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The main parameters of the ultrasonic horn quantitative cross-section rod longitudinal vibration ultrasonic horn is the simplest and most commonly used types are: conical, exponential, catenary and stepped. Such horn is called a single horn. The performance of the ultrasonic horn with a number of parameters to describe the most commonly used are: In practical applications, the resonance frequency (resonance length), the zoom factor, the shape factor [1].

Consider the uniform, isotropic material composed of variable cross-section rod, without taking into account the mechanical loss, and plane longitudinal wave propagation along the rod axis direction, that is, the stress distribution on the cross-section of the rod is balanced [1]. 1 is a bar with variable section, the axis of symmetry axis x, the role of stress in a small volume element defined interval (x, x + dx) σxdx, according to Newton's law can write the kinetic equation: (S, sigma) xdx = S

the ρ2ξt2dx (1) wherein S = S (x) as the rod cross-sectional function, ξ = ξ (x) for the particle displacement function, sigma = sigma (x) = Eξx stress function sigma as the density of the material of the rod member, E is Young's modulus.

In the case of simple harmonic motion, equation (1) can be written as: 2ξx2 +1 SSxξx + κ2ξ = 0 (2) formula (2) is variable cross-section rod longitudinal vibration of the fluctuation equation, which κ2 = ω2/c2, kappa for the circular wave number, omega for round frequency, c = (E / ρ) is the velocity of propagation of longitudinal waves in thin rods.

Using the equation below (2) the Index-shaped, conical, catenary and stepped half-wavelength horn deduced commonly used parameters [1,3].

Exponential half-wave resonant horn exponential horn. (1) the frequency equation and the resonant length area function: S = S1E for-2βxβ = 1lln to 12 = 1lln (S1/S2) (R1/R2) = 1llnNN = (S1/S2) 12 = R1/R2 which beta-shape coefficient; area coefficient; S as a variable cross-sectional area; S1 x as a variable area for large end;

Frequency equation: sink'l = 0, k'l = pi (3) where k '= (k2-beta2) 12; l as a half wave resonant length. (2) displacement of nodes: x0: x0 = 1πarccot ​​(lnNπ) (4) (3) amplification factor MP: MP = eβl = N (5) (4) form factor strain maxima equation: tg (k'xM,) = -k'β (6) form factor: = Nk'βe-βxM1sin (k'xM) (7) conical half-wave resonant horn conical horn.

Half-wave of the catenary the resonant horn catenary horn, 4. Catenary horn (1) Frequency equation and the length of the resonant frequency equation: TG (k0'l) =-rk0'th (rl) (14) where K0 '= (k2-r2) 1/2 (15 ) half-wave resonant length: lp = λ2 (k0'l) 2 + (arcchN) 2π2

1/2 (16) where, k is the wave number; l horn length variable; r2 radius of the small end surface; N = r1r2; lambda is the wavelength.

(2) displacement of the nodes x0: TG (k0'x0) =-k0'rcth (rl) (17) (3) amplification factor Mp: to mp = Ncosk0'l (18) (4) shape factor:

The: = 2rkcos (k0'l + ψ) cos (k0'xM + ψ) shr (l-xM) (19) wherein, tgψ = rk0'thrl (20) TG (k0'xM + ψ) = rk0'thr (l-xM) -12 (rk0 '+ k0'r) cthr (l-xM) (21) 2.4 stepped half-wave resonant horn stepped horn by two separate cross-sectional area of ​​the uniform bar. Such as 5 above.

Ladder-shaped horn (1) the frequency equation and the resonant length kl = pi, l = lambda / 2 (22) (2) displacement nodes x0: x0 = lambda / 4 (23) (3) amplification factor Mp: Mp = S1S2 = N2 (24) are approximate analysis, in fact, to obtain an amplification factor Mp is less than N2.

Conclusions from the preceding analysis and calculation can be seen: (1) N the same area index, the amplification factor of the stepped horn, followed by the catenary, exponential, the smallest conical. (2) Index-shaped and conical resonator length L with N increases.

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