly, which cause the true sensitive axis

of the instrument to be not quite perpendicular or parallel (depending

33
on design) to the mounting surfaces or other fiducial line. However,

even if the instrument is mounted so that the sensitive axis is exactly

perpendicular or paralled to the mounting, a minimum amount of cross talk will be present, referred to as "inherent" cross talk. Cross talk

is also a function of the position of the mass of the spring mass system. In general, the effect of transverse accelerations on the output

of the instrument is apparently greater when there is also full scale

acceleration applied along the sensitive axis than when no acceleration

is applied along the sensitive axis.

Referring to section 5> which discussed some design principles of

bonded strain gage accelerometers, the deflection of the end of the single cantilever beam due to gravity is given by u = ri±_ . Thus, the

3IY

deflection due to "G" units of accelerations will be uG. If in addition

a transverse acceleration of B "G" units of acceleration acts along the

beam or the weight W, at the end of the beam, it will produce a moment

at the root of the beam of BW(uG). The moment produced by acceleration

acting along the sensitive direction will equal GWL, where L is the

length of the beam. Within elastic limits, strain, and consequently

strain gage output, are proportional to the bending moment at the section where the gages are attached. Therefore, the ratio of output due

to acceleration along the sensitive direction will be equal to the ratio

of the respective bending moments B:vlG' = B -. By using a configuration

GWL L

consisting of two cantilever beams in a Z-shaped arrangement connected

to a common seismic mass, output due to transverse accelerations along

the long dimension of the beam can be cancelled out almost completely.

Tests on two bonded strain gage accelerometers show responses to

3h
transverse excitation ranging from 0.4$ to 1.7$.

Experimental values obtained for a low range (±1.5G) accelerameter

of the unbonded strain gage type show the transverse response to he less

than the estimated experimental limits of error which range from about

1.2$ to 1.8$ of transverse acceleration. For a similar ±50G accelerometer, the transverse response was 0.3$ of the acceleration. A gas

damped unbonded strain gage accelerometer (±10 G's) had a transverse response of 0.9$.

Since transverse response appears to be greater when accelerations

are also applied along the sensitive axis, tests are often performed byapplying steady state acceleration at some known angle to the sensitive

axis. This results then in two components of the accelerations; one

along the sensitive axis and the other transverse to it. Unless, however, the location of the center of mass of the seismic system is known

accurately, the components of acceleration cannot be accurately determined. Some of the above data may be inaccurate for this reason.

A promising way of determining the steady state transverse response

appears to be one which the manufacturer can perform before the instrument is assembled. A known force (such as a spring) pulling the seismic

mass transversely, while weights hanging from the mass simulate acceleration along the sensitive direction, would allow determination of the

transverse response quite accurately.

7-6-2. Transverse Response to Vibrational Accelerations .

These strain gage accelerometers will generally also show a trans- verse response to vibrational accelerations, (sinusoidal or transient)

as well as to steady state, accelerations. The effect of poor assembly

35
methods during instrument construction may "be magnified by resonance.

An unbonded strain gage accelerometer with a natural frequency of ^-3 CPS

showed maximum sinusoidal vibrational transverse response of 3»*$ at 20

cps (for one transverse direction) and of 3*6$ at 89 cps in another one

at right angles to the first one. Another unbonded strain gage accelerometer showed a transverse response of about 5$ over a frequency range

from 20 to 200 cps for sinusoidal vibrations. The transverse response

for a third one did not exceed 2$ over a frequency range from 25 to 125

cps.

Laboratory measurements of the response to transverse vibrational

accelerations on the assembled instrument can be quite good, since only

the direction of the sensitive axis need be known.

7-7. Temperature Effects .

7-7-1. Slowly Changing Ambient Temperatures .

Slow changes in the ambient temperature may effect the operation of

strain gage accelerometers in three ways by giving rise to zero shifts,

changes in sensitivity and, by changing the viscosity of the damping

fluid, thereby changing the damping ratio and consequently the dynamic

response of the instrument. This is true for bonded as well as unbonded

strain gage accelerometers.

7-7-1-1. Zero Shift .

Zero shift may be due to unsymmetrical changes in dimensions with

temperature causing strain in the strain wires or it may be caused by

temperature gradients causing unbalanced resistance changes in the strain

gage bridge. The amount as well as the direction of zero shift due to

slowly changing ambient temperatures are not readily predictable for any

36
instrument "but seem generally reproducible for any particular instrument

and may "be determined by test. It is, therefore, feasible in most cases

to reduce this zero shift by a process of temperature compensation.

This takes the form of a small resistor, which when added to one arm of

the bridge, will undergo a change in resistance with temperature which

will oppose the zero shift. While complete compensation appears impossible, in the case of unbonded strain gage accelerometers zero shifts

normally ranging from about 0.02$ to 0.05$ of full scale per degree

Fahrenheit, may be reduced to 0.01$ of full scale per degree F (for a

temperature range from -20°F to +200°F). Such compensation will not be

effective for rapidly changing temperatures (thermal transients ) . It

may, in fact, result in an even larger zero shift. Zero shifts occurring in bonded strain gage accelerometers have not been determined. One

would expect them to be slightly larger than those of unbonded instruments due to the larger physical size with consequently larger possible

changes in dimensions with temperature and greater possibilities for

temperature gradients.

7-7-1-2. Sensitivity Change .

A change in sensitivity is primarily due to the temperature coefficient of the modulus of elasticity of the spring materials of the instrument ' s seismic system. For unbonded strain gage accelerometers, the

sensitivity of the instrument may be expected to increase with increasing ambient temperature at the rate of from about 0.02$ FS/°F to 0.03$

F3/°F. The larger value applies where the strain wires supply most of

the elastic restraint of the system. This agrees with the value of temperature coefficient of the modulus of elasticity for "constantan" wire

37
of about -0.00033/°F. As in the case of zero shift, it is possible to

reduce the changes in sensitivity of the unbonded instrument with temperature by a process of compensation. In this case, the compensating

resistor is put in series with the entire bridge. Instruments, thus

compensated, require a higher excitation voltage (generally about 15$

higher than non- compensated ones) to make up for the loss in the compensating resistor. Such a process of compensation will reduce the change

in sensitivity to about 0.01$ of full scale per degree Fahrenheit.

In the case of bonded strain gage accelerometers, changes of the

modulus of elasticity with temperature of the cantilever beam on which

the strain gages are mounted will determine the temperature variation

of sensitivity. Alloys commonly used as the beam material like beryllium

copper or phosphor bronze have temperature coefficients of the modulus

of elasticity of about -0. 00020/° F and -0. 00021/° F respectively. This,

then, would be expected to result in an increase of sensitivity with

increasing temperature for a bonded strain gage accelerometer of about

0.02$ F3/°F. The result of a test on such an instrument showed a decrease in sensitivity of 2.3$ FS for a decrease in temperature of about

103°C. This is equivalent to a rate of change of sensitivity of about

0.012$ FS/°F.

While semiconductor strain gages are sensitive to temperature

changes, these can be compensated. Test data are not available, but

manufacturers literature claims zero shift and sensitivity change to be

less than 1$ per 100° F temperature change.

38
7-7-l-3« Effects on Dynamic Characteristics .

Section 6 "Frequency Response of Strain Gage Accelerometers" shows

how the value of the damping ratio "will affect the frequency response

characteristics of strain gage accelerometers and, thereby, the accuracy

of dynamic measurements performed with these accelerometers. The most

commonly used damping fluids are silicones. While their temperature

coefficients of viscosity are considerably smaller than that of most

other damping fluids they are still quite appreciable. A typical fluid

(lOO centistokes nominal viscosity) will show a variation in kinematic

viscosity at 77°F (room temperature) of approximately 1.1$/°F. As

pointed out in section 6, the damping ratio is directly proportional to

the kinematic viscosity, consequently for this particular damping fluid,

the damping ratio of the instrument using it would also be expected to

vary 1.1$/° F. It can be seen that for the above fluid an increase in

ambient temperature of about l8°F would change the damping ratio from

0.707 toO.59 with attendant possible increase of instrument response of

10$ (at O.56 of the natural frequency).

Also, the damping may be affected by temperature induced changes

in the dimensions of the passages in the instrument through which the

damping fluid must pass. Such dimensional changes may be used in some

cases to compensate for the change of viscosity of the damping fluid.

If an increase in temperature, which results in a decrease in damping

fluid viscosity, would also decrease the size of the passages, the damping ratio would not change as much. A practical way of reducing error

due to viscosity variations with temperature as well as other tempera39
ture errors is by the temperature control of the entire instrument.

This is done by putting an electrical heater jacket around the instrument with a thermostat controlling the heating current mounted inside

the accelerometer preferably in close contact with the damping fluid.

The control temperature is usually in the range of 110°F to 135° F, permitting temperature control of the instrument to be effective up to

these temperatures (within limits of the thermostat) and down to temperatures as low as 0°F to -65°F. The low temperature limit depends on an

available heater power, instrument size, insulation, and whether air

surrounding instrument is moving or still. A bonded accelerometer had

its heater on continuously when in moving air at 50° F, or, in still air

at -20°F.

Tests for two such instruments showed temperature control to be

effective from -65°F to +119°F and -65°F to +113°F. The range of temperature control for another unbonded strain gage accelerometer was

found to be from -V?°F to +136°F. Tests on an unbonded strain gage accelerometer with gas damping showed the frequency response to be down

7$ (at the equivalent of 0.5 of the natural frequency) for a temperature

rise above ambient of about 120° F. This instrument was not temperature

controlled.

7-7-2. Thermal Transients .

The location of an instrument in close proximity to a rocket engine

or to the skin of a high speed missile may result in the instrument's

exposure to thermal transients. The effect of such transients would

probably manifest itself in a zero shift, which would be a function of

the magnitude and duration of the transient. Temperature compensated

ko
instruments may be even more effected than uncompensated ones due to

the gradients between the pickoff and its compensating element.

A gas damped unbonded strain gage accelerometer showed a transient

zero shift of about 5$ of the range when subjected to a step function

heat flux of 138 cal/minute through the base of the instrument.

7-8. Tolerance to Environmental Extremes .

While all environmental changes affect the measuring accuracy of

strain gage accelerometers to some extent, if the environmental changes

are severe enough, the instrument may be temporarily or even permanently

disabled.

7-8-1. Steady Acceleration Overload.

If a steady state acceleration with an amplitude much larger than

the full scale range of the instrument acts along the sensitive axis of

a strain gage accelerometer, it may be damaged due to over-ranging, that

is, by exceeding the elastic limit of strain gage wires, springs, or

beam material (in the case of bonded strain gage accelerometers), permanent set may be introduced. In extreme cases, strain gage wires may

actually break and thereby ruin the instrument.

To prevent this, the manufacturer generally builds stops into the

instrument which prevent the seismic mass from travelling more than some

nominal percentage beyond full scale range. Instruments using the "zero

length strain gage" are Immune to strain wire breakage, since the strain

in the wires remains relatively constant with the displacement of the

mass.

The limit stops are placed (frequently unsymmetrically) so as to

kl
limit displacement of the seismic mass corresponding to acceleration

values ranging from about 110$ to 190$ of the range, with the majoritynear 120$.

7-8-2. Vibration and Shock Along the Sensitive Axis .

The use of limit stops does not preclude damage due to overloads.

Large vibrational accelerations within the operating frequency range of

the accelerameter may cause the seismic mass to pound the stops very

hard and damage the instrument. The same may be true of large amplitude

shock accelerations.

Tests on a bonded strain gage accelerometer (±5G) (stop at -t8G and

-9G) revealed a changed calibration and open circuited thermostat after

the instrument had been subjected to a vibrational overload of +9G at

15 cps.

An unbonded strain gage accelerometer (±1.5G) showed no apparent

damage due to a vibrational overload of ±1^G at 35 cps. It is extremely

difficult to determine the effect of the environmental extremes experienced by a telemetering instrument in flight on the accuracy of the data

obtained by means of this instrument. This is not only due to difficulties in simulating such environmental extremes in the laboratory, but

also due to the fact that it is hard to predict and determine their magnitudes during flight tests. In addition, while the failure of an instrument due to environmental extremes is quite clear cut, "damage" or

"unsatisfactory operation" allows a wide latitude of interpretations.

Another difficulty exists in the fact that many cases of failure or

"damage" are due to imperfections of materials, poor assembly, improper

inspection, and other factors pertaining to a particular instrument and

k2
not necessarily to all instruments of the same type or class. Thus,

failure of one instrument does not automatically imply failure of others

of the same type under similar circumstances.

7-8-3. Acoustic (Airborne) Noise .

With the advent of high power jet engines and rocket engines, high

acoustic sound levels generated by them created another environmental

problem. These high level sound pressures may excite to resonance structural members on which instruments are mounted thereby producing vibration effects in the instruments. The remarks above on vibration effects

would apply then. A more direct effect has been reported for the case

of an unbonded strain gage accelerameter. This instrument when exposed

to an acoustic field of about 165 DB intensity at 600 cps showed outputs

of the order of 10$ to 30$ of full scale. This was apparently due to

resonant excitation of the instruments ' top cover plate and transmission

of this vibration to the mass through the damping fluid.

7-8-4. Extremes of Ambient Temperatures .

7-8-4-1. Effects on Unbonded Strain Gages .

In the case of conventional unbonded strain gage accelerometers,

one of the factors establishing the operating temperature range is the

maximum allowable strain in the wire.

Assuming a typical design with a one inch gage length of "Advance"

wire, a brass frame, and a full scale range of strain of ±0.0015 inches/

inch, a temperature range from -40°F to +200°F will set up strains of

±0.0003 inches/inch. Since the strain wires must be mounted under enough

initial tension to allow for both of the above values of strain, a maxi43
mum strain of O.OO36 inches/inch may exist at full scale range and +200° F.

This value of strain is close to that which caused permanent set in some

experiments on strain wire characteristics. Again, "zero length" strain

gages are not subject to this.

Another factor is the change in characteristics of "Advance" with

time at high temperatures (500°F). Oxidation and corrosion apparently

take place and gradually change the electrical and mechanical properties

of the strain wire. 500° F appears to be the present upper limit for

reliable performance of unbonded strain gages.

7-8-4-2. Effects on Bonded Strain (3ages .

Manufacturers recommendations for bonded strain gages indicate

that "Advance" (constantan) gages with paper backs may be used at temperatures up to l80°F, those with Bakelite backs may be used up to about

300°F without damage. Tests performed at NBS2 on temperature characteristics of bonded strain gages indicate that paper backed gages are not

reliable above about 100° F, bakelite or epoxy resin backed gages are

good up to about 200° F. Creep may be present at temperatures as low as

100° F if a strain level exists for any length of time. It appears to

increase with temperature. Some of the creep originates in the bonding

cement. Local strains at the end of the wire loops and at junctions

between gage wires and lead wires will also contribute to the creep.

Strain gages have been tested at temperatures as low as -310° F,

and appeared to perform satisfactorily. The gage factor for "Advance"

gages seems to decrease in the order of one percent between room temperature and about -200°F. Other tests indicate that the gage factors of

some "Advance" gages decrease in the order of 3$ between room tempera-
ture and about +250° F. Reports on test results show a wide variety of

results and the above values only indicate a general trend. The properties of bonded strain gages appear to vary not only among specimens of

the same type, but depend on mounting procedures, type of current used,

temperature and humidity prevailing at the time of mounting, curing temperature and curing time for bonding cement, etc.

It has been definitely established that strain cycling and temperature cycling of the gages after mounting is beneficial in reducing creep

and zero shifts and generally stabilize the characteristics of the gages.

High temperature strain gages (for temperatures beyond 250° F) are

available and have been tested. Again, a rather wide range of results

was obtained. Apparently high temperature gages made of "Advance" wire

or foil are satisfactory up to about 500° F with a gage factor somewhat

higher than at room temperature. Some "Advance" gages show resistance

changes with time and temperature independent of strain. Other materials

have been used for high temperature gages; gages made with Nichrome V

wire or foil seem satisfactory up to about 600°F with a gage factor lower

than at room temperature. Another material, Karma, may be suitable for

even higher temperatures (up to 1000° F) although some tests have indicated temperature hysteresis. Commercial high temperature gages claim

operating ranges up to l800°F, although presumably zero drift would make

steady state measurements unreliable.

One type of ceramic bonding cement, recommended for high temperature gages, appears rather soft and might easily be eroded by the action

of damping fluid in motion.

Semiconductor strain gages are advertised as being suitable for

45
operation at temperatures from -320° F to +650°F.

7_8-4-3. Effects on Cantilever Beam (Spring) Materials .

In addition to changes of the modulus of elasticity with temperature, other effects occur at elevated temperatures. These are plastic

readjustments as a result of stress at time and temperature: "relaxation",

which refers to constant strain, and "creep", which refers to constant

stress. Practically speaking, "both have the same effect on measurements

with cantilever beam type strain gage accelerometers : they cause zero

shift and may cause eventual operation of the beam in a nonlinear stressstrain region. For alloys like beryllium copper or phosphor bronze,

these effects are apparently very small at ambient temperatures up to

near 400°F.

7-8-4-4. Damping .

Large changes in temperature will change the viscosity of the damping fluid radically, and thereby change the dynamic characteristics of

a fluid damped instrument. As an example, a silicone damping fluid with

a viscosity of 100 centistokes at +77° F, will have a viscosity of 490 at

-30°F, and 32 at +200° F. If an accelerometer, filled with this damping

fluid, has a damping ratio of 0.707 at 77°F, the corresponding damping

ratios at -30°F and +200°F will be about 3.5 and O.23. The significance

of this on the frequency response can be seen by considering the response

of the accelerometer to a sinusoidal acceleration at frequency of 0.57

of the natural frequency where at 77°F, and damping ratio of 0.707> the

frequency will be down 5$ from the steady state value. At +200° F, the

response will be 38$ above the steady state response. At -30° F, damping

46
ratio 3« 5, the response will nave dropped to about 25$ of the steadystate response. Some of the silicones solidify between -40°F and -70°

and, thereby, prevent functioning of the instrument. (it appears, then,

that temperature control is imperative for acceleration measurements at

low ambient temperature with fluid damped accelerometers .

At high ambient temperatures, the damping fluid Imposes other limitations. While the flash point for a DC 200 fluid of 100 centistokes is

near 600°F, for a 5 centistokes fluid it is about 275 °F. If these

fluids are kept at high temperatures for a period of time, some of the

fluid is lost through evaporation, the viscosity of the remainder will

have changed somewhat. Thus the shelf life of the instrument would be

limited by the storage temperature. Based on the characteristics of the

damping fluids above, an upper limit of ambient temperature of about

300° F would seem a reasonable one for future design. A typical silicone

damping fluid with a viscosity of 100 centistokes will show a change in

volume of 8$ over a temperature range from 0°F to +200°F. Most manufacturers provide an elastic expansion chamber in the instrument to prevent

leakage or the formation of air bubbles in the fluid when the ambient

temperature changes. Gas damping varies much less with temperature as

shown in section k-k-3 f and shows promise for high temperature operation.

7-8-5- Ambient Pressure Variations .

While ambient pressure variations have no effect as such on the

operation of strain gage accelerometers. It has been found that some of

these instruments (supposedly "pressure tight") have leaked damping fluid

under comparatively mild pressure variations. The loss of damping fluid

hi
may cause air bubbles in the fluid and consequent spurious dynamic

responses.

7-8-6. Effects of Nuclear Radiation .

The physical properties of many materials are altered in the presence of high energy radiation!^-The changes vary with the type, density

and duration of the radiation, and the type and structure of the material. Organic compounds appear to be affected harmfully by beta, gamma,

and neutron radiation. Metals seem to be affected chiefly by neutrons.

Organic insulators will break down after prolonged exposure and

also lose structural strength. Inorganic insulators can be used instead.

For bonded strain gages, the susceptibility of the cements poses the

most serious problem at present.

Irradiation appears to increase the hardness and tensile strength

of metals and decrease their ductility. In addition, metals exhibit an

increase in electrical resistance.

Absorption of nuclear radiation by a strain gage will increase its

internal temperature, thereby affecting its gage factor and linearity.

Semiconductor strain gages will undergo severe permanent changes

in electrical characteristics.

Finally, there may be hazards to personnel due to the radioactivity

induced in the materials of the instruments. This radioactivity will

persist for a period of time depending on the characteristics of the

radiation and the materials.

7-8-7. Other Environmental Conditions .

Humidity, salt spray, fungus, sunshine, rain, sand and dust would

not be expected to have any appreciable effect on the instruments. Some

kd
of these effects may decrease the leakage resistance between the electrical terminals on the outside of the accelerometer, but since the instruments are essentially low resistance devices, the effect of the changed

leakage resistance should be negligible.

h9
TABLE I

CHARACTERISTICS OF SOME COMMERCIAL UNBONDED STRAIN GAGE ACCELEROMETERS

TYPE RANGE

±G-UNTTS

Q

±mv/volt cps

E

VOLTS

BRIDGE

RESISTANCE

OHMS

m = £b!

G

'Brl ±025 2.00 21 11 350 882

S-2 ±2.0 3-89 100 9 350 5000

S-3 ±5.0 4.55 190 11 350 7220

s-4 ±200 4.00 850 11 350 3610

S-5 ±50 4.58 550 12 350 6050

S-6 ±10 4.00 350 8 300 12250

S-7 ±0.5 2.22 5 9 350 50

S-8 ±20 2.08 12 12 350 7.2

S-9 ±50 4.00 360* 5 350 2500*

S-IO ±25 4.00 790* 5 350 24700*

C-ll ±5 4.00 300 5 350 18000

C-12 ±500 4.00 2900 5 350 16800

* Computed. These are gas damped accelerometers

.

50
TABLE 2

A. CHARACTERISTICS OF SOME COMMERCIAL BONDED STRAIN GAGE ACCELEROMETERS

TYPE

RANGE Q fn E

+G--UNITS ±mv/volt cps VOLTS

BRIDGE

RESISTANCE

OHMS

M = fn2

T-l ±2 2.5 25 15 300

T-2 ±30 2.5 110 15 300

B-3 ±3 4.0 8 8 120

B-4 ±100 4.7 75 8 120

B-5 ±100 3-1 185 8 120

313

4o4

21

342

B. CHARACTERISTICS OF SOME COMMERCIAL ACCELEROMETERS

WITH SEMICONDUCTOR STRAIN GAGES

K-l ±1 50 no 20 4oo* 12100

K-2 ±20 50 500 20 4oo* 12500

* Output Impedance

51
REFERENCES

1. M. Hetenyi. "Handbook of Experimental Stress Analysis," John Wiley

and Sons, Inc., New York, 1950.

2. "Characteristics and Applications of Resistance Strain Gages."

National Bureau of Standards Circular No. 528, issued 195^.

3. U. Yarnell. "Resistance Strain Gages," Electronic Engineering,

London, 1951.

k. M. R. Behar. "The Handbook of Measurement and Control," Instruments

Publishing Company, Inc., Pittsburgh, Pa., 1951-

5. "Statham Transducer Element" Bulletin 1.0, Statham Laboratories,

Inc., Los Angeles, California, 1956.

6. "The Statham Zero-Length Unbonded Strain Gage" Bulletin 1.02,

Statham Laboratories, Inc., Los Angeles, California, 1957*

7. "A Study of Force and Displacement Measuring Techniques", Part I -

"Linear and Angular Displacement Measurement Techniques", WADD,

ARDC, Wright-Patterson Air Force Base, Ohio, i960.

8. "Pressure Transducing and Instrumentation Techniques" Vol. I, Book

2 - Part B "Transmitting Techniques", WADD Technical Rept. No. 59-

7^3, WADD, ARDC, Wright-Patterson Air Force Base, Ohio, i960.

9. D. E. Weiss. "Design and Application of Accelerometers," Proceedings of the Soeiety for Experimental Stress Analysis, Vol. IV,

No. 2, 1947, PP. 89-99.

10. W. V. Basset. Discussion following reference 9, pp. 100-102.

52
11. "Instrument Notes" Statham Laboratories, Inc., (Statham Instruments, Inc.), Los Angeles, California:

No. 2. "Response Characteristics of a Simple Instrument", 1950.

No. 5* "Temperature Compensation of Bridge Type Transducers", 1951*

No. 9« "Design Parameters for Linear Accelerometers , 1952.

No. 12. "The Meaning of "Natural Frequency", 19^9.

No. 13. "The Mass Effect in Fluid Damping", 1950.

No. 23. "Secondary Effects in Seismic Systems", 1952.

No. 33» "Some Characteristics of Gas-Damped Accelerometers", 1958.

12. S. Levy and W. Kroll. "Response of Accelerometers to Transient

Accelerations," Journal of Research of the National Bureau of Standards, Vol. k-5, No. k, October, 1950.

13. "Characteristics of Resistance Strain Gages? B. L. Bloss. Paper No.

90-NY60, Instrument Society of America, Sept., i960.

Ik. "SR-4 Strain Gage Evaluation Report", Technical Data No. 4310-3,

Baldwin-Lima-Bamilton, August, 1958*

15. "Materials for Instruments in Radiation Service", RP 25.1, Instrument Society of America, December, 1951*

16. "Shock and Vibration Handbook", McGraw-Hill Book Co., Inc., 1961.

53
LIST OF SYMBOLS USED

A Peak acceleration amplitude, inches per second per second

B Transverse acceleration, "G" units

E Excitation voltage, volts

G Maximum range of instrument, "G" units

I Moment of inertia of beam, inches^"

Ks Gage factor of strain wire

L Length of beam, inches

Q Sensitivity, millivolts out per volt of excitation

R Resistance of each active arm of strain gage bridge, ohms

S Total length of wire in active arms of bridge, inches

V Electrical output, volts

W Weight at end of beam, pounds

Y Modulus of elasticity, pounds per square inch

Z Distance along beam from fixed end, inches

a Acceleration due to gravity, inches per second per second

c Equivalent viscous damping constant, pounds per inch per second

Cc 2 tf km, the critical damping constant, pounds per inch per second

d Diameter of strain wire, inches

fn Natural frequency, cycles per second

h Height of beam, inches

k Spring constant, pounds per inch

m Mass of seismic weight, pounds

n n _ , the damping ratio

c c

5^
> €> natural circular frequency, radians per second

u Deflection of end of beam, inches

w Circular frequency of case displacement, radians per second

x Relative displacement between seismic mass and case, inches

^oeak Maximum displacement of seismic mass from its zero position,

inches

y Displacement of case, inches

£ Strain in Fibre, inches per inch

p Resistivity of strain wire, ohms per circular mil foot

n* Stress in fibre, pounds per square inch

55
STRAIN WIRES

STOP LIMITS TRAVEL OF MASS

SOFT SPRINGS RESTRICT MASS TO

RECTILINEAR MOTION

SEISMIC MASS

STOP LIMITS TRAVEL OF MASS

STRAIN WIRES

CASE OF INSTRUMENT

SENSITIVE DIRECTION

Figure 1 Principle of Unbonded Strain Gage Accelerometer

56
SEISMIC MASS

SOFT SPRINGS RESTRICT MASS

TO RECTILINEAR MOTION

STRAIN WIRES

SLIDING CONTACTS

NG, SOFT SPRINGS

CASE OF INSTRUMENT

- SENSITIVE DIRECTION

Figure 2 Principle of "Zero Length" Strain Gage

Accelerometer

57

U. S. GOVERNMENTPRINTING OFFICE : 1962 O - 648032

U. S. DEPARTMENT OF COMMERCE

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NATIONAL BUREAU OF STANDARDS

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