请帮忙介绍蜂鸣器原理 - 基础理论室 - 声学楼论坛

INTRODUCTION TO PIEZO TRANSDUCERS

Transducers convert one form of energy to another. Piezo actuators convert electrical energy to mechanical energy. This is why they are referred to as "motors" (often linear motors). Piezo sensors convert mechanical energy into electrical energy. This is why they are referred to as "generators". In most cases, the same element can be used to perform either task.

Single sheets: can be energized to produce motion in the thickness, length, and width directions. They may be stretched or compressed to generate electrical output.

Thin 2-layer elements are the most versatile configuration of all. They may be used like single sheets (made up of 2 layers), they can be used to bend, or they can be used to extend. "Benders" achieve large deflections relative to other piezo transducers. "Extenders", being much stiffer, produce smaller deflections but higher forces.

Multilayered piezo stacks can deliver and support high force loads with minimal compliance, but they deliver small motions.

PIEZO ACTUATORS (MOTORS) Piezo motors convert voltage and charge to force and motion.

SINGLE-LAYER MOTORS
(Sheets & Plates)
When an electric field having the same polarity and orientation as the original polarization field is placed across the thickness of a single sheet of piezoceramic, the piece expands in the thickness or "longitudinal" direction (i.e. along the axis of polarization) as shown in Figure-1. At the same time, the sheet contracts in the "transverse" direction (i.e. perpendicular to the axis of polarization) as shown in Figure-2. When the field is reversed, the motions are reversed.

Sheets and plates utilize this effect. The motion of a sheet in the thickness direction is extremely small (on the order of tens of nanometers). On the other hand, since the length dimension is often substantially greater than the thickness dimension, the transverse motion is generally larger (on the order of microns to tens of microns) . The transverse motion of a sheet laminated to the surface of a structure can induce it to stretch or bend, a feature often exploited in structural control systems.

Figure-1: Single Layer Longitudinal (d33) Motor
Getting Thicker

Figure-2: Single Layer Transverse (d31) Motor
With Sides Contracting

2-LAYER MOTORS
(Benders & Extenders)
2 -layer elements can be made to elongate, bend, or twist depending on the polarization and wiring configuration of the layers. A center shim laminated between the two piezo layers adds mechanical strength and stiffness, but reduces motion.

"2-layer" refers to the number of piezo layers. A "2-layer" element actually has nine layers, consisting of: four electrode layers, two piezoceramic layers, two adhesive layers, and a center shim. The two layers offer the opportunity to reduce drive voltage by half when configured for parallel operation.

Extension Motors:
A 2-layer element behaves like a single layer when both layers expand (or contract) together. If an electric field is applied which makes the element thinner, extension along the length and width results. Typically, only motion along one axis is utilized, as demonstrated in Figure-3. Extender motion on the order of microns to tens of microns, and force from tens to hundreds of Newtons is typical.

Bending Motors:
A 2-layer element produces curvature when one layer expands while the other layer contracts. These transducers are often referred to as benders, bimorphs, or flexural elements. Bender motion on the order of hundreds to thousands of microns, and bender force from tens to hundreds of grams, is typical. Figures-4, 5 and 6 show several common bending configurations. The variety of mounting and motion options make benders a popular choice of design engineers.

Figure-3: 2-Layer Extension (d31) Motor
With sides Extending

For extension motors of the same thickness:
Free Deflection (Xf)

L
Blocked Force (Fb)

W
Resonant Frequency (Fr)

I / L
Capacitance (C)

L x W

Figure-4: 2-Layer Bending Motor
Mounted as a Cantilever

For standard cantilevered benders of the same thickness:
Free Deflection (Xf)

L²
Blocked Force (Fb)

W / L
Resonant Frequency (Fr)

I / L²
Capacitance (C)

L x W
Characteristics: End takes on an angle. Easy to mount.

Figure-5: 2-Layer "S" Bending Motor
Mounted as a Cantilever

To convert standard cantilever performance to "S" bender performance:
Free Deflection (Xf) = 1 / 2 x cantilever motion
Blocked Force (Fb) = 1 / 2 x cantilever force
Resonant Frequency (Fr) = same as cantilever frequency
Capacitance (C) = same as cantilever capacitance
Characteristics: end moves up and down in a parallel plane

Figure-6: 2-Layer Bending Motor
Mounted as a Simple Beam

To convert cantilever performance to simple beam performance:
Free Deflection (Xf) = 1 / 4 X cantilever motion
Blocked Force (Fb) = 4 X cantilever force
Resonant Frequency (Fr) = 3 X cantilever frequency
Capacitance (C) = same as cantilever capacitance
Characteristics: center moves up and down in a parallel plane.

MULTI-LAYER MOTORS
(Stacks)
Any number of piezo layers may be stacked on top of one another. Increasing the volume of piezoceramic increases the energy that may be delivered to a load. As the number of layers grows, so does the difficulty of accessing and wiring all the layers.

Stack Motors:
The co-fired stack shown in Figure-7 is a practical way to assemble and wire a large number of piezo layers into one monolithic structure. The tiny motions of each layer contribute to the overall displacement. Stack motion on the order of microns to tens of microns, and force from hundreds to thousands of Newtons is typical.

Figure-7: Co-fired Multi-Layer Stack Motor

MOTOR PERFORMACE
Piezoelectric actuators are usually specified in terms of their free deflection and blocked force. Free deflection (X_f) refers to displacement attained at the maximum recommended voltage level when the actuator is completely free to move and is not asked to exert any force. Blocked force (F_b) refers to the force exerted at the maximum recommended voltage level when the actuator is totally blocked and not allowed to move. Deflection is at a maximum when the force is zero, and force is at a maximum when the deflection is zero. All other values of simultaneous displacement and force are determined by a line drawn between these two points on a force versus deflection line, as shown in Figure-8. Generally, a piezo motor must move a specified amount and exert a specified force, which determines its operating point on the force vs. deflection line. An actuator is considered optimized for a particular application if it delivers the required force at one half its free deflection. All other actuators satisfying the design criteria will be larger, heavier, and consume more power.

Figure-8: Piezo Motor Performance
(Force versus Deflection Diagram)

POLING AND WIRING Poling and wiring determine how the same transducer can be used many ways.

Making a 2-layer piezo element either bend or extend is determined by how it is polarized and wired.

SERIES AND PARALLEL OPERATION

Series Operation: Series operation refers to the case where supply voltage is applied across all piezo layers at once. The voltage on any individual layer is the supply voltage divided by the total number of layers. A 2-layer device wired for series operation uses only two wires (one attached to each outside electrode), as shown in Figure-17.

Parallel Operation: Parallel operation refers to the case where the supply voltage is applied to each layer individually. This means accessing and attaching wires to each layer. A 2-layer bending element wired for parallel operation requires three wires (one attached to each outside electrode and one attached to the center shim), as shown in Figure-18. For the same motion, a 2-layer element poled for parallel operation needs only half the voltage required for series operation.

Figure-17: 2-Layer Bending Element Poled for Series Operation (2-wire)

Figure-18: 2-Layer Bending Element Poled for Parallel Operation (3-wire)

"X" AND "Y" POLING CONFIGURATIONS

X-Poled: refers to the case where the polarization vectors for each of the 2 layers point in opposite directions, generally, towards each other.

Y-Poled: refers to the case where the polarization vectors for each of the 2 layers point in the same direction.

Figure-19: X-Poled Element

Figure-20: Y-Poled Element

ltem	Symbol(Unit)	P-1	P-2	P-3	P-4
Relative Dielectric Constant	ε11T/ε0	1490	1670	1930	3200
Relative Dielectric Constant	ε33T/ε0	1510	1780	2100	4720
Loss Coefficient	tanδ (%)	0.4	1.2	1.4	2.2
Electro-mechanical Coupling Factor	Kp Radial (%)	56	57	65	65
	K31 Length (%)	32	32	38	36
	K33 Longitudinal (%)	62	65	71	68
	Kt Thickness (%)	45	48	51	47
	K15 Shear (%)	60	61	66	57
Piezoelectric Constant	d31 (10-12m/V)	-131	-148	-207	-303
	d33 (10-12m/V)	271	311	410	603
	d15 (10-12m/V)	400	431	550	592
	g31 (10-3V.m/N)	-10	-9	-11	-7
	g33 (10-3V.m/N)	20	20	22	14
	g15 (10-3V.m/N)	30	29	32	21
"Frequency Constant"	Np Radial (%)	2250	2210	2050	1960
	N31 Length (%)	1610	1540	1430	1370
	N33 Longitudinal (%)	1550	1540	1400	1350
	Nt Thickness (%)	2060	2060	2000	1970
	N15 Shear (%)	1010	1000	930	930
		1010
Mechanical Q	Qm	970	110	80	70
"Elastic Constant"	S11^E (10-12m2/N)	12.4	13.4	15.8	16.7
	S12^E (10-12m2/N)	-4.1	-4.8	-5.7	-5.9
	S13^E (10-12m2/N)	-5.2	-5.4	-7.0	-7.5
	S33^E (10-12m2/N)	14.3	14.5	18.1	18.8
	S44^E (10-12m2/N)	34.0	34.2	40.6	38.8
	S66^E (10-12m2/N)	33.0	36.5	43.0	45.4
	Y11^E (1010N/m2)	8.1	7.5	6.3	6.7
Poisson's Ratio	σ E	0.33	0.36	0.36	0.36
Density	ρ (103Kg/m3)	7.8	7.9	7.8	8.0
"Temperature Coefficient"	TK(fr) (ppm/℃）	115	38	59	336
"Temperature Coefficient"	TK(cf) (ppm/℃）	3500	-	4500	13500
Curie Temperature	TC (℃）	280	280	300	180
Linear Expansion Ratio	α (10-6/℃）	4	4	2	2
Bending Strength	τ (106N/m2)	113	103	99	85
Compressive Strength	K_1c (106N/m1.5)	1.1	0.9	0.8	0.9
Applications		Ultrasonic cleaners for high power"	Sensors	Ultrasonic- sensors pickups Actuators Acoustic- application	Actuators Acoustic- application
Note:This table shows typical values measured on standard test piece.Qm,TK(fr) and TK(Cf) are measured for radial vibration mode.

比较复杂!
楼主所说的方式已经改变了震动模式.

压电陶瓷主要性能及参数

自由介电常数εT33（free permittivity）

电介质在应变为零（或常数）时的介电常数，其单位为法拉/米。

相对介电常数εTr3（relative permittivity）

介电常数εT33与真空介电常数ε0之比值，εTr3=εT33/ε0，它是一个无因次的物理量。

介质损耗（dielectric loss）

电介质在电场作用下，由于电极化弛豫过程和漏导等原因在电介质内所损耗的能量。

损耗角正切tgδ（tangent of loss angle）

理想电介质在正弦交变电场作用下流过的电流比电压相位超前90 0，但是在压电陶瓷试样中因有能量损耗，电流超前的相位角ψ小于900，它的余角δ（δ+ψ=900）称为损耗角，它是一个无因次的物理量，人们通常用损耗角正切tgδ来表示介质损耗的大小，它表示了电介质的有功功率（损失功率）P与无功功率Q之比。即：电学品质因数Qe（electrical quality factor）

　　电学品质因数的值等于试样的损耗角正切值的倒数，用Qe表示，它是一个无因次的物理量。若用并联等效电路表示交变电场中的压电陶瓷的试样，则 Qe=1/ tgδ=ωCR

机械品质因数Qm（mechanical quanlity factor）

　　压电振子在谐振时储存的机械能与在一个周期内损耗的机械能之比称为机械品质因数。它与振子参数的关系式为：

泊松比（poissons ratio）

　　泊松比系指固体在应力作用下的横向相对收缩与纵向相对伸长之比，是一个无因次的物理量，用δ表示：

δ= - S 12 /S11

串联谐振频率fs（series resonance frequency）

　　压电振子等效电路中串联支路的谐振频率称为串联谐振频率，用f s 表示，即　　　

并联谐振频率fp（parallel resonance frequency）

　　压电振子等效电路中并联支路的谐振频率称为并联谐振频率，用f p 表示，即f p = 谐振频率fr（resonance frequency）

　　使压电振子的电纳为零的一对频率中较低的一个频率称为谐振频率，用f r 表示。

反谐振频率fa（antiresonance frequency）

　　使压电振子的电纳为零的一对频率中较高的一个频率称为反谐振频率，用f a 表示。

最大导纳频率fm（maximum admittance frequency）

压电振子导纳最大时的频率称为最大导纳频率，这时振子的阻抗最小，故又称为最小阻抗频率，用f m表示。

最小导纳频率fn（minimum admittance frequency）

　　压电振子导纳最小时的频率称为最小导纳频率，这时振子的阻抗最大，故又称为最大阻抗频率，用f n表示。

基频（fundamental frequency）

　　给定的一种振动模式中最低的谐振频率称为基音频率，通常成为基频。

泛音频率（fundamental frequency）

　　给定的一种振动模式中基频以外的谐振频率称为泛音频率。

温度稳定性（temperature stability）

　　温度稳定性系指压电陶瓷的性能随温度而变化的特性。

　　在某一温度下，温度变化1℃时，某频率的数值变化与该温度下频率的数值之比，称为频率的温度系数TKf。

另外，通常还用最大相对漂移来表征某一参数的温度稳定性。

　　正温最大相对频移=△f s (正温最大)/ f s(25℃)

　　负温最大相对频移=△f s (负温最大)/ f s(25℃)

机电耦合系数（ELECTRO MECHANICAL COUPLING COEFFICIENT）

　　机电耦合系数K是弹性一介电相互作用能量密度平方V122与贮存的弹性能密度V1与介电能密度V2乘积之比的平方根。

压电陶瓷常用以下五个基本耦合系数

A、平面机电耦合系数KP（反映薄圆片沿厚度方向极化和电激励，作径向伸缩振动时机电耦合效应的参数。）

B、横向机电耦合系数K31（反映细长条沿厚度方向极化和电激励，作长度伸缩振动的机电耦合效应的参数。）

C、纵向机电耦合系数K33（反映细棒沿长度方向极化和电激励，作长度伸缩振动的机电耦合效应的参数。）

D、厚度伸缩机电耦合系数KT（反映薄片沿厚度方向极化和电激励，作厚度方向伸缩振动的机电效应的参数。）

E、厚度切变机电耦合系数K15（反映矩形板沿长度方向极化，激励电场的方向垂直于极化方向，作厚度切变振动时机电耦合效应的参数。）

压电应变常数D（PIEZOELECTRIC STRAIN CONSTANT）

　　压电应变常数是在应力T和电场分量EM(M≠I)都为常数的条件下，电场分量E变化所引起的应变分量SI的变化与EI变化之比。

压电电压常数G(PIEZOELECTRIC VOLTAGE CONSTANT)

　　该常数是在电位移D和应力分量TN（N≠I）都为常数的条件下，应力分量TI的变化所引起的电场强度分量EI的变化与TI的变化之比。

居里温度TC(CURIE TEMPERATURE)

　　压电陶瓷只在某一温度范围内具有压电效应，它有一临界温度TC，当温度高于TC时，压电陶瓷发生结构相转变，这个临界温度TC称为居里温度。

温度稳定性(TEMPERATURE STABILITY)

　　指压电陶瓷的性能随着温度变化的特性，一般描述温度稳定性有温度系数或最大相对漂移二种方法。

十倍时间老化率(AGEING RATE PER DECADE) Y表示某一参数

频率常数(FREQUENCY CONSTANT)

　　对于径向和横向长度伸缩振动模式，其频率常数为串联谐振频率与决定此频率的振子尺寸（直径或长度）的乘积。对于纵向长度厚度和伸缩切变振动模式，其频率常数为并联谐振频率与决定此频率的振子尺寸（长度或厚度）的乘积，其单位：HZ.M

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