JP3683365B2 - Method and apparatus for measuring unsteady aerodynamic forces - Google Patents

Description

[0001]
BACKGROUND OF THE INVENTION
The present invention relates to a method and apparatus for measuring unsteady aerodynamic forces, in which a wind tunnel test is performed using a model of the structure to investigate the structural mechanical characteristics of a suspended long structure subjected to wind force. .
[0002]
[Prior art]
The long structure body of the above-mentioned type of interest here is, for example, a huge suspension bridge. In recent years, construction of large bridges, especially suspension bridges and cable-stayed bridges, has continued. Suspension bridges connecting Honshu and Shikoku are several kilometers long, especially the longest of which is 4 kilometers. When the blowing wind hits the structure of the bridge, a so-called Karman vortex is generated behind it, and a force or moment, that is, aerodynamic force, is applied to the bridge. This aerodynamic force naturally increases with increasing wind power. It was this wind that caused the collapse of the bridge built in the Tacoma Valley, Colorado, USA. Therefore, in designing this kind of low-rigidity bridge, elucidate the various loads to be loaded, the winds of various wind speeds to be blown, the characteristics of the inclination angle, the vibration characteristics of the structure, and their mutual interference effects. It is essential.
[0003]
Conventionally, various methods have been used to address this problem. One of them is the wind tunnel test method with spring support. FIG. 1 shows the concept of this method. The model M of the structure housed in the wind tunnel wall WT is supported by a spring and exposed to various wind forces to examine the dynamic characteristics of the model. In other words, each of the other support rods SR2 orthogonal to the support rods SR1 fixed on both sides of the model M has four ends (a total of four locations), each having a pair of upper and lower springs. It is supported by springs SP1 to SP4 and SP'1 to SP'4. Then, the force applied to the model M in the vertical direction and the vertical displacement, and the moment and rotation around the support rod SP1 of the model M are examined. In that case, in order to change the direction of the wind, that is, the elevation angle of the wind with respect to the model M, the ends of the springs SP1 to SP4 and SP'1 to SP'4 (opposite the connecting end to SR2) are turntables. It is fixedly connected to the structure of TT. Further, springs SP9, which are flow prevention mechanisms, are connected to the support rods SR1 at both ends of the model M so that the model M is not swept away by wind power. The spring constants of the springs SP1 to SP4 and SP'1 to SP'4 are selected according to the rigidity of the structure. Hereafter, the vertical direction shown in the figure is the Z axis, the longitudinal direction of the model M is the Y axis, and the longitudinal direction of the model M corresponding to the wind direction is the X axis. In this test facility, the turntable TT can be rotated in the ω direction from the Z direction shown (see also FIG. 2a). Therefore, vibration in the ω direction and rotational vibration around the longitudinal axis of the model, that is, the support rod SP1, are allowed. Therefore, the phenomenon that the model M vibrates depending on the wind speed can be measured while being controlled by the vibration damping mechanism or the like, and the aerodynamic characteristics of the model can be clarified.
[0004]
As another method, an unsteady aerodynamic force measurement method is known. The method described above observes the behavior of the model M supported by the spring in the air flow and measures the displacement of the model due to the air flow to obtain the aerodynamic force. At that time, the aerodynamic force generated in the model is directly measured. A detector that measures a two component force, which is a moment about the Z direction and the Y axis, suitable for this measurement is disclosed in Japanese Patent Laid-Open No. 51-36985, which has already been proposed by the applicant as one of the inventors. . A vibrating device that applies displacement vibration in the Z direction and rotational vibration around the Y axis to the model is also disclosed in Japanese Patent Publication No. 4-57972 proposed by the present applicant.
[0005]
It is known that a recent huge suspension bridge is several kilometers long, and the displacement in the X direction due to wind is remarkably large. In fact, a huge suspension bridge of about 4 kilometers, such as Akashi Bridge, receives a crosswind of 75 meters per second (which corresponds to the instantaneous maximum wind speed of Muroto Typhoon), and the middle of the bridge moves in the longitudinal direction (X direction). It is expected to be displaced by about 38 meters. The occurrence of such a large displacement requires a fundamental review of the material to be used and its shape from the viewpoint of vibration and displacement in the wind flow direction (X direction). In other words, it is necessary to actually verify not only the two components as described above, the displacement in the Z direction and the rotation around the Y axis, but also the displacement in the X direction and the corresponding component force. No elucidation has yet been made.
[0006]
When designing this type of suspension bridge, increase the manufacturing cost by making the weight more than necessary or making the bridge structure more complex than necessary to achieve the desired structural stability in various suspensions and loads. Detailed experimental verification is desired so that there is no problem.
[0007]
[Problems to be solved by the invention]
Therefore, an object of the present invention is to create a state corresponding to an arbitrary suspended state by an excitation mechanism that generates vibrations in the Z and X directions and the Y axis, and the Z direction and X applied to the structure under this state. An object of the present invention is to provide an unsteady aerodynamic force measuring method and apparatus capable of actually measuring directional forces F _{Z and} F _X and a moment M _Y around the Y axis.
[0008]
[Means for Solving the Problems]
According to the present invention, the above-described problems are solved by the fact that the vibration is performed at the same frequency in the vertical and longitudinal directions and the longitudinal axis, and the amplitude of each vibration can be varied independently, and the mutual vibration phase can be varied at the same time. The
[0009]
Furthermore, the problem is, this invention, both ends detector D _L of the model M that are arranged in the wind tunnel _MT, a mounting support MB which holds through D _R, a solid the mounting support MB on the ground An apparatus for measuring unsteady aerodynamic forces applied to a model M by applying vibration mechanisms VB _{1 to} VB ₃ that vibrate the installed base B and applying winds of various wind speeds to the model M , The vibration mechanisms VB _{1 to} VB ₃ are used to model the reciprocating motion displacement transmitted from the eccentric crank mechanism having the motors MT _{1 to} MT ₃ and the flywheels FW _{1 to} FW _{3 and} FW ₁ ^' FW ₃ ^'. A mechanism for converting vibration displacement around the vertical (Z-axis) direction, the front-rear (X-axis) direction and the longitudinal axis (Y-axis) of the model, and the detectors D _{L and} D _R are at least vertically maybe forces longitudinal force F _Z, a moment M _Y around the the F _X longitudinal axis can be measured An output unit, can be changed by the eccentricity of the amplitude of the signal can be mechanically manual adjustment of the eccentric crank EC ₁ ~EC _3, frequency and vibration of the phase of the vibration control motor MT ₁ to MT ₃ a pulse width modulation This is solved by providing an electrical control unit 14 that performs the following.
[0010]
Other advantageous configurations according to the invention are described in the dependent claims.
[0011]
DETAILED DESCRIPTION OF THE INVENTION
According to the above configuration, the model of the structure to be tested is subjected to three component forces, that is, a Z-direction force (vertical force) F _z
Force in the X direction (front / rear force) F _x
Moment around Y axis (rotational force) _MY
It is fixed to a support base via a three-component force detector that can detect the above, and this support base is supported to be displaceable with respect to a base fixed on the ground. Further, an excitation mechanism that allows displacement vibration in the X and Z directions and rotational vibration about the Y axis is connected to the support base. And the model supported in this way is arrange | positioned in the wind path of a wind tunnel. The vibration mechanism can move in three directions, that is, linear movement in the X and Z directions and rotational movement around the Y axis, independently of amplitude and phase, and at the same time, the angular frequencies ω _v, ω _{h, and} ω _r have three components. Can be varied independently. In this case, the vibration of each component A _V, A _H, A _R
Vibration in the Z direction (up and down): A _V = a _v sin (ω _v t)
X-direction (front-rear) vibration: A _H = a _h sin (ω _h t + φ _h )
Rotational vibration around Y: A _R = _ar sin (ω _r t + φ _r )
It can be expressed as Here, a _v, a _{h, and} a _r mean the amplitude of each vibration, and φ _h and φ _r mean the phase difference of each component with respect to the vibration in the Z direction.
[0012]
With the three kinds of vibration degrees of freedom that can be selected in this way, it is possible to easily collect experimental data that cannot be obtained in the spring support test and the two-way unsteady aerodynamic force measurement test that belong to the prior art described above. In particular, the dynamics of structures exposed to wind at various wind speeds in the presence or absence of vibration or displacement in the front-rear direction (X direction), which was not taken into account in both of the tests that have been adopted conventionally. The characteristics can be examined in detail.
[0013]
In addition, since the vibration of the former model is in the ω direction (see FIG. 1b), the latter is in the Z direction. According to the present invention, if the phase φ _h of the longitudinal vibration with respect to the vertical vibration is selected to be 0 ° or 180 ° and at the same time ω _h and ω _v are selected to be equal (such vibration is referred to as coupled vibration), the combined vibration The direction ω is
tan α = A _H / A _V = a _h / a _v
(See Figure 2b). Thus, if the vertical vibration and the longitudinal vibration are selected in the same phase and the amplitude of both vibrations is adjusted, the variable resistance of the electric control device can be used without using a large-scale device such as the turntable TT shown in FIG. The vibration direction can be easily adjusted simply by setting a value.
[0014]
【Example】
Hereinafter, the present invention will be described in more detail based on preferred embodiments with reference to the drawings.
FIG. 3 schematically shows the overall configuration of the unsteady aerodynamic force measuring apparatus according to the present invention. A model M of the structure to be tested is connected to a model support MB via a detector D. As will be described in detail later, the model support part MB is supported to be displaceable with respect to a base B fixed on the ground. In actual use, the model M is disposed in the wind tunnel WT. Then, the wind indicated by the arrow W is applied to the model M. The base B is provided with three independent vibration mechanisms VB _1, VB _{2, and} VB ₃ that give three-way component forces F _Z, F _{X, and} M _Y to the support portion MB. The displacement or rotation of the support portion due to the vibration application is detected by the vibration detectors DD _1, DD _2, DD ₃ , and the rotation angle of the motor that is the power of the vibration mechanisms VB _1, VB _2, VB ₃ is also detected by the rotation angle detector RD. _1, RD _{2 and} RD ₃ are detected. The detection signal of the component component of the three components of the detector D is introduced into the amplification unit 12 via the conducting wire L ₁ . The vibration detectors DD _1, DD _2, DD ₃ and the rotation angle detectors RD _1, RD _2, RD ₃ are connected via conductors L ₄ and L _2. The vibration control unit 14 is introduced, and a predetermined control signal is supplied from the vibration control unit 14 to the vibration mechanisms VB _1, VB _{2, and} VB ₃ via the conductor L ₃ . The detection signal of the detector D filtered or processed in the response frequency band by the amplification unit 12 and the detection signal and control signal introduced into the vibration control unit 14 are introduced into the comprehensive evaluation unit 16, and comply with predetermined rules regarding structural mechanical properties. In response, it is output to an electromagnetic oscilloscope or an appropriate recording device.
[0015]
FIG. 4 is a front view of the unsteady aerodynamic force measuring apparatus according to the present invention as viewed from the windward side. The model M in the wind tunnel WT are fixed each mounting flange FG _L, suitable means FG _R 3 component force detector D _L, D _R at both ends, for example by bolting. Both detectors D _{L and} D _R are connected to a model support portion hidden in the cover of the base B.
FIG. 5 is a plan view of the unsteady aerodynamic force measuring apparatus according to the present invention. In this case, the model is removed. The motors MT _1, MT _2, MT ₃ are fixed to the base in order to apply vertical and longitudinal vibrations and rotational vibrations. These motors MT _1, MT _2, MT ₃ rotate at their ends with shafts SF _1, SF ₂ with flywheels FW _1, FW ₁ ′, FW _2, FW ₂ ′, FW _3, FW ₃ ′, respectively. _, SF ₃ . Eccentric crank mechanisms EC _1, EC _{2 and} EC ₃ (details will be described later) are further attached to these shafts SF _1, SF _{2 and} SF ₃ . The rotational motions transmitted to the eccentric crank mechanisms EC _1, EC _2, EC ₃ are converted into reciprocating motions by connecting rods CR _1, CR _2, CR ₃ , and the second shafts SF ₁ ′ _, SF ₂ ′, SF ₃ Is transmitted as a reciprocating reciprocating motion. This reciprocating motion is further transmitted to a pair of second connecting rods CR _1L, CR _1R, CR _2L, CR _2R, CR _{3L, and} CR _3R , respectively. Transmitted to the department. The balance weights BL _L, BL _L ′ _, BL _R, BL _R ′ connected to each mounting support portion perform reverse vertical movement when the mounting support portion moves up and down, and the center of gravity of each mounting support portion Is adjusted according to the weight and lever length of the balance weights BL _L, BL _L ′ _, BL _R, BL _R ′ so that they are maintained at a substantially constant vertical position. In this way, vibration is prevented from being transmitted to the outside of the base when the mounting support portion moves up and down.
[0016]
FIG. 6 is a schematic side view showing how three kinds of vibration motions of the mounting support portion are generated. A mechanism for generating rotational vibrations, b for vertical vibrations, and c for longitudinal vibrations are schematically shown. The reciprocating motion transmitted to the first connecting rod CR is via a link portion LK ₀ that is rotatably supported by the bearing SP _0. Is transmitted to the second connecting rod CR _a or CR _b or CR _c.
[0017]
The rotational vibration in Figure 6a, the reciprocating motion transmitted to the second connecting rod CR _a is introduced via the link LK _R to rotate lever LV _R, which is rotatably fixed to the rotating pin SP _R. Pivoting movement of the lever LV _R is transmitted to the linked lever CP detector D which is rotatably supported by the rotary shaft DC via a connecting bar CB, detector D is an arrow about an axis of rotation DC Rotate vibration as shown.
[0018]
The vertical vibration of 6b, the reciprocating motion transmitted to the second connecting rod CR _b is introduced via the link LK _U to rotate lever LV _U which is rotatably fixed to the rotating pin SP _U. Pivoting movement of the lever LV _U, the detector D and the support, it is transferred to both sides in guide rolls GR ₁ ~GR slidably retained the support frame SPR at _4, the detector D as shown by arrow Is given vertical vibration. Although not shown in this figure, each lever having the balance weight shown in FIG. 5 is actually connected to both sides of the support frame SPR, and the rotatable fulcrum of this lever is fixed to the base. ing. At this time, when the support frame SPR moves up, the balance weight moves down, and when the support frame SPR moves down, the balance weight moves up. In this way, the center of gravity of the system including the support frame SPR and the balance weight is designed so as not to fluctuate.
[0019]
The vertical vibration of Figure 6c, the reciprocating motion transmitted to the second connecting rod CR _C is introduced via the link LK _F to rotate lever LV _F which is rotatably fixed to the rotating pin SP _F. The swinging motion of the lever LV _F gives a back-and-forth vibration in the front-rear direction to the detector D as indicated by an arrow.
FIG. 7 shows details of the flywheel FW and the eccentric crank mechanism EC. As shown in the figure, a screw SCW that penetrates the center of the shaft C from the side is provided near the tip of the axis C of the first shaft that penetrates the center of the flywheel FW, and the movement can be moved according to the rotation of the screw SCW. Mount the base CRP. A cylindrical projection CRC is provided at the center of the movable table CRP, and the bearing portion AB of the first connecting rod CR is rotatably fitted to the cylindrical projection CRC. If necessary, for example, a ball bear rig may be interposed between the circular protrusion CRC and the bearing portion AB. With this structure, the eccentricity of the eccentric crank is determined by the distance between the center of the axis C and the center of the cylindrical protrusion CRC. That is, if the eccentricity of the eccentric crank is increased, the amplitude of the corresponding vibration, that is, the vertical vibration, the longitudinal vibration, or the rotational vibration can be increased accordingly. In other words, the eccentricity of the eccentric crank mechanisms EC _1, EC _{2, and} EC ₃ of FIG. 5 can be varied independently, and the amplitudes of vertical, front and rear, and rotational vibrations can be arbitrarily selected.
[0020]
Although not shown, the amplitude of the actually applied vibration is measured by a rotation detector such as a potentiometer directly connected to the second shafts SF ₁ ′ _, SF ₂ ′, SF ₃ ′ of FIG. In that case, it is necessary to measure in advance the proportionality coefficient between the actual displacement or rotation amount and the output value of the rotation detector.
3 component force detector to be used in this invention, 2 component force detector used in the unsteady aerodynamic force measuring device disclosed in JP-A-51-36985 (F _Z and M _Y component force measurement ) In principle. That is, the component force to be measured is highly accurate, and the component force generated by the weight of the detection itself needs to be offset. For this reason, a sensing part is provided on the fixed base of the support part via a gimbal mechanism, and a balance weight against lift and moment that cancels the component force generated by its own weight is attached. FIG. 8 schematically illustrates the principle functions of the extendable joint, the gimbal mechanism, the balance weight, and the sensing part (F _X, F _Z, M _Y ) that connect the model M and the detector. Here, lift force and drag force correspond to component forces of F _Z and F _X , respectively. The actual structure is for detecting two-component force, but it is disclosed in 1977 by the Ministry of International Trade and Industry, Corona Corporation, Vol. 26, No. 7 Please refer to.
[0021]
Further, the detection signals of the detectors D _{R and} D _L attached to both ends of the model M are added in the amplification unit 12. Subsequent measurement processing of the unsteady aerodynamic force is performed using this addition signal.
Next, FIG. 9 shows a schematic block diagram of an electric circuit that generates a control current for controlling the motor MT of the vibration exciting mechanism. A reference signal is output from a waveform generation circuit 22 that generates a sine wave that gives a desired vibration, and this is introduced into the delay circuit 24 via a switch SW. On the other hand, the deviation signal is obtained by subtracting the output signal of the rotation angle detector RD to which the rotation shaft of the motor MT is attached and the output signal of the delay circuit 24 from each other at the subtraction point 25. A carrier wave signal (mainly a triangular wave signal) supplied from the carrier wave generating circuit 28 is compared with the deviation signal, and two drive signals, so-called pulse width control signals Q and Q , which are inverted from each other by making the difference signal a rectangular wave are generated. . These control signals are sent to the switching elements 30 and 32, respectively, and these switching elements are on / off controlled. The positive and negative voltages of the DC power supply 34 are applied to one terminal of each switching element 30, 32. The other terminals of the switching elements 30 and 32 are connected in common and connected to a common return line of the DC power supply via the motor MT. This circuit system is a so-called inverter circuit and can generate drive currents of various frequencies. According to the present invention, the rotation frequency ω of the corresponding motor MT can be set by the variable resistor VR ₁ attached to the waveform generation circuit 22, and the rotation phase φ can be changed by the variable resistor VR ₂ attached to the delay circuit 24. .
[0022]
According to this invention, the motor control circuit attached to each of the vibrations of up and down, front and rear, and rotation can be adjusted independently. That is, ω and φ can be arbitrarily changed for each of the _three motors MT _1, MT _{2, and} MT ₃ . If the switch SW is connected as shown in FIG. 9, the drive signal of the common angular frequency ω ₀ adjusted by the common waveform generator 20 is used as an inverter corresponding to each motor MT _1, MT _2, MT _3. Can be introduced into the circuit. Then, the delay circuit 24 of each channel adds an appropriate phase difference φ and introduces it to the gate of the switching element. For example, the other channel 40 is implied by a broken line. Such a case where the three types of vibrations are excited at a common frequency is referred to as coupled excitation. That is, individual vibration excitation and coupled vibration excitation can be performed according to the switching mode of the switch SW.
[0023]
FIG. 10 shows a specific example in the case where the setting unit and the display unit of the vibration unit are configured by digital circuits. Here, the driving unit 100 for driving the motor is configured by an analog circuit, and a signal of a tachometer TG attached to each motor is used as a feedback signal. The signal of the rotation angle detector RD is used for rotation angle measurement (counting by a counter), and the set frequency and phase difference can be set by a digital switch. Although the description of the individual elements of the digital circuit is omitted, the variable resistor shown in FIG. 9 is configured by a digital switch.
[0024]
The specifications of the actual excitation unit thus obtained are as follows.
Excitation amplitude back and forth / up and down ± 20 mm
Direction of rotation ± 5 °
Excitation frequency range 0.1 to 10 Hz
Maximum excitation acceleration front / rear / vertical direction ≤ 0.5 G
Direction of rotation ≤ 1.0 G
Excitation mode Variable phase difference in single independent mode or coupled mode coupled mode 360 °
The weight of the model that can be mounted is 5 kg and the size is 0.6 to 1.6 m.
[0025]
Furthermore, the detector performance is drag (F _X ) ± 2.0 kgf
Lifting force (F _Z ) ± 2.0 kgf
Pitching ( _MY ) ± 0.2 kgf-m
Linearity and temperature characteristics ± 1% FS or less.
[0026]
The wind tunnel test of a long suspension bridge divides the bridge into tens of ones, performs wind tunnel tests on each divided segment, measures aerodynamic forces, and combines these results comprehensively. The dynamic mechanical properties of the entire bridge can be measured.
Various modifications and improvements can be made to the unsteady aerodynamic force measuring apparatus and the measuring method having the configuration described here. However, it goes without saying that all configurations defined in the claims belong to the category of the present invention.
[0027]
【The invention's effect】
As described above, the unsteady aerodynamic force measurement method according to the present invention and the apparatus that implements the method can provide a state corresponding to an arbitrary suspended state by the vibration generating mechanism that generates vibrations in the Z and X directions and around the Y axis. In this state, the forces F _{Z and} F _{X in the} Z direction and the X direction applied to the structure under this state and the moment M _Y about the Y axis can be measured.
[Brief description of the drawings]
FIG. 1 is a schematic diagram showing the principle of a spring support measurement method;
FIG. 2 is a schematic diagram defining the vibration of the model,
FIG. 3 is a functional block diagram of the entire system of the unsteady aerodynamic force measuring apparatus according to the present invention;
FIG. 4 is a front view of the unsteady aerodynamic force measuring device.
FIG. 5 is a plan view of the unsteady aerodynamic force measuring device,
FIG. 6 is a schematic side view showing various vibration mode generation principles;
FIG. 7 is an enlarged side view of an eccentric crank mechanism,
FIG. 8 is a principle diagram of a three component force detector,
FIG. 9 is a schematic block circuit diagram for explaining the function of the vibration control unit;
FIG. 10 is a block circuit diagram showing a digital configuration of setting and display of an excitation control unit.
[Explanation of symbols]
M Model WT Wind tunnel D Detector B Base MB Mounting support RD _{1 to} RD ₃ Rotation detector DD _{1 to} DD ₃ Displacement detector VB _{1 to} VB ₃ Excitation mechanism EC Eccentric crank 12 Component force detection amplifier 14 Excitation Control unit 16 Comprehensive evaluation unit

Claims (4)

A mounting support part that holds both ends of the model arranged in the wind tunnel via a detector, and an excitation mechanism that vibrates the mounting support part with respect to a base fixed to the ground. The body is vibrated with respect to the model in the vertical (Z-axis) direction, the longitudinal (X-axis) direction, and the longitudinal axis (Y-axis) of the model, and the forces in the vertical and longitudinal directions and the moments around the longitudinal axis are at least Measure the component force applied to the model using a multi-component force detector capable of measuring three component forces. Apply unsteady aerodynamic force applied to the model under vibration conditions by applying wind of various wind speeds to the model. In the method
The method is characterized in that the excitation is performed at the same frequency in the vertical direction, the front-rear direction, and the longitudinal axis, the amplitude of each vibration can be varied independently, and the mutual vibration phase can be varied at the same time. A mounting support part (MB) for holding both ends of the model (M) arranged in the wind tunnel (MT) via detectors (D _L, D _R ), and the mounting support part (MB) are fixed to the ground. Provided with a vibrating mechanism (VB _{1 to} VB ₃ ) for vibrating the base (B), the model (M) under a vibrating state by applying winds of various wind speeds to the model (M). In the device for measuring the unsteady aerodynamic force applied to
The eccentric mechanism (VB _{1 to} VB ₃ ) has three eccentric cranks each provided with one electric motor (MT _{1 to} MT ₃ ) and a corresponding flywheel (FW _{1 to} FW _3, FW ₁ ^′ FW ₃ ^′ ). Three mechanisms that separately convert the reciprocating displacement motion transmitted from the mechanism into vibration displacements in the vertical (Z-axis) direction, the longitudinal (X-axis) direction, and the longitudinal axis (Y-axis) of the model,
Said detector (D _L, D _R) is up and down with respect to models, be perhaps force detector capable of measuring at least three component force is a moment M _Y of the about the longitudinal axis longitudinal force F _Z, and F _X ,
The amplitude of each signal can be varied by the eccentricity of the eccentric crank (EC _{1 to} EC ₃ ) that can be manually adjusted mechanically,
An electric control unit (14) that controls the electric motors (MT _{1 to} MT ₃ ) by pulse width modulation to vary the frequency and phase of three types of vibration within a predetermined range;
A device characterized by that.   The device according to claim 2, characterized in that the electrical control unit (14) provides an independent vibration excitation mode in which the vibration is independently performed in the vertical and longitudinal directions and around the longitudinal axis in terms of frequency and amplitude. .   The electric control unit (14) performs excitation at the same frequency in the vertical and longitudinal directions and around the longitudinal axis, and the vibration amplitude can be varied independently and the mutual vibration phase can be varied. The apparatus according to claim 2, wherein a mode is provided.

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