Optical pointing platform based on three-degree-of-freedom piezoelectric actuator and working method thereof

Abstract

The invention discloses an optical pointing platform based on a three-degree-of-freedom piezoelectric actuator and a working method thereof, the device comprises a piezoelectric vibrator, a rotor, an improved bearing, a shell and an adjusting module, and the adjusting module comprises a connecting cylinder, an adjusting end cover and a disc spring. The three-degree-of-freedom piezoelectric actuator is used for direct driving, a traditional optical pointing platform formed by connecting three single-degree-of-freedom motors in series and in parallel is replaced, a transmission mechanism and a speed reducer do not need to be used, the structural complexity of the device is greatly reduced, and the structural function integrated design is achieved. The three-degree-of-freedom positioning mechanism is simple in structure, high in positioning precision, capable of achieving three-degree-of-freedom rotating motion and high-precision positioning, wider in application scene and higher in applicability.

Description

Technical Field

[0001] The present invention relates to the technical field of piezoelectric actuators, and in particular to an optical pointing platform based on a three-degree-of-freedom piezoelectric actuator and a working method thereof. Background Art

[0002] In areas such as optical pointing and satellite attitude adjustment, existing precision multi-dimensional drive systems are mainly driven by multiple single-degree-of-freedom rotating electromagnetic motors, which transmit multi-degree-of-freedom motion through transmission mechanisms and reducers. These structures often lead to complex structures and cumulative stroke errors, making it difficult to further improve accuracy. Summary of the invention

[0003] The technical problem to be solved by the present invention is to provide an optical pointing platform based on a three-degree-of-freedom piezoelectric actuator and a working method thereof in view of the defects involved in the background technology.

[0004] The present invention adopts the following technical solutions to solve the above technical problems: An optical pointing platform based on a three-degree-of-freedom piezoelectric actuator, comprising a piezoelectric vibrator, a rotor, an improved bearing, a housing and an adjustment module; The piezoelectric vibrator comprises a driving prism, a fixing plate, first to fourth columns, and first to eighth piezoelectric ceramic sheets; The driving prism is a regular quadrangular prism, the upper bottom surface area of ​​which is smaller than the lower bottom surface area, and the lower bottom surface is provided with a first V-shaped groove and a second V-shaped groove; the first V-shaped groove and the second V-shaped groove are perpendicular to each other at the center of the lower bottom surface, dividing the lower bottom surface of the driving prism into first to fourth squares of the same shape; The fixing plate is square; The first to fourth columns have the same structure, and their upper ends are fixedly connected to the first to fourth squares on the bottom surface of the driving prism in a one-to-one correspondence, and their lower ends are fixedly connected to the fixing plate vertically, so that the axis of the driving prism passes through the center of the fixing plate; the two side surfaces outside the first to fourth columns are the first to eighth side surfaces in a clockwise direction; The first to eighth piezoelectric ceramic sheets have the same structure, are arranged one by one at the same height of the first to eighth side surfaces, are polarized along the thickness direction, and the polarization direction is from outside to inside; The housing is a hollow regular prism or a hollow cylinder, and a first blind hole for cooperating with the radial spherical bearing is provided at the center of the upper end surface, and a through hole for the bottom surface of the driving prism to pass through is provided at the center of the first blind hole; The piezoelectric vibrator is arranged in the shell, the fixing plate is fixed on the lower end surface of the shell, and the driving prism and the shell are coaxial; The improved bearing adopts a deep groove ball bearing with the inner ring removed or a thrust ball bearing with the inner ring removed, comprising an outer ring, a retainer and a plurality of balls; The rotor comprises an output platform, a connecting column and a driving spherical segment, wherein the connecting column is cylindrical, and the driving spherical segment is a hollow spherical surface in the shape of a spherical segment; the lower end of the connecting column is fixedly connected to the center of the outer wall of the driving spherical segment, and the upper end is vertically fixedly connected to the center of the output platform, and the axis of the connecting column passes through the center of the driving spherical segment; the radius of the bottom surface of the driving spherical segment is larger than the outer diameter of the original inner ring of the improved bearing, and smaller than the inner diameter of the outer ring of the improved bearing; The outer ring of the improved bearing and the first blind hole on the upper end surface of the housing are clearance-matched and can slide freely up and down relative to the housing. The driving spherical segment has an opening facing downward, and its inner wall abuts against the upper end surface of the driving prism, and its outer wall abuts against each ball of the improved bearing; the output platform and the connecting column are both located outside the housing; The adjustment module comprises a connecting tube, an adjustment end cover and a disc spring; The connecting tube is a hollow cylinder with openings at both ends, which is sleeved outside the improved bearing, and the lower end is coaxially fixedly connected to the upper end surface of the shell; the outer wall of the connecting tube is provided with external threads; The regulating end cover is cylindrical, and the center of its lower end surface is provided with a threaded blind hole for matching with the thread on the outer wall of the connecting tube, and the center of the threaded blind hole is provided with a through hole through which the rotor output shaft extends; The disc spring is arranged between the adjusting end cover and the radial spherical bearing, one end of which abuts against the outer ring of the improved bearing, and the other end abuts against the bottom surface of the threaded blind hole; The adjusting end cover is threadedly connected to the connecting tube and is used for adjusting the pre-pressure between the driving ball segment and the driving prism through the disc spring.

[0005] As a further optimization solution of the optical pointing platform based on the three-degree-of-freedom piezoelectric actuator of the present invention, the piezoelectric vibrator is made of any one of titanium alloy, aluminum alloy and brass.

[0006] As a further optimization solution of the optical pointing platform based on the three-degree-of-freedom piezoelectric actuator of the present invention, the first to eighth piezoelectric ceramic sheets are adhered to the first to eighth side walls in a one-to-one correspondence by epoxy resin glue.

[0007] The present invention also discloses a working method of the optical pointing platform based on the three-degree-of-freedom piezoelectric actuator, comprising the following steps: The center of gravity of the piezoelectric vibrator is taken as the origin of the Cartesian coordinate system, the axis passing through the origin and parallel to the polarization direction of the second piezoelectric ceramic piece is the X-axis, the axis passing through the origin and parallel to the polarization direction of the first piezoelectric ceramic piece is the Y-axis, and the axis of the housing is the Z-axis; If you need to drive the rotor to rotate positively around the X axis: A first excitation signal is applied to the fourth and fifth piezoelectric ceramic sheets, a second excitation signal is applied to the first and eighth piezoelectric ceramic sheets, and a third excitation signal is applied to the second, third, sixth, and seventh piezoelectric ceramic sheets, wherein the first to third excitation signals are all AC harmonic signals of the same frequency and amplitude, the first excitation signal leads the third excitation signal by π / 2 in terms of time phase difference, and the first excitation signal is opposite in phase to the second excitation signal; If it is necessary to drive the rotor to rotate in the opposite direction around the X-axis, the phase of the third excitation signal can be reversed; If you need to drive the rotor to rotate positively around the Y axis: Applying a first excitation signal to the second and third piezoelectric ceramic sheets, applying a second excitation signal to the sixth and seventh piezoelectric ceramic sheets, and applying a third excitation signal to the first, fourth, fifth, and eighth piezoelectric ceramic sheets; If it is necessary to drive the rotor to rotate in the opposite direction around the Y axis, the phase of the third excitation signal can be reversed; If you need to drive the rotor to rotate positively around the Z axis: Applying a first excitation signal to the second and third piezoelectric ceramic sheets, applying a second excitation signal to the sixth and seventh piezoelectric ceramic sheets, applying a third excitation signal to the fourth and fifth piezoelectric ceramic sheets, and applying a fourth excitation signal to the first and eighth piezoelectric ceramic sheets; the fourth excitation signal is an AC harmonic signal with the same frequency and amplitude as the first excitation signal, and the fourth excitation signal is opposite in phase to the third excitation signal; If it is necessary to drive the rotor to rotate in the opposite direction around the Z axis, the first excitation signal can be changed to lag behind the third excitation signal by π / 2 in terms of time phase difference.

[0008] Compared with the prior art, the present invention adopts the above technical solution and has the following technical effects: 1. The present invention uses a three-degree-of-freedom piezoelectric actuator for direct drive, replacing the traditional optical pointing platform composed of three single-degree-of-freedom motors connected in series and parallel. It does not require a transmission mechanism and a reducer, greatly reducing the structural complexity of the device and realizing an integrated design of structure and function. 2. It can directly realize the rotation drive of the optical pointing platform in three orthogonal directions, which increases the positioning accuracy of the optical pointing platform while simplifying the mechanical system, making it more applicable to a wider range of scenarios and more versatile. BRIEF DESCRIPTION OF THE DRAWINGS

[0009] Figure 1 It is a cross-sectional structural schematic diagram of the present invention; Figure 2 It is a schematic diagram of the structure of the piezoelectric vibrator in the present invention; Figure 3 is a schematic diagram of the polarization directions of the first to eighth piezoelectric ceramic sheets in the present invention; Figure 4 It is a schematic diagram of the structure of the rotor in the present invention; Figure 5 It is a schematic diagram comparing the bending vibration modes of the piezoelectric vibrator in the present invention in two X-axis directions with a phase difference of π; Figure 6 It is a schematic diagram comparing the bending vibration modes of the piezoelectric vibrator in the present invention in two Y-axis directions with a phase difference of π; Figure 7 It is a schematic diagram comparing the longitudinal vibration modes of the piezoelectric vibrator in the present invention at two phase differences of π; Figure 8 It is a schematic diagram of the working state of the piezoelectric vibrator when the output platform is controlled to rotate around the X-axis according to the present invention; Fig. 9 It is a schematic diagram of the working state of the piezoelectric vibrator when the output platform is controlled to rotate around the Y axis of the present invention; Fig.10 It is a schematic diagram of the working state of the piezoelectric vibrator when the output platform is controlled to rotate around the Z axis of the present invention.

[0010] In the figure, 1- piezoelectric vibrator, 2-rotor, 3-improved bearing, 4-housing, 5-connecting tube, 6-adjusting end cover, 7-disc spring, 8-driving prism, 9-fixing plate, 10-first column, 11-second column, 12-first piezoelectric ceramic sheet, 13-second piezoelectric ceramic sheet, 14-third piezoelectric ceramic sheet, 15-driving spherical segment, 16-connecting column, 17-output platform. DETAILED DESCRIPTION

[0011] The technical solution of the present invention is further described in detail below in conjunction with the accompanying drawings: The present invention can be implemented in many different forms and should not be considered to be limited to the embodiments described herein. On the contrary, these embodiments are provided to make this disclosure thorough and complete, and will fully express the scope of the present invention to those skilled in the art. In the accompanying drawings, components are enlarged for clarity.

[0012] It should be understood that although the terms first, second, third, etc. can be used here to describe various elements, components and / or parts, these elements, components and / or parts are not limited by these terms. These terms are only used to distinguish elements, components and / or parts from each other. Therefore, the first element, component and / or part discussed below can become the second element, component or part without departing from the teaching of the present invention.

[0013] like Figure 1 As shown, the present invention discloses an optical pointing platform based on a three-degree-of-freedom piezoelectric actuator, comprising a piezoelectric vibrator, a rotor, an improved bearing, a housing and an adjustment module; like Figure 2 As shown, the piezoelectric vibrator comprises a driving prism, a fixing plate, first to fourth columns, and first to eighth piezoelectric ceramic sheets; The driving prism is a regular quadrangular prism, the upper bottom surface area of ​​which is smaller than the lower bottom surface area, and the lower bottom surface is provided with a first V-shaped groove and a second V-shaped groove; the first V-shaped groove and the second V-shaped groove are perpendicular to each other at the center of the lower bottom surface, dividing the lower bottom surface of the driving prism into first to fourth squares of the same shape; The fixing plate is square; The first to fourth columns have the same structure, and their upper ends are fixedly connected to the first to fourth squares on the bottom surface of the driving prism in a one-to-one correspondence, and their lower ends are fixedly connected to the fixing plate vertically, so that the axis of the driving prism passes through the center of the fixing plate; the two side surfaces outside the first to fourth columns are the first to eighth side surfaces in a clockwise direction; The first to eighth piezoelectric ceramic sheets have the same structure, are arranged one by one at the same height of the first to eighth sides, are polarized along the thickness direction, and the polarization direction is from outside to inside. Figure 3 As shown; The housing is a hollow regular prism or a hollow cylinder, and a first blind hole for cooperating with the radial spherical bearing is provided at the center of the upper end surface, and a through hole for the bottom surface of the driving prism to pass through is provided at the center of the first blind hole; The piezoelectric vibrator is arranged in the shell, the fixing plate is fixed on the lower end surface of the shell, and the driving prism and the shell are coaxial; The improved bearing adopts a deep groove ball bearing with the inner ring removed or a thrust ball bearing with the inner ring removed, comprising an outer ring, a retainer and a plurality of balls; like Figure 4 As shown, the rotor comprises an output platform, a connecting column and a driving spherical segment, wherein the connecting column is cylindrical, and the driving spherical segment is a hollow spherical surface in the shape of a spherical segment; the lower end of the connecting column is fixedly connected to the center of the outer wall of the driving spherical segment, and the upper end is vertically fixedly connected to the center of the output platform, and the axis of the connecting column passes through the center of the driving spherical segment; the radius of the bottom surface of the driving spherical segment is larger than the outer diameter of the original inner ring of the improved bearing, and smaller than the inner diameter of the outer ring of the improved bearing; The outer ring of the improved bearing and the first blind hole on the upper end surface of the housing are clearance-matched and can slide freely up and down relative to the housing. The driving spherical segment has an opening facing downward, and its inner wall abuts against the upper end surface of the driving prism, and its outer wall abuts against each ball of the improved bearing; the output platform and the connecting column are both located outside the housing; The adjustment module comprises a connecting tube, an adjustment end cover and a disc spring; The connecting tube is a hollow cylinder with openings at both ends, which is sleeved outside the improved bearing, and the lower end is coaxially fixedly connected to the upper end surface of the shell; the outer wall of the connecting tube is provided with external threads; The regulating end cover is cylindrical, and the center of its lower end surface is provided with a threaded blind hole for matching with the thread on the outer wall of the connecting tube, and the center of the threaded blind hole is provided with a through hole through which the rotor output shaft extends; The disc spring is arranged between the adjusting end cover and the radial spherical bearing, one end of which abuts against the outer ring of the improved bearing, and the other end abuts against the bottom surface of the threaded blind hole; The adjusting end cover is threadedly connected to the connecting tube and is used for adjusting the pre-pressure between the driving ball segment and the driving prism through the disc spring.

[0014] The piezoelectric vibrator is preferably made of any one of titanium alloy, aluminum alloy and brass.

[0015] The first to eighth piezoelectric ceramic sheets are adhered to the first to eighth side walls in a one-to-one correspondence by epoxy resin glue.

[0016] The present invention also discloses a working method of the optical pointing platform based on the three-degree-of-freedom piezoelectric actuator, comprising the following steps: The center of gravity of the piezoelectric vibrator is taken as the origin of the Cartesian coordinate system, the axis passing through the origin and parallel to the polarization direction of the second piezoelectric ceramic piece is the X-axis, the axis passing through the origin and parallel to the polarization direction of the first piezoelectric ceramic piece is the Y-axis, and the axis of the housing is the Z-axis; If you need to drive the rotor to rotate positively around the X axis: A first excitation signal is applied to the fourth and fifth piezoelectric ceramic plates, a second excitation signal is applied to the first and eighth piezoelectric ceramic plates, and a third excitation signal is applied to the second, third, sixth, and seventh piezoelectric ceramic plates. The first to third excitation signals are all AC harmonic signals of the same frequency and amplitude. The first excitation signal leads the third excitation signal by π / 2 in time phase difference, and the first excitation signal is opposite in phase to the second excitation signal. The piezoelectric vibrator is caused to simultaneously excite the longitudinal vibration mode and the bending vibration mode in the Y-axis direction, such as Figure 5 and Figure 7 As shown; through the coupling of the two vibration modes, a slight elliptical motion perpendicular to the X-axis is formed on the driving surface of the piezoelectric vibrator, and the spherical rotor is driven to rotate around the X-axis through friction, as shown Figure 8 As shown; If it is necessary to drive the rotor to rotate in the opposite direction around the X-axis, the phase of the third excitation signal can be reversed; If you need to drive the rotor to rotate positively around the Y axis: Apply a first excitation signal to the second and third piezoelectric ceramic sheets, apply a second excitation signal to the sixth and seventh piezoelectric ceramic sheets, and apply a third excitation signal to the first, fourth, fifth, and eighth piezoelectric ceramic sheets; so that the piezoelectric vibrator excites the longitudinal vibration mode and the bending vibration mode in the X-axis direction at the same time, such as Figure 6 and Figure 7As shown; through the coupling of the two vibration modes, a slight elliptical motion perpendicular to the Y axis is formed on the driving surface of the piezoelectric vibrator, and the spherical rotor is driven to rotate around the Y axis through friction, as shown Fig. 9 As shown; If it is necessary to drive the rotor to rotate in the opposite direction around the Y axis, the phase of the third excitation signal can be reversed; If you need to drive the rotor to rotate positively around the Z axis: A first excitation signal is applied to the second and third piezoelectric ceramic plates, a second excitation signal is applied to the sixth and seventh piezoelectric ceramic plates, a third excitation signal is applied to the fourth and fifth piezoelectric ceramic plates, and a fourth excitation signal is applied to the first and eighth piezoelectric ceramic plates; the fourth excitation signal is an AC harmonic signal with the same frequency and amplitude as the first excitation signal, and the fourth excitation signal is opposite in phase to the third excitation signal; the piezoelectric vibrator is caused to simultaneously excite the bending vibration mode in the X-axis direction and the bending vibration mode in the Y-axis direction, such as Figure 5 and Figure 6 As shown; through the coupling of the two vibration modes, a slight elliptical motion perpendicular to the Z axis is formed on the driving surface of the piezoelectric vibrator, and the spherical rotor is driven to rotate around the Z axis through friction, as shown Fig.10 As shown; If it is necessary to drive the rotor to rotate in the opposite direction around the Z axis, the first excitation signal can be changed to lag behind the third excitation signal by π / 2 in terms of time phase difference.

[0017] It will be understood by those skilled in the art that, unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as generally understood by those skilled in the art in the art to which the present invention belongs. It should also be understood that terms such as those defined in common dictionaries should be understood to have meanings consistent with the meanings in the context of the prior art, and will not be interpreted with idealized or overly formal meanings unless defined as herein.

[0018] The specific implementation methods described above further illustrate the objectives, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above description is only a specific implementation method of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. An optical pointing platform based on a three-degree-of-freedom piezoelectric actuator, characterized in that: It includes a piezoelectric vibrator, a rotor, an improved bearing, a housing and an adjustment module; The piezoelectric vibrator comprises a driving prism, a fixing plate, first to fourth columns, and first to eighth piezoelectric ceramic sheets; The driving prism is a regular quadrangular prism, the upper bottom surface area of ​​which is smaller than the lower bottom surface area, and the lower bottom surface is provided with a first V-shaped groove and a second V-shaped groove; the first V-shaped groove and the second V-shaped groove are perpendicular to each other at the center of the lower bottom surface, dividing the lower bottom surface of the driving prism into first to fourth squares of the same shape; The fixing plate is square; The first to fourth columns have the same structure, and their upper ends are fixedly connected to the first to fourth squares on the bottom surface of the driving prism in a one-to-one correspondence, and their lower ends are fixedly connected to the fixing plate vertically, so that the axis of the driving prism passes through the center of the fixing plate; the two side surfaces outside the first to fourth columns are the first to eighth side surfaces in a clockwise direction; The first to eighth piezoelectric ceramic sheets have the same structure, are arranged one by one at the same height of the first to eighth side surfaces, are polarized along the thickness direction, and the polarization direction is from outside to inside; The housing is a hollow regular prism or a hollow cylinder, and a first blind hole for cooperating with the radial spherical bearing is provided at the center of the upper end surface, and a through hole for the bottom surface of the driving prism to pass through is provided at the center of the first blind hole; The piezoelectric vibrator is arranged in the shell, the fixing plate is fixed on the lower end surface of the shell, and the driving prism and the shell are coaxial; The improved bearing adopts a deep groove ball bearing with the inner ring removed or a thrust ball bearing with the inner ring removed, comprising an outer ring, a retainer and a plurality of balls; The rotor comprises an output platform, a connecting column and a driving spherical segment, wherein the connecting column is cylindrical, and the driving spherical segment is a hollow spherical surface in the shape of a spherical segment; the lower end of the connecting column is fixedly connected to the center of the outer wall of the driving spherical segment, and the upper end is vertically fixedly connected to the center of the output platform, and the axis of the connecting column passes through the center of the driving spherical segment; the radius of the bottom surface of the driving spherical segment is larger than the outer diameter of the original inner ring of the improved bearing, and smaller than the inner diameter of the outer ring of the improved bearing; The outer ring of the improved bearing and the first blind hole on the upper end surface of the housing are clearance-matched and can slide freely up and down relative to the housing. The driving spherical segment has an opening facing downward, and its inner wall abuts against the upper end surface of the driving prism, and its outer wall abuts against each ball of the improved bearing; the output platform and the connecting column are both located outside the housing; The adjustment module comprises a connecting tube, an adjustment end cover and a disc spring; The connecting tube is a hollow cylinder with openings at both ends, which is sleeved outside the improved bearing, and the lower end is coaxially fixedly connected to the upper end surface of the shell; the outer wall of the connecting tube is provided with external threads; The regulating end cover is cylindrical, and the center of its lower end surface is provided with a threaded blind hole for matching with the thread on the outer wall of the connecting tube, and the center of the threaded blind hole is provided with a through hole through which the rotor output shaft extends; The disc spring is arranged between the adjusting end cover and the radial spherical bearing, one end of which abuts against the outer ring of the improved bearing, and the other end abuts against the bottom surface of the threaded blind hole; The adjusting end cover is threadedly connected to the connecting tube and is used for adjusting the pre-pressure between the driving ball segment and the driving prism through the disc spring.

2. The optical pointing platform based on a three-degree-of-freedom piezoelectric actuator according to claim 1, characterized in that: The piezoelectric vibrator is made of any one of titanium alloy, aluminum alloy and brass.

3. The optical pointing platform based on a three-degree-of-freedom piezoelectric actuator according to claim 1, characterized in that: The first to eighth piezoelectric ceramic sheets are adhered to the first to eighth side walls in a one-to-one correspondence by epoxy resin glue.

4. The working method of the optical pointing platform based on the three-degree-of-freedom piezoelectric actuator according to claim 1, characterized in that: The following steps are involved: The center of gravity of the piezoelectric vibrator is taken as the origin of the Cartesian coordinate system, the axis passing through the origin and parallel to the polarization direction of the second piezoelectric ceramic piece is the X-axis, the axis passing through the origin and parallel to the polarization direction of the first piezoelectric ceramic piece is the Y-axis, and the axis of the housing is the Z-axis; If you need to drive the rotor to rotate positively around the X axis: A first excitation signal is applied to the fourth and fifth piezoelectric ceramic sheets, a second excitation signal is applied to the first and eighth piezoelectric ceramic sheets, and a third excitation signal is applied to the second, third, sixth, and seventh piezoelectric ceramic sheets, wherein the first to third excitation signals are all AC harmonic signals of the same frequency and amplitude, the first excitation signal leads the third excitation signal by π / 2 in terms of time phase difference, and the first excitation signal is opposite in phase to the second excitation signal; If it is necessary to drive the rotor to rotate in the opposite direction around the X-axis, the phase of the third excitation signal can be reversed; If you need to drive the rotor to rotate positively around the Y axis: Applying a first excitation signal to the second and third piezoelectric ceramic sheets, applying a second excitation signal to the sixth and seventh piezoelectric ceramic sheets, and applying a third excitation signal to the first, fourth, fifth, and eighth piezoelectric ceramic sheets; If it is necessary to drive the rotor to rotate in the opposite direction around the Y axis, the phase of the third excitation signal can be reversed; If you need to drive the rotor to rotate positively around the Z axis: Applying a first excitation signal to the second and third piezoelectric ceramic sheets, applying a second excitation signal to the sixth and seventh piezoelectric ceramic sheets, applying a third excitation signal to the fourth and fifth piezoelectric ceramic sheets, and applying a fourth excitation signal to the first and eighth piezoelectric ceramic sheets; the fourth excitation signal is an AC harmonic signal with the same frequency and amplitude as the first excitation signal, and the fourth excitation signal is opposite in phase to the third excitation signal; If it is necessary to drive the rotor to rotate in the opposite direction around the Z axis, the first excitation signal can be changed to lag behind the third excitation signal by π / 2 in terms of time phase difference.

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