Accelerometers

An accelerometer is a transducer that responds to acceleration in one or more axes. The sensing element consists of a spring-mass system that deflects when subject to acceleration in the direction of its sensitive axis (ill. 19-1). This mass is normally known as the seismic element, and the spring-mass combination as the seismic system.

ill. 19-1. A simplified diagram of a spring-mass type accelerometer.

The seismic mass responds to acceleration by producing a force proportional to applied acceleration. The spring deflects until an equal reaction force is developed. This deflection is a linear function of applied acceleration within the constraints imposed by the natural frequency and damping ratio of the seismic system. The actual “spring” involved does not have to be a mechanical one. It can just as well be electrical, and the seismic mass can be part of the transducer itself (e.g., the core of an LVDT). Alternatively, a seismic system can be coupled to a separate displacement-sensitive transducer element to produce a transducer whose output is proportional to the acceleration applied to the seismic system. The transducer thus formed is referred to as an open-loop accelerometer because the measurement does not involve output-to-input feedback.

In a simple spring-mass system the mass position is directly proportional to acceleration only as long as the acceleration is considerably less than the undamped frequency of the system. This affects the choice of transducer normally employed. At low frequencies the position of the mass can be detected with a displacement sensor. At higher frequencies a strain-gauge transducer or piezoelectric transducer becomes a more realistic choice. Even more demanding requirements are set by accelerometers designed for measuring shock and vibration.

OPEN-LOOP ACCELEROMETERS

Two important parameters of any open-loop accelerometer are natural frequency and damping ratio. The natural frequency of the spring-mass system is the frequency at which the seismic mass will vibrate with no damping. it's a measure of the speed with which the system can move in response to an impulse. The natural frequency of an undamped accelerometer must be several times the highest frequency of interest in the measurement if the output of the instrument is to be a correct representation of the applied acceleration. However, high natural frequency implies a relatively stiff, and therefore relatively insensitive, measuring system. The sensitivity of an undamped accelerometer is inversely proportional to the square of the natural frequency (ill. 19-2). Thus, a high natural frequency permits acceleration measurement over a wider range of frequencies, whereas a low natural frequency gives greater sensitivity.

DAMPING

This relationship can be modified by adding damping to the system. Unless an open-loop accelerometer is damped, the seismic system will continue to vibrate and give readings long after the applied acceleration has disappeared. Further, a very small acceleration at frequencies near the natural frequency of an undamped accelerometer will cause an unduly large response from the instrument. Damping ratios of approximately 0.6-0.7 of critical will ex tend the range of usefulness of an accelerometer to nearly three-fourths of its natural frequency.

In reproducing a complex wave pattern, phase distortion generally results from the lack of linearity between the phase lag of the responding element (seismic system) and the frequency components of the applied wave pattern. A damping ratio in the range of 0.6 to 0.7 produces an almost linear phase lag relationship for frequencies up to the natural frequency of the instrument, and thus this range of damping ratios eliminates phase distortion within the operating range of the instrument.

ill. 19-2. Sensitivity-vs.-damping curve for a spring-mass accelerometer. As the natural frequency increases, the sensitivity drops off rapidly.

Open-loop accelerometers use either fluid (viscous) or magnetic (eddy-current) damping. Silicon fluids having a low temperature coefficient of viscosity must be used for viscous damping to make any change in damping ratio with temperature relatively small, if not negligible. Magnetic damping is commonly used in applications requiring a constant damping ratio, because magnetic damping is essentially unaffected by temperature.

Specifically, the output of an accelerometer or spring-mass system is linearly proportional to input acceleration only for frequencies up to about 40 percent of its damped natural frequency. However, when the frequency components of the motion under study are higher than about 2.5 times the natural frequency of the spring-mass system, the relative motion of the seismic system is proportional to the applied displacement.

The response of a spring-mass system is thus proportional to the applied acceleration or to the applied displacement, depending on whether the frequencies involved are lower of higher, respectively, than the natural frequency of the spring-mass system. e.g., an accelerometer having a natural frequency of 20 Hz and designed to measure low-frequency accelerations up to about 10 Hz may also be used to measure displacements involving frequencies beyond about 50 Hz.

SERVO ACCELEROMETERS

Servo accelerometers are closed-loop, force-balance transducers with much greater accuracy and stability than that obtainable with open-loop accelerometers. They normally feature a rugged acceleration sensor integrated with dc-operated solid-state circuitry that pm vides a dc signal proportional to acceleration.

A block diagram of a servo accelerometer is given in ill. 19-3. A pendulous mass reacts to an acceleration input and begins to move. A position sensor detects this minute motion and develops an output signal. This signal is demodulated, amplified, and applied as negative feedback to an electrical torque generator (or torquer) coupled to the mass. The torquer develops a torque proportional to the current applied to it. The magnitude and direction of this torque just balance out the torque attempting to move the pendulous mass as a result of the acceleration input, preventing further movement of the mass.

ill. 19-3. Block diagram of a servo accelerometer.

Because both torques are equal, and because the torque generator output is proportional to its input current, the input current is proportional to the torque attempting to move the pendulous mass. This torque is equal to the product of moment of inertia (a constant) and acceleration. Therefore, the torque generator cur rent is proportional to applied acceleration. If this current is passed through a stable resistor, the voltage developed is proportional to applied acceleration.

The dynamic ratings of the servo accelerometer are unusual in that neither the natural frequency nor the damping ratio is directly and unavoidably related to the accelerometer range, as in open-loop types. The damping in the sensitive axis is accomplished electrically by a passive network.

The natural frequency of a servo accelerometer is a function of loop gain multiplied by the moment of inertia of the pendulous mass. Thus, the natural frequency can also be determined electrically, within reasonable limits. it's possible therefore to provide high natural frequency for low-range accelerometers without sacrificing sensitivity or affecting scale factor. However, small accelerations are generally related to the relatively slow movements of large bodies, and large accelerations are generally related to the relatively fast movements of small bodies. So, as a practical matter, high response is not generally required in low-range accelerometers.

PRACTICAL ACCELEROMETERS

The majority of accelerometers in use today are of the piezoelectric or semiconductor strain-gauge type. Piezoelectric accelerometers fall into two distinct categories: piezoresistive (pr) and piezoelectric (pe). Piezoresistive (pr) accelerometers have the ad vantage of offering dc response with a sensitivity usually sufficiently high that no pre-amplification of output is necessary. Also, because they use an external source of energy, they have an inherently low output impedance. They are, however, largely limited to low- frequency measurement yielding signal pulses of relatively long duration.

Note. The piezoresistor (pr) transducer is a strain gauge, al though not all strain gauges are of pr type (see later description of strain-gauge accelerometers and also Chapter 18 on pressure transducers).

Piezoelectric (pe) accelerometers are self-generating as regards electrical output signal and so don't require any external power supply. Artificially polarized ceramic crystals, having a much greater a shape configuration chosen to further enhance specific characteristics:

- Single-ended compression for high sensitivity and high resonant frequency. A suitable choice for low-level measurement and for general-purpose use.

- Shear for miniaturized accelerometers with low mass. By locating the sensitive element isolated from the base, shear accelerometers provide the best protection against pickup from base bending and acoustic noise. Also, shear excitation reduces crystal sensitivity to temperature transients. Shear crystals are, however, less sensitive than compression types.

With pe accelerometers, low-frequency amplifier cutoff is usually 2-5 Hz to reject piezoelectric output produced by many pe transducers. Special isolated designs can be used at much lower frequencies. Piezoelectric accelerometers tend to have very predictable nonlinearity, which can be expressed as a percentage in crease in sensitivity with applied acceleration (typically on the order of 1 percent per 500 g). The upper limit of g is normally determined by peak crystal stress and /or maximum nonlinearity.

Note. Careless handling of pe transducers can produce very high g levels (several thousand if dropped from a height of 4-5 feet onto a hard floor).

THERMAL EFFECTS

The sensitivity of piezoelectric acceleration also varies with temperature. A temperature-range rating gives the operating range over which this effect can be regarded as negligible for most practical purposes. Typically, this is from 0 to 180 to 260 °C. for pe types, and -50° to +120°C. for pr types.

A sudden change in temperature may also affect the output, giving a momentary spurious signal generated by pyroelectric effect.

EXAMPLES OF DESIGN

Modern pe accelerometers are highly developed designs, largely individual to specific manufacturers and aimed at overcoming the limitation of conventional designs. With conventional compression designs, non-vibrating forces can be transmitted through the mass or crystal, producing a spurious noise signal. With conventional shear design, extraneous forces transmitted through the mass or base again produce noise, but not to the same extent.

The following are examples of optimized designs.

Isobase

Isobase accelerometers (ill. 19-4) are a premium compression design. They use a specially contoured internal base to make the crystals less sensitive to stress at the mounting point. This gives a significant improvement in isolation from base bending and thermal transients. Isobase accelerometers also operate in high g levels and at high temperatures.

ill. 19-4. A compression (isobase) accelerometer.

Shear Designs

Shear designs also give improved isolation. Electrical output is derived from shearing forces caused by the mass which is mechanically attached or bonded to the periphery of the pe element (ill. 19-5). This provides excellent base strain protection because base bending produces negligible shearing forces on the element. Similarly, with acoustic excitation and thermal transients. In addition, shear elements are not subject to primary pyroelectric out put caused by uniform temperature change. Annular shear accelerometers offer additional advantages such as small size, light weight, and wideband frequency response. They are also popular for shock measurements. But sensitivity is low, and high- temperature models are not available.

Isoshear

Isoshear is the optimum design. It offers the best isolation characteristics of both the Isobase and shear principles for applications that don't require extremely small size or light weight. It also has high sensitivity and high operating temperatures.

ill. 19-5. A shear-type accelerometer.

Isoshear accelerometers use flat-plate shear elements that are bolted to a central post. Multiple elements can be stacked for greater sensitivity. Compensators can be added for flatter temperature response. and electrical insulators can be added to isolate the signal from the case. Isoshear offers such excellent insulation from non-vibration environments that measurements can readily be made down to 0.1 Hz in environments of severe thermal, acoustic, or base-bending conditions.

SIGNAL CONDITIONING

A signal conditioner is normally used to interface a pe accelerometer to a readout instrument or recorder. In the case of a pr-type circuit, requirements can be minimal. A pair of transducer elements and a pair of fixed resistors are connected in a Wheatstone bridge configuration, with the external power supply connected as in ill. 19-6. Output is then taken from the bridge; it may or may not need amplification before being fed to a dc-indicating readout. For increased sensitivity all four arms of the bridge may be active (transducer) elements.

ill. 19-6. A method of signal conditioning for use with accelerometer transducers (X).

Piezoelectric type accelerometers may be treated either as volt age or charge generators requiring no external supply. The voltage- generator mode is the simplest to condition by using a voltage amplifier (ill. 19-7). However, the disadvantage of this system is that sensitivity is affected by cable length.

ill. 19-7. A simple voltage amplifier.

For that reason the charge-generator mode, which is independent of cable length, is normally preferred, and thus the initial calibration of the transducer is made without the use of extra long cables.

A typical circuit is shown in ill. 19-8, where the transducer is connected to a charge amplifier. A charge amplifier is essentially an operational amplifier with integrating feedback. Output voltage is proportional to the charge generated by the transducer. Low- frequency response is determined by feedback capacitor C and the dc stabilizing resistor R.

ill. 19-8. A charge amplifier using an operational amplifier.

Care must be taken on critical measurements to avoid overloading the amplifier input because, if saturated, the recovery will be at the low-frequency time constant of the amplifier, which is typically 2 seconds or longer. In unattended airborne systems the accelerometer sensitivity and amplifier gain are matched to provide a wide dynamic range.

It is a feature of some pe accelerometers that they are available with integral electronics. Strain-gauge-type accelerometers may also be available with integral electronics, but it's more usual to connect to an external compensation module. The main disadvantage of integral electronics (with both types) is that the maximum series temperature of the accelerometer is that for the electronics, which may be considerably lower than that of the accelerometer itself.

STRAIN-GAUGE ACCELEROMETER

An example of modern strain-gauge accelerometer construction is given in ill. 19-9. The moving mass is mounted on a cantilever beam to which strain gauges are bonded top and bottom. Under acceleration forces, the g effect on the mass causes the beam to bend; the resulting bending movement produces a strain proportional to acceleration and detected by the strain gauges. The strain gauges are connected to a bridge circuit with either two or four “active” arms (two or four strain gauges on the beam, respectively). With a voltage applied to the bridge, bridge unbalance results in a circuit charge proportional to acceleration.

ill. 19-9. A strain-gauge accelerometer.

Accelerometers of this type can have an extremely linear response, such as a design full-scale range well within a 1-percent error band for nonlinearity, or overall nonlinearity of better than 99 percent. If it's used for higher g measurement than the design range, however, nonlinearity will become increasingly marked.

Accelerometers of this type are also designed with different natural frequencies as well as different g ranges—the higher the g range the higher the natural frequency of the system, and vice versa. The main point here is that the maximum frequency of vibration applied should be substantially less than the natural frequency; otherwise the accelerometer may be damaged by over-ranging. This is most likely to occur with low-g-range accelerometers (with low natural frequency), when a damped accelerometer would be the preferred choice. With an undamped accelerometer approaching its natural frequency, sensitivity may be measured by up to 100 times its linear output.

SIGNAL CONDITIONING

The strain gauges are arranged in a Wheatstone bridge con figuration, normally connected to a compensation module (although the same function can be performed by discrete resistors). This pro vides sensitivity compensation for thermal sensitivity shift with a dropping resistor in one of the supply lines, zero offset trim, and zero offset drift.

It is important to use the specified excitation voltage for the specific model of accelerometer used, because higher or lower voltages can affect both the sensitivity and the amount of compensation required (resistor values). However, it's easy to adjust the circuit, if you know what you are doing.

In the case of a typical Entran accelerometer, e.g., the sensitivity is directly proportional to the input voltage, and all compensation and trimming has been done in the compensation module for the design voltage. If the exciting voltage is lowered, with no other changes in circuitry, the sensitivity decreases, but all other specifications remain the same. If it's necessary to lower the in put voltage with either no reduction or a partial reduction in sensitivity, the value of the thermal sensitivity resistor (Re) can be reduced. This allows more of the applied voltage to be directed to ward the bridge but, in turn, reduces the effectiveness of the thermal sensitivity compensation. The compensating resistor (Re) is expressed as the difference between the input impedance (Ri) and the output impedance (R). With no resistor at all, the thermal sensitivity shift (tss) is approximately — 15 percent per 100 degrees Fahrenheit for most of Entran’s standard devices.

The following relationships are approximate and indicate the effect of sensitivity change versus input voltage and thermal sensitivity shift. By selecting the maximum tss you can accept and the desired input voltage, you can calculate approximate sensitivities.

For...

Vids = Input voltage from data sheet

Vi = Desired Input voltage

Vods = Sensitivity from data sheet

Vo = New sensitivity

tss = Thermal sensitivity shift (0 to — 15%/100° F.)

Ro = Output impedance from data sheet

Example. Entran’s EGA-125-250 accelerometer.

Vids = 15 V

Vods = 1 mV/g

Ro =500 Ohm

...would like to operate 10 Vdc with maximum thermal sensitivity shift of -15%/100 ° F.

For maximum stability of zero offset, lower input voltages are recommended. Sensitivity can also be increased by placing a higher voltage on the accelerometer. This should be discussed with Entran before purchase.

The following notes also apply to Entran accelerometers.

Zero G Offset

All transducers have some no load or zero g offset. When the transducer is powered, the no-load output will not be exactly 0 mV. If the zero offset value is not specified in the data sheet, it's typically between ± 10 mV, but in some cases it can be as high as ± 15 mV. This usually represents a small percentage of full-scale output. Off set values closer to 0 mV can be provided on special request. Most recording devices have their own zero balance circuit to null out transducer offsets. If you zero the transducer yourself, don't shunt one of the transducer legs externally. This procedure will change the thermal zero shift compensation provided with the unit. don't shunt the accelerometer to reduce zero offset. This will alter the thermal zero shift performance. Adjustable zero offsets are also available from Entran as an option.

The actual value of the zero offset will drift to its final value while the accelerometer is being “warmed up.” Typical warm-up times can vary from 5 minutes to 2 hours, depending upon the transducer and desired level of stability. For critical dc measurements, where ultimate stability is required, a 4-hour warm up may be advisable. Once the zero reaches equilibrium, it will then exhibit a small drift over time. When minimal drifting is required, the following four alternatives yield better results.

For Best Zero Stability

- Choose Entran’s high-impedance option. Because drifting is due to power dissipated, the higher gauge resistance is stabler for a given voltage.

- Operate the transducer with a lower input voltage. Power dissipated is proportional to the square of the voltage. Using one- half the typical input voltage dissipates one-fourth the power.

- Select a damped accelerometer. Oil damping creates a better heat distribution internal to the accelerometer and is inherently stabler.

- Provide better heat sinking for the accelerometer when mounted.

When making dynamic measurements, the output of the accelerometer can be AC-coupled. This completely eliminates the zero offset, and all its effects may be ignored.

Zero Offset Shift with Temperature (Thermal Zero Shift)

The change of zero offset with temperature is minimized in Entran’s thermal compensation process. Standard units are provided fully compensated and the actual maximum shift is described in the accelerometer bulletins. Typical compensations are in the range of ±1 to ±2 percent of full scale per 100 degrees Fahrenheit. This means that the stabilized zero offset will change a maximum of 1 to 2 percent of the full-scale output per 100 degrees Fahrenheit. e.g., for a transducer with 1-percent compensation and a 250-mV full-scale output, if the stable zero is + 3 mV, it will shift to a maximum of either + 0.5 mV or + 5.5 mV over a 1000 F. change. These values apply within the compensated temperature range of the transducer.

Sensitivity Shift with Temperature (Thermal Span Shift)

The change of sensitivity with temperature is minimized in Entran’s thermal compensation process. Standard units are provided fully compensated (except for low-cost units), and the actual maximum shift is described in their accelerometer bulletins. Typical Compensations are in the range of ±1 to ±2.5 percent per 100 degrees Fahrenheit. This means that the sensitivity of the accelerometer will only change a maximum of 1 to 2.5 percent of the calibrated value per 100°F. e.g.,; a transducer with 1-per cent compensation and a 1.00 mV/g sensitivity, will shift to a maximum of either 0.99 or 1.01 mV/g over a 100° F. change. These values apply within the compensated temperature range of the transducer.

Compensated TemperatureRange

The compensated temperature range is the range in which the accelerometer will meet the specifications for zero and span shift as posted in the data sheets. Above and below this range, the transducer will continue to operate, but the specification will gradually increase from the data sheet values. The transducer is compensated for equilibrium values of temperature, not for fast temperature changes, pulses, or excursions. If the accelerometer is compensated from 80° F. to 180° F. and the actual 100° F. differential occurs in a rapid excursion, the accelerometer must be allowed to come to an equilibrium temperature before it will meet the listed specifications. Compensation is only valid for equilibrium or slow changes in temperature, not for thermal shocks. In cases where fast temperature changes are required, we suggest using a damped accelerometer or a unit with a larger housing to act as a better heat sink.

All standard accelerometers are compensated from 80 F to 180 F. unless otherwise specified. However, Entran will compensate your accelerometer over any 100° F. band within the operating temperature without additional charge. For intervals of greater than 100°F., compensation can be achieved by special request. For large differentials, such as a 2000 F. or 300° F. bandwidth, the tightest compensation can only be achieved over a 100 °-150 ° F. section, but you may specify this section. e.g., an accelerometer can be compensated from 0° to 300° F. with any 100° F. section at a compensation of percent per 100 degrees Fahrenheit while the other intervals are at a compensation of percent per 100 degrees Fahrenheit. Most of Entran’s standard units are available for compensated ranges from -40° to +250° F.; however, ranges from -100° to +500° F. are available on special order.

PREV: Pressure Transducers
NEXT: Measurement of Force and Torque

Fundamentals of Transducers (all articles)