CN113589754B - Groove grinding processing method of variable helix angle micro drill bit - Google Patents

Groove grinding processing method of variable helix angle micro drill bit Download PDF

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CN113589754B
CN113589754B CN202110834865.8A CN202110834865A CN113589754B CN 113589754 B CN113589754 B CN 113589754B CN 202110834865 A CN202110834865 A CN 202110834865A CN 113589754 B CN113589754 B CN 113589754B
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CN113589754A (en
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杨晓钧
胡永祥
李兵
徐魏斌
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Shenzhen Graduate School Harbin Institute of Technology
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B19/00—Programme-control systems
    • G05B19/02—Programme-control systems electric
    • G05B19/18—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form
    • G05B19/19—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form characterised by positioning or contouring control systems, e.g. to control position from one programmed point to another or to control movement along a programmed continuous path
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B2219/00—Program-control systems
    • G05B2219/30—Nc systems
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    • G05B2219/35349—Display part, programmed locus and tool path, traject, dynamic locus

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Abstract

The invention provides a groove grinding processing method of a variable helix angle micro drill bit, which comprises the following steps: extracting a spiral line of the variable-helix-angle micro drill bit to be processed, dividing the spiral line into a plurality of equal-helix-angle curve segments, and dispersing the equal-helix-angle curve segments in an equal radian mode to obtain a series of micro line segments; reading in each tiny line segment, respectively calculating the geometric characteristics of each tiny line segment, and smoothing the corner of each tiny line segment through a PH curve in a control point constructing mode to obtain a primary processing path which can achieve four-order parameter continuity, curvature continuity and symmetrical distribution; carrying out prospective speed planning to determine the speed of the speed dangerous point, and determining the acceleration, constant speed and deceleration time of each tiny line segment by adopting an acceleration and deceleration strategy based on fourth-order polynomial jump; and performing interpolation operation on the primary processing path after the fairing and speed planning to obtain a final processing path. The invention has the advantages of easy real-time interpolation, speed fluctuation reduction and machine tool vibration influence reduction.

Description

Groove grinding processing method of variable helix angle micro drill bit
Technical Field
The invention belongs to the field of numerical control machining, and particularly relates to a groove grinding machining method for a variable helix angle micro drill bit, which is easy to interpolate and reduce the influence of speed fluctuation and machine tool vibration.
Background
The rapid development of the electronic industry promotes the prosperity of the PCB industry, and the market puts forward higher processing requirements on the PCB; electronic equipment mainboard size is getting smaller and smaller, and the chip height is integrated and arranges more densely, and this has proposed higher requirement to the position precision in the PCB diaphragm orifice of connecting the chip pin.
In fact, the precision of the drill used for processing the PCB greatly influences the positioning precision of the PCB drilling. At present, the general research focuses on the influence of the shape and geometric parameters of the grinding wheel on the geometric structure of the spiral groove, the removal mechanism of the micro-cutting material, the vibration resistance of the micro-cutting platform and the like.
In order to improve the rigidity of the micro drill, the drill is designed into a shape with a variable helical angle, however, the traditional machining method cannot meet the characteristic of the variable helical angle, and researches are rarely made at home and abroad on how to machine the micro drill with high precision and the variable helical angle.
Based on the above, a groove grinding method for a variable helix angle micro drill is provided.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a groove grinding machining method capable of realizing a variable helix angle micro-drill which is easy to interpolate and reduces the influence of speed fluctuation and machine tool vibration.
In order to achieve the purpose, the invention provides a groove grinding processing method of a variable helix angle micro drill, which comprises the following steps:
the method comprises the following steps: extracting a spiral line of the variable-helix-angle micro drill bit to be processed, dividing the spiral line into a plurality of equal-helix-angle curve segments, and dispersing the equal-helix-angle curve segments in an equal radian mode to obtain a series of micro line segments;
step two: reading in each micro line segment, respectively calculating the geometric characteristics of each micro line segment, and smoothing the corner of each micro line segment through a PH curve in a control point constructing mode to obtain a primary processing path which can achieve four-order parameter continuity, curvature continuity and symmetrical distribution;
step three: carrying out prospective speed planning to determine the speed of the speed dangerous point, and determining the acceleration, constant speed and deceleration time of each tiny line segment by adopting an acceleration and deceleration strategy based on fourth-order polynomial jump;
step four: and performing interpolation operation on the primary processing path after the fairing and speed planning to obtain a final processing path.
As another specific embodiment of the present invention, the XOY plane coordinates are established in step two, and P is used as P i-1 、P i 、P i+1 The method comprises the following steps of (1) setting a starting point, a turning point and an end point of each corner of a tiny line segment, wherein the geometric characteristics of the tiny line segment comprise:
Figure BDA0003176780200000021
The direction from the starting point to the turning point;
Figure BDA0003176780200000022
is the direction from turning point to end pointThe direction of the solution is as follows;
Figure BDA0003176780200000023
is composed of
Figure BDA0003176780200000024
To
Figure BDA0003176780200000025
The bisector of (a);
Figure BDA0003176780200000026
to
Figure BDA0003176780200000027
Angle of turning
Figure BDA0003176780200000028
As another specific embodiment of the present invention, the configuration of each control point in step 2 is as follows:
Figure BDA0003176780200000031
wherein B is i ＝[x i ，y i ] T : i is 0, and 1 … 15 is the control point of the PH curve; epsilon is the fairing approximation error, and the control polygon length l, l' is:
Figure BDA0003176780200000032
Figure BDA0003176780200000033
by substituting the above-mentioned control points
Figure BDA0003176780200000034
To obtain corner fairingC 4 Wherein t is a curve parameter,
Figure BDA0003176780200000035
is the Bernstein basis function.
As another embodiment of the present invention, the preliminary processing path obtained in the second step includes a linear path section and a PH curve path section.
As another embodiment of the present invention, the velocity hazard point in step three is located at the center of symmetry of each PH curve path segment.
As another specific embodiment of the present invention, the prospective speed planning in step three includes a forward scan, the constraint conditions to be satisfied in the forward scan include interpolation bow-height error, maximum normal acceleration, maximum jerk, machine feed command speed, and constraints of an acceleration and deceleration strategy of fourth-order polynomial jerk under the maximum acceleration and the maximum jerk, wherein the prospective window size is N1, and the speeds of the starting point and the end point of the window are initialized during the forward scan
Figure BDA0003176780200000041
0, the forward scan speed for each hazard point is:
Figure BDA0003176780200000042
Figure BDA0003176780200000043
Figure BDA0003176780200000044
v f ＝min(v m 、v J 、v A )
wherein, T s Indicates the interpolation period, delta indicates the interpolation bow-height error, kappa indicates the curvature of each dangerous point, A max Represents the maximum normal acceleration, J max Represents the maximum jerk, F cmd Indicating the feed command speed v of the machine tool m For interpolating speed v under the constraint of bow height error, maximum normal acceleration, maximum acceleration and machine tool feed command speed J And v A The velocity of the quartic polynomial jump acceleration and deceleration strategy under the constraints of the maximum acceleration and the maximum jerk is obtained.
As another specific embodiment of the present invention, the look-ahead speed planning in step three further includes a reverse scan, wherein the reverse scan is performed after the initial determination of the speed of the dangerous point, so as to ensure that the tool can stay at the end point with the look-ahead speed window size N1; during reverse scanning, the starting point and the end point of the window
Figure BDA0003176780200000051
Figure BDA0003176780200000051
0, and v ═ min (v) for each dangerous point after the reverse scan f 、v J 、v A )。
As another specific embodiment of the present invention, after the speeds of the dangerous points in the step three are finally determined, a process of determining the acceleration and deceleration type between the dangerous points is performed.
As another specific embodiment of the present invention, in the fourth step, the linear path segment adopts the traditional interpolation operation, and the PH curve path segment adopts the FV iteration mode to solve the parameter points, thereby realizing the interpolation operation.
As another specific embodiment of the present invention, in step four, if the interpolation point is in the linear path segment, the interpolation point position is represented as:
Figure BDA0003176780200000052
wherein S, E is the start and end points of the linear segment, A, B is the danger point of two adjacent corners, C (kTs) is the point of the curve between S, E in the kth interpolation period, and the arc length of A, S, E, C (kTs) is S A 、S S 、S E 、
Figure BDA0003176780200000053
If the interpolation point is in the PH curve segment, performing parameter point solution by adopting an FV iteration mode to realize interpolation operation, firstly constructing an equation without speed fluctuation, and then solving the equation by adopting an FV iteration method, wherein deltas represents the arc length from the point A to the interpolation point or the arc length from the point E to the interpolation point, and the equation is as follows:
Figure BDA0003176780200000054
Figure BDA0003176780200000055
the invention has the following beneficial effects:
the invention can meet the requirement of the micro drill with the variable helical angle, improves the rigidity of the processed micro drill, has the advantages of easy real-time interpolation, speed fluctuation reduction and machine tool vibration influence reduction, and can grind the variable helical groove line of the micro drill at high speed and high precision.
The present invention will be described in further detail with reference to the accompanying drawings.
Drawings
FIG. 1 is a schematic flow diagram of the present invention;
FIG. 2 is a schematic illustration of the linear path fairing of the present invention;
FIG. 3 is a flow diagram of the look-ahead speed planning of the present invention;
FIG. 4 is a schematic flow chart of an acceleration/deceleration strategy according to the present invention;
FIG. 5 is a schematic diagram of a real-time interpolation according to the present invention.
Detailed Description
In order that the above objects, features and advantages of the present invention can be more clearly understood, a more particular description of the invention will be rendered by reference to the appended drawings. It should be noted that the embodiments and features of the embodiments of the present application may be combined with each other without conflict.
In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present invention, however, the present invention may be practiced otherwise than as specifically described herein and, therefore, the scope of the present invention is not limited by the specific embodiments disclosed below.
Example 1
The embodiment provides a groove grinding processing method of a variable helix angle micro drill, as shown in fig. 1, comprising the following steps:
the method comprises the following steps:extracting a spiral line (groove line) with a variable spiral angle to be processed, dividing the spiral line into a plurality of equal spiral angle curve segments, and dispersing the equal spiral angle curve segments in an equal radian mode to obtain a series of tiny line segments;
Step two:reading in each micro line segment, respectively calculating the geometric characteristics of each micro line segment, and smoothing the corner of each micro line segment through a PH curve in a control point constructing mode to obtain a primary processing path which can achieve four-order parameter continuity, curvature continuity and symmetrical distribution;
as shown in FIG. 1, wherein P i-1 、P i 、P i+1 The starting point, the turning point and the end point of each corner of the micro line segment of the XOY plane are as follows:
Figure BDA0003176780200000071
is the direction from the starting point to the turning point;
Figure BDA0003176780200000072
the direction from the turning point to the end point;
Figure BDA0003176780200000073
is composed of
Figure BDA0003176780200000074
To
Figure BDA0003176780200000075
The bisector of (a);
Figure BDA0003176780200000076
to
Figure BDA0003176780200000077
Angle of turning
Figure BDA0003176780200000078
Further, as shown in fig. 2, the position information and distribution of each control point of the PH curve, a preferred rule of the structure of each control point is as follows:
Figure BDA0003176780200000079
wherein B is i ＝[x i ，y i ] T : i is 0, and 1 … 15 is the control point of the PH curve; epsilon is the fairing approximation error, and the control polygon length l, l' is:
Figure BDA0003176780200000081
Figure BDA0003176780200000082
by substituting the above-mentioned control points
Figure BDA0003176780200000083
The corner fairing C can be obtained 4 Wherein t is a curve parameter,
Figure BDA0003176780200000084
is the Bernstein basis function, where the resulting initial processing path is composed of a mixture of linear and PH curve segments.
Step three:
when the constraint conditions are met, prospective speed planning is carried out to determine the speed of the speed danger points, and an S-type acceleration and deceleration strategy based on fourth-order polynomial jump is adopted to determine the acceleration, uniform speed and deceleration time of each tiny line segment;
A look-ahead velocity planning procedure as shown in fig. 3, in which the velocity risk point is located at the center of symmetry of the curve of each corner fairing;
the look-ahead velocity plan includes a forward scan and a reverse scan.
Various constraints are considered in the forward scan, including: and (3) interpolating the constraints of the acceleration and deceleration strategies of the height error, the maximum normal acceleration, the maximum acceleration, the machine tool feeding command speed and the fourth-order polynomial jump degree on the maximum acceleration and the maximum acceleration.
With the size of the look-ahead window being N1, the speed of the starting point and the end point of the window is initialized during the forward scanning
Figure BDA0003176780200000091
Figure BDA0003176780200000091
0, the forward scan speed for each hazard point is:
Figure BDA0003176780200000092
Figure BDA0003176780200000093
Figure BDA0003176780200000094
v f ＝min(v m 、v J 、v A )
wherein, T s Indicates the interpolation period, delta indicates the interpolation bow-height error, kappa indicates the curvature of each dangerous point, A max Represents the maximum normal acceleration, J max Represents the maximum jerk, F cmd Indicating machine feed commandsVelocity v m For interpolating speed v under the constraint of bow height error, maximum normal acceleration, maximum acceleration and machine tool feed command speed J And v A The velocity of the quartic polynomial jump acceleration and deceleration strategy under the constraints of the maximum acceleration and the maximum jerk is obtained.
Further, a reverse scan is performed after the initial determination of the dangerous point speed to ensure that the tool can stay at the end point with the look-ahead speed window size of N1.
During reverse scanning, the starting point and the end point of the window
Figure BDA0003176780200000095
A value of 0 corresponds to a value of v ═ min (v) at each risk point after the reverse scan since the reverse scan starts from the end point and the forward scan starts from the start point f 、v J 、v A )。
Furthermore, after the speed of each dangerous point is finally determined, the acceleration and deceleration process among the dangerous points needs to be judged, and specifically, two criteria, namely displacement l, are determined first 1 The displacement l is the displacement which can just reach the maximum command speed in the acceleration and deceleration process 2 The displacement is just achieved by pure acceleration or pure deceleration in the acceleration and deceleration process, and specifically comprises the following steps:
Figure BDA0003176780200000101
Figure BDA0003176780200000102
see the flow of the entire acceleration/deceleration determination shown in FIG. 4, where v s 、v s Representing the initial and terminal velocities of a planning segment, l representing the arc length between two points of danger, T a 、T c 、T d And the acceleration time, the uniform speed time and the deceleration time of the acceleration and deceleration process of the two dangerous points are shown.
The specific judgment process is as follows:
(1) if the maximum of the start and end speeds is equal to the commanded speed, i.e., max (v) s ,v e )＝F cmd The section must include one of an acceleration section or a deceleration section, and the specific type is compared with the starting speed and the ending speed. The acceleration or deceleration section has a time of
Figure BDA0003176780200000103
Time T of uniform velocity segment c The determination is made by 1- (a) and 1- (b), which are determined by the arc length remaining after acceleration or deceleration. If not, entering the flow (2);
(a) If the time of the uniform velocity section
Figure BDA0003176780200000104
The segment does contain a uniform segment, and the acceleration and deceleration type is type1 or type2 in fig. 4;
(b) if the time T of the uniform velocity section c If the speed is less than 0, the initial speed or the terminal speed cannot be reached under the acceleration and deceleration strategy; therefore, a speed adjustment is required, consisting of
Figure BDA0003176780200000105
The relation between the initial and final speeds and the arc length is obtained, and the rules (1) - (b) -i, (1) - (b) -ii of the speed are adjusted;
i. if v is e ＞v s By adjusting the tip speed first, i.e. solving
Figure BDA0003176780200000106
If the velocity v is solved e(new) ＞v e(old) Then the adjustment of the terminal speed is abandoned, the terminal speed is kept unchanged, and the initial speed is adjusted, i.e. the solution is solved
Figure BDA0003176780200000111
The acceleration and deceleration type is type3 in FIG. 4;
ii. If v is e ＜v s By adjusting the initial speed, i.e. solving
Figure BDA0003176780200000112
Velocity v if solved s(new) ＞v s(old) Then the initial speed is abandoned and the terminal speed is adjusted, i.e. the equation is solved
Figure BDA0003176780200000113
The acceleration and deceleration type is type4 in FIG. 4;
(2) if the arc length of the segment is greater than l 1 It is stated that this segment necessarily includes the acceleration, uniform velocity and deceleration stages, and the acceleration and deceleration type is type5 in fig. 4; if less than l 1 Then, the flow proceeds to the flow (3).
(3) If the arc length of the segment is less than l 2 The section is determined to be one of an acceleration stage or a deceleration stage, and the specific type is compared with the initial speed and the final speed; because the arc length l is less than the criterion l 2 When the initial speed or the terminal speed cannot reach the planned value, the speed adjustment is also needed, and the adjustment method is the same as (1) - (b) -i, (1) - (b) -ii, and is not repeated here; the acceleration and deceleration type is type3 or type4 in FIG. 4; if it is greater than l 2 Then, the flow proceeds to the flow (4).
(4) If the arc length of the segment is l 1 And l 2 In between, the segment is illustrated as containing only acceleration and deceleration. The acceleration and deceleration type is type6 in FIG. 4. Ta can be obtained by solving the following equation, and Td can also be obtained:
Figure BDA0003176780200000114
Figure BDA0003176780200000115
specifically, the six types of acceleration/deceleration time solution results are shown in table 1 below:
table 1: time solution result
Figure BDA0003176780200000121
And 4, step 4:
and performing interpolation operation on the primary processing path after the fairing and the speed planning to obtain a final processing path.
As shown in fig. 5, if the interpolation point is in a linear path, the interpolation point position can be represented as:
Figure BDA0003176780200000122
wherein S, E is the start and end points of the linear segment, A, B is the danger point of two adjacent corners, C (kTs) is the point of the curve between S, E in the kth interpolation period, and the arc length of A, S, E, C (kTs) is S A 、S S 、S E 、
Figure BDA0003176780200000123
If the interpolation point is in the PH curve path section, performing parameter point solution by adopting an FV iteration mode to realize interpolation operation, specifically:
The method for solving the PH parameter curve based on FV iteration comprises the steps of firstly constructing an equation without speed fluctuation, and then solving the equation by the FV iteration method, wherein deltas represents the arc length from the point A to the interpolation point or the arc length from the point E to the interpolation point:
Figure BDA0003176780200000131
Figure BDA0003176780200000132
although the present invention has been described with reference to the preferred embodiments, it is not intended to limit the scope of the invention. It will be appreciated by those skilled in the art that changes may be made without departing from the scope of the invention, and it is intended that all matter contained in the above description or shown in the accompanying drawings shall be interpreted as illustrative and not in a limiting sense.

Claims (8)

1. A groove grinding processing method of a variable helix angle micro drill bit is characterized by comprising the following steps:
the method comprises the following steps: extracting a spiral line of the variable-helix-angle micro drill bit to be processed, dividing the spiral line into a plurality of equal-helix-angle curve segments, and dispersing the equal-helix-angle curve segments in an equal radian mode to obtain a series of micro line segments;
step two: reading in each micro line segment, respectively calculating the geometric characteristics of each micro line segment, and smoothing the corner of each micro line segment through a PH curve in a control point constructing mode to obtain a primary processing path which can achieve four-order parameter continuity, curvature continuity and symmetrical distribution;
Wherein, the XOY plane coordinate is established in the second step, and P is used as the coordinate i-1 、P i 、P i+1 The starting point, the turning point and the end point of each corner of the tiny line segment are shown, wherein the geometrical characteristics of the tiny line segment are as follows:
Figure FDA0003690360120000011
is the direction from the starting point to the turning point;
Figure FDA0003690360120000012
the direction from the turning point to the end point;
Figure FDA0003690360120000013
is composed of
Figure FDA0003690360120000014
To
Figure FDA0003690360120000015
The bisector of (a);
Figure FDA0003690360120000016
to
Figure FDA0003690360120000017
Angle of turning
Figure FDA0003690360120000018
And the construction mode of each control point in the step two is as follows:
Figure FDA0003690360120000019
wherein B is i ＝[x i ，y i ] T I is 0, and 1 … 15 is the control point of the PH curve; epsilon is the fairing approximation error, and the control polygon length l, l' is:
Figure FDA0003690360120000021
Figure FDA0003690360120000022
by substituting the above-mentioned control points
Figure FDA0003690360120000023
To obtain corner fairing C 4 Wherein t is a curve parameter,
Figure FDA0003690360120000024
is the Bernstein basis function;
step three: carrying out prospective speed planning to determine the speed of the speed dangerous point, and determining the acceleration, constant speed and deceleration time of each tiny line segment by adopting an acceleration and deceleration strategy based on fourth-order polynomial jump;
step four: and performing interpolation operation on the primary processing path after the fairing and speed planning to obtain a final processing path.
2. The groove grinding method for a variable helix angle micro drill according to claim 1, wherein the preliminary processing path obtained in the second step includes a linear path section and a PH curve path section.
3. The slot grinding method for a variable helix angle micro drill according to claim 2, wherein the risk point of velocity in the third step is located at the symmetrical center of each PH curve path segment.
4. The slot grinding method for the micro drill with the variable spiral angle as claimed in claim 3, wherein the prospective speed planning in the third step comprises a forward scanning, the constraint conditions to be met in the forward scanning comprise interpolation bow height error, maximum normal acceleration, maximum jerk, machine feed command speed and the constraint of an acceleration and deceleration strategy of fourth-order polynomial jump under the maximum acceleration and the maximum jerk, and the prospective window has a size N 1 Speed of initialization start point and window end point during forward scanning
Figure FDA0003690360120000031
0, the forward scan speed for each hazard point is:
Figure FDA0003690360120000032
Figure FDA0003690360120000033
Figure FDA0003690360120000034
v f ＝min(v m 、v J 、v A )
wherein, T s Indicates the interpolation period, delta indicates the interpolation bow-height error, kappa indicates the curvature of each dangerous point, A max Represents the maximum normal acceleration, J max Represents the maximum jerk, F cmd Indicating the feed command speed v of the machine tool m For interpolating speed v under the constraint of bow height error, maximum normal acceleration, maximum acceleration and machine tool feed command speed J And v A The velocity of the quartic polynomial jump acceleration and deceleration strategy under the constraints of the maximum acceleration and the maximum jerk is obtained.
5. The slot grinding method for a variable helix angle micro-fine drill according to claim 4, wherein the look-ahead speed planning in step three further comprises a reverse scan, wherein the reverse scan is performed after the initial determination of the dangerous point speed to ensure that the tool can stay in the look-ahead speed window with a size of N 1 The terminal point of (1); during reverse scanning, the starting point and the end point of the window
Figure FDA0003690360120000035
0, and v ═ min (v) for each dangerous point after the reverse scan f 、v J 、v A )。
6. The method of claim 5, wherein after the final determination of the speed of each dangerous point in the third step, the determination of the type of acceleration and deceleration between the dangerous points is performed.
7. The slot grinding method for a variable helix angle micro drill according to claim 2, wherein the linear path section in the fourth step is processed by conventional interpolation, and the PH curve path section is processed by parameter point solution in FV iteration mode to realize interpolation.
8. The groove grinding method for a variable helix angle micro drill according to claim 7, wherein in the fourth step, if the interpolation point is in the linear path segment, the interpolation point position is represented as:
Figure FDA0003690360120000041
wherein S, E is the start and end points of the linear segment, A, B is the danger point of two adjacent corners, C (kTs) is the point of the curve between S, E in the kth interpolation period, and the arc length of A, S, E, C (kTs) is S A 、S S 、S E 、
Figure FDA0003690360120000042
If the interpolation point is in the PH curve segment, performing parameter point solution by adopting an FV iteration mode to realize interpolation operation, firstly constructing an equation without speed fluctuation, and then solving the equation by adopting an FV iteration method, wherein deltas represents the arc length from the point A to the interpolation point or the arc length from the point E to the interpolation point, and the equation is as follows:
Figure FDA0003690360120000043
Figure FDA0003690360120000044
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