Variable curvature diaphragm balanced mode radiator

Abstract

An audio device and a method for designing and manufacturing a diaphragm, the audio device comprising a diaphragm and a transducer, the diaphragm having a curved profile adapted to radiate audio signals from a plurality of flexural modes and piston modes, one or more of the plurality of flexural modes having a consistent nodal line position, the diaphragm having a front side and a rear side, the transducer being coupled to the rear side of the diaphragm, the transducer being adapted to drive the diaphragm to radiate audio signals with reduced audio distortion, wherein each of the plurality of flexural modes has a minimum position across the entire diaphragm, and wherein the transducer is mounted at one of the minimum positions of the plurality of flexural modes, and one or more impedance components are mounted at at least one of the remaining minimum positions to inertially balance the diaphragm based on a predetermined relative average modal velocity limit.

Description

[0001] Cross-reference to related applications

[0002] This application claims priority to U.S. Provisional Application 63 / 029,857, filed May 26, 2020, which is incorporated herein by reference in its entirety. Technical Field

[0003] This disclosure generally relates to the field of audio systems, and particularly, but not exclusively, to a curved diaphragm balanced mode radiator for reproducing signals over an audio frequency range and a method of manufacturing the radiator. Summary of the Invention

[0004] Balanced modal radiators (BMRs) are acoustic loudspeaker transducers designed and capable of providing wide-directional, full-range sound across multiple frequency ranges in a single diaphragm audio device. These ranges include bass, treble, and midrange frequencies, and sometimes ultrasonic frequencies. These devices are commonly referred to as BMRs and are typically created using a flat disc as the diaphragm element to radiate acoustic energy from vibrations generated by the electromechanical components of the transducer. These BMR transducers include multiple interoperable components, typically including one or more magnets, pole pieces, steel spacers (in some, but not all, embodiments), a backplate, a frontplate, a coil frame, a voice coil wound around a portion of the coil frame, a roll surround suspension element, and optional secondary suspension elements made of corrugated fabric, one or more flexible armatures, or additional roll surrounds. The coil frame is coupled to the diaphragm and extends from the diaphragm into an air gap defined between the outer diameter of the pole pieces and the inner diameter of the frontplate. The portion of the coil frame on which the voice coil is wound is placed in an air gap near the magnet and pole pieces, such that the voice coil is positioned within a radially oriented static magnetic field that extends between the pole pieces and the front plate. In effect, the static magnetic field in the air gap interacts with a time-varying alternating current signal flowing within the voice coil used to transmit audio signals. This interaction between the static magnetic field and the alternating current signal generates an electrodynamic force, which, according to Lorentz's law, acts perpendicular to the direction of the flowing current and the direction of the static magnetic field, driving the movement of a diaphragm connected to the coil frame based on the time-varying audio signal flowing through the voice coil. This driven movement of the diaphragm causes the BMR to radiate acoustic energy (e.g., audio sound waves).

[0005] A more significant difference between BMR and conventional driver units (often referred to as "audio transducers") involves the intended vibrational behavior of the diaphragm. In conventional driver units, the diaphragm is largely expected to vibrate as a rigid structure to avoid structural standing waves, often referred to as "bending modes," which are considered undesirable due to their largely uncontrolled nature. In contrast, the diaphragm in a BMR driver unit is expected to vibrate both as a rigid structure and by intentionally employing multiple bending modes within the desired signal band, where the outputs from two vibrational schemes complement each other. The frequencies of these bending modes can vary depending on the size of the speaker diaphragm, the material used to construct the diaphragm, and the mechanical impedance of any components connected to the diaphragm. In a BMR, the acoustic energy radiated from these vibrating bending modes is summed in a complex manner with the energy radiated by the piston-like motion of the diaphragm. However, in a BMR, the acoustic energy from the vibrating bending modes contributes little or no to the net axial radiation. Each bending mode is characterized by the number of nodal lines (concentric circles for a circular diaphragm) across the diaphragm in that particular mode. The nodal line is defined as a region of the diaphragm that is not subjected to translational motion from the modal excitation at a given modal frequency (i.e., in a direction perpendicular to the plane of the diaphragm), even though piston motion still occurs at that nodal line. While complementary, an alternative definition of the nodal line is that it is the minimum point in the mechanical admittance function of the diaphragm when drawn from the center to the edge at a given modal frequency (referred to as the "eigenfrequency"). An examination of the mechanical admittance function for a given bending mode reveals that the Nth order bending mode is characterized by having N nodal lines across the diaphragm (N minimums in the mechanical admittance function).

[0006] In mechanical systems such as loudspeaker diaphragms, mechanical admittance is the reciprocal of mechanical impedance, and it quantifies how easily a force can be converted into velocity when applied to the system. The mechanical admittance function is defined based on axisymmetric geometry, specifying the value of the mechanical admittance at every location on the diaphragm from its center to its edge. The mechanical admittance function for non-axisymmetric diaphragm geometries is defined relative to their respective geometries. Analyzing the mechanical admittance at the diaphragm's eigenfrequency is beneficial because mechanical resonance is accompanied by high mechanical admittance. Furthermore, the total mechanical admittance at each individual eigenfrequency includes the combination of its eigenmode shape, all low-frequency bending mode shapes, and the mechanical admittance of the piston mode. Subtracting the piston mode admittance from the total mechanical admittance yields the modal mechanical admittance. Modal mechanical admittance includes only the bending mode shape. In fact, the physical manifestation of the eigenmode shape is a shape function. The shape function represents the form of displacement, velocity, or acceleration of the eigenmode at that eigenfrequency. Typically, the modal mechanical admittance function at the highest eigenfrequency in the bandwidth used should be analyzed, which is usually the third or fourth bending mode. The shape function of lower-order bending modes is weakened because their eigenfrequency differs increasingly from the observed eigenfrequency. For example, the mechanical admittance of the piston mode halves with each additional octave. Other eigenmodes have varying rates of decrease in mechanical admittance above and below their respective eigenfrequency.

[0007] Finite element analysis is typically used to determine the mechanical admittance functions of all bending modes occurring within the target bandwidth of the device. These in-band mechanical admittance functions of the bending modes are combined in a weighted sum manner to determine the location of the minimum modal mechanical admittance of the most utilized bending mode, which is typically dominated by the highest bending mode considered in the sum. These locations of the minimum modal mechanical admittance define specified locations where the voice coil frame and corresponding inertial balancing mechanical impedance elements can be mounted to the diaphragm. The mechanical impedance elements are components that include mechanical properties such as mass, stiffness, and damping. Inertial balancing is a process in which these mechanical impedance elements are attached to the diaphragm at specified locations to compensate for the necessary additional force input components, including the voice coil assembly. In inertial balancing devices such as BMR, the radiation from all bending modal vibrations is summed in a manner that produces zero or near-zero net on-axis acoustic radiation.

[0008] Generally, any of the minimum values ​​of the modal mechanical admittance function can be used to attach the voice coil frame, and the remaining positions are used to attach mechanical impedance elements for inertial balancing. Typically, the outermost (i.e., largest diameter) position is where the roller surround suspension element is attached. In all electrically driven units, this roller surround element is practically necessary, providing a secondary suspension plane for the movement of the moving parts and creating an air seal to prevent (i.e., eliminate) pressure equalization around the edges of the diaphragm. Therefore, by using the roller surround as the outermost balancing impedance element, the number of components required to attach to the diaphragm can be minimized. This is desirable from a cost and ease of assembly perspective.

[0009] If the drive position coincides with a region of the diaphragm exhibiting relatively high modal velocities, thereby generating an electromotive force opposite to the drive force through the motor structure, resulting in a reduction in acoustic output at the frequency corresponding to that bending mode, some form of distortion may occur. Positioning the voice coil carrier attachment to the diaphragm at the nodal line of the bending mode significantly reduces modal excitation and thus reduces or eliminates the associated modal velocity at the drive position. To create a BMR drive unit with the lowest possible distortion, there exists an optimal position where the voice coil carrier element should be attached to the diaphragm. This position is specific to one implementation where the bending modes up to the fourth bending mode are inertially balanced. In this configuration (commonly referred to as "four-mode balance"), the minimum of the third modal mechanical admittance among the four total minimums (approaching the third nodal line of the fourth bending mode counted radially outward from the center of the diaphragm) is used as the position of the voice coil carrier. The optimal location is due to the close intersection of the minimum mechanical admittance function of the first bending mode, which appears at 68% of the diaphragm diameter, and the third minimum (the third nodal line of the fourth bending mode), of the modal mechanical admittance function of the fourth bending mode, which appears at 69% of the diameter of the flat circular diaphragm.

[0010] While this configuration is known to reduce or eliminate distortion associated with high-speed motion in the first bending mode of a BMR, it presents significant commercial disadvantages and growing concerns because the required voice coil carrier must have a diameter that is 69% of the diameter of a flat, circular diaphragm. This requirement for a voice coil carrier with this relative diameter limits the radial space available for the secondary suspension assembly and often precludes the use of ceramic magnet types due to their large volume required beyond the coil diameter. This requirement for a voice coil carrier of this size inevitably results in a large, heavy motor assembly in which magnets and metalwork account for a significant portion of the cost and weight of the drive unit. Therefore, there is a significant and growing need for improved BMR designs that can deliver low-distortion output while utilizing the voice coil, and thus reduce the cost of associated magnets and metalwork. Attached Figure Description

[0011] Non-limiting and non-exhaustive embodiments are described with reference to the following figures, wherein, unless otherwise stated, the same reference numerals refer to the same parts in the various views.

[0012] Figure 1 This is an axisymmetric cross-sectional view of the curved diaphragm balanced mode radiator in the embodiment.

[0013] Figure 2 This is an axisymmetric diagram of the electromechanical transducer used to drive the diaphragm of the balanced mode radiator in the embodiment.

[0014] Figure 3A This is a flowchart illustrating a method for selecting parameters of the curved diaphragm of the balanced mode radiator in an embodiment.

[0015] Figure 3B This is a diagram showing the nodal line positions of the relative edge height and diaphragm thickness of the balanced mode radiator in the embodiment.

[0016] Figure 3C This is a graph showing the variation of the eigenfrequency ratio of the balanced mode radiator in the embodiment with respect to the relative edge height.

[0017] Figure 3D This is a graph showing the variation of the eigenfrequency ratio of the balanced mode radiator in the embodiment with respect to the relative edge height.

[0018] Figure 3E This is a graph showing the variation of the eigenfrequency ratio of the balanced mode radiator in the embodiment with respect to the relative edge height.

[0019] Figure 3F This is a graph showing the variation of the eigenfrequency ratio of the balanced mode radiator in the embodiment with respect to the relative edge height.

[0020] Figure 3G This is a flowchart illustrating the balancing method of the curved diaphragm of the balanced modal radiator in the embodiment.

[0021] Figure 4A This is a graph showing the mechanical admittance and shape function of the first bending mode of the bending diaphragm balanced mode radiator in the embodiment.

[0022] Figure 4B This is a graph showing the mechanical admittance and shape function of the second bending mode of the bending diaphragm balanced mode radiator in the embodiment.

[0023] Figure 4C This is a graph showing the mechanical admittance and shape function of the third bending mode of the bending diaphragm balanced mode radiator in the embodiment.

[0024] Figure 4DThis is a graph showing a comparison between the modal mechanical admittance and the modal shape function of the first mode of the curved diaphragm balanced modal radiator in the embodiment.

[0025] Figure 4E This is a graph comparing the modal mechanical admittance and modal shape function of the second mode of the curved diaphragm balanced modal radiator in the embodiment.

[0026] Figure 5A This is a graph illustrating the simulated volumetric velocity of the unbalanced bending diaphragm of the balanced mode radiator in the embodiment.

[0027] Figure 5B This is a graph showing the relative average modal velocity of the unbalanced curved diaphragm of the balanced modal radiator in the embodiment.

[0028] Figure 5C This is a graph illustrating the simulated volumetric velocity of the balanced bending diaphragm of the balanced mode radiator in the embodiment.

[0029] Figure 5D This is a graph showing the relative average modal velocity of the balanced bending diaphragm of the balanced modal radiator in the embodiment.

[0030] Figure 6A This is a diagram illustrating the on-axis acoustic response of an unbalanced bending mode caused by excessive mass placed within the first section of the balanced modal radiator in an embodiment.

[0031] Figure 6B This is a diagram illustrating the on-axis acoustic response of an unbalanced bending mode caused by excessive mass placed on the periphery of the first section of the balanced modal radiator in an embodiment.

[0032] Figure 7A This is a plan view of the free, flat, circular diaphragm of the balanced mode radiator in the embodiment.

[0033] Figure 7B This is a plan view of the freely bending circular diaphragm of the balanced mode radiator in the embodiment.

[0034] Figure 8A This is a graph showing the curvature function of the diaphragm profile of the balanced mode radiator in the embodiment.

[0035] Figure 8B This is a diagram showing the axisymmetric diaphragm profile of the balanced mode radiator in the embodiment.

[0036] Figure 8C This is a diagram showing the position of the nodal lines on the diaphragm of the balanced mode radiator in the embodiment.

[0037] Figure 8DThis is a graph comparing the relative average modal velocity and diaphragm curvature rate of the balanced modal radiator in the embodiment.

[0038] Figure 9 This is a graph showing the on-axis sound pressure level of an embodiment of an inertial balanced bending diaphragm compared to an embodiment of an inertial unbalanced bending diaphragm. Detailed Implementation

[0039] In the following description, various aspects of embodiments of the radiation diaphragm of the balanced mode radiator will be described, and specific configurations will be illustrated. Numerous and specific details are given to provide an understanding of these embodiments. The aspects disclosed herein can be practiced without one or more specific details, or practiced using other methods, components, systems, services, etc. In other instances, structures or operations have not been shown or described in detail to avoid obscuring the relevant inventive aspects.

[0040] Throughout this specification, the phrase "in one embodiment" or "in an embodiment" means that a particular feature, structure, or characteristic described in connection with that embodiment is included in at least one embodiment. Therefore, the phrases "in one embodiment" or "in an embodiment" appearing in various places throughout this specification do not necessarily refer to the same embodiment. Furthermore, in one or more embodiments, a particular feature, structure, or characteristic may be combined in any suitable manner.

[0041] Figure 1 This is an axisymmetric cross-sectional view of an embodiment of a balanced modal radiator (“BMR”) with a curved diaphragm adapted to radiate acoustic signals in the audio and ultrasonic frequency ranges. The BMR 100 includes a diaphragm 104, a plurality of impedance components 106a, 106b, a roller-wrap suspension element 108 mechanically grounded to a frame 109, and a coupler 102 (typically a voice coil frame, but sometimes may include additional components) for transferring energy from an electromechanical transducer to the rear side of the diaphragm 104. The curved shape of the diaphragm 104 of the BMR allows for the generation of a desired curved mode of the diaphragm 104 that transmits signals in the Z direction perpendicular to the diaphragm surface at its center. In an alternative non-circular embodiment of the BMR, the Z direction can be identified as the direction in which the diaphragm 104 moves during piston-like operation when a voltage is applied to the voice coil. In curved diaphragm BMR design, the curved shape of the diaphragm is manipulated in both analog and physical ways to produce an acoustic output signal with desired performance in terms of radiation bandwidth, signal frequency, directivity, sound pressure level, low distortion, and output signal acoustic power response.

[0042] Figure 2This is an axisymmetric view of the operating components of the electromechanical transducer 200 in the embodiment. In the illustrated embodiment, the transducer 200 includes a voice coil frame 204 coupled at its upper portion to the rear side of a diaphragm (not shown), a wire (referred to as voice coil 218) wound around the lower portion of the voice coil frame 204, and a corrugated suspension element 206 (referred to as a "spider frame"). The spider element 206 is connected at one end (its inner diameter) to a position on the upper part of the voice coil frame 204 and at the opposite end (its outer diameter) to a fixed frame 219 of the BMR. The spider element 206 and the roller-wrap suspension element 108 work together to provide a restoring force to the moving assembly to keep the voice coil 218 positioned in the gap. If the radial width of the spider element 206 is small, the restoring force will rise too quickly when the moving assembly moves away from the rest position, which will result in harmonic distortion. In this case, the moving assembly is an assembly that includes a diaphragm, a roller surround (other than the outside of the fixed frame to the BMR), a voice coil 218 and a voice coil frame 204 assembly, any impedance components, and a spider frame (other than the outside of the fixed frame to the BMR), plus any adhesives for bonding these parts and lead wires of connectors extending from the voice coil to the frame of the BMR.

[0043] Voice coil 218 carries an electrical signal representing a given desired audio input. As the electrical signal is conducted through voice coil 218, an electromotive force (EMF) is generated by the electromagnetic interaction between the static magnetic field and the electrical signal flowing through voice coil 218. This EMF is a driving force acting on voice coil 218 and coupled to the rear side of the diaphragm via voice coil holder 204 (on which voice coil 218 is wound), which in turn generates a piston-like acceleration (i.e., a piston mode) and excites one or more bending modes (not shown) of the diaphragm. When applied to the diaphragm using the voice coil, this driving force generates radiated audio signals from the excited bending and piston modes, and these radiated signals include the audio signal and measurable audio signal distortion, referred to as the measurable distortion component. Each excited bending mode is located at the center of the frequency, but the lowest resonant bending frequency is the vibration frequency of the first bending mode, referred to as the first lowest frequency bending mode. The second bending mode has a different resonant frequency and is typically the second lowest frequency among the various vibration frequencies of the bending modes. This frequency is also known as the second lowest frequency, and it is lower than the other subsequent bending modes, but still higher than the resonant bending frequency of the first bending mode (i.e., the first lowest frequency). In practice, the voice coil 218 is mounted on the back side of the diaphragm at a position corresponding to the nodal line location of the first lowest frequency. When a driving force is applied, bending modes of the audio signal radiate from the surface of the diaphragm, wherein nodal line locations do not have bending mode radiation, and each bending mode has one or more specific nodal line locations. It is advantageous to drive the BMR transducer using a voice coil 218 mounted at a position corresponding to the nodal line location of the first lowest frequency because the driving force applied at this location will tend to have a lower distortion component in the first lowest frequency bending mode, and therefore a lower overall distortion level in the radiated audio signal.

[0044] In one embodiment, when mounted on a voice coil frame 204, the voice coil 218 is situated within a gap defined between a plurality of components forming a magnetic circuit, including pole pieces 208, a backplate 210, and a front plate 212 adjacent to the magnet 214. In alternative embodiments, the relative positions of these components may vary, even if the functional operation of the transducer 200 remains similar. In the described embodiment, the magnet 214 is a ceramic ferrite magnet, while in alternative embodiments, the magnet may be a rare-earth magnet or an electromagnet. Regardless of the specific magnet used, a steady-state magnetic field is inserted into the voice coil 218 wound on the voice coil frame 204. The interaction between the magnetic field in the gap and the current flowing through the voice coil 218 generates an electrodynamic force that causes the voice coil frame 204 to drive the diaphragm 202, which in turn generates a piston-like motion and a diaphragm bending mode that induces a signal radiated from the outer surface of the diaphragm 202 at a desired acoustic and / or ultrasonic frequency. Structurally, the voice coil frame 204 is a cylindrical element, and when placed within the gap, the voice coil 218 is mounted or wound on this cylindrical element.

[0045] The pole piece 208 is a centralized structure within the electromechanical transducer 200 and provides a structure defining a first side of an air gap in which the voice coil 218 is placed. In a common arrangement, the opposite sides of the gap are defined by the front plate 212 and the magnet 214. In an embodiment, the back plate 210 completes the magnetic circuit and provides the base of the gap on which the pole piece 208 and the magnet 214 are placed. In the illustrated embodiment, the magnetic circuit is formed by the arrangement of the magnet 214, the pole piece 208, the air gap, the front plate 212, the back plate 210, and the voice coil 218, which is located within the air gap such that it intersects orthogonally with the magnetic field present in the air gap.

[0046] Figure 3AThis is a flowchart illustrating an embodiment of the process for manufacturing a curved diaphragm BMR. As shown in flowchart 300, the design and generation of a curved diaphragm BMR requires receiving multiple input parameters, as shown in step 302, which define the general shape of the candidate curved diaphragm. The input parameters are used to define the diaphragm geometry within a curvature function with initial conditions. One input parameter used to establish the curvature function is a distance, and more specifically, a distance (i.e., arc length) from the center of the diaphragm along the diaphragm surface. Other parameters used to establish the curvature function must have some non-zero values ​​to avoid forming a flat diaphragm geometry. Other initial parameters relate to the initial conditions of the diaphragm profile, such as the slope near the diaphragm center when the radius is close to zero (which is set to zero for smooth and continuous surfaces on axisymmetric diaphragms), the Y-intercept of the diaphragm curvature profile set, and an initial set of estimates for these values. Once generated, as shown in step 304, a curvature function is used to generate the shape of the diaphragm, and as shown in step 306, the generated diaphragm shape is simulated and its output characteristics are analyzed to determine the general distribution of eigenfrequency (the diaphragm's natural resonant frequency) and eigenmode (the diaphragm's vibrational behavior at the resonant frequency). As used in the context of this embodiment of the described methods, apparatus, and systems, the eigenmode of the diaphragm is one of a bending mode or a piston mode, all of which are vibrational modes of the diaphragm. In this context, each of these bending modes consists of an active region having amplitude, phase, and oscillation frequency. The spatial pattern generated by the oscillations from the bending modes also has certain zero-translation nodal lines or regions, which are essentially locations where there is almost no diaphragm movement. Based on the output analysis performed in step 306, as shown in step 308, a comparison is made between the generated output nodal line distribution and the desired output nodal line distribution. The output pattern from the candidate diaphragm is compared with the desired nodal line location to evaluate the output acoustic performance. The comparison of the output intrinsic frequency patterns requires not only a comparison of the signal output patterns but also a systematic comparison of the target nodal line position and the generated output nodal line position of the output pattern (as shown in step 308). During the comparative analysis, as shown in step 310, a relative error value between the desired nodal line position and the nodal line position of the candidate diaphragm is calculated, and as shown in step 312, a comparison is made between the calculated error and a predetermined tolerance. In one embodiment, the tolerance is established by measuring the width of the adhesive region formed by the bonding between the voice coil frame and the diaphragm. However, in alternative embodiments, particularly those involving manipulation of multiple bending modes, a cost function will be needed to determine the optimal curvature. When comparing the relative error value with the tolerance, the determined relative error value is further evaluated to check if it is equal to or less than the tolerance. As shown in step 314, if the error is equal to or less than the tolerance, the relative error value is considered acceptable. Then, as shown in step 316, parameters defining the diaphragm profile are compiled to generate the diaphragm profile.Alternatively, if the relative error value exceeds the tolerance, as shown in step 314, a new set of candidate parameter values ​​is generated and inserted into the iterative process shown in the flowchart until the relative error value falls within the tolerance.

[0047] More generally, a normalization method can be used to determine the desired degree of curvature in the reference embodiment, thereby determining alternative embodiments of the diaphragm. This reference embodiment can be used to determine a curvature function that shifts the nodal line of a first bending mode inward by a certain amount to achieve an inertial balance configuration, wherein the voice coil velocity in the first mode is equal to or less than the voice coil velocity in the second mode. When using this method to determine such alternative embodiments, the following conditions and limitations should be used. These conditions and limitations used to determine the degree of curvature are representative, and do not preclude the use of alternative or additional conditions and limitations as may be known to those skilled in the art.

[0048] • The plan view of the diaphragm is circular.

[0049] Isotropic materials are used in membranes.

[0050] • The thickness of the diaphragm is constant.

[0051] • The magnitude of curvature increases with the increase of radius.

[0052] • The curvature at the center of the diaphragm is zero.

[0053] Although this reference embodiment was created using a linear curvature function, other functions will provide similar results provided the conditions described above are met. Higher-order curvature functions and constant curvature functions do not deflect the nodal line position as significantly as linear curvature functions. Constant curvature functions are the least effective when deflecting the nodal line of the first bending mode in the functions being tested, as they require a slightly higher edge height to achieve a similar nodal line position for the first bending mode. The reference embodiment is described in dimensionless terms to provide a general description of the movement of the position of the diaphragm's first nodal line. This is achieved by dividing or "scaling" each relevant distance by the diaphragm radius. The relative diaphragm thickness (T) is a control parameter and includes the diaphragm thickness as a percentage of the radius. Another control parameter is the relative edge height (H) at the diaphragm periphery, measured as a minimum point on the same surface, and scaled as a percentage of the diaphragm radius. This parameter can be obtained using any number of curvature profiles that follow the stated constraints.

[0054] Figure 3BThe plot shows the nodal line position of the first intrinsic mode as a function of the relative edge height and diaphragm thickness of the linear curvature diaphragm profile. Linear functions are used in this plot because they provide the most accurate comparison, and nodal line manipulation is performed in 5% increments in the data given below. The table below provides a quick approximation of the relative edge height (H). The values ​​shown in the table provide the relative edge height (H) of the diaphragm for a given nodal line position and relative diaphragm thickness (T).

[0055]

[0056] As the relative diaphragm edge height increases, the intrinsic frequencies also increase, which tends to have a larger and more pronounced effect on thinner diaphragms (i.e., diaphragms with a relative thickness of 2% or less). For a given diaphragm geometry, dividing each intrinsic frequency by the intrinsic frequency of the first mode of a disk with the same thickness reveals a normalization tendency that can be used to further manipulate modal behavior. Significant performance advantages can be achieved by controlling the diaphragm's intrinsic frequencies in this way. In particular, the grouping of modes can be increased within a certain bandwidth to provide additional acoustic radiation, or a lighter diaphragm can be used, since the first mode frequency is significantly higher for diaphragms with low relative thickness. The combination of relative diaphragm thickness, curvature profile, and diaphragm material controls the diaphragm's intrinsic frequencies. In some embodiments, the diaphragm is made of a single sheet material, such as aluminum with a thickness ranging from 0.15 mm to 0.3 mm and paper with a thickness ranging from 0.2 mm to 0.5 mm. Other alternatives to material composites include composites with typical thicknesses ranging from 1 mm to 5 mm (e.g., skin, cell core, outer sheath) or foamed materials with thicknesses ranging from 0.5 mm to 5 mm (e.g., Rohacell). Often, a more important design consideration is the stiffness-to-weight ratio and the ability to fabricate films with low thicknesses (i.e., thin materials), as the effects of curvature are more pronounced with thinner materials. Figure 3C , 3D Figures 3E and 3F show the effect on the ratio of eigenfrequencys as a function of the relative diaphragm edge height (defined as the ratio of a given eigenfrequency in a flat diaphragm to the eigenfrequency of the first flexural mode) to further illustrate the effect of the method. Figure 3C The variation of the intrinsic frequencies of the first four bending modes as a function of the relative edge height (H) is shown for a diaphragm with a relative diaphragm thickness of 0.5% and a linearly varying diaphragm curvature profile. Figure 3D The variation of the intrinsic frequencies of the first four bending modes as a function of the relative edge height is shown for a diaphragm with a diaphragm curvature profile that has a relative diaphragm thickness of 1% and a linear variation. Figure 3E The first four bending modal eigenfrequency values ​​as a function of relative edge height are shown for a diaphragm with a 2% relative diaphragm thickness and a linearly varying diaphragm curvature profile. Figure 3F The first four bending modal eigenfrequency values ​​as a function of relative edge height are shown for a diaphragm with a 4% relative diaphragm thickness and a linearly varying diaphragm curvature profile.

[0057] Figure 3G This is a flowchart illustrating an embodiment of the process for inertial equilibrium bending of a diaphragm to form a BMR. As shown in step 322, method 320 begins by receiving shape parameters that define the geometry of the diaphragm to be simulated and created, generated from the process used to manufacture diaphragm 300. Once the shape parameters have been received, as shown in step 324, an eigenfrequency output analysis is performed, which simulates the reproduction of the eigenmodes of the diaphragm. For N eigenfrequencys up to the highest eigenfrequency within the target bandwidth of the diaphragm, a simulation representation of the bending behavior of the output eigenmodes is performed. Typically, these are the eigenfrequency of the third or fourth bending mode. Once the simulated output frequency analysis has been performed as shown in step 324, as shown in step 326, the mechanical admittance functions of the highest bending mode and all lower frequency bending modes are generated.

[0058] As shown in step 328, the identification of intrinsic mode shapes is a means of determining, simulating, and analyzing the mechanical admittance function of bending modes. The mechanical admittance function of a given bending mode quantifies how readily a vibrational force from an external source (such as a voice coil assembly) can be transmitted to the bending velocity of the diaphragm in that given mode, within a range of locations on the diaphragm. The minimum value of the given mechanical admittance function is the nodal line of the given mode. These regions are areas where, if an input force is applied, the energy transfer to the bending behavior of the diaphragm is inefficient for each corresponding mode when the diaphragm is driven in these regions. The peaks of the mechanical admittance function identify antinodes, or locations where energy can be readily converted into the bending behavior of the diaphragm and where the applied force results in a high bending velocity. For each bending mode, the center and edges of the diaphragm are antinodes. For each bending mode, the mechanical admittance function is generated.

[0059] In designing the optimal bending diaphragm, the working assumption is the existence of N applicable bending modes within the desired bandwidth of the shape geometry. Once a set of mechanical admittance functions containing distinct functions of each of the N bending modes is generated, these functions are combined in a weighted sum to generate the modal mechanical admittance function. The minimum locations calculated from the modal mechanical admittance function, as shown in step 330 and step 328, are used together to determine the physical locations for mounting the voice coil assembly and one or more mechanical impedance components to balance the generated geometry of the BMR diaphragm. Distortion associated with the first mode is reduced by placing the voice coil assembly at the modal mechanical admittance minimum closest to the nodal line of the first mode. The locations of one or more balancing impedance components are set at the other N-1 minimum locations, where such locations are determined based on an Nth-order analysis of the mechanical admittance function for each bending mode of the diaphragm geometry. In summary, the Nth-order mechanical admittance functions of the bending modes form the modal mechanical admittance function. The addition of a mechanical impedance component results in bringing the bending behavior into an inertial equilibrium state, where the Z-direction component of the total surface velocity tends towards the value of the piston mode. Furthermore, for a flat diaphragm, inertial equilibrium of the behavior of the highest frequency mode also corrects for the lower modes. Under this condition, the diaphragm is inertially balanced over a frequency range covered by N selected modes. A similar approach can be used for a curved diaphragm (BMR), but the lower modes intentionally behave differently from those of a flat plate. An improved method must be used to inertially balance the lower modes. To inertially balance a curved diaphragm in a BMR, the modal mechanical admittance and relative average modal velocity must be determined for the curved plate.

[0060] The determination of the inertial equilibrium of a diaphragm depends on its modal mechanical admittance function. Typically, when modeling a flat diaphragm, the mechanical admittance function for any single mode is analytically derived. However, for non-flat structures, analytical solutions are more difficult to determine and may be impossible to derive. A practical method for determining the modal mechanical admittance function is to identify the highest eigenfrequency used. This highest eigenfrequency can be used for frequency domain simulations, where a ring force is applied in increasing radii, starting from the center of the axisymmetric diaphragm and ending at the edges. The average velocity amplitude should then be calculated for each drive radius and assigned to that location. The total mechanical admittance is obtained by dividing this average velocity amplitude by the total input force at each radial location (including the mechanical admittance component from the piston-like motion). For use with inertial equilibrium, only the bending mode should be considered, so the piston-like component of the total mechanical admittance function is subtracted to identify the modal mechanical admittance.

[0061] The diaphragm can be simulated in the frequency domain at its highest intrinsic frequency using finite element analysis, constrained to prevent bending over the operating bandwidth, and using the same input force as used in the bending analysis. The modal mechanical admittance can then be identified by subtracting the mechanical admittance of the piston mode from the total mechanical admittance function. In the table below, the modal column represents the number of intrinsic modes, the shape function column represents the diaphragm velocity as a function of the radial position from the intrinsic frequency analysis, the excitation shape column is the output from the frequency domain analysis and is proportional to the total mechanical admittance, and the modal admittance column represents the modal mechanical admittance of the intrinsic modes. In the table, the constant “Cn” changes for each row. “Psi” represents the normalized shape for each intrinsic mode, and “F” represents the input force.

[0062]

[0063] Figure 4A , 4B Figures 4C and 4C are plots showing the positions of the modal mechanical admittance and shape function relative to their percentages as diaphragm radius at the frequencies of the first, second, and third bending modes of the flexural diaphragm balanced modal radiator in the embodiments. Figure 4A In this configuration, the diaphragm uses a linear curvature profile with a relative diaphragm thickness (T) of 2%, and the nodal line of the first bending mode has been manipulated inward by 9% from 69% of the radius to 60% of the radius. For example... Figure 4A The first bending mode shown has a shape function that is almost identical in shape to the modal mechanical admittance. In the second bending mode (as shown...) Figure 4B (as shown) and the third bending mode (as shown) Figure 4C This performance is repeatedly illustrated in the comparison of modal mechanical admittance and shape function (as shown in the figure). When normalized, as... Figure 4D As shown, the modal mechanical admittance and shape function of the first bending mode match at the center of the diaphragm and can be directly compared because the diaphragm motion is primarily determined by the piston motion and the bending motion of the first bending mode. In higher bending modes, the diaphragm motion includes the motion of that bending mode, the motion of all lower bending modes, and the motion of the piston mode. Figure 4E As shown, when comparing the modal mechanical admittance of the second bending mode with the shape function of that bending mode, no perfect match was observed. Because the modal mechanical admittance of each mode includes the mechanical admittances of all lower modes, the minimum of the modal admittance is slightly offset from the minimum of the shape function. The location of the minimum obtained from the modal mechanical admittance function is ideal for placing the inertial balancing mass.

[0064] The degree to which the diaphragm is inertially balanced can be determined by assessing how close the average bending velocity at any frequency within the operating bandwidth is to the piston velocity. This assessment is determined by measuring the amplitude and phase of the surface velocity on the vibrating surface of the diaphragm. Both the average volumetric velocity and the root mean square (“RMS”) volumetric velocity on the vibrating surface of the diaphragm can be evaluated at high-frequency resolution within the operating bandwidth (typically 24 points per octave as the minimum resolution) to accurately quantify the degree of inertial balance of the diaphragm. Analytically, the average volumetric velocity can be evaluated using the following integral expression:

[0065]

[0066] RMS speed can be evaluated using the following expression:

[0067]

[0068] Where Psi(ψ) represents the surface velocity on the diaphragm, and S represents the area of ​​the region being evaluated.

[0069] The final required expression relates to the volumetric velocity of the piston assembly, which can be determined using the following methods. In a first method, if a digital FEA simulation incorporating coupled mechanical, acoustic, and electromagnetic physics is used to model the entire BMR, the diaphragm can be constrained within the simulation to prevent bending while preserving all other electromechanical properties of the BMR. In a second method, low-frequency piston behavior is matched to a lumped-element simulation model of the BMR to estimate the piston velocity at high frequencies. This estimate of the high-frequency piston velocity can be combined with the lower-frequency piston velocity to determine the piston velocity over the entire operating bandwidth of the BMR. In both simulation and measurement, a current-driven source is used to suppress electromotive force effects and the effects of rising mechanical impedance at high frequencies to improve the correlation between measurements and simulations.

[0070] The following analytical expression is used to determine how much the average velocity in the Z direction differs from the piston velocity, which is equal to the relative average modal velocity:

[0071]

[0072] The following expressions analytically define the “mean volume velocity” and the “RMS volume velocity”. In practical implementations, these expressions are defined based on operators derived from a discrete dataset of observations. In these expressions, A is defined as the evaluated area, ΔA is the incremental area, N is the total number of elements, and n is the number of elements in the summation.

[0073]

[0074] Typically, in a balanced diaphragm, the relative average modal velocity should be below 25%, but in a well-balanced diaphragm, it should be below 18%. These values ​​can be determined using a scanning laser vibrometer to evaluate audio equipment and finite element analysis to evaluate analog audio equipment. A spatially discrete version of the formula above can be used if the measurement locations are distributed to provide at least five locations for each bending wavelength at the highest frequency in the operating bandwidth to ensure sufficient spatial resolution.

[0075] Typically, the performance of a complete transducer can be simulated with or without an inertial balancing component. For example... Figure 5A , 5B As shown in Figures 5C and 5D, in a simulated embodiment using a 40mm diameter aluminum diaphragm, various relative average modal velocities were determined before and after balancing. Below 20kHz (i.e., the operating frequency range most useful for audio applications), the inertial balancing diaphragm exhibited a relative average modal velocity of less than 18%, indicating that it was well balanced. Figure 5A The RMS, average, and piston-like components of the volumetric velocity are shown in the embodiment using a finite element analysis (“FEA”) model used to simulate the volumetric velocity of an unbalanced 40 mm diameter bent aluminum diaphragm. Figure 5B The FEA simulation results for the relative average modal velocity of the unbalanced 40mm diameter bent aluminum diaphragm in the embodiment are shown. The 25% standard for an inertial balanced diaphragm is indicated by a horizontal line, which is exceeded in this unbalanced example. Conversely, Figure 5C The FEA simulation results for the volumetric velocity, RMS, average value, and piston component of the balanced 40 mm diameter bent aluminum diaphragm in the embodiment are shown. Figure 5D The FEA simulation results for the relative average modal velocity of the balanced 40mm diameter curved aluminum diaphragm in the embodiment are shown. The 18% standard for a well-balanced inertial diaphragm is indicated by a horizontal line, which is not exceeded in this inertial balance example.

[0076] Typically, a diaphragm becomes essentially “inertially unbalanced” with the addition of voice coil components. An inertially unbalanced diaphragm will have a relative average modal velocity greater than 25% across the entire operating frequency band. To inertially balance the diaphragm and reduce the relative average modal velocity to below 25%, preferably to 18% or less, one or more mechanical impedance components must be added. The number of components added typically corresponds to the number of minimum values ​​of the modal mechanical admittance function of the highest in-band intrinsic modes. In some embodiments, one or more internal balancing masses can be combined into a single balancing disk.

[0077] In the case of a flat BMR, the mass of each mechanical impedance component is proportional to the mass of the required voice coil components and their radial position on the diaphragm. However, for ideal balance, the mass of the mechanical impedance components placed on the periphery of the diaphragm can be reduced by up to 25%. The mass proportions and positions of flat BMRs are shown in the table below, and they are scaled based on the mass of the voice coil components located at one of these positions.

[0078]

[0079] This method provides a good starting point when balancing a bent diaphragm BMR. The mass is placed at the minimum of the bent diaphragm modal mechanical admittance up to the highest intrinsic frequency within the operating bandwidth, and the voice coil assembly mass and their relative radial position should initially be minimized. The minimums of the bent diaphragm modal mechanical admittance cannot be tabulated in general form because these minimums vary with different curvature profiles. Due to the manipulation of the nodal line position, the mass of the mechanical impedance assembly must be adjusted to achieve optimized inertial balance.

[0080] Starting with the lowest bending mode, mass adjustments can be made to correct for each mode. For the first mode, if the mass within the region enclosed by the nodal line of the first bending mode is too large, on-axis acoustic measurements will show something similar to... Figure 6A The response in the first bending mode. If the mass on the periphery of the nodal line is too large, the on-axis response will be similar to... Figure 6B Inertial balancing of the first mode can also be achieved by increasing the mass on the other side of the nodal line in either case, but when possible, the excessive efficiency loss related to mass will be minimized. The masses inside and outside the nodal line of the first bending mode can be adjusted until the on-axis response is as flat as possible and until the relative average modal velocity of the mode is minimized.

[0081] A similar method can be implemented to balance the second mode. However, the first mode must be kept in balance. This is achieved by scaling all added masses up or down depending on how unbalanced the diaphragm is. Doing so maintains the radial moment exerted by each mass around the nodal line, and thus maintains its balance. If multiple masses on either side of the nodal line of the first bending mode require further adjustment, they should be adjusted to maintain the radial moment around the first mode. For the second mode, there are two nodal lines, and the bending regions separated by the nodal lines have alternating polarities. As a result, the innermost and outermost regions have the same polarity. If the voice coil is in the middle region and the mass is too low, the acoustic response in the second mode will be similar to... Figure 6A The acoustic response is shown in the figure. If the mass is too large, the acoustic response will be similar to... Figure 6B The response shown.

[0082] The method can still be used for modes above the second mode, although implementation becomes very difficult to maintain the inertial balance of the lower-order bending modes. Higher modes are least affected if the diaphragm has a bending profile consisting of zero or one inflection point. Conventional flat diaphragm BMR balancing mass schemes should provide low relative average modal velocities and therefore should minimize any adjustments to the mass to balance the first and second modes as much as possible. All mass adjustments should be made in increments not exceeding 10%, and refined to 5% or less when an approximate solution is found.

[0083] Figure 7A This is a planar view of the distribution of nodal lines in a free, flat, circular diaphragm in the embodiments. In the illustrated embodiment 700, a series of lines representing the nodal line positions of the first four different bending modes present in the flat circular diaphragm of the BMR are shown. The nodal line of the first bending mode is illustrated by a single-ring circle 702, and the three nodal lines of the third bending mode 704 are illustrated by a series of dashed lines and dots. Each bending mode has a nodal line, which is a region of zero translation, velocity, or acceleration caused by modal excitation of the diaphragm. Essentially, these are locations on the diaphragm that contribute little to the radiated acoustic power from the bending mode operation. In the illustration, the nodal line of the first bending mode 702 coincides with the third nodal line of the fourth bending mode 708. Typically, each bending mode of the flat diaphragm has a different oscillation frequency and a different nodal line position, and the combined or constructive radiated acoustic power of these bending modes enables the BMR to radiate acoustic signals simultaneously with piston-like acoustic radiation across a wide range of acoustic and ultrasonic frequencies. The movement of the BMR diaphragm is primarily generated by the electromotive force of the voice coil frame, which is activated by the interaction between a static magnetic field and a current flowing through the voice coil, which is wound around the voice coil frame within an assembly including an electromechanical transducer. However, performance advantages are achieved by modifying the shape of the BMR diaphragm, allowing the nodal line position to be offset or adjusted through physical warping or by creating a curved structure from the BMR diaphragm's previous flat-plate structure.

[0084] When obtaining this performance advantage, Figure 3A and 3BThe previously described process shown is used to generate an optimized set of diaphragm shape parameters to produce a diaphragm profile with a curved shape, iteratively evaluate the intrinsic frequency output of the curved diaphragm profile, and directly manipulate the distribution of the curved modes of the selected BMR diaphragm profile. When iteratively determined, the selected diaphragm profile can produce acoustic output with reduced acoustic distortion, reduced material costs measured in the form of smaller voice coils and smaller coil frame diameters, and lower cost of the magnets used in the electromechanical transducers driving the diaphragm compared to conventional flat diaphragm BMRs. Additionally, the smaller magnet size significantly reduces the overall weight, size, and cost of the transducers used to drive the BMR diaphragm. In the selection of magnets, ceramic magnets can be used to further reduce costs, but may also lead to an increase in weight due to their significantly lower energy storage density compared to rare-earth magnets.

[0085] Figure 7B This is a plan view of the curved, circular BMR diaphragm in the embodiment. In this illustrated embodiment, the curved shape of the alternative diaphragm profile has offset the first segment line 702 of the first curved mode to align with the second segment line of the third curved mode 704. The ability to control and manipulate the shape of the BMR diaphragm through the offset of the curved modes provides functional advantages in reducing signal directivity, reducing distortion, and manufacturing a BMR with a reduced voice coil size. This reduced size significantly reduces the cost of materials used as components in the electromechanical transducer. The structural modification enables lower distortion through the availability of additional internal space to extend the spider element that provides connection between the coil frame and the fixed frame of the BMR. The extended length of the spider element in the BMR due to the curvature of the diaphragm and the corresponding reduction in the size of the internal components allows the spider frame to have more linear stiffness behavior, thereby providing greater flexibility and more significantly reducing the distortion of audio signal frequencies transmitted from the curved BMR diaphragm.

[0086] Figure 8A This is a diagram illustrating a representative set of curvature functions used to create the profile of a curved BMR diaphragm. Multiple lines are shown, representing the curvature relative to the arc length of a potential curved diaphragm used in BMR. Experiments have shown that the curvature K, defined as the product of the curvature rate and the arc length, satisfies the relationship K = 250s (where s represents the arc length in meters, and 250 represents the curvature rate in units of 1 / m). 2This involves optimizing the positioning of the nodal line between the first and third bending modes. In a diaphragm embodiment with this curvature profile, the nodal line of the first bending mode of the BMR diaphragm has been closely aligned with the second nodal line of the third bending mode. When the nodal lines are aligned or closely aligned, it has been found that applying a driving force to those nodal lines suppresses the excitation of the modes associated with those nodal lines, thus achieving reduced acoustic output distortion at those modal frequencies. Because the distortion from the bending mode is proportional to the surface velocity at the driving position, the lowest mode has the highest surface velocity when driven near the antinode (i.e., the point or line of maximum translation) compared to other bending modes. Therefore, it has the highest potential to generate acoustic distortion. By manipulating its nodal line to align or closely align with the driving position to control the excitation of the first bending mode, reduced acoustic radiation output is generated from this bending mode, and acoustic distortion is minimized. In this way, the inertial balance known as "three-mode balance" can be implemented by redistributing the nodal line through the curvature of the diaphragm to reduce distortion at the frequency of the first bending mode. More specifically, distortion reduction is achieved by suppressing the modal velocity experienced by the voice coil by positioning the diameter of the voice coil frame at a diameter closely aligned with the nodal line of the bending mode. By closely aligning the nodal line of the first bending mode with the nodal lines of higher-order modes, the balanced modal behavior of the BMR can be maintained more effectively.

[0087] Figure 8B This is a cross-sectional diagram showing the range of the axisymmetric membrane profile of the BMR in the embodiment. The diagram illustrates the curvature variation of the membrane profile. It has been found that as the observed arc length moves outward from the center to the edge, it increases from 250 / m... 2 Advantageous embodiments for generating linear curvature rates.

[0088] Figure 8C This is a graph illustrating the effect of the rate of curvature on the nodal line position, measured in meters, relative to a diaphragm radius of 0.1 meters in this representative example. The graph shows how the diaphragm's curvature profile causes a shift or modification in the nodal line position of lower-order curvature modes. In this case, a radial shift in the nodal line position of the first curvature mode is depicted, consistent with the second nodal line of the third curvature mode.

[0089] Figure 8D This is a graph showing the relative average modal velocity as a function of the curvature rate of the curved diaphragm in the embodiment. The graph depicts, in a comparative form, the acoustic output generated in the Z-direction by the strong or weak interference of the curved modes from the surface of the piston assembly operated by the curved diaphragm. The relative average modal velocity is determined by calculating the average modal volume velocity and dividing it by the RMS modal volume velocity. Values ​​below 25%, preferably below 18%, indicate that the mode is inertially balanced. (The last sentence appears to be incomplete and possibly refers to a graph with a curvature rate of 250 / m.) 2The corresponding curved diaphragm has been identified and the optimized position is shown on the diagram. The relative average modal velocities from this particular curved profile have inertial balance in the first, third, and fourth curved modes, thereby reducing interference with the acoustic radiation generated from the piston-like motion. The sound radiated from the second curved mode is shown in the Z direction as approximately 0.34% to 0.35% of the RMS velocity of that curved mode. The curved modes with low percentage relative average modal velocities are primarily off-axis radiates and provide broad directionality.

[0090] Figure 9 This is a graph showing the on-axis sound pressure level of an embodiment of an inertial balanced curved diaphragm compared to an embodiment of an inertial unbalanced curved diaphragm. Both diaphragms use 0.2mm thick diaphragms with a diameter of 40mm and a relative edge height of 10%. The curvature profiles of the two embodiments of the curved diaphragm were chosen to provide a first nodal position close to the second nodal position of the fourth mode, which corresponds to the placement of a 19.05mm diameter voice coil. By comparison, the inertial balanced flat 40mm diameter diaphragm BMR would require a voice coil diameter of 27.6mm to suppress the excitation of the first curved mode. Suppressing the excitation of the first curved mode is desired to reduce the level of distortion present in the radiated acoustic signal. The maximum relative average modal velocity of the unbalanced curved diaphragm is 42%. After inertial balancing, the maximum relative average modal velocity decreases to 21%, which is below the 25% inertial balancing threshold considered for a loudspeaker with BMR.

[0091] While specific embodiments have been shown and described herein, those skilled in the art will understand that various alternatives and / or equivalent implementations may be used instead of the specific embodiments shown and described without departing from the scope of this disclosure. This application is intended to cover any modifications or variations of the embodiments discussed herein.

Claims

1. A method for designing an inertially balanced audio transducer diaphragm, characterized by, The method comprises: receiving a plurality of input parameters of the diaphragm; generating a first diaphragm shape having a curved profile based on the received plurality of input parameters; performing a first frequency analysis of the first diaphragm shape; determining a nodal line distribution of the first diaphragm shape based on the performed frequency analysis, the nodal line distribution comprising a minimum translational velocity amplitude of each resonant frequency of one or more vibrational bending modes resonating throughout the first diaphragm shape; comparing the determined nodal line distribution to a desired nodal line distribution of the first diaphragm shape; determining a relative error value from the comparison of the determined nodal line distribution to the desired nodal line distribution of the first diaphragm shape; comparing the relative error value to a predetermined nodal line distribution tolerance; iteratively adjusting the plurality of input parameters of the first diaphragm shape when the relative error value is greater than the predetermined nodal line distribution tolerance; and generating a plurality of diaphragm shape parameters when the relative error value of the plurality of diaphragm shape parameters is below the predetermined nodal line distribution tolerance.

2. The method of claim 1, wherein, The determined nodal line distribution comprises a plurality of locations of a minimum translational velocity amplitude of each resonant frequency of the one or more vibrational bending modes resonating throughout the first diaphragm shape.

3. The method of claim 1, wherein, further comprising: generating a simulated diaphragm based on the generated plurality of diaphragm shape parameters; performing a second frequency analysis of the simulated diaphragm; generating a modal mechanical mobility function of the simulated diaphragm based on the second frequency analysis; determining a plurality of minimum value locations of the generated modal mechanical mobility function; identifying, based on the simulated diaphragm, a coupling location on a surface of a generated diaphragm of each of a voice coil assembly and one or more mechanical impedance assemblies; and coupling the voice coil and the one or more mechanical impedance assemblies to the surface of the generated diaphragm at each identified coupling location, wherein the generated diaphragm including the coupled voice coil and the one or more mechanical impedance assemblies comprises an inertially balanced audio transducer diaphragm.

4. The method of claim 3, wherein, The first frequency analysis is an eigenfrequency analysis of the first diaphragm shape, wherein the second frequency analysis is an eigenfrequency analysis of the simulated diaphragm, wherein the performed second frequency analysis comprises identifying a highest vibrational bending mode frequency in a target operating bandwidth of the diaphragm, and wherein the generation of the modal mechanical mobility function of the simulated diaphragm is performed using the identified highest vibrational bending mode frequency in the target operating bandwidth.

5. The method of claim 3, wherein, The coupling location of the voice coil assembly coincides with a nodal line of a first vibrational bending mode within the predetermined nodal line distribution tolerance.

6. The method of claim 1, wherein, The plurality of input parameters comprises one or more parameters defining a curvature profile of the diaphragm.

7. The method of claim 6, wherein, The plurality of input parameters comprises at least a curvature function and an arc length of the diaphragm defining the curvature profile.

8. A method of manufacturing an electrodynamic transducer diaphragm, characterized by, The method comprises: receiving an iteratively adjusted plurality of input parameters; generating a curvature profile of the diaphragm from the iteratively adjusted plurality of input parameters; determining a modal mechanical mobility of the diaphragm based on the generated curvature profile; determining one or more locations of a voice coil assembly and one or more inertial balance masses on a surface of the diaphragm based on the determined modal mechanical mobility of the diaphragm; mounting the voice coil assembly and the one or more inertial balance masses on the surface of the diaphragm at the determined one or more locations; measuring a modal velocity of the diaphragm with the mounted voice coil assembly and the one or more inertial balance masses; determining a relative average modal velocity of the diaphragm from the measured modal velocity of the diaphragm; and adjusting a mass of the one or more inertial balance masses until the determined relative average modal velocity is within a relative average modal velocity limit.

9. The method of claim 8, wherein, The iteratively adjusted plurality of input parameters defines at least a curvature function and an arc length.

10. The method of claim 8, wherein, The relative average modal velocity limit is less than one of 18% or 25%.

11. The method of claim 8, wherein, Determining the one or more locations of the voice coil assembly and the one or more inertial balance masses on the surface of the diaphragm includes: determining a modal mechanical mobility function for each vibrational bending mode of the diaphragm; determining a highest frequency vibrational bending mode within an operating bandwidth of the diaphragm; determining the modal mechanical mobility function for the determined highest frequency vibrational bending mode within the operating bandwidth of the diaphragm; identifying one or more minimum value locations of the modal mechanical mobility function; and evaluating a match closeness between a measured velocity average of the diaphragm and a piston-like velocity of the diaphragm over a range of the operating bandwidth.

12. An audio device, comprising: includes: a diaphragm (104) having a bending profile adapted to radiate audio signals from a plurality of bending modes and a piston mode, one or more of the plurality of bending modes having a uniform nodal location, the diaphragm having a front side and a back side, the bending profile of the diaphragm generated from a plurality of input parameters iteratively adjusted; and a transducer (200) coupled to the back side of the diaphragm, the transducer adapted to drive the diaphragm to radiate audio signals with reduced audio distortion, wherein the plurality of bending modes each have one or more minimum value locations across the diaphragm, and wherein the transducer (200) is mounted on one of the one or more minimum value locations of the plurality of bending modes, and one or more impedance assemblies are mounted on at least one of the remaining one or more minimum value locations to inertially balance the diaphragm based on a predetermined relative average modal velocity limit.

13. The audio device of claim 12, wherein, The plurality of bending modes are within an operating bandwidth of the diaphragm.

14. The audio device of claim 12, wherein, The transducer includes one or more magnets (214), a pole piece (208), a back plate (210), a front plate (212), a bobbin (204), a voice coil (218), and a first suspension element (206).

15. The audio device of claim 14, wherein, The first suspension element is a roll-around suspension element.

16. The audio device of claim 15, wherein, Further including a second suspension element that is one of a corrugated fabric, a flexible armature, or a second roll-around suspension element.

17. The audio device of claim 12, wherein, The predetermined relative average modal velocity limit is less than one of 18% or 25%.

18. The audio device of claim 12, wherein, The thickness of the flexural profile of the diaphragm is less than 5% of the radius of the diaphragm.

19. The audio device of claim 14, wherein, A driving force applied to the diaphragm using the voice coil of the transducer produces radiation of the audio signal from the plurality of flexural modes and the piston mode, each radiation of the audio signal having a measurable distortion component, the measurable distortion component from a first lowest frequency flexural mode of the plurality of flexural modes being less than a distortion component from a second lowest frequency flexural mode of the plurality of flexural modes, wherein the voice coil is mounted at a location on the back side of the diaphragm that coincides with a nodal position of the first lowest frequency flexural mode of the plurality of flexural modes.

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