Sensors - September 2000-The Art of Fabricating a Rotational Accelerometer

The Art of Fabricating a
Rotational Accelerometer

Bimorph and quartz-based piezoelectric sensors, together with the required system configurations, have recently been developed to accurately measure rotational acceleration for use in design research.

Michael D. Insalaco, Kistler Instrument Corp.

The acceleration experienced by a rotating member or structure is often a

Photo 1. With all the electronics housed in a small, hermetic package, a very rugged and dependable sensor is achieved for use in automotive crash studies.

very important parameter during system design. Mechanical structures deform dynamically at resonant frequencies, and the resulting stresses can be damaging. An automobile crash, for example, imparts tremendous energy to the occupants, typically in the form of rotational inertia. Impact dynamics and modal analysis are used to investigate the characteristics of these mechanical systems or structures, and finite element analysis (FEA) to model them mathematically. This technique uses an appropriate stress/strain relationship to relate the deformation at one surface of a discrete elemental section to that at opposing surfaces.

In a computer model, each surface displacement and rotation represents a degree of freedom (DOF) of the system. Attachments such as welds and bolted joints can introduce a significant error into the FEA model because the required stiffness estimates are generated from engineering judgement and empirical data. The stiffness at these connections is dependent on many variables such as weld homogeneity and thickness, and mounting torque. A dynamic measurement or analysis must be performed when the results may have critical consequences. A correlation can be forced between the experimental and analytical study and by applying a modification or “assumption adjustments” to the computer model. Once this correlation is obtained and the model assumptions are verified, accurate predictions can be made with confidence regarding improvements to the existing design.

Measurement techniques have been used to estimate rotational DOFs, but it was not until recently that sensors designed specifically to perform these measurements have been available. Assembly and calibration procedures also have been developed to optimize these sensors for a specific field of study.

A dynamic experimental study is typically performed on a structure with linear accelerometers attached at appropriate meas urement sites. If the accelerometers are close to one another, their differing linear outputs can yield an estimate of rotation in the system but it remains difficult to obtain an accurate measurement near interfaces such as bolted joints. Because these interfaces often experience considerable relative rotation and minimal displacement, direct rotational measurement is important.

Figure 1. A symmetrical bimorph accelerometer usually has a simple mechanical design. Adhesive attachment is adequate because the seismic element has an extremely low mass.

Figure 2. As shown in this visualization of the beam’s deformation during operation, internal stresses proportional to the resulting charge are directly related to the deformation. Linear input is shown in (A) and rotational input in (B).

Figure 3. Slicing a single beam into separate elements yields a uniform and consistent arrangement.

Various techniques have been attempted, using a pair of spatially separated, sensitivity-matched accelerometers to determine rotational acceleration. When attached to a fixture, at a prescribed distance apart, the output signal difference between them is proportional to rotational acceleration. If the path between them is short and rigid, such that there is no local rotation between the matched accelerometers, the rotation at the base of the fixture can be computed. This approach can be used in many situations to obtain a reasonable estimate, under favorable, but not all, conditions. The major problem is that the prevailing levels of output signal generated by the translational components of the structure’s movement tend to overshadow those due to the rotational motions, making the data questionable [1].

This undesirable ratio places a high-precision requirement on the sensitivity-matching process. The effect of sensitivity mismatch error has been analyzed and shows that an error in sensitivity-matching as small as ¹/₄% can contribute 12.3% error to the computed rotational acceleration, even on a simple cantilever beam structure [2]. This error analysis was performed with the assumption of an infinitely rigid attachment between the two sensors. Transverse influences were excluded by an appropriate selection of specimen and test conditions. Clearly, producing an accurate rotational accelerometer from commercially available hardware is a very challenging task.

Designing an accelerometer always entails the optimization of a “parameter compromise.” Experimental modal analysis (EMA) usually incorporates a sensor well suited to the following conditions/characteristics:

These conditions are satisfied by a piezoelectric element in the form of a bimorph made of two inversely polarized piezoelectric plates sandwiched together and sliced to form a rectangle mounted on a central support (see Figure 1). This element also serves as the seismic mass since it allows beam flexure when exposed to acceleration. When configured as a cantilever beam, the rectangular shape results in an extremely flexible seismic system in its sensitive axis as compared to the two orthogonal directions defining the transverse planes. Even though the system lacks the extreme stiffness typical of most accelerometers, the obtainable frequency response is well suited for EMA.

This arrangement is symmetric about the central fulcrum. Any rotation about this center point generates equal magnitude but inverted charges from each of the symmetric beam halves. A self-cancellation occurs when rotations are presented. Linear acceleration creates similar bending in each beam half and the charges then sum, resulting in an output proportional to the imposed linear acceleration (see Figure 2).

When this dual cantilever beam arrangement is stressed, it produces a voltage, V, across the element. V is related to the charge, Q, generated on the surface of the piezoelectric material by the relationship V = Q/C, where C is the capacitance of the element itself.

A high insulation resistance characteristic, R, exists at the element stage of all piezoelectric sensors. If it did not, the energy developed in the system would dissipate rapidly since a system time constant is formed by the relationship t = RC. These high-impedance signals are very susceptible to any adverse environmental influences (e.g., EMI and triboelectric); electronic devices and circuits have therefore been developed to transform the high-impedance signals into manageable, low-impedance voltages. Hence, the high-impedance voltage generated in the seismic system can be converted into a low-impedance voltage using a simple unity gain operational amplifier. Other techniques incorporate a feedback loop and process the high-impedance charge signal into a low-impedance voltage. This electronic circuit is called a charge amplifier. Either an impedance converter (voltage amplifier) or charge amplifier can be integrated with any piezoelectric system. Each method has application-specific advantages. When a bimorph is integrated into a package with an internal charge amplifier, an extremely lightweight sensor is realized and a very high voltage sensitivity can be achieved.

Referring to Figure 2, it is apparent that if the output from the two halves of the bimorph can be acquired independently, both rotational and linear acceleration can be determined. These separate beams act as independent seismic systems with their centroids a prescribed distance apart. The rectangular beam element is inherently insensitive to transverse acceleration. Incorporating creative assembly and process techniques such as epoxy mounting a single, long, rectangular beam across the fulcrum as shown in Figure 1 and then cutting the assembled beam in half as shown in Figure 3 provides for an extremely well aligned system.

Figure 4. Miniature electronics easily fit into a small, compact package, making the sensor small and lightweight.

Because each independent system is made of the same piezoelectric material, each has exactly the same material-dependent characteristics. Any inherent flaws such as poling alignment or temperature variations tend to be self-canceling. One additional critical design requirement must be met: the sensitivity from each channel must be identical. Even minor variations in the epoxy fillet from side to side can have excessive influence on sensitivity matching. The problem can be solved most easily by an electrical matching technique. The recent miniaturization of hybrid charge amplifiers allows the inclusion of an additional internal charge amplifier into the housing without adding excessive weight to the package. The low-impedance voltage outputs from each of the independent channels are connected to a remote signal conditioner capable of powering the sensor’s internal electronics and processing the independent channel signals. Precision potentiometers can be used to adjust each channel’s sensitivity, with the goal of an exact match to its counterpart. Sum and difference electronic circuits further process the independent channels and provide as output both a linear and rotational acceleration channel.

The result, the Kistler TAP system (see Figure 4), appears somewhat complex but is not significantly different from a typical low-impedance measuring chain. Low-impedance accelerometers require an external power supply typically referred to as a coupler. The TAP’s coupler does a little more work, but makes both linear and rotational data available from a coincident meas urement point on a structure.

Having done all that, it is possible to incorporate a set of “well matched” accel erometers into a structural test where the minimized sensor footprint has negligible influence on the test conditions. Still, the “well-matched” criterion requires further improvement. With the external postprocessing electronic package containing a provision for fine-tuning the independent channel signals, achieving a matched condition would appear straightforward. Accel erometer calibration is typically performed with the test accelerometer connected directly to a back-to-back reference accel erometer and excited by a calibration shaker at the common reference frequency of 100 Hz. This is a dynamic measurement, and all electromagnetic shakers exhibit some rotational motion. Since the centroids of the internal beams are offset from the shaker centerline, an associated error exists that is related to twice the rotation. Adjusting each channel’s sensitivity for an exact match, at a frequency where the shaker exhibits minimal rotational motion, provides reasonable accuracy. An improvement is readily achievable using an iterative test method on a rotational member, as shown in Figure 5.

The oscillating bar is rigid within the meas urement frequency range, and reference accelerometers are used to determine the input acceleration. The central T-shaped supporting member is attached to a rigid base; the heavy bar twists the T, which rotates without any bearing noise or lost motion. The fixture is driven at its resonant frequency so that a significant input level is presented to the unit under test. Rotational sensitivity is measured with the test unit mounted as shown in Figure 5. The unit is then rotated 180º and the sensitivity is again measured. The output should have the same amplitude as the previous measurement, but the phase will be opposite. An ultra precision tuning is performed on the independent channel gain control and the process is repeated until convergence is achieved. This technique provides the best matching possible, from an overall system standpoint, and has proved to provide the accuracy required for reasonable rotational data extraction during EMA studies.

A Robust System for Vehicle Crash Testing

Figure 5. A rigid rotating bar driven into resonance provides a reference signal that is adequate for calibration purposes.

Rotational accelerometers are needed in areas other than structural testing. Auto motive crash studies have identified rotational acceleration as extremely harmful to occupants of a vehicle during a collision or an impact. Unfortunately, the remote electronic system approach incorporated in the modal sensor solution is not well suited for the types of tests common in automotive studies. The postprocessing electronics require a substantial number of components, limiting the technique to the benchtop or laboratory.

A rugged version of the electronics package can be designed specifically for installation into a crash text vehicle with proper consideration of adequate isolation from major impacts. This arrangement is not ideal, though, and other, more robust integral piezoelectric systems are more suitable for this application. Furthermore, a bimorph is not the best piezoelectric material for a crash test sensor. The qualities of quartz, on the other hand, are unsurpassed in this type of environment.

Quartz is an extremely rigid material whose natural piezoelectric characteristics are based on fundamental properties of its molecular structure. These characteristics are absolutely stable. They do not change. Quartz can be cut into various configurations where the characteristics, or piezoelectric coefficients, are dependent on the resulting orientation of the crystalline lattice with respect to the physical geometry. A common orientation, referred to as the shear cut, integrates well into an accelerometer design that is optimized for low transverse sensitivity and negligible base strain effects. These are the same important parameters typical of those of an EMA accelerometer. Compared to a bimorph construction with equivalent package size and weight, however, a relatively low voltage sensitivity is realized. Fortunately, the accelerometers used by the crash study industry require low sensitivities, thereby providing capability to measure the large accelerations common to these events. A candidate for a rotational accelerometer with high acceleration meas uring capabilities is found in a quartz shear mode design. It is possible to create a convenient package rigidly supporting two spatially separated quartz element assemblies (see Figure 6).

The solution to the remaining problem of accommodating the required rugged postprocessing signal conditioning lies in the fundamental design of the transducer itself. Also, a dramatic simplification of the overall sensitivity matching can be realized by appropriate management of the primary charges generated within each half of the seismic system.

The piezoelectric coefficient of quartz is defined as a ratio of the output charge (picocoulombs) resulting from an applied force (newtons). The applied force, F, in the accelerometer is dependent on the seismic mass, m, by the equation F = ma. It is important to note here that the charge, Q, generated by the crystal is a function of a single variable, the seismic system’s mass. All geometric parameters (plate thickness, width, and height) have no influence on the generated charges but do affect the capacitance of the system to a significant degree. A shear quartz based seismic system similar to that in Figure 6, and with each leg of the symmetric system considered as half of the total seismic system, has an electrical equivalent circuit as shown in Figure 7.

The voltage, V, across the parallel capacitor network results from the generated charges created on the surfaces of the crystals and their interaction with the capacitance of each leg of the system. The equation describing the relationship is:

V = Q/C

Figure 6. A symmetric shear quartz package provides a rugged assembly. The center through-hole makes installation convenient and simple.

V = output voltage from the seismic system or potential input to an impedance converter

A review of this equation shows that for the case where q2 = –q1, the resulting voltage is zero. Referring to Figure 6, consider the quartz plates on the right side of the symmetric package to be inverted with respect to the opposite side. The total mass on each side is selected to be exactly equal, so the charges illustrated in Figure 7 are exactly equal and opposite when a linear acceleration is applied to the base. During a rotation, the acceleration experienced by each half will be different and a resulting voltage will exist at the input to the impedance converter. This voltage will be proportional to the rotational acceleration by a constant related to both the separation of the elements and the total capacitance of the input network.

The electrical arrangement of this system is very simple and the controlling factor of charge generation, mass, is easily measured with extreme accuracy. This is a simple, static, weighing measurement whose inherent benefits include a significant increase in the measurable rotational acceleration amplitude range. Because the linear acceleration components are cancelled by the parallel charge connection before entering the range-limiting impedance converter, the angular range of measurement is significantly increased.

The sensitivity of the device is dependent on the total mass and input capacitance of the seismic system. It is measured as described previously using the rigid rotating test fixture. A 180° degree rotation of the unit yields a signal with the same amplitude but inverted phase as compared to the reference.

Overall system simplification is provided by this design. The industry standard two-wire Piezotron signal conditioning approach is used, with its associated cost and convenience advantages. Another variation on the design incorporates the Piezotron coupling electronics with a constant current diode internal to the transducer itself. This yields an extremely rugged assembly well adapted to vehicle crash studies without the need for additional external electronics (see Photo 1). It is powered by a simple 20 VDC supply.

Conclusions

Figure 7. The electrical schematic is fundamentally very simple. Precision components permit negligible variance among the few variables.

Rotational acceleration data are important in many experimental studies. Bimorph and quartz-based piezoelectric sensors, together with the required system configurations, have recently been developed to accurately meas ure this parameter. A configuration using a bimorph is tailored for high sensitivity within a small, lightweight sensor. It is coupled to a remote signal processor to accommodate long-term changes, an inherent characteristic of the bimorph sensing element. This system provides both linear and rotational acceleration signals from a single meas urement site. For more rugged applications such as automotive crash studies, a shear quartz approach is used. The electronics are miniaturized and integral to the transducer itself.

The assembly and calibration techniques discussed here have been optimized to achieve the precision necessary to resolve small differences between slightly separated linear acceleration signals. This low-level signal difference is proportional to rotational acceleration but is susceptible to minute design flaws such as transverse influences or component alignment.

For the bimorph design, a satisfactory component alignment technique assembles a single beam and then slices it into two independent segments. This both ensures alignment and provides part homogeneity between the two beams so they tend to change in a similar fashion. Processing the independent signals externally permits any necessary future adjustments.

The rugged shear quartz design is fabricated by means of a static weighing process that achieves an exact charge output from separate halves of the seismic system. This static process is extremely accurate, and the stability of the natural crystal makes postprocessing of independent signals unnecessary.

The assembly technique permits internal connection of the separate seismic halves, thus forming a single seismic system with a single output that is proportional to rotational acceleration. A charge due to linear acceleration is self-canceling and does not exist at the input to the internal electronics, thus providing a single output related only to the rotational acceleration but with a very large dynamic range.

The method of calibration using a rigid member excited into rotational resonance provides the accuracy required for accurate sensitivity-matching in the time-varying bimorph design. It also provides confirmation of accuracy for the shear quartz approach. These assembly and calibration techniques have evolved over the past few years and have been found to satisfy the accuracy requirements of these demanding sensors.

1. D.J. Ewens. 1984. Modal Testing: Theory and Practice, Research Studies Press Ltd.

2. Li Shumin et al. 1994. “The Development of a Six-Axis Arrayed Transducer,” Proc IMAC 12.