3D printed waveguides

[Ro808]

My post was a quick write-up based on numerous documents and literature I have gathered over the last few years. I'll will post some links later.
Before posting, I discussed this topic with an engineer in fluid dynamics who develops his own horns for high end loudspeakers.

As stated earlier in this thread, there is no consensus or general theory on waveguides for dome tweeters. Why?
It is my - slightly educated - guess this is due to (small) differences in the construction from one dome tweeter to another. As with compression drivers: some work better with a specific horn/wg than others, because the exit angle/diaphragm of the driver provides a wavefront that may or may not be appropriate for a given horn/wg (throat).

Brendon, if you compare the "dome area" of the tweeters you mention, seemingly tiny features are clearly distinguishable: ring radiator vs full vs flattened dome, size and shape of the surround, the "grille" covering the RS28 dome etc.
Looking at the SB26, I suspect it to work better with a rather shallow WG, with a wide throat angle that provides some space around the dome/surround similar to the original faceplate.
On the other hand: this contradicts - at least partly - with the Arendal tweeter-waveguide combo from my previous post, which features an OEM tweeter with a customized dome by Dr. Kurt Mueller.
To narrow this down: the space around the dome/surround area appears to be crucial here.


Quote:
"BTW when you say tangent to the dome, do you mean perpendicular (normal)? Since these are only partial spheres I don't see a way for the mouth opening to actually meet tangent to the dome."

The tangency might be related to more than a few aspects of the dome. It may even turn out to be "tangent to the wavefront in the operational frequency range of the waveguide", or no tangency at all. This is rather experimental territory, not yet fully understood, explored, let alone completely covered by science. I'll try to post some additional info on this.

[Ro808]

This is one of the COMSOL documents.

[TN Allen]

"As stated earlier in this thread, there is no consensus or general theory on waveguides for dome tweeters. .."

The above may be at the crux of the design and testing problems. There are plenty of theories, plenty of design objectives, and plenty of people designing WGs. Some modeling and predicting response curves using FEA algorithms, some milling, turning, molding and testing WGs. There seems to me to be little consensus about what objectively defines successful WG design and integration within a set of speaker cabinets to produce a pleasant listening expereince. This is not a surprise given WGs are designed and used for different effects and purposes, and that a significant range of shapes and dimensions can be used for WGs.

It is easier to setup to test a single WG and driver using OmniMic or a similar system, than to quantify the subjective nature of listening to a completed set of speakers. However, theory and FEA models need to be correlated to actual listening experiences. What use is test data if it is not related to listening experience?

Brandon, I am thinking of ways to quantify subjective listening impressions, and to account for different effects of WGs, as well as better test equipment that more closely measures what the listener hears. In the past I have suggested that people on this forum who are interested in WGs put together a systematic procedure for quantifying listening experiences. Although such a process would not be as objective as testing using OmniMic, it could produce more practical data that could be related to response curves.

[augerpro]

Tim> While not directly about waveguides, Harman/Toole/Olive's listener preference studies and predictive model are the basis most of us have when considering waveguides, since it is very difficult to meet those requirements tightly without some sort of directivity control. So in that way, a lot of the data you are looking for is in those studies. Waveguides are just the vehicle to get you there.

[TN Allen]

Brandon,

I am interested in ways to evaluate the effect of specific waveguides in a complete system, not generalized listener preferences.

Listening is ultimately the proof of the quality of a waveguide's effect. In my opinion, generating response curves without also listening carefully, and without correlating response curves to heard effects, is an inadequate approach to evaluating waveguides. It is at best a limited method, that could be significantly improved by combining it with a well thought out series of methodical listening exercises and scoring.

[Ro808]

Both posts are relevant in the context of this thread:

- It makes sense to conform to standards derived from fundamental research in the field of listener preferences
- in setting up an evaluation system.

Moreover, I think it's mandatory to define some constraints in order to limit the number of variables. The same with the selection of tweeters vs number of waveguides per tweeter to be tested.

The differences between tweeter/waveguide combinations are expected to be largely determined by the (sound)quality of the tweeters, provided the waveguides are optimized (i.e. do not cause interferences).

[Ro808]

Here is some info on waveguide theory and the development of tweeter waveguides (Source: Harman International):

Often times, loudspeakers consist of a transducer or driver unit coupled to a waveguide. A waveguide can also be commonly referred to as a horn or acoustic waveguide. A waveguide functions to provide gain for the transducer, i.e., increases the acoustic sensitivity of the loudspeaker in a region of frequencies. A waveguide can also assist in the control of dispersion on and off-axis as well as assist with directivity mating with other transducers and can simplify loudspeaker system integration.

Typical waveguides include a “throat” or entrance at one end and a “mouth” or exit at the opposing end. The throat end of the waveguide is typically coupled to the transducer or driver and receives the initial input of sound from the driver. The waveguide then usually increases in cross-sectional area or flares out as it approaches the mouth. The sound is then dispersed through the mouth, which is the exit of the waveguide. Thus, the throat end of the waveguide is typically narrower in cross-section in both the horizontal and vertical directions and generally defines a bounded region that directs the sound from the throat to the mouth of the waveguide. This interior bounded region may be referred to as the waveguide profile. The sound produced as planar surfaces parallel to the throat, are referred to as wave fronts.

In operation, the surfaces of the waveguide in a loudspeaker typically produce a coverage pattern of a specified total coverage angle that may differ horizontally and vertically. The coverage angle is a total angle in any plane of observations, although horizontal and vertical orthogonal planes are typically used. The coverage angle is evaluated as a function of frequency and is defined to be the angle at which the intensity of sound (Sound Pressure Level—SPL) is half of the SPL on the reference axis, which is the axis direction usually normal to the throat of the driver.

Acoustic energy radiates into the throat from the transducer at high pressure, with a wave front that is nominally flat and free of curvature. As the wave front expands outward to toward the mouth of the waveguide, the axial area increases in a uniform and monotonically increasing fashion. Analogous to electrical transformers in the electrical domain, waveguides can be considered as acoustical transformers in the acoustical domain. In the acoustical domain, waveguides contain impedance along the profile with resistive and reactive components. However, sound pressure level is produced primarily by the acoustical resistance of the waveguide. That is, acoustical reactance does not contribute to the sound pressure level. In the work presented, the rate of increasing area is controlled by an area expansion function designed to provide minimal acoustic reactance (or maximum acoustic radiation resistance at the throat). This approach increases the sensitivity and ultimately, the efficiency of the transducer and waveguide assembly.

The determined area expansion rate is intended to create a uniform dispersion pattern on and off-axis by manipulating the acoustical impedance as a function of frequency to theoretically lower frequency range of operation. The coupling of the waveguide acoustic impedance source to the acoustic impedance of the surrounding environment; provides an action analogous to an electrical transformer. The winding ratio is equivalent to the ratio of the radiation resistance seen by the driver and the radiation resistance of the surrounding environment. In this analogy, the change in pressure from the throat to the mouth of the waveguide is equivalent to the change in voltage across an electrical transformer.

The shape of an acoustic waveguide affects the frequency response, polar pattern and the level of harmonic distortion of sound waves as they propagate away from the acoustic waveguide. As loudspeakers produce sound waves, waveguides are used to control the characteristics of the acoustic wave propagation. As previously stated, the increase in area of the waveguide from throat to mouth is typically controlled by an area expansion function designed to provide appropriate acoustic impedance. Many different theories on waveguide design have been developed in the past to help determine the optimal expansion functions for waveguide designs.

One common design approach, developed by Keele, involves a two-section waveguide or horn design. In this design approach, an exponential design is used on the section near the throat, while the outer section utilizes a conical design approach. Similarly, Geddes developed an alternative design approach that is a well known in the industry. This approach uses exponential algebraic equations and functions developed by Geddes to determine the optimal contour of a waveguide once required values for the throat radius and coverage angle have been determined.

Current design approaches, such as those taught by Keele and Geddes, first determine the desired performance standards of the waveguide and then design the waveguide using established exponential functions or algebraic equations that are designed to model a waveguide to achieve the desired standards. No design method currently exists, however, that uses the performance standards of a waveguide of known contours and dimensions as a design metric. Additionally, no design method currently exists that captures the change in acoustic impedance, in particular the change in acoustic reactance, along the profile of the waveguide as part of the design standard. A need therefore exists for a waveguide design method such that one can predict the performance standards of waveguides having various contours and dimensions without the necessity of building a prototype. Under this proposed approach, design iterations can be made before the prototype stage of the waveguide since the performance standards may be predicted in advance of the design.

[TN Allen]

The following from the last paragraph is interesting, particularly that which I have underlined:

"No design method currently exists, however, that uses the performance standards of a waveguide of known contours and dimensions as a design metric. Additionally, no design method currently exists that captures the change in acoustic impedance, in particular the change in acoustic reactance, along the profile of the waveguide as part of the design standard. A need therefore exists for a waveguide design method such that one can predict the performance standards of waveguides having various contours and dimensions without the necessity of building a prototype. Under this proposed approach, design iterations can be made before the prototype stage of the waveguide since the performance standards may be predicted in advance of the design."

I wonder if listening to the effect of the WG with a specific driver, and comparing the effect of a flat baffle on the same driver, is an important part of evaluating the prototype? I imagine a considerable amount of money is spent setting up to research and quantify the phenomena described above.

[Ro808]

That text is part of a patent in which a waveguide modeling and design system is described and here is another part :


SUMMARY

This invention provides a method of designing waveguides capable of sustaining a generally constant change in impedance and pressure gradient along the transition of the waveguide from throat to mouth by using design metrics known to correlate with the physical dimensions, contours, and acoustical measurements of waveguides. The design methodology captures the change in acoustical impedance within the area expansion function and explicitly determines the waveguide profile required by providing a predicted frequency response, without the use of a discrete prototype.

With an established set of design metrics, waveguide profiles can be design by dividing the waveguide profile into two or more different exponential profiles having two or more different slopes. The slopes are then altered by applying functions derived from the set of design metrics. Once altered, the resulting waveguide profiles from the different slopes are then concatenated together and smoothed to produce a design key for prototyping a waveguide that can achieve the desired design performance specifications; for which the design metric is based.

In one embodiment, the design metric is the change in acoustic reactance along the profile of the waveguide. The waveguide is divided into ten sections. Initial values are then assigned for the radius or diameter of the throat of the waveguide as well as values for the initial slope of the waveguide along the major and minor (or x and y) axis, polynomial smoothing order for the ten concatenated profiles, and the desired depth of the waveguide. The values for the slopes of each section are then altered based upon functions derived from the design metrics. In this example implementation, each slope is adjusted to minimize the change in acoustic reactance along the waveguide profile, which is the desired performance standard. Once the slopes of each section are adjusted to achieve minimal change in acoustic reactance, the sections are concatenated together and the curve is smoothed using a polynomial function order curve fit to create a continuous waveguide profile. The profile correlates with the design measurements, which allows for the prediction of the performance standards or dispersion characteristics of the waveguide. Design iterations may then be made to adjust for desired performance measurements without the necessity of building a prototype.

Furthermore, since the uniform acoustical reactance along the waveguide profile provides stable and predictable dispersion on-axis and off axis, the invention may be used to design waveguides having elliptical cross-sectional areas that produce circular dispersion patterns (i.e. an elliptical waveguide that produces the same horizontal and vertical dispersion patterns from 1 kHz to 10 kHz). Conversely, the design allows for the design of waveguides having circular cross-sectional areas yet provide elliptical dispersion patterns (i.e. a circular waveguide that produces different horizontal and vertical dispersion patterns from 1 kHz to 10 kHz).
Other systems, methods, features and advantages of the invention will be or will become apparent to one with skill in the art upon examination of the following figures and detailed description. For example, this design method could be used to design transducers diaphragms found in tweeters, mid-ranges, mid-bass, woofers, and subwoofers commonly used in loudspeaker systems. Similarly, this work could be used to design waveguides that are found in radar and communication applications using analogous partitions, concatenations, and design metrics. It is intended that all such additional systems, methods, features and advantages be included within this description, be within the scope of the invention, and be protected by the accompanying claims.


The complete text with images can be found here.

[TN Allen]

After reading the first two paragraphs a second time, and all of this summary one time, I wonder how the inventor arrived at the "known metrics", what was the basis for the math used to caculate the WG contours, and how were the results verified? A protoype is mentioned. Perhaps various prototypes were produced and tested, perhaps used in listening evaluations?

If what I think I understand from the description of this design methodology is correct, it appears a person could design a WG to meet a specified effect on sound, and then produce the WG confident that the WG would function as intended. It would be interesting to see how effective and reliable this methodology is. I am sceptical at best.

[Ro808]

Most likely HSpice or MatLab are used to derive functions from the design metrics.

To sum up the steps to create a (virtual) waveguide profile:
- The waveguide is divided in 10 sections
- Initial values are set for throat radius, initial slope along the x and y-axis, polynomial smoothing order for the 10 concatenated profiles and depth
- Altering of the slopes based upon functions from the derived design metrics
- Concatenating of the sections and polynomial smoothing to create a smooth continious wg profile.

As stated in the patent, waveguides created by use of the method basically consist of altered exponential curves with elliptical or circular cross-sections.

The curves shown in the patent are similar to the exponential horns I have created with a modeling tool that incorporates the metrics and complex functions of the classic horn types (Conical, Exponential, Hyperbolic, Spherical) based on the initial settings (throat radius, flare type, cut-off frequency etc.). Similar to Harman's method, there's a lot of engineering math involved and it requires some knowledge of horn theory.

So what's the use of all of this to us?
In practice probably not very much, but it might help to get a better understanding of the science behind waveguides and more specifically: the factors involved.

If we compare Brendon's curves with those from Revel, it becomes clear that his waveguides match or - in some cases - even surpass performance of Revel's waveguides.

[TN Allen]

It would be interesting to know what of empirical listening experience and psycho-acoustics is factored into the metrics.

[Ro808]

After reading the first two paragraphs a second time, and all of this summary one time, I wonder how the inventor arrived at the "known metrics", what was the basis for the math used to caculate the WG contours, and how were the results verified? A protoype is mentioned. Perhaps various prototypes were produced and tested, perhaps used in listening evaluations?

If what I think I understand from the description of this design methodology is correct, it appears a person could design a WG to meet a specified effect on sound, and then produce the WG confident that the WG would function as intended. It would be interesting to see how effective and reliable this methodology is. I am sceptical at best.

Tim, I think it's safe to say this patent describes only 1 part of Harman's rapid prototyping process.
The output of this stage presumably defines the parameters of a CAD model which is subsequently FEA optimized in COMSOL. The final stage consists of creating a physical prototype by use of Harman's advanced CNC and (lately) 3D printing machinery.

This proces was used to develop the Progressive Transition (PT) Waveguides more than 10 years ago. Ever since, the science and technology involved have progressed considerably.

The effectiveness and reliability ratios of this sort of methodology - which has become a common practice in many high tech industries - can be very high. Think: 0.1% margin, deviation, accuracy etc.

Revel is known for its extensive post-design/pre-market testing which involves several cycles of double-blind listening tests followed by small modifications.

Here you'll find more info and this huge thread is about a double blind shoot-out between the JBL M2 and the Revel Ultra Salon 2 with some input from Floyd Toole.

[TN Allen]

All very complex, and as I think you wrote above somewhere, not really all of that useful for DIY.
I wonder how cost effective the methodology is, seems like a considerable investment in hardware, software and human intelligence and endeavor.

Ro808, are you working on guides at present, if so, are you willing to describe these?

[TN Allen]

This invitation arrived from Comsol for an Acoustical Modeling and Simulation Webinar, perhaps it will interest someone:

https://event.on24.com/eventRegistration/EventLobbyServlet?target=reg20.jsp&referrer=https%3A%2F%2Fwww.comsol.com%2Fevents%2Fwebinars&eventid=1515799&sessionid=1&key=1D8E718ADC4B3DB14669E4AF9EBACF86&regTag=&sourcepage=register