Speaker Transducer Design and Manufacturing

This project’s aim is to design a low frequency loudspeaker transducer and it’s manufacturing methods. This project is being used as a senior project as well as a component in the Cal Poly AES System Design Project. This is a work in progress and will be updated as the project progresses.

 

Transducer Basics

A transducer is a device that converts one form of energy into another. In the case of a loudspeaker transducer an electrical waveform is converted into a pressure wave, transforming electrical energy into acoustic energy. The frequency that the transducer outputs varies harmonically as the electrical input signal varies harmonically. The sound level of acoustic output, commonly measured in decibels (dB), varies with the amplitude of the electrical input signal.

While there are exotic loudspeaker transducers that operate differently (e.g. electrostatic, plasma, magnetostatic, moving magnet), the most common type used in loudspeakers is the moving coil electro-dynamical transducer (see figure below).

 
Figure 1: Section view of a moving coil electrodynamical transducer (Klippel, "Linear Lumped Parameter Measurement").

Figure 1: Section view of a moving coil electrodynamical transducer (Klippel, "Linear Lumped Parameter Measurement").

 


The motor (voice coil, voice coil former, pole plate, backplate, magnet) is the component that does the actual transduction. It generates a Lorentz force Fcoil = Bli, where B is magnetic flux density (often measured in Tesla), l is the length of wire (measured in meters) immersed in the magnetic flux, and i is the electrical current (measured in amperes) running through the wire. In addition, as the coil moves at velocity v, a back electro-motive force (EMF = Blv) is generated.

 
Figure 2: A diagram of electrodynamical transduction (Klippel, "Linear Lumped Parameter Measurement").

Figure 2: A diagram of electrodynamical transduction (Klippel, "Linear Lumped Parameter Measurement").

 

The mechanical structure of the transducer (cone/dust cap, surround, spider) can be modeled as a damped mass-spring system (see Figure 7 below). The lumped mass of all moving parts (cone/dust cap, voice coil/voice coil former, partial masses of the spider and surround) is designated the moving mass, Mms. As the system moves with acceleration a, the mass has inertial force Fm. When the system is displaced from its resting position, the force Fk results in proportion to displacement x as the suspension components (spider and surround) deform. The magnitude of this restorative force can be characterized by the spring constant Kms. Mechanical resistance of the system, Rms, damps the system with force Fr in proportion to the velocity of the system, v.

 
Figure 3: Damped mass-spring diagram of an electrodynamical transducer (Klippel, "Linear Lumped Parameter Measurement").

Figure 3: Damped mass-spring diagram of an electrodynamical transducer (Klippel, "Linear Lumped Parameter Measurement").

 

This method of modeling a transducer as a mechanical can be represented with the electro-mechanical circuit diagram in Figure 8 below. The electrical components are represented on the left side (ZL(f) being the electrical impedance from the voice coil’s inductance as a function of frequency f) and the mechanical components are represented on the right side. The transduction of electrical signal to mechanical output is represented as a transformer with Bl as the coupling constant.

 
Figure 4: The electromechanical system of a transducer as an equivalent circuit (Klippel, "Linear Lumped Parameter Measurement").

Figure 4: The electromechanical system of a transducer as an equivalent circuit (Klippel, "Linear Lumped Parameter Measurement").

 

Thiele-Small Parameters

Thiele-Small parameters are a set of electromechanical parameters commonly used in the loudspeaker industry to characterize the low frequency performance of a loudspeaker transducer. These parameters can be used to simulate the frequency and impedance response of a transducer, making them a useful tool for designing loudspeaker enclosures for PA and HiFi systems. These parameters assume that the transducer operates in completely linear “pistonlike” motion, at small signal levels well within the mechanical operating limits of the transducer.

 
Thiele Small Parameters.JPG
 

Large Signal Parameters and Power Compression

Large signal parameters are used for simulating the output of a transducer at higher output levels when the transducer is close to or at its mechanical and electrical limits. These parameters can be hard to characterize due non-linearities from design or from increased thermal conditions, generally known as power compression.

 
Larger signal parameters.JPG
 

Power compression in its most basic form is the reduction of acoustic output at higher electrical inputs. This non-linearity can be due to multiple factors, sometimes compounding on each other.

On the mechanical side, the culprits are the spider and surround. These components, while characterized by a constant parameter, do not perform as constant parameters over the entire range of excursion. As the system gets further from x = 0 in displacement, the spring constant k increases, reducing how far the cone moves in relation to the magnetic force. This compresses the amplitude of the output as the displacement of the cone increases. In addition to the spring constant being nonlinear, it can also be unsymmetrical about x = 0. This can unevenly distort the signal, reducing amplitude more on one side of a waveform’s cycle. An example is plotted in the figure below.

 
Figure 5: An example of a non-linear, unsymmetrical spring constant in a transducer’s suspension (Glazer, "An Engineering Student's Guide to Loudspeaker Design").

Figure 5: An example of a non-linear, unsymmetrical spring constant in a transducer’s suspension (Glazer, "An Engineering Student's Guide to Loudspeaker Design").

 

On the magnetic side, power compression can occur when the magnetic Bl force factor isn’t constant over the transducer’s operating displacement. The Bl force factor can be plotted as a function of displacement x to determine if the transducer provides constant Bl force factor. In addition to not being constant, the Bl(x) curve can also be unsymmetrical. Unsymmetrical BL(x) curves can usually be corrected by re-positioning the voice coil’s at-rest position in the magnetic flux gap.

 
Figure 6: Example of an unsymmetrical Bl(x) force factor curve. The dashed curve represents the mirrored characteristic to display the asymmetry of the non-linearity (Glazer, "An Engineering Student's Guide to Loudspeaker Design").

Figure 6: Example of an unsymmetrical Bl(x) force factor curve. The dashed curve represents the mirrored characteristic to display the asymmetry of the non-linearity (Glazer, "An Engineering Student's Guide to Loudspeaker Design").

 

On the thermal side, power compression can occur when the motor of a speaker begins to heat up. As the aluminum or copper electrical winding on the voice coil begin to heat up, the electrical resistance increases, putting a higher load on the amplifier that inputs the electrical signal into the transducer, which results in a lower acoustic output. This effect can be mitigated by properly venting the voice coil to allow for heat to dissipate.

An example of a subwoofer (a very low frequency speaker) measured for power compression is shown below (Figure 7). The Figure 7 shows frequency responses taken at different gain levels (usually 3dB increments). The increments are then plotted in reference to the first curve to highlight where the power compression occurs, in this case around 20 Hz where linear excursion is at a maximum (Figure 8).

 
Figure 7: Example power compression measurement (Sanfilipo, “Efficiency, Power Compression & Max SPL”).

Figure 7: Example power compression measurement (Sanfilipo, “Efficiency, Power Compression & Max SPL”).

 
 
 
Figure 8: Example power compression curve, normalized to the reference curve (Sanfilipo, “Efficiency, Power Compression & Max SPL”).

Figure 8: Example power compression curve, normalized to the reference curve (Sanfilipo, “Efficiency, Power Compression & Max SPL”).

 

Transducer Design

Our solution uses a blend of components designed and manufactured in-house and components sourced from a third party. The cone, motor, spider, and basket are custom designed, the surround and voice coil are sourced from an online supplier. All models were created in Solidworks.

Cone

The cone is six inches in diameter, made from 6061-T6 aluminum. Aluminum was chosen due to its high strength to weight ratio, its availability, and its machine-ability. A nonuniform, randomly generated lattice on the back surface of the cone was created with nTopology’s Element software. Its function is to increase stiffness and provide a structure that doesn’t readily resonate at a frequency within the operating bandwidth of the transducer. This should reduce the harsh breakup characteristics commonly associated with metal cones and minimize distortion due to standing waves over the surface of the cone.

 
Figure 9: Generated random surface lattice on the back of the cone.

Figure 9: Generated random surface lattice on the back of the cone.

 

The manufacturing method determined for the cone is to machine it out of billet aluminum. The complex geometry of the surface lattice requires a manufacturing method that can produce detailed features. This design can be milled in two operations, using a soft jaw fixture to securely hold the part during the second operation. While this process is normally too time intensive for higher volume production transducers, time is less of an issue for the low volumes of this project.

Motor

The motor is an XBL (eXtreme BL Linearity) type design, chosen for its ability to minimize harmonic distortion at high cone excursions. The voice coil is two inches in diameter, utilizing a Kapton former for high heat resistance. The magnetic structure uses a carbon steel top plate and pole piece to secure the radial array of N52 grade neodymium magnets. The open magnetic structure exposes the voice coil, which allows the air between the cone and the pole piece to be forced out over the voice coil into free air. Typical non-vented ring magnet designs can suffer from power compression as the voice coil cannot cool freely. The forced cooling of the voice coil in this open-air design reduces long term power compression effects due to thermal effects.

 
Figure 10: Cutaway view of motor assembly in Solidworks.

Figure 10: Cutaway view of motor assembly in Solidworks.

 

The XBL motor design reduces harmonic distortion by providing a more consistent BL force (force generated from a current in a length of wire [L] and a magnetic flux [B]) over the transducer’s range of excursion. The split in the magnetic gap creates two high intensity fields of magnetic flux and the voice coil is located with equal portions in each magnetic field when at rest. When the coil moves, constant flux is integrated resulting in a constant BL force. Since the force remains constant when at excursion, the transducer tracks closer to the input waveform, resulting in less distortion of the original waveform. Note that the XBL motor was developed by Dan Wiggins and is a patented design. The three figures below are not simulations run on our motor, but are sourced from Wiggins’ “XBL: A Primer” to demonstrate the benefit of the XBL design.

 
Figure 11: Example of FEA simulation run on XBL motor (Wiggins. "XBL: A Primer")

Figure 11: Example of FEA simulation run on XBL motor (Wiggins. "XBL: A Primer")

 
 
Figure 12: The BL plot from the example simulation above (Wiggins. "XBL: A Primer")

Figure 12: The BL plot from the example simulation above (Wiggins. "XBL: A Primer")

 
 
Figure 13: The Total Harmonic Distortion (THD) plot from the example simulation above (Wiggins. "XBL: A Primer").

Figure 13: The Total Harmonic Distortion (THD) plot from the example simulation above (Wiggins. "XBL: A Primer").

 

Spider

The spider utilizes an arachnid design, creating a spring force from the deflection of the S-curved “legs” running from the inner ring to the outer ring. This geometric solution offers a linear and symmetrical spring constant over the transducers operating excursion range. The exact material used is still being determined, but the material assumed for simulation purposes is polycarbonate. Other possible materials include polypropylene, a TPX/PP mix, or a fiber composite sheet.

 
Figure 14: Solidworks model of the arachnid spider geometry.

Figure 14: Solidworks model of the arachnid spider geometry.

 

FEA simulations were run in Solidworks to determine how far the central ring would displace for a certain force. After running many of these simulations, results were used to calculate the compliance (N/mm) over an operating excursion range of the transducer, then visualized with the graph below. As you can see, the arachnid design is more symmetrical and linear than a conventional cup spider.

 
Figure 15: FEA simulation of spider  displacement for a specified force in solidworks.

Figure 15: FEA simulation of spider displacement for a specified force in solidworks.

 
 
Figure 16: Stiffness (N/mm) plotted over excursion from resting position (a basic cup spider is plotted in orange; arachnid design is plotted in blue).

Figure 16: Stiffness (N/mm) plotted over excursion from resting position (a basic cup spider is plotted in orange; arachnid design is plotted in blue).

 

This geometrical design is also easily manufacturable with the equipment available at Cal Poly. A prototype can be cut out of sheet material on a water jet cutter or laser cutter. Should the final material choice be an injection-mold-able polymer, a mold can be CNC milled and used to easily produce parts in a short amount of time. Either of these manufacturing methods should be able to produce spiders with more constancy between lots than the typical textile cup spiders.

 

Basket

The basket is currently a pretty typical design, providing rigid mounting for the motor, spider, and surround. The current design calls for the entire part to be milled out of a single billet of aluminum, which is beneficially rigid and requires no further assembly. However, since billet is very expensive, the basket will be redesigned to be made in pieces, then assembled and adhered with epoxy and fasteners. While requiring more assembly, the overall cost of the basket should be reduced.

 
Figure 17: A Solidworks model of the basket

Figure 17: A Solidworks model of the basket

 

Current Status of the Project

The project is currently under some design changes regarding the cone lattice and basket design. Detailed manufacturing methods are being developed for each unique part and will be ready for making parts by the end of March 2019. Stay tuned for more updates!

Sources

  • Klippel, W., & Schlechter, J. (2010). Fast Measurement of Motor Suspension

    Nonlinearities in Loudspeaker Manufacturing. Journal of the Audio Engineering Society,

    58(3), 115-125.

  • Klippel, W., & Schlechter, J. (2011). Dynamic Measurement of Transducer Effective

    Radiation Area. Journal of the Audio Engineering Society, 59(1/2), 44-52.

  • Wiggins, Dan. “XBL: A Primer.” Acoustic Development International, 2008,

    www.acousticdev.com/Files/XBLPrimer.pdf.

  • Klippel, Dr. Wolfgang. “Linear Lumped Parameter Measurement.” Klippel GmbH, 2013,

    www.klippel.de/training/attachments/training1/Training_1_Linear_Lumped_Parameter

    _Measurement_en.pdf.

  • Glazer, Mark. “An Engineering Students Guide for Loudspeaker Design.” Cal Poly Audio

    Engineering Guest Speakers. An Engineering Students Guide for Loudspeaker Design, 20

    Apr. 2018, San Luis Obispo, Fisher Science.

  • “Thiele/Small Parameters.” Wikipedia, Wikimedia Foundation, 27 Oct. 2018,

    en.wikipedia.org/wiki/Thiele/Small_parameters.

  • Sanfilipo, Mark. “Efficiency, Power Compression & Max SPL.” Audioholics Home Theater,

    HDTV, Receivers, Speakers, Blu-Ray Reviews and News, Audioholics Home Theater,

    HDTV, Receivers, Speakers, Blu-Ray Reviews and News, 6 Mar. 2008,

    www.audioholics.com/loudspeaker-design/subwoofer-measurement-part-1/efficiency.