Application of MEMS accelerometers for modal analysis Ronald Kok Cosme Furlong and Ryszard J. Pryputniewicz NEST NanoEngineering Science and Technology CHSLT Center for Holographic Studies and Laser micro-mechatronics Mechanical Engineering Department Worcester Polytechnic Institute Worcester MA 0609 ABSTRACT In this paper feasibility of using MEMS accelerometers for experimental modal analysis is investigated. MEMS accelerometers are small have low dynamic mass require low actuation power and provide high measurement resolution which may provide an optimal alternative to traditional electromechanical transducers. Investigations presented in this paper include analytical computational and experimental characterization of specific MEMS accelerometers. Case studies are performed based on the methodologies developed in this research to investigate the boundaries and limitations of applying MEMS accelerometers for modal analysis. Results show that MEMS accelerometers could potentially be applied for health monitoring. This research is further extended to integrate MEMS accelerometers with telemetry systems for real-time monitoring of structures. Keywords: MEMS accelerometers experimental modal analysis measuring accuracy telemetry computational modeling.. INTRODUCTION Experimental modal analysis consists of subjecting a structure to an excitation function and measuring its response. Conventional devices used for monitoring the response of a structure to an excitation function are based on piezoelectric transducers which are usually heavy and may require large power excitations. As a result their application to modal analysis of meso scale and micro scale structures is limited since they may modify the dynamic characteristics of the structures being measured. The rapid developments of microelectromechanical systems (MEMS) have led to the progressive designs of lightweight low actuation power and high-resolution MEMS accelerometers. Although MEMS accelerometers have been mostly utilized as inertial sensors their applicability to experimental modal analysis has not yet been fully demonstrated. Such applicability depends on their measuring accuracy for a given application and frequency ranges [-3]. Measuring accuracy of MEMS accelerometers is directly related to the dynamic characteristics of the proof mass folded springs and electrostatic comb drives that define the MEMS sensor. Due to material and geometrical uncertainties introduced during the micromachining processes dynamic characteristics of specific MEMS accelerometers may vary from the specifications provided by the manufacturer. To verify measuring accuracy computational and experimental analyses are performed to validate the frequency responses of the MEMS accelerometer utilized in this study. Such analyses provide information on the applicable frequency ranges at which MEMS accelerometer can be reliably applied. In addition damping characteristics can also be determined. To transfer signals from MEMS accelerometers to signal analyzers traditional wiring methods are utilized. Such methods provide reliable data transfer and are simple to integrate. However in order to perform modal analysis of complex structures multiple accelerometers attached to different locations on the structure may be required. In this case wiring and integration of multiple MEMS accelerometers might become complicated and the weight of the additional components may modify the dynamic characteristics of the structures being measured. Therefore a wireless telemetry system is under development [4].. MEMS ACCELEROMETERS MEMS inertial sensors comprising acceleration and angular rate sensors (i.e. microaccelerometers and microgyroscopes respectively) are used in a wide range of consumer industrial and automotive applications [-3]. A schematic of a MEMS accelerometer is shown in Fig.. The central part of the MEMS accelerometer is a micromechanical proof mass attached to a reference frame by spring elements. When an external acceleration is applied the proof mass moves with respect to the moving frame of reference as shown with an arrow. Motion of the proof mass is proportional to the applied acceleration.
Capacitive electrodes defined by the proof mass and fixed finger-electrodes subjected to a static potential difference Vst are used for detection of motion of the proof mass. Spring elements x Proof mass Mechanical anchors Fixed electrodes Fig.. Schematic of a MEMS accelerometer sensitive to motions acting along the x-axis. Vst.. MEMS accelerometers utilized In this paper dual-axes MEMS accelerometers are utilized. They contain on a single monolithic integrated circuit (IC) a polycrystalline silicon surface micromachined proof mass as well as signal conditioning circuitry to implement an acceleration measurement. These MEMS accelerometers are capable of measuring not only positive and negative accelerations to at least ± g but also static acceleration forces such as gravity allowing them to be used as tilt sensor [-35]. Table summarizes pertinent characteristics of the MEMS accelerometers studied herein and Figs and 3 depict electronic packages of the MEMS accelerometers used. Figure shows the 5.0 4.5.78 mm 3 leadless package of the device and electronic board set to the [0-5000] Hz bandwidth configuration. Figure 3 shows the inside configuration of the package. The proof mass has dimensions of 600.0 600.0 3.0 µm 3 [5-7]. Table. Pertinent characteristics of the MEMS accelerometers utilized. Measuring Resonance Operating Operating Temperature Sensitivity Weight range frequency voltage temperature drift ± g 0 khz 3 mv/g 3.0 to 5.5 V 60 mgr -40 to 85 C ± 0.5 % Proof mass 4 sets folded springs (dual axes) 4 sets electrostatic combs (capacitive electrodes) Substrate Fig.. Two different packages of the MEMS accelerometers utilized. Fig. 3. Inside configuration of a MEMS accelerometer package. 3. ANALYTICAL CONSIDERATIONS Referring to Fig. the relative displacement Z of the proof mass m with respect to the reference frame can be written as [589] Z = X Y () where X and Y are displacements of the proof mass and the reference frame respectively. If sinusoidal motion of the reference frame of the form Y = β sin(ω t) is assumed the governing equation of motion is expressed as mz && + cz & + kz = mω β sin( ωt). ()
In Eq. c is the damping coefficient between the proof mass and the surrounding medium and k is the spring constant of the spring elements while β and ω are the amplitude and frequency of motion of the reference frame respectively. Solution of Eq. indicates that the steady-state component of motion is where and ( ω φ ) Z = H sin t (3) H = ω ωn ω β ωn ω + ζ ωn ω ζ ωn φ = tan (5) ω ω n in which ω n is the natural frequency and ζ = c / mω n is the damping ratio. Analysis of Eq. 4 indicates that the quantity ω Γ = ω ω + ζ n ω n approaches unity when ω / 0 so that β ω n ω n H = ω (7) indicating that Z as defined in Eq. 3 is proportional to the acceleration ω β of the reference frame. Therefore Equations 3 to 7 indicate that by measuring the motion of the proof mass it is possible to measure accelerations applied to the reference frame [58]. Equation 7 is only valid when ω / ω n 0. However according to Eqs 3 and 4 measured accelerations include the effects of the function shown in Eq. 6. Therefore indicating the existence of measuring errors. Figure 4 shows /Γ as a function of frequency ratio for various damping ratios. According to Fig. 4 the effects of errors can be minimized by: (a) utilizing an accelerometer with a high natural frequency (b) limiting the measuring range to a fraction of the natural frequency of the accelerometer and (c) controlling the damping ratio. Due to their large stiffness to mass ratios MEMS accelerometers are characterized by high natural frequencies therefore providing high measuring accuracy in wide frequency ranges while providing minimum distortions in the measurements. Such characteristics make MEMS accelerometers an optimal alternative to traditional piezoelectric transducers. (4) (6) /Γ Frequency ratio (ω / ω n ) Fig. 4. Measuring error /Γ as a function of frequency ratio for specific damping ratios.
4. COMPUTATIONAL CONSIDERATIONS As shown in Section 3 the high natural frequency of a MEMS accelerometer allows high measuring accuracy in wide frequency ranges. Therefore accurate characterization of natural frequencies of a MEMS accelerometer helps determining their operational frequency range. Finite element method (FEM) is applied to investigate the modal characteristics of the MEMS accelerometers utilized in this study. An axisymmetric model of the proof mass constrained according to the MEMS configuration shown in Fig. 3 was created. Figure 5 shows the computation model of the proof mass and corresponding boundary conditions [50]. Polycrystalline silicon with material properties characterized by the modulus of elasticity E of 60 GPa and mass density ρ of.33 gr/cm 3 are utilized. Thickness of the proof mass is 3 µm according to manufacturer s specifications [67]. Solving an eigenvalue problem corresponding to undamped and free-vibrations conditions allows determination of modal characteristics of the proof mass. Figure 6 displays FEM predicted mode shape at the fundamental natural frequency of 8.48 khz. Table summarizes the FEM results for the first five modes of vibration and the corresponding frequencies. Experimental verifications of the FEM results are described in Section 5. Symmetry constrains Table. FEM determined modes of vibrations of the proof mass: E is 60GPa ρ is.33 gr/cm 3 and thickness is 3µm. Mode number Frequency khz Modes of vibration 8.48 st bending 77.0 In-plane (x-axis) 3 77.4 In-plane (y-axis) 4 86.0 nd bending 5 90.68 Torsion Fig. 5. FEM model of the proof mass and corresponding boundary conditions. Fully constrained Fig. 6. Fundamental mode of vibration of the proof mass predicted at 8.48 khz. 5. EXPERIMENTAL CONSIDERATIONS Experimental investigations are performed to study the dynamic characteristics of the MEMS accelerometers utilized including determination of their frequency responses and damping ratios. Experiments consist of exciting MEMS accelerometers with a piezoelectric shaker and measuring their output frequency responses with a dynamic signal analyzer. Laser vibrometer measurements are also performed for verification purposes. Circuitry for signal conditioning of the output responses of the MEMS accelerometers is described. 5. Experimental setup Figure 7 depicts major components of the experimental setup utilized for performing characterization of the frequency responses and damping ratios of MEMS accelerometers of interest. In the configuration shown in Fig. 7 a dynamic signal analyzer (SA) is utilized for generating excitation signals to drive a piezoelectric shaker (PZT) through PZT amplifier (AMP). SA is also utilized for analyzing the output signals generated by the MEMS accelerometer under test (MEMS) and the laser vibrometer (VM) which consists of optical head (OH) fiber optic interferometer (FI) and vibrometer controller (VC). MEMS accelerometer is mounted to a reference mirror (MR) which in turn is mounted to PZT. MR is used as a reference surface to the OH. MEMS accelerometer is driven by a variable power source (PS).
VC VM OH FI Displacement PS MR MEMS AMP SA PZT Source Fig. 7. Experimental setup utilized for performing characterization of the frequency responses and damping ratios of MEMS accelerometers of interest. 5... Laser vibrometer Laser vibrometer is a noninvasive and noncontact optoelectronic system for measuring dynamic characteristics of objects. The laser vibrometer system utilized in this study is based on a Mach-Zehnder interferometer. This system allows measurement of displacements much smaller than the wavelength of light by exploiting the sinusoidal relationship between the output of an interferometer and the difference in optical path length traveled by its beams. By allowing the motion of the surface of interest in this case the reference mirror MR to modulate the path length traveled by a laser beam the interferometer can be used to detect vibrational signals with subnanometer measuring resolution []. Quantitative determination of motions using laser vibrometer is achieved by extracting the time dependent optical phase difference θ (t) introduced by the MR from the detected intensity I(t) given as [3] I( t) = I o{ + cos[π f + θ ( t)]} (8) B where I o is the magnitude of the detected intensity and f B is a known frequency shift introduced by a Bragg cell modulator mounted in one of the beams of the interferometer. The extracted time dependent optical phase difference θ (t) is described by π θ ( t) = L( t) (9) λ where L(t) is the distance traveled by the MR related to its velocity v and to the induced Doppler frequency shift f D by ( t) = π L( t) = π θ v t = π f D t. (0) λ λ Equations 9 and 0 indicate that displacements and velocities of an object as a function of time can be obtained with laser vibrometer measurements. 5... Low-pass filter circuit The MEMS accelerometer utilized in this study requires decoupling of its output signal from the implicit signal noise generated by the power supply. Figure 8 shows the block diagram of the low-pass filter circuit utilized for decoupling and reduction of high-frequency noise in the analog and digital output signals of the MEMS accelerometer [67]. Decoupling is accomplished by placing a 0. µf capacitor between the power source and the COM terminal and a MΩ resistor is required for setting the duty cycle of the digital output modulated signal. In addition a 0.00 µf capacitor is utilized to provide a limiting frequency bandwidth of 5 khz. SA MEMS Fig. 8. Block diagram of the low-pass filter circuit.
5.. Experimental results Simple harmonic random noise and sweep sinusoidal functions were utilized in the experiments. Different frequency spans were considered to investigate the measuring range and applicability of the MEMS accelerometers utilized. A 4.5 Vdc signal was applied to drive the MEMS accelerometers in all of the experiments. 5... Determination of frequency responses Experiments were conducted to verify the functionality of the MEMS accelerometers and to observe their sensitivity to input excitations. Initial experiments consisted of exciting MEMS accelerometers with simple harmonic motions using forcing functions characterized by amplitude of 5 mv corresponding to displacement amplitude of 0.80 nm and frequencies ranging from khz to khz using 0.5 khz intervals. MEMS accelerometers were excited along their principal axes. Power spectra from both MEMS accelerometers and laser vibrometer were recorded and compared to observe their similarities and deviations. Figure 0 shows representative power spectra obtained with a MEMS accelerometer and laser vibrometer corresponding to a forcing function characterized by khz and 3. mg (g = 9.8 m/s ). Results indicate excellent agreement between the two measurement methodologies. Offset observed in Fig. 0 is due to different electronic gains implicit in the instrumentation utilized. Real structures are not usually subjected to single frequency excitations but rather to excitation functions containing a wide spectrum of frequencies and amplitudes. In order to verify the frequency response of MEMS accelerometers to a generic loading situation experiments were performed by exciting MEMS accelerometers with random noise containing all frequencies included within specific frequency spans. Figure shows representative power spectra obtained with a MEMS accelerometer and laser vibrometer and corresponding to a random noise forcing function containing frequencies in the [0.8] khz range and accelerations in the [0 0.35] g (g = 9.8 m/s ) range. Results once again indicate excellent agreement between the two measurement methodologies. Offset observed in Fig. is due to different electronic gains implicit in the instrumentation utilized. Power spectra shown in Fig. indicate main harmonics occurring at 8.6 8.93 and 0.4 khz. It is suspected that one of these frequencies corresponds to the fundamental natural frequency of the proof mass of the MEMS accelerometer as determined by the FEM predictions described in Section 4. Future work will concentrate on identifying fundamental natural frequency of the proof mass of the MEMS accelerometer. LogMag (Vrms^).0E-0.0E-03.0E-04.0E-05.0E-06.0E-07.0E-08.0E-09.0E-0 Comparsion of power spectra measured by MEMS accelerometer and laser vibrometer (PZT excited by simple harmonic motion of khz).0e+00 0.0E-0 500 000 500 000 500 3000 Power spectrum measured by MEMS Power spectrum measured by laser vibrometer Frequency (Hz) Fig. 0. Power spectra measured with MEMS accelerometer and laser vibrometer corresponding to a simple harmonic motion of khz at 3. mg. LogMag (Vrms^).0E-05.0E-06.0E-07.0E-08.0E-09.0E-0 Comparsion of power spectra measured by MEMS accelerometer and laser vibrometer (PZT excited by random noise with frequency span of 0 -.8 khz).0e+00 0.0E-0 000 4000 6000 8000 0000 000 Power spectrum measured.0e-0 by MEMS.0E-03 Power spectrum measured by vibrometer.0e-04 Frequency (Hz) Fig.. Power spectra measured with MEMS accelerometer and laser vibrometer corresponding to random excitation containing frequencies in the [0.8] khz range and accelerations in the [0 0.35] g. 5... Determination of damping ratio Results obtained in Section 5.. facilitate determination of damping ratios corresponding to the MEMS accelerometers. Damping ratios can be determined by calculating the Q factor given as [8] ωr Q = = () ω ω ζ where ω and ω define the half-peak power bandwidths (also referred to as side bands) that are measured as the two frequencies on either side of reference frequency ω r at -3dB. The Q factor is used for characterizing sharpness of
resonance. According to Fig. 0 ω r is measured as 06 Hz therefore ω and ω are calculated as 45.3 Hz and 606.67 Hz respectively. Consequently the Q factor is.7 which corresponds to a damping ratio ζ of 0.93. Referring to Fig. 4 using the value of ζ equal to 0.93 it can be observed that the MEMS accelerometer utilized in this study has a 5% maximum measurement error at approximately 5% of its natural frequency. With the natural frequency computationally predicted at 8.48 khz this MEMS accelerometer is capable to provide measurements of up to. khz with a maximum error of 5%. 6. TELEMETRY SYSTEM Feasibility of implementing a wireless data acquisition system for the remote measurement of the dynamic characteristics of structures is being investigated [4]. Commercially available RF components are utilized in the system. The major criteria for selecting RF components include small size light weight fast data transfer rates and low actuation power. To verify reliable transmission of data the preliminary telemetry system being developed utilizes a single transmitter (Tx) and a single receiver (Rx). Characteristics of the transmitter and receiver components utilized in preliminary investigations are shown in Tables 3 and Table 4 respectively while Figs and 3 show the preliminary experimental setup and the corresponding block diagram of the telemetry system [44]. Figure 4 shows comparisons between power spectra corresponding to signals sent and received with the telemetry system. These spectra correspond to a transmitted single frequency signal characterized by khz and amplitude of V. Result shown in Fig. 4 indicates good correlation between the transmitted and received signals because small frequency distortions are observed. Such preliminary results demonstrate reliability of the telemetry system. Table 3. Major characteristics of the transmitter subsystem Driving Operating Transmitting Data rates voltage frequencies range.5 to 3 V 400 bps 48 MHz 300 ft Table 4. Major characteristics of the receiver subsystem Driving voltage Data Rates Operating frequencies Receiving range 4.5 to 5.5 V 000 bps 48 MHz 50 ft Tx MEMS (a) Fig.. Experimental setup of the telemetry system. Comparsion of power spectra measured between the input and output signal of the telemetry system Rx SA Vrms^ 5 4 3 Power spectrum of input signals (to transmitter) Power spectrum of output signals (from receiver) (b) 0 0 500 000 500 000 500 3000 Frequency (Hz) Fig. 3. Block diagram of the telemetry system being developed: (a) transmitter and (b) receiver. Fig. 4. Comparison between power spectra corresponding to signals sent and received with the telemetry system.
7. CONCLUSIONS AND FUTURE WORK This study presents an investigation of the feasibility of utilizing MEMS accelerometers for experimental modal analysis. It is shown that measuring accuracy is proportional to the magnitude of the fundamental natural frequency that characterizes a specific accelerometer. Due to their large stiffness to mass ratios MEMS accelerometers are characterized by high natural frequencies therefore providing high measuring accuracy in wide frequency ranges while providing minimum distortions in the measurements. Analytical computational and experimental solution (ACES) methodology was utilized to validate the results obtained. It was determined that MEMS accelerometers utilized in this study are characterized by a Q factor of.7 and a damping ratio of 0.93. With the natural frequency computationally predicted at 8.48 khz the MEMS accelerometers used in this study are capable to provide measurements of up to. khz with a maximum error of 5%. Investigations will continue on the determination of the fundamental natural frequency of the proof mass of the MEMS accelerometers including determination of their transfer and coherence functions. Future work will also include application of multiple MEMS accelerometers to monitor dynamic responses of real structures using telemetry systems. 8. ACKNOWLEDGEMENTS The authors gratefully acknowledge support by the NanoEngineering Science and Technology (NEST) Program at the Worcester Polytechnic Institute Center for Holographic Studies and Laser micro-mechatronics Mechanical Engineering Department. 9. REFERENCES [] Kovacs G. T. A Micromachined transducers sourcebook McGraw-Hill New York 998. [] Hsu T-R. MEMS & microsystems: design and manufacture McGraw-Hill New York 00. [3] Pryputniewicz R. J. and Furlong C. MEMS and nanotechnology Worcester Polytechnic Institute Worcester MA 00. [4] Kok R. Application of MEMS accelerometers to modal analysis of structures MS Thesis Worcester Polytechnic Institute Worcester MA in preparation. [5] Furlong C. and Pryputniewicz R. J. Characterization of shape and deformation of MEMS by quantitative optoelectronic metrology techniques Proc. SPIE 4778:-0 00. [6] Application Note ADXL0 / ADXL0 - low cost ± g / ±0 g dual axis imems accelerometers with digital output Analog Devices Inc. Norwood MA 00. [7] Analog Devices Inc. http://www.analog.com Norwood MA March 003. [8] Thomson W. T. and Dahleh M. D. Theory of vibration with applications 5th ed. Prentice Hall Upper Saddle River New Jersey 998. [9] Rao S. S. Mechanical vibrations 3rd ed. Addison-Wesley New York 995. [0] Pro/Engineer User s guide v. 00 Parametric Technology Corporation Waltham MA 00. [] Furlong C. and Pryputniewicz R. J. New opto-mechanical approach to quantitative characterization of fatigue behavior of dynamically loaded structures SPIE 544:45-56 995. [] Polytec PI Vibrometer operator s manual for OSF-3000/OFV-50 Auburn MA 994. [3] Furlong C. Hybrid experimental and computational approach for the efficient study and optimization of mechanical and electro-mechanical components Ph.D. Dissertation Worcester Polytechnic Institute Worcester MA 999. [4] ABACOM Technologies Inc. http://www.abacom-tech.com Etobicoke ON Canada 003.