A Survey of Loudspeaker Diaphragm Materials
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The Audio Technology Authority Article prepared for www.audioXpress.com An Engineering Materials Update, Part 1 By Steve Mowry he diaphragm, cone, and/or membrane assemblies of the ρ is the material mass density, kg/m3. Taudio transducer are critical components. The material t is the material thickness, m. requirements include not just high stiffness to mass ratio, but δ is the material damping, typically small, ~ 0.010 for also robustness and good looks. Companies such as B&W, fiber−epoxy composite to ~ 0.005 for light metals, unit- Focal, Accuton, Genesis, Infinity, and Revel have aban- less. doned paper and polypropylene in favor of light metals and Q• is the quality factor related to mechanical losses within alloys, ceramics, CVD diamond, and/or composite materials. the diaphragm, unit-less. Applications and implementations of engineering materi- x is the AC velocity of the diaphragm, m/s. The magnitude als from the defense, aerospace, automotive, and consumer of this complex velocity is just 2πf |x| m/s, remembering industries have clearly raised the state-of-the-art for audio that |x| is the magnitude of displacement of the diaphragm, transducers; however, there is still work to be done. The fol- m and f is frequency, Hz, while 2πf is the angular frequency, lowing is a tutorial discussion of a high-frequency diaphragm 1/s. model, a low-frequency moving assembly model, and high- The RLC model illustrated in Fig. 1 shows by the performance materials suitable for cones and domes. electromechanical analogy that when an AC force of The objective is to identify the industry’s current state- increasing frequency is applied to the diaphragm, at some of-the-art material development and implementation—that limit there is a natural fre- is, determine the best diaphragm material—and to indicate quency at which the dia- future opportunities for additional development. The mys- phragm begins to bend. The tique of black magic, secret cone formulae, and potions has diaphragm cannot resonate been replaced by the clarity of organic chemistry, structural without bending. This engineering, and material science that in effect tend to unlock bending frequency depends technology and innovation. However, specialized FEA simu- on the material properties FIGURE 1: High-frequency diaphragm model. lation and design capabilities are essential for effective audio and diaphragm geometry, where, for a given material, there transducer R&D and technology implementation. is an optimum geometry within a mass budget that will SIMPLIFIED LUMPED MECHANICAL DIAPHRAGM MODEL maximize the first bending frequency, I will begin by using a voltage, V, to Force and current, I, to velocity electromechanical analogy with an inductance, Hz and where . The damping at this frequency is L, to mass, capacitance, C, to compliance and resistance, related to the material loss property. The material damping R, to mechanical loss analogies to illustrate the first natural of high and very high performance materials is typically bending frequency of a diaphragm, Hz and small. The objective is then to push bending modes to fre- with damping at that frequency 1/Q quencies greater than 12kHz and ideally to 30kHz rather than damp in band natural frequency bending modes. where The problem in practice is much more entailed than the model indicates; although the critical parameters of S is the surface area of the diaphragm, m2. modulus, density, thickness, and surface area are identified. E is the tensile modulus or Young’s modulus of the material, Typically, cone and dome depth or height is limited by N/m2. In isotropic materials (homogeneous properties) the process as is minimum thickness. Finite Element Analysis is shear modulus, µ is related to the tensile modulus, E by the used to simulate the effects of geometry and material prop- Poisson’s ratio, ν, where N/m2. erty perturbations on the natural frequencies and bending mode shapes of the diaphragm assembly. However, clearly Voice Coil 2008 1 a large cone will have lower bending frequencies than a TABLE 1: COMMON LIGHT METAL MATERIAL PROPERTIES. small cone and then implicitly, a large cone needs to be Property Beryllium Aluminum Magnesium Titanium thicker than a small cone. The methodology is to itera- Density, ρ 1,840kg/m3 2,699kg/m3 1,740kg/m3 4,500kg/m3 tively converge on an optimum design solution. Loudsoft’s Young’s Modulus, E 303 × 109 Pa 68 × 109 Pa 44 × 109 Pa 116 × 109 Pa FINECone is a convenient and powerful FEA software Speed of sound, √E/ρ 12,832 m/s 5,019 m/s 5,029 m/s 5,077 m/s application for the simulation and design of single laminate Tensile strength 240 × 106 Pa yield 90 × 106 Pa yield 115 × 106 Pa yield 140 × 106 Pa yield cones and domes. Poisson’s ratio, ν 0.07 – 0.18 0.33 0.35 0.34 Thermal conductivity 216W/m – K 210W/m – K 159W/m – K 17W/m – K COMMON METALS FOR Electrical conductivity 2.3 × 107 1/Ω - m 3.7 × 107 1/Ω - m 2.2 × 107 1/Ω - m 1.8 × 106 1/Ω - m CONE AND DOME APPLICATIONS Beryllium is a chemical element with the symbol Be COMMON CERAMICS and atomic number 4 on the periodic table of the elements. Beryllia or Beryllium Oxide (BeO) is a white crystal- Beryllium is a steel grey, strong, very lightweight yet brittle line oxide. It is notable as an electrical insulator with a alkaline earth metal. The element is not known to be neces- thermal conductivity higher than any other non-metal. Its sary or useful for either plant or animal life. The use of beryl- high melting point leads to its use as a refactory. It occurs lium metal presents technical challenges due to the toxicity, in nature as the mineral bromellite. Historically beryllium especially by inhalation of dusts containing beryllium. oxide was called glucina or glucinium oxide. Beryllium is a relatively rare element in both the Earth Alumina or Aluminum Oxide is an amphoteric oxide and the universe. Beryllium reserves are located around the of aluminum with the chemical formula Al2O3. Aluminum world excepting in the Middle East. The US is currently oxide is an electrical insulator but has a relatively high ther- the largest producer of beryllium products and while it does mal conductivity. In its most commonly occurring crystal- have large known reserves, particularly in Utah, there are line form, it is called corundum. several other important known global deposits of beryllium. Magnesia or Magnesium Oxide is a white solid mineral Estimates are that more than 50% of the planet’s beryllium that occurs naturally as periclase and is a source of magne- deposits are located in Brazil, Uganda, and Russia. sium. It has an empirical formula of MgO. It is formed by Aluminum is a ductile member of the boron group of an ionic bond between one magnesium and one oxygen chemical elements. It has the symbol Al and atomic number atom. Magnesium oxide is easily made by burning magne- 13. It is not soluble in water under normal circumstances. sium ribbon which oxidizes in a bright white light, resulting Aluminum is the most abundant metal in the Earth’s crust, in a powder. and the third most abundant element overall, after oxygen Titania or Titanium Oxide is the naturally occurring and silicon. It makes up about 8% by weight of the Earth’s oxide of titanium, chemical formula TiO2. It occurs in solid surface. Aluminum is too reactive chemically to occur nature as the well-known naturally occurring minerals in nature as a free metal. Instead, it is found combined in rutile, anatase, and brookite. The most common form over 270 different minerals. The chief source of aluminum is rutile, which is also the most stable form; anatase and is bauxite ore. brookite both convert to rutile on heating. Magnesium is a chemical element with the symbol Mg The change in material properties after oxidation and and atomic number 12. Magnesium is the ninth most from metal to ceramic is quite remarkable and not always abundant element in the universe by mass. It constitutes intuitive. Caution is advised; ceramics are brittle. The about 2% of the Earth’s crust by mass, and it is the third material properties of four common ceramics are listed in most abundant element dissolved in sea water. Magnesium Table 2. ions are essential to all living cells, and is the 11th most abundant element by mass in the human body. The free ele- TABLE 2: COMMON CERAMIC MATERIAL PROPERTIES. ment (metal) is not found in nature. Once produced from Property Beryllia (BeO) Alumina (Al2O3) Magnesia (MgO) Titania (TiO2) magnesium salts, this alkaline earth metal is now mainly Density, ρ 2,850kg/m3 3,960kg/m3 3,400kg/m3 4,000kg/m3 obtained by electrolysis of brine and is used as an alloying Young’s Modulus, E 350 × 109 Pa 370 × 109 Pa 250 × 109 Pa 250 × 109 Pa agent to make aluminum-magnesium alloys. Speed of sound, √E/ρ 11,000m/s 9,700m/s 8,600m/s 7,900m/s 6 6 6 6 Titanium is a chemical element with the symbol Ti Tensile strength 220 × 10 Pa 300 × 10 Pa 165 × 10 Pa 140 × 10 Pa and atomic number 22. It is a fairly light, strong, lustrous, Poisson’s ratio, ν 0.26 0.22 0.28 0.27 Thermal conductivity 285W/m – K 30W/m – K 9W/m – K 12W/m – K corrosion-resistant (including to sea water and chlorine) Electrical conductivity ~0 ~0 ~0 ~0 transition metal with a grayish color. The element occurs within a number of mineral deposits, principally rutile and ilmenite, which are widely distributed in the Earth’s crust LIGHT METAL ALLOYS FOR and lithosphere, and Ti is found in almost all living things, CONE AND DOME APPLICATIONS rocks, water bodies, and soils.