Design and characterization of an enclosed coaxial carbon nanotube speaker

Thermoacoustics describes the interaction between rapid temperature oscillations and acoustic pressure waves. Due to alternating current (ac) Joule heating of a thin conductor (diameter in nanometers), its surface temperature undergoes rapid oscillations. These oscillations result in the generation of pressure waves, i.e., sound in the fluid medium surrounding the conductor. The speakers that operate on this principle are known as thermophones. Braun discovered the first thermophone in 1898.¹ In 1917, Arnold and Crandall first demonstrated this effect using a thin platinum film of 700 nm thickness.² However, the surface temperature of the platinum film had a maximum oscillation rate of 16 Hz, which is below the audible frequency range of 20 Hz–20 kHz. This constraint was eliminated by the discovery of aligned carbon nanotube (CNT) thin films.

CNT films are extremely lightweight, stretchable, flexible, transparent, and can easily adhere to substrates and CNT speakers can be manufactured in any desired shape and size.^3,4 The simplest form of a CNT speaker is fabricated by stretching the CNT film between two parallel linear electrodes, known as a planar speaker. Xiao et al. studied various designs of CNT speakers (planar, cylindrical) and performed tests to study the output sound pressure level (SPL) of planar speakers for different designs along with their light transmittance.⁵ Several studies characterized the performance of planar CNT speakers under various operating conditions, multiple stack arrangements of speakers, different mediums surrounding the speaker, and efficiency.^6–16 Arnold and Crandall,² in their study, also discovered that thermophones are non-linear, squaring the input signal upon its output, thus doubling the frequency of output sound. Bouman et al. studied different drive signals for the speaker with an aim to minimize this nonlinearity and compared their efficiencies and total harmonic distortion.¹⁷ One method used was to amplitude modulate the input signal with a high frequency carrier signal (>20 kHz). Another method was to add a fixed direct current (dc) offset to the input signal. Asgarisabet et al. performed COMSOL simulations for the planar and spherical CNT speakers to understand the temperature distribution on the surface of the CNT film along with near-field acoustic holography measurements.^18,19

Passive noise control systems, in the form of mufflers, dominate the market for automotive exhaust noise reduction.^20–28 Mufflers have resonant chambers that reflect the exhaust sound back onto itself or absorptive materials which absorb the sound energy resulting in attenuation.^29–32 For low frequencies with large wavelengths, the required size of the muffler increases drastically. Passive systems also cannot adapt to any changes in the exhaust noise spectrum due to fixed dimensions. Soot and dust particles clog the absorptive material used in the muffler, causing negative performance changes over time. Finally, mufflers add backpressure to the engine, reducing fuel economy of the vehicle.

Active control systems work on the principle of constructive and destructive interference,³³ using a moving coil loudspeaker.^34–36 The speaker generates a signal that is used for cancellation of the exhaust noise. These active systems provide much needed flexibility of frequency and amplitude in real time. However, loudspeakers have a working temperature limit, up to 40 °C, much lower than the exhaust gas temperature range of 160 °C–250 °C. This makes it essential for the loudspeakers to be isolated from the high temperature region of the exhaust with the help of a side branch.^34–36 The side branch and the loudspeaker add weight to the tailpipe and affect the space considerations in the exhaust system. This shortcoming defines the need for a speaker that is small in size, lightweight, and can be mounted in-line with the axis of the tailpipe to reduce backpressure.³⁷ 

CNT speakers, due to their distinct characteristics, are suitable to overcome the shortcomings of both passive and active noise control systems. The CNT speakers can be designed to keep their overall size small, independent of the frequency of the sound that needs to be controlled. In addition, a CNT speaker will act as a point source due to its small size compared to the wavelength of exhaust noise, radiating sound equally in all directions. Second, CNT speakers can operate at high temperatures compared to normal loudspeakers, eliminating the need for separating the speakers from the exhaust tailpipe. Third, CNT speakers are extremely lightweight; the material itself weighs only 160 mg/m² of thin film. With these factors in mind, an enclosed coaxial CNT speaker was designed and manufactured.

For the enclosed coaxial CNT speaker, a simple spool type design was selected. It consisted of two end plates in which the electrodes were anchored. A concentric electrode arrangement allowed for more CNT film areas with small speaker dimensions [Fig. 1(B)]. For the designed prototype, two rings, each containing six electrodes, were used with continuous CNT film wrap in each ring. Alternate electrodes in each ring were wired to the positive and negative [Fig. 1(C)] electrical terminals. The end plates were manufactured at the Michigan Technological University workshop out of an insulating material, PEEK plastic, to electrically isolate the electrodes. The coaxial design of the speaker allows mounting in-line with the longitudinal axis of the tailpipe. This speaker is designed to be used in tandem with the passive muffler, ideally positioned after it [Fig. 1(A)].

The two end plates were mounted on a tailpipe and extended through the length of the speaker. This pipe was slotted, where the open area of the slots was matched to that of the CNT film between two electrodes to allow sound to travel into the pipe. CNT films are weak in the transverse direction, meaning fluid flow in this direction would risk tearing the film, causing failure of the speaker. To protect the CNT film from the exhaust gases, a thin protective film (Kapton–thickness 1 mm) was wrapped around the slots of the internal pipe. Insertion loss testing was performed on the Kapton film for one-third octave band frequencies (sine wave input) from 20 Hz to 20 kHz. Insertion loss was less 14.9 dB over the entire frequency range (Fig. 2). In the target frequency range of 20–500 Hz, insertion loss of the Kapton film was less than 12 dB, and much lower in the 100–200 Hz region. A metal cover protected the CNT film from damage due to atmosphere and reflected the generated sound back into the exhaust pipe.

Two parameters to consider for the design of a CNT speaker are resistance and power density. A single square layer of a multi-walled CNT film has a resistance of 750 Ω/square and each additional square layer is connected to all the other layers in parallel.⁴ As a standard for good frequency response from the CNT speaker, five layers are used to wrap the speaker,⁵ with an estimated resistance of 150 Ω/square. For the coaxial speaker, the CNT films in each ring are connected in parallel. CNT surface temperature increases with input power, resulting in a lower speaker resistance. The resistance of the speaker was selected to have output impedance at least 2 Ω at operating temperature to prevent amplifier overload.

Power density of a CNT speaker is the ratio of the input electrical power to the total surface area of the CNT film. When the medium surrounding the speaker is air and 5 layers of CNT film are used in the thermophone, the maximum power density has been empirically determined to be about 20 kW/m² prior to catastrophic failure of the speaker.⁵ The power density of the coaxial CNT speaker was designed so that it was below 10 kW/m², representing a safety factor of 2, for maximum input power of 500 W.

Because it is desired for the speaker to act like a plane wave point source in the pipe, the length of the CNT speaker is crucial for effective noise cancellation. The target was to keep the source length to less than 1/6th of target sound wavelength. The concentric ring design helps to reduce the speaker length compared to the wavelength of sound. The final prototype had two concentric electrode rings of 64 and 78 mm diameter. The diameter of the electrodes was 3.175 mm with six electrodes in each ring. The CNT wrap length was 123 mm. The speaker had resistance of 2.4 Ω and power density of 8.4 kW/m² for an input power of 500 W. The electrodes were made of copper and the end plates were made of PEEK high-temperature plastic. The outer cover of diameter 85 mm was made of aluminum and it enclosed the end plates to provide protection to the CNT film.

CNT speaker impedance was measured using a white noise input in the frequency range of 0 Hz–20 kHz. An arbitrary function generator (Sony AFG 310) was used to provide white noise input to the speaker through a Crown XTi 2002 amplifier and National Instruments compact RIO (cRIO), that measured the input voltage and the current through the speaker. The voltage and current values were stored for 45 input power levels from 0.3 to 120 W.

The SPL of the coaxial speaker was measured at the center of the pipe, axially, and at the outlets of the speaker. To measure the pressure at the center of speaker, a probe microphone (PCB 345E21) was used [Fig. 3(A)]. The speaker was driven with a multiple frequency sine wave at varying input electrical power.

True power efficiency was measured as the ratio of the acoustic output power to the corresponding input electrical power using a multi-tone signal input. Because of the non-linearity in the CNT speaker, the input sine wave was amplitude modulated using a custom LabVIEW code. Two 45.7 cm (18 in.) long, 5.1 cm (2 in.) diameter tailpipes were connected to the two ends of the coaxial speaker. The output from the speaker was measured at the two ends of the tailpipe using 1/4 in. array microphones [Fig. 3(B)]. The sound intensity at both pipe ends was computed from the measured pressure, then multiplied by the cross-sectional area of the pipe to obtain net acoustic power.

A frequency response function was calculated between the voltage and the current, using the current as the reference, to obtain the impedance of the CNT speaker. The result shows that the CNT speaker behaves as a pure resistor up to a frequency of 20 kHz (Fig. 4). Identical resistance behavior is seen for all values of input power. The behavior of the CNT speaker as a pure resistor in the desired frequency range is highly beneficial. A similar result for planar CNT speakers was obtained by Bouman et al.¹⁷ 

One of the main objectives of the coaxial speaker was to achieve SPLs above 100 dB (re 20 μPa) in the low frequency range (0–500 Hz) inside the pipe. The results indicate that the speaker is capable of producing up to 120 dB (re 20 μPa) of sound with an input power of 105 W at specific frequencies [Fig. 5(A)].

The efficiency measurement results are shown in Fig. 5(B). For reference, standard moving coil loudspeakers have power efficiency on the order of 1%. The efficiency of the speaker is highly frequency dependent and it is proven that the efficiency of open thermophones increases monotonically with frequency.^6,9 The measured results show that the efficiency of the coaxial thermophone is not monotonically increasing and it can be attributed to the acoustic modes in the cylindrical semi-closed design of the coaxial speaker.

An enclosed coaxial CNT speaker was designed for an automotive exhaust system, with a focus on exhaust noise cancellation. The components of the speaker were copper electrodes, two end plates made of insulating material, a slotted pipe, a diaphragm to isolate the CNT film from the exhaust gases, and a cover. The speaker dimensions and CNT film length were selected based on the resistance and power density calculations while ensuring that the entire speaker acted as a point source. Using the prototype, resistance, in-pipe axial SPL, and efficiency measurements were performed using sinusoidal input signals. The coaxial CNT speaker showed a pure resistive behavior up to 20 kHz frequency. For an input power of 105 W, axial SPL reached 120 dB at 250 Hz. The power efficiency of the speaker is lower than a conventional moving coil loudspeaker. Frequency dependent peaks observed in the power efficiency may be attributed to acoustic modes in the housing of the coaxial speaker, but further work is recommended in this area.

The results obtained provide proof-of-concept of the coaxial CNT speaker. It is time-consuming to redesign and manufacture such a speaker for multiple vehicle platforms without having a validated model which would enable performance predictability. The next step is to model the speaker [two-dimensional and three-dimensional (3D)] and perform simulations that can be experimentally validated. The results obtained from the tests in this study will be used to validate a model in the future. A coaxial speaker could be optimized for a specific vehicle exhaust system using this validated model. This optimized design would provide estimates of size, weight, power, and cost of the speaker for a specific platform, which are crucial for automotive manufacturers and suppliers.

The authors would like to acknowledge the Michigan Economic Development Corporation for partially funding this work under the Michigan Translational Research and Commercialization grant. In addition, the authors would like to acknowledge the contributions of Siddharth Parmar and Martin Toth for their work in manufacturing the prototype.