JP5476079B2 - Ultrasonic motor - Google Patents

Description

  The present invention relates to an ultrasonic motor that vibrates a rectangular laminated piezoelectric vibrator in a multiple vibration mode.

  2. Description of the Related Art Conventionally, a technique is known in which an electrode for a sensor is provided on an ultrasonic motor or actuator using a multilayer piezoelectric element, and the operation of the multilayer piezoelectric element is controlled by a signal extracted therefrom (Patent Document 1). 2, 3).

  The actuator described in Patent Document 1 includes an actuator portion and a sensor portion that are integrally laminated with an insulating material layer interposed therebetween. Piezoelectric ceramics that have been subjected to polarization treatment in the thickness direction as a piezoelectric material layer are used for the sensor portion. It has been. Then, when the actuator part is displaced in the thickness direction, the electric field of the sensor part is displaced according to the displacement amount, and the displacement amount of this electric field is sampled and held as a voltage signal and fed back to the control unit. Sensing sensitivity is improved by detecting non-linear stress fluctuations.

  The laminated piezoelectric element described in Patent Document 2 is a laminated piezoelectric element in which a plurality of piezoelectric element plates each having an electrode formed on one side of a piezoelectric ceramic are laminated in the thickness direction, and a part of the piezoelectric ceramic layer is used as a sensor phase. An electrode for extracting a sensor phase signal is provided on the piezoelectric element plate. A sensor electrode having one wavelength width is provided in non-contact with the conduction hole, while the uppermost piezoelectric element plate is formed with an electrode that conducts with the sensor electrode by a through hole or the like. The drive control of the drive device is going to be performed with high accuracy.

  In the vibration wave motor described in Patent Document 3, the surface electrode layer is disposed in the first layer and the piezoelectric layer is disposed in the second layer in the laminated piezoelectric element. In the layers from the third layer to the Nth layer, different piezoelectric layers are alternately arranged, and an internal electrode divided into four is formed on the surface of the piezoelectric layer. On the surface of the piezoelectric layer, four internal electrodes are formed, and in each piezoelectric layer, only the internal electrode which is the sensor phase and the internal electrode arranged in the same phase are exposed to the outside of the piezoelectric layer. Thus, the traveling wave unevenness of a small vibration wave motor is reduced.

Japanese Patent No. 3059038 Japanese Patent No. 3729781 JP 2007-13039 A

  As described above, there are piezoelectric actuators provided with electrodes for sensors. However, an ultrasonic motor driven in a multiple vibration mode that combines a spread vibration mode and a bending vibration mode has a configuration in which sensing is performed by electrodes. It has not been developed and efficient detection and control of the drive is not performed.

  The present invention has been made in view of such circumstances, and in an ultrasonic motor driven in a multiple vibration mode that combines a spread vibration mode and a bending vibration mode, efficient detection of driving with a compact configuration is possible. An object of the present invention is to provide an ultrasonic motor that enables control.

  (1) In order to achieve the above object, an ultrasonic motor of the present invention is a rectangular ultrasonic motor used for vibration in a multiple vibration mode, and is formed by stacking piezoelectric layers and the stacked piezoelectric layers. Drive electrodes and ground electrodes that are alternately layered, and a sensing electrode that is layered in a plane where the drive electrode is layered on one main surface side of the stacked piezoelectric layers that are used for drive detection. And when the length of one side of the two sets is L and the length of the side of the other set is w, the resonance frequency of the spread vibration and the resonance frequency of the bending vibration are substantially It is characterized by being formed based on the value of w / L which is the same.

  Thus, the inactive layer volume ratio that does not contribute to the operation can be reduced by providing the drive electrode and the sensing electrode in the same plane. In addition, an ultrasonic motor that vibrates a rectangular laminated piezoelectric vibrator in multiple modes of spreading vibration and bending vibration can be configured compactly. As a result, since the ratio of the piezoelectric active layer is larger than when the sensing layer is separate from the drive layer, it is possible to provide an efficient high performance ultrasonic motor.

  (2) Further, the ultrasonic motor of the present invention is characterized in that two sensing electrodes are provided at symmetrical positions with respect to the center of the whole. As a result, the structure is symmetrical to eliminate the bias of operation.

  (3) Further, in the ultrasonic motor of the present invention, the sensing electrode has a half electrode area, and the driving electrode in the plane in which the sensing electrode is installed has a half electrode area. It is characterized by having. As a result, the driving state can be detected while driving the ultrasonic motor, without being disturbed by the sensing layer.

  (4) Further, the ultrasonic motor of the present invention is characterized in that the inner layered drive electrode, ground electrode and sensing electrode are connected to input, ground and detection terminals by external electrodes, respectively. As described above, the volume ratio of the inactive layer that does not contribute to the operation can be reduced by increasing the volume ratio of the active layer by using the external connection without using the through hole.

  (5) In the ultrasonic motor of the present invention, the piezoelectric layer is polarized in two polarization directions in the same layer, and a one-phase driving voltage is applied to the inner layer driving electrode. It is characterized by that. As described above, when one-phase driving is performed, the operation can be sensed by obtaining a constant voltage waveform in the operation direction voltage using the sensing electrode. Therefore, the sensor circuit can be simplified if only a certain voltage waveform can be sensed without sensing the phase difference.

  ADVANTAGE OF THE INVENTION According to this invention, the efficient detection and control of a drive can be enabled by a compact structure in the ultrasonic motor driven by the multiple vibration mode which combined the expansion vibration mode and the bending vibration mode.

It is a front view of the ultrasonic motor concerning the present invention. It is a figure which shows a mode that the ultrasonic motor which concerns on this invention is spreading and vibrating. It is a figure which shows a mode that the ultrasonic motor which concerns on this invention is carrying out bending vibration. It is a figure which shows a frequency spectrum when a rectangular-shaped piezoelectric vibrator is vibrated in a plurality of types of vibration modes. It is a figure which shows an example of a structure of the sheet | seat lamination at the time of preparation of a piezoelectric vibrator. 1 is a perspective view of a piezoelectric vibrator according to the present invention. It is a top view which shows the electrode pattern on a drive layer. It is a top view which shows the pattern of a ground electrode. It is a top view which shows the electrode pattern on a sensing layer. It is a top view which shows the electrode pattern on a sensing layer. It is a figure which shows the wiring with respect to the electrode on the drive layer of the ultrasonic motor which concerns on 1st Embodiment. It is a figure which shows the wiring with respect to the electrode on the sensing layer of the ultrasonic motor which concerns on 1st Embodiment. It is a graph which shows the input voltage with respect to time in 1st Embodiment. It is a graph which shows the sensing voltage with respect to time in 1st Embodiment. It is a graph which shows the sensing voltage with respect to time in 1st Embodiment. The It is a figure which shows the application example of the ultrasonic motor which concerns on 1st Embodiment. It is a figure which shows the application example of the ultrasonic motor which concerns on 1st Embodiment. It is a figure which shows the wiring with respect to the electrode on the drive layer of the ultrasonic motor which concerns on 2nd Embodiment. It is a graph which shows the input voltage with respect to time in 2nd Embodiment. It is a graph which shows the sensing voltage with respect to time in 2nd Embodiment.

  Next, embodiments of the present invention will be described with reference to the drawings. In order to facilitate understanding of the description, the same reference numerals are given to the same components in the respective drawings, and duplicate descriptions are omitted.

[First Embodiment]
FIG. 1 is a front view of the ultrasonic motor 10. As shown in FIG. 1, the ultrasonic motor 10 includes a piezoelectric vibrator 1 and a sliding chip 2, and can be driven by vibrating the rectangular laminated piezoelectric vibrator 1 in a multiple vibration mode. The piezoelectric vibrator 1 is formed of rectangular laminated piezoelectric ceramics, and each layer is polarized in either the positive or negative direction in the z direction of FIG. A known material such as a lead zirconate titanate ceramic can be used for the piezoelectric vibrator 1. The piezoelectric vibrator 1 is manufactured according to a general ceramic manufacturing process, for example, a manufacturing process of forming (degreasing), firing, and processing of piezoelectric ceramic powder. By applying a silver paste to the manufactured piezoelectric vibrator 1 in a predetermined pattern by screen printing or the like and baking it, two electrodes described later can be provided on one main surface.

  In addition, a sliding chip 2 for transmitting a driving force is provided in the central portion on the upper side with respect to the paper surface of the piezoelectric vibrator 1. The sliding tip 2 is made of a material having excellent wear resistance. For example, ceramic parts such as alumina, zirconia, silicon nitride, and silicon carbide, wear-resistant metal parts such as super-rigid, parts having a hard metal material coated with a ceramic thin film or a diamond thin film, and the like are preferably used.

  In addition, as shown by a dotted line in the drawing, sliding tips 3a and 3b may be provided at both ends of the y-direction end of the piezoelectric vibrator 1. When the sliding tip 2 is provided at the center of the y-direction end of the piezoelectric vibrator 1, it is suitable for driving a rotating body such as a disk or a sphere. When the sliding tips 3a and 3b are provided at both ends, it is suitable for driving a sliding body that operates linearly. Also, as shown in FIG. 1, the length of one set of the two sides of the rectangular piezoelectric vibrator 1 is L, and the length of the other set of sides is w.

  FIG. 2 is a diagram illustrating a state in which the ultrasonic motor 10 is expanding and vibrating. The spreading vibration is vibration in which the rectangular piezoelectric vibrator 1 repeats expansion and contraction in the direction of four sides from the center. The potential distribution of the piezoelectric vibrator 1 becomes higher toward the end face with equipotential lines almost in parallel. FIG. 3 is a diagram illustrating a state in which the ultrasonic motor 10 is bending-vibrated. Bending vibration means that the rectangular piezoelectric vibrator 1 bends two-dimensionally, but in the potential distribution, potentials having opposite signs are generated at the output-side central portion and both sides in the width direction. When the expansion vibration mode shown in FIG. 2 and the bending vibration mode shown in FIG. 3 are combined (degenerated), the sliding tip 2 or the sliding tips 3a and 3b perform an elliptical motion, and a driving force is generated.

  Next, the driving principle of the ultrasonic motor will be described. FIG. 4 is a diagram showing a frequency spectrum when the rectangular piezoelectric vibrator 1 is vibrated in an expansion vibration mode (Expand Mode) and a bending vibration mode (Flexural Mode). Of the two sets of sides of the rectangular piezoelectric vibrator 1, the length of one set of sides is L and the length of the other set of sides is w. As shown in FIG. Using / L as a variable, w / L and the resonance frequency of the vibration mode of the piezoelectric vibrator are made to correspond, and w / L and the resonance frequency of the bending vibration mode are made to correspond.

  In FIG. 4, L is fixed at 20 mm, and only w (Width) is changed. In this case, w is 17.0 mm, that is, the ratio between the two sides in the vertical and horizontal directions (hereinafter referred to as “side ratio”) w / L is about 0.85, the resonance frequencies of both coincide, and the two vibrations are degenerated To do. The resonance frequency at this time is 107 kHz to 108 kHz. In this way, the side ratio is 0.85, and the side becomes a square having a side of about 20 mm, so that the size can be reduced.

  FIG. 5 is a diagram illustrating an example of a configuration of sheet lamination when the piezoelectric vibrator 1 is manufactured. In the figure, the sheet number indicates the number of sheets to be laminated, the sheet thickness indicates the thickness of each sheet, and the type of inner layer printing indicates the pattern of inner layer printing. The print patterns J1, GND, S1, and S2 correspond to electrode patterns that will be described later. In the example shown in FIG. 5, the third to sixth sheets, the 11th to 14th sheets, the 25th to 28th sheets, and the 33rd to 36th sheets of the piezoelectric vibrator are sheets serving as driving layers, and the third sheet and the 11th sheet. Driving electrodes are printed on the 29th and 37th sheets. The drive layer is a piezoelectric layer that causes displacement when a voltage is applied.

  A ground electrode is printed on the seventh, fifteenth, twenty-fifth, and thirty-third sheets. Further, the 15th to 18th sheets and the 21st to 24th sheets are sheets that become sensing layers, and sensing electrodes and drive electrodes are printed in the same plane on the layers. The piezoelectric vibrator 1 is obtained by firing the formed body formed by laminating the sheets in this way. The sensing layer is a piezoelectric layer for detecting driving. Note that the above laminated structure is an example, and the order is not necessarily in this order, but the electrode patterns are preferably laminated so that the positions of the electrode patterns are centrosymmetric.

  FIG. 6 is a perspective view of the piezoelectric vibrator 1. The piezoelectric vibrator 1 is formed of rectangular laminated piezoelectric ceramics, and the polarization direction of each layer coincides with either positive or negative in the z-axis direction of the coordinate axis shown in FIG. The piezoelectric vibrator 1 spreads in the direction of the xy plane and vibrates in the vibration mode. The length of the piezoelectric vibrator 1 in the x-axis direction is L and the length in the y-axis direction is w.

  The piezoelectric vibrator 1 has a ground electrode and a drive electrode that are alternately provided on the surface or between layers of the stacked piezoelectric layers. The piezoelectric vibrator 1 includes a sensing electrode that is provided in the same plane as the drive electrode and detects the operation of the piezoelectric vibrator 1 as a signal. That is, the sensing electrode is layered on the one main surface side of the drive layer in a plane on which the drive electrode is layered.

  FIG. 7A is a plan view showing an electrode pattern J1 on the drive layer. The drive electrodes 4a and 4b are each equally divided into approximately half the area of the main surface. And it has the extraction part exposed to the side surface of the piezoelectric vibrator 1, respectively. A predetermined alternating voltage is applied to each of the drive electrodes 4a and 4b having a diagonal relationship in the electrode pattern, and a voltage having a phase different by π / 2 from the voltage applied to the drive electrode 4a is applied to the drive electrode 4b.

  FIG. 7B is a plan view showing a ground electrode pattern GND. When an electric field is generated between the ground electrode 4c and the drive electrodes 4a, 4b, 4d, and 4f, the piezoelectric layer 1b therebetween is displaced. Further, when the piezoelectric layer 1b between the ground electrode 4c and the sensing electrodes 4e and 4g is displaced, a voltage is generated in the sensing electrodes 4e and 4g, and the driving of the piezoelectric vibrator 1 can be detected.

  7C and 7D are plan views showing electrode patterns S1 and S2 on the sensing layer, respectively. The sensing layer is used for driving detection among the stacked piezoelectric layers. The sensing electrodes 4e and 4g are formed in one rectangular shape when the entire main surface is divided into two, and have a half electrode area. The drive electrodes 4d and 4f are also formed in one rectangular shape when the entire main surface is divided into two and have a half electrode area. As a result, the driving state can be detected while driving the ultrasonic motor, without being disturbed by the sensing layer.

  Thus, the drive electrodes 4d and 4f are provided on the same plane as the sensing electrodes 4e and 4g. Thereby, the volume ratio of the inactive layer that does not contribute to the operation can be reduced, and the external extraction electrode can be configured in a compact manner. An ultrasonic motor that vibrates the rectangular laminated piezoelectric vibrator 1 in a multiple vibration mode combined with a bending vibration mode can be configured compactly. As a result, since the ratio of the piezoelectric active layer is larger than when the sensing layer is separate from the driving layer, the ultrasonic motor 10 can be provided with a sensing layer and have high performance.

  The drive electrodes 4a, 4b, 4d, and 4f are connected to input terminals by external electrodes. The ground electrode 4c is connected to the ground terminal by an external electrode. Each sensing electrode 4e, 4g is also connected to the detection part 6 mentioned later via the detection terminal by the external electrode. In this way, by making external connection without using a through hole, the volume ratio of the active layer can be increased, and the volume ratio of the inactive layer that does not contribute to the operation can be decreased.

  The same voltage as that of the drive electrode 4b is applied to the drive electrodes 4d and 4f. The two sensing electrodes 4e and 4g are provided at symmetrical positions with respect to the center of the piezoelectric vibrator 1, respectively. As a result, the structure is symmetrical to eliminate the bias of operation. The drive electrodes 4a, 4b, 4d, and 4f are preferably provided symmetrically with respect to the center.

  FIG. 8 is a diagram showing wiring for electrodes on the drive layer of the ultrasonic motor 10. In FIG. 8, the electrode surface on the drive layer of the piezoelectric vibrator 1 is schematically cut out. As shown in FIG. 8, in the ultrasonic motor 10, the drive electrode 4a and the drive electrode 4b are provided on the drive layer so that one main surface of the rectangular piezoelectric layer 1b is divided into two. A ground electrode 4c is provided on the other main surface of the drive layer and is grounded. The drive electrodes 4a and 4b are individually provided in a state of being insulated from each other.

The drive circuit of the ultrasonic motor 10 is composed of two AC voltage sources 5a and 5b. The AC voltage source 5a applies a voltage of V ₀ sin ωt to the drive electrode 4a, and the AC voltage source 5b applies a voltage of V ₀ cos ωt to the drive electrode 4b. As described above, when the voltages V ₀ sin ωt and V ₀ cos ωt having a phase shift of π / 2 with respect to the drive electrodes 4a and 4b of the piezoelectric vibrator 1 are applied, the piezoelectric vibrator 1 is applied with FIGS. As shown in FIG. 4, the vibration in the spread vibration mode that spreads on the xy plane and the vibration in the bending vibration mode that curves on the xy plane are generated.

When the resonance frequency of the spreading vibration mode is equal to the resonance frequency of the bending vibration mode, both vibration modes are combined (degenerate), and the chip of the piezoelectric vibrator 1 (not shown in FIG. 8) has an elliptical vibration. Will occur. The voltages V ₀ sin ωt and V ₀ cos ωt correspond to the first AC voltage and the second AC voltage, respectively. There is no problem even if the two are interchanged.

  As described above, since two electrodes are arranged side by side on either one of the main surfaces, the main surface is divided into four regions as in the L1F2 mode, and electric power is arranged in each region. The configuration can be made simpler than the configuration in which the electrodes positioned at the corners must be connected.

In the above example, the configuration of a two-phase signal input is described, but a configuration of a one-phase signal input may be adopted. In this case, it is also possible to operate by applying an AC signal of V ₀ sin ωt to one drive electrode 4a by the AC voltage source 5a and opening the other drive electrode 4b.

  FIG. 9 is a diagram illustrating wiring for electrodes on the sensing layer of the ultrasonic motor 10. As shown in FIG. 9, the same voltage as that of the drive electrode 4a shown in FIG. 8 is applied to the drive electrode 4d. As a result, the sensing layer is displaced in the same manner as the driving layer, and efficient driving is possible. On the other hand, the voltage generated in the sensing electrode 4e by driving is detected by the detection unit 6 connected to the sensing electrode 4e. Similarly, the voltage generated at the sensing electrode 4g is detected by the detection unit connected to the sensing electrode 4g.

Next, the operation when the ultrasonic motor 10 is driven in two phases will be described. FIG. 10A is a graph showing the input voltage with respect to time. The drive voltage Va shown in FIG. 10A is a voltage applied to the drive electrode 4a by the AC voltage source 5a and can be expressed as Va = V ₀ sin ωt. The drive voltage Vb is a voltage applied to the drive electrode 4b by the AC voltage source 5b and can be expressed as Vb = V ₀ cos ωt.

10B and 10C are graphs showing the sensing voltage with respect to time, respectively. The detection voltage V _S1 shown in FIG. 10B is a voltage generated at the sensing electrode 4e. Also, the detection voltage V _S2 shown in FIG. 10B is a voltage generated at the sensing electrode 4g. In the example shown in FIGS. 10B and 10C, the detection voltage V _S1 is a sine wave having a wave phase obtained by combining the drive voltages Va and Vb. The detection voltage V _S2 is a sine wave whose phase is changed by π from the detection voltage V _S1 . These indicate that the driving of the ultrasonic motor is normal. For example, if the phase of the detection voltage V _S1 and the detection voltage V _S2 is opposite to that in the above case, it is understood that a malfunction has occurred. In that case, the phases of the drive voltages Va and Vb are reversed and the magnitude of the voltage is adjusted to adjust the drive of the ultrasonic motor 10 to be normal.

  FIG. 11A is a diagram illustrating an application example of the ultrasonic motor 10. The ultrasonic motor 10 employs a configuration in which one sliding tip 2 is provided at the center of the side surface of the drive layer. This configuration is suitable for driving a rotating body such as a disk or a sphere, and rotates the disk 50 in the direction of the arrow in FIG. 11A.

  FIG. 11B is a diagram illustrating an application example of the ultrasonic motor 10. The ultrasonic motor 10 employs a configuration in which two sliding chips 3 a and 3 b are provided at both ends at the left end with respect to the paper surface of the piezoelectric vibrator 1. This configuration is suitable for driving a sliding body that operates linearly. In the second embodiment, a slider 61 that is slidably disposed on the linear guide 60 is slid in the direction of the arrow in FIG. 11B.

  As described above, according to this embodiment, the piezoelectric vibrator 1 is formed based on the value of w / L at which the resonance frequency of the spreading vibration and the resonance frequency of the bending vibration are substantially the same. Therefore, the shape of the main surface of the piezoelectric vibrator can be made closer to a square than when driven in another mode, for example, the L1F2 mode. As a result, the overall dimension does not become flat, and the depth dimension can be reduced. Thereby, it becomes possible to take a power input larger than the conventional one.

[Second Embodiment]
In the above embodiment, voltages having different phases are applied to the drive electrodes 4a and 4b, but voltages having the same phase as b may be applied. In that case, the piezoelectric layer between each drive electrode 4a, 4b and the ground electrode is previously polarized in the opposite direction. Thus, the piezoelectric layer is polarized in two polarization directions in the same layer, and a one-phase driving voltage is applied to the driving electrode.

  As described above, when the one-phase driving is performed, the operation of the ultrasonic motor 10 can be sensed by obtaining a constant voltage waveform in the operation direction voltage using the two sensing electrodes. Therefore, it is sufficient that only a certain voltage waveform can be sensed without sensing the phase difference, and the sensor circuit can be simplified.

FIG. 12 is a diagram showing wiring for electrodes on the drive layer of the ultrasonic motor 10. The wiring for the sensing layer is the same as in the above embodiment. 13A and 13B are graphs showing the input voltage with respect to time. The detection voltages V _S1 and V _S2 shown in FIG. 13B are detection voltages generated at the sensing electrodes 4e and 4g. In the example shown in FIG. 12B, the detection voltages V _S1 and V _S2 are sine waves having a wave phase obtained by synthesizing the drive voltages Va and Vb. This indicates that the driving of the ultrasonic motor is normal. For example, if the phases of the detection voltages V _S1 and V _S2 are opposite to those in the above case, it is understood that a malfunction has occurred. In that case, the drive voltages Va and Vb are reversed in phase, and the magnitude of the voltage is adjusted to adjust the drive of the ultrasonic motor 10 to normal.

DESCRIPTION OF SYMBOLS 1 Piezoelectric vibrator 2 Slide tip 3a, 3b Slide tip 4a, 4b, 4d, 4f Drive electrode 4c Ground electrode 4e, 4g Sensing electrode 5a, 5b AC voltage source 6 Detection part 10 Ultrasonic motor 50 Disc 60 Linear guide 61 Slider GND Ground electrode pattern J1 Electrode pattern S1 on drive layer, S2 Electrode pattern Va, Vb on sensing layer Drive voltage V _S1 , V _S2 detection voltage

Claims (5)

A rectangular ultrasonic motor used for vibration of multiple vibration modes by spreading vibration and bending vibration ,
Laminated piezoelectric layers;
Drive electrodes and ground electrodes alternately layered between the laminated piezoelectric layers;
On one main surface side of the laminated piezoelectric layer used for drive detection, the sensing electrode is provided in an inner layer in the surface on which the drive electrode is provided,
Of the two sets of sides, when the length of one set of sides is L and the length of the other set of sides is w, the value of w / L is formed to be 0.85 ,
The ultrasonic motor is characterized in that two sensing electrodes are provided at symmetrical positions with respect to the center of the whole . The sensing electrode has a half electrode area;
The ultrasonic motor according to claim 1 , wherein the drive electrode in the plane in which the sensing electrode is provided has a half electrode area. 3. The ultrasonic motor according to claim 1, wherein the inner layer drive electrode, ground electrode, and sensing electrode are connected to input, ground, and detection terminals by external electrodes, respectively. The piezoelectric layer is polarized in two polarization directions within the same layer,
The ultrasonic motor according to claim 1 , wherein a one-phase driving voltage is applied to the inner layer driving electrode. A determination method for determining whether or not the drive is normal using the ultrasonic motor according to claim 1,
When the ultrasonic motor is normally driven, the phase of the detection electrode detected by one of the two sensing electrodes coincides with the phase of the voltage obtained by synthesizing the drive voltage applied to the drive electrode. Having an electrode structure,
When the phase of the detection electrode detected by the other of the two sensing electrodes matches the phase of the voltage obtained by synthesizing the drive voltage applied to the drive electrode with respect to the electrode structure, the ultrasonic motor A determination method characterized by determining that a malfunction has occurred.

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