DETAILED DESCRIPTION OF A PREFERRED EMBODIMENT

[0017] As shown in FIG. 1 , a prior art muffler 20 incorporates an inlet pipe 22 leading to a downstream end 24 . An exhaust gas passes into the inlet pipe 22 and through the downstream end 24 into a chamber 26 defined between walls 25 and 27 . An intermediate pipe 30 has its inlet 28 communicating with the chamber 26 , and leading to its own downstream end 32 . Thus, exhaust gas to be muffled passes from inlet pipe 22 , into chamber 26 , into intermediate pipe 30 , and into a chamber 34 defined in part by wall 35 . From chamber 34 , the exhaust gas passes into the inlet 36 of the outlet pipe 38 , and eventually outwardly of the outlet end 40 of the muffler 20 . Thus, the nominal flow of the exhaust gas is torturous and serially through pipes 22 , 30 and 38 .

[0018] As also shown, a Helmholtz resonator throat 42 communicates between chamber 26 and a Helmholtz resonator volume 44 . There is only the throat 42 leading to the Helmholtz resonator volume 44 , and thus there is not free flow of the exhaust gas between the chamber 26 and Helmholtz resonator volume 44 . Instead, gases within the Helmholtz resonator volume 44 work in cooperation with the throat 42 to provide a spring effect that dampens the particular frequency of noise passing through chamber 26 . The description above is as known in the prior art. A worker of ordinary skill in the art would recognize that a Helmholtz resonator is a very effective way of eliminating noises at a particular frequency in a muffler.

[0019] The present invention, and the first embodiment shown in FIG. 2 , provide the designer with a second degree of freedom such that a second frequency can also be addressed within the same approximate muffler size.

[0020] FIG. 2 shows a muffler 50 including an inlet pipe 52 leading to a downstream end 54 . The downstream end 54 empties into a chamber 56 defined between walls 55 and 57 . An inlet 58 of an intermediate pipe 60 reverses the flow of exhaust gas back to a downstream end 62 and empties into a chamber 64 . Chamber 64 is defined in part by an internal wall 65 . From chamber 64 the exhaust gas passes into an inlet 66 of an outlet pipe 68 , and eventually to the outlet 70 of the muffler 50 . Thus, the exhaust gas experiences a torturous flow as in the prior art. The two degrees of freedom Helmholtz resonator is defined by two separate Helmholtz resonator volumes 72 and 74 . A first throat 76 communicates chamber 56 into first Helmholtz resonator volume 72 . A second throat 78 communicates first Helmholtz resonator volume 72 into second Helmholtz resonator volume 74 . An intermediate wall 75 separates the Helmholtz resonator volumes 72 and 74 . As will be shown below, this serial Helmholtz resonator dampens two separate frequencies by the combination of the two throats and two Helmholtz resonator volumes.

[0021] The designer of the muffler 50 can select two distinct frequencies to be addressed by the muffler.

[0022] A second embodiment muffler 80 is shown in FIGS. 3A and 3B . In this embodiment, the second throat is longer than is the case in the FIG. 2 embodiment.

[0023] As shown in FIGS. 3A and 3B , the inlet pipe 82 again empties to a downstream end 84 communicating with a chamber 86 defined between walls 85 and 87 . An intermediate pipe 88 communicates from chamber 86 back to a downstream end 90 and into a chamber 91 defined between walls 90 and 105 . From chamber 91 the exhaust gas passes into an inlet end 92 of outlet pipe 93 and eventually to an outlet 94 . Again, a throat 98 communicates with a first Helmholtz resonator volume 100 . From Helmholtz resonator volume 100 , a second throat 102 communicates to a downstream end 104 associated with a second Helmholtz resonator volume 106 . The Helmholtz resonator volumes 100 and 106 are sealed other than the communication between the throats 98 and 102 . Again, the use of this embodiment will allow the muffler designer to successfully dampen two distinct frequencies. The second throat extends through the remote side of chamber 86 . In these embodiments, the two Helmholtz resonator volumes are spaced at the two ends of muffler 80 .

[0024] The formulas which are relevant to the design of the two degree of freedom Helmholtz resonator will be described, with particular reference to the disclosed embodiments.

[0025] As known, the prior art FIG. 1 Helmholtz resonator can be described by an equivalent vibration system. This allows the development of a formula to calculate its natural frequency.

[0026] Equation 1 is the classic equation for a Helmholtz resonator natural frequency calculation. 1 $\begin{array}{cc}f=\frac{\omega }{2\pi }=\frac{1}{2\pi }\sqrt{\frac{m}{k}}=\frac{c}{2\pi }\sqrt{\frac{A}{LV}}& \left(1\right)\end{array}$

[0027] m=ρAL with L being the length of the throat, ρ the density of air and A the cross-sectional area of the throat. The k quantity can be determined from the following equation: 2 $\begin{array}{cc}k=\frac{\rho c^2A^2}{V}& \left(2\right)\end{array}$

[0028] The c quantity is the speed of sound and the V quantity is the volume of the Helmholtz resonator volume.

[0029] Again, the above formula is known in the design of Helmholtz resonators.

[0030] FIG. 4 is a schematic of an equivalent vibration system for the inventive serially mounted Helmholtz resonators. By modeling the Helmholtz resonator on an equivalent vibration system, a new formula, similar to the formula 1 can be developed.

[0031] Applying Newton's second law to this system, the equation of motion of this system can be written as:

m ₁ x ₁ +k ₁ ( x ₁ −x ₂ )=0 (3)

m ₂ x ₂ +k ₂ x ₂ +k ₁ ( x ₂ −x ₁ )=0 (4)

[0032] Since equations 3 and 4 are both harmonic equations, they can be solved by substituting x _l =X ₁ sin ωt and x ₂ =X ₂ sin ωt. Equations 3 and 4 can be rewritten as

−m ₁ X ₁ ω ² sin ω t+k ₁ X ₁ sin ω t−k ₁ X ₂ sin ω t =0 (5)

−m ₂ X ₂ ω ² sin ω t+k ₂ X ₂ sin ω t+k ₁ ( X ₂ sin ω t−X ₁ sin ω t )=0 (6)

[0033] Simplifying equations 5 and 6, equations 7 and 8 are obtained.

(− m ₁ ω ² +k ₁ ) X ₁ =k ₂ X ₂ (7)

(− m ₂ ω ² +k ₁ +k ₂ ) X ₂ =k ₁ X ₁ (8)

[0034] Rearrange both equations 7 and 8, 3 $\begin{array}{cc}\frac{X_2}{X_1}=\frac{k_1-m_1{\omega }^2}{k_1}& \left(9\right)\\ \frac{X_2}{X_1}=\frac{k_1}{k_1+k_2-m_2{\omega }^2}& \left(10\right)\end{array}$

[0035] Equation 11 is obtained by substituting Equation 9 into Equation 10 and rearranging.

m ₁ m ₂ ω ⁴ −[k ₁ m ₂ +m ₁ ( k ₁ +k ₂ )]ω ² +k ₁ k ₂ =0 (11)

[0036] The frequency, ω, is obtained by solving Equation 11. 4 $\begin{array}{cc}{\omega }_{1,2}=\sqrt{\frac{1}{2}\left(\frac{k_1+k_2}{m_2}+\frac{k_1}{m_1}\right)\pm \sqrt{\frac{1}{4}{\left(\frac{k_1+k_2}{m_2}+\frac{k_1}{m_1}\right)}^2-\frac{k_1k_2}{m_1m_2}}}& \left(12\right)\end{array}$

[0037] As at equation 2, the k quantity includes physical variables such as ρ and c, and also relates to the area of the throat and the Helmholtz resonator volume. The m quantity again relates to a physical variable, namely the density of air, and generally the volume of the throat that is defined by its area multiplied by its length.

[0038] Equation 12 gives the frequency of the lump mass system. Since it is a 2 DOF system, two frequencies are obtained. Both of them are the resonance frequencies of the 2 DOF Helmholtz resonator.

[0039] As can be appreciated, the size of the throat factors into the m quantities. Generally, a worker in this art would select the two frequencies that are to be addressed and work backward to design an appropriate throat and volume for the two Helmholtz resonators. There will generally be restrictions on the total envelope size, and thus the total volumes available. However, the L quantity does allow the designer some freedom, particularly given the two distinct embodiments shown in FIG. 2 and FIGS. 3A and 3B . That is, a designer who is faced with a desire to have a greater m ₂ might consider using the embodiments of FIGS. 3A and 3B as it has a greater L than the earlier embodiment.

[0040] While preferred embodiments have been disclosed, a worker of ordinary skill in the art would recognize that certain modifications would come within the scope of this invention. In particular, three or even more Helmholtz resonators could be incorporated into the inventive mufflers. For that reason, the following claims should be studied to determine the true scope and content of this invention.