High-speed and high-precision numerical control flanging machine and flanging beam displacement solving method
Technical Field
The invention relates to the field of metal plate processing, in particular to a high-speed and high-precision numerical control flanging machine and a flanging beam displacement solving method.
Background
The flanging machine is a simple bending machine, can be operated manually or mechanically, is mechanical equipment for processing the edge of a product, can only realize single up-down flanging action and cannot realize complex flanging tracks in the conventional flanging machine. Along with the development of social economy, people's demand scope to the work piece is wider and wider, and traditional flanging machine can't satisfy customer's demand. In addition, the traditional flanging machine has a too simple structure, low transmission precision and poor product quality.
The Chinese patent application with the application number of CN201610497320.1 is named as a flanging mechanism of a metal sheet flanging machine and comprises a frame, wherein a supporting table is arranged at the lower end of the front side of the frame, a pressing beam is arranged above the supporting table, a flanging beam is arranged in the front side of the frame, vertical driving mechanisms for driving the flanging beam to swing up and down are respectively arranged on the left side and the right side of the lower end of the flanging beam, and a horizontal driving mechanism for driving the flanging beam to swing back and forth is arranged at the rear end of the flanging beam. The vertical driving mechanism drives the flanging beam to swing up and down to realize vertical direction movement, the horizontal driving mechanism drives the flanging beam to swing back and forth to realize horizontal direction movement, and the flanging beam and the horizontal driving mechanism are linked to realize complex flanging tracks and meet the requirements of different customers.
However, the above patent application, in use, has the following disadvantages, and needs to be further improved:
1. the horizontal driving mechanism moves in the horizontal direction and has additional swing; the vertical drive mechanism has additional swing while driving vertical motion, so that a single translation of X, Y to two degrees of freedom in an absolute sense cannot be achieved. Therefore, the accurate control of the tool nose track cannot be realized, the control precision is poor, the angle correction can be performed only through manual correction parameter input for many times during the bending process, the calculation of the correction value cannot be automatically completed through accurate mathematical calculation, the efficiency is low, and the intelligent control is difficult to realize. In addition, the precision of the tool nose track is poor, so that the problem of indentation left on the plate surface in the bending process is inevitable.
2. The machining precision of equipment depends on the machining and assembling precision of each hinge point, so the machining and manufacturing difficulty is high, the mass production is difficult to realize, and the large-scale popularization of the equipment is limited. In addition, in CN201610497320.1, the hinge point is not only used for driving, but also used for guiding the folding beam or limiting the degree of freedom. Therefore, the manufacturing error of the hinge point can influence the parallelism of the horizontal direction and the vertical direction of the folding beam during the movement process to generate influence.
3. Due to the existence of additional swing, real-time feedback of the movement position of the folding beam is difficult to realize (a feedback measurement sensor is installed everywhere), closed-loop feedback and control of the movement position of the folding beam are difficult to realize, and therefore the machining precision is difficult to guarantee.
4. The abrasion of the hinge point, the elastic deformation of each rod piece in the mechanism under stress and the temperature deformation of the component can greatly influence the processing precision.
Disclosure of Invention
The invention aims to solve the technical problems of the prior art and provides a flanging transmission mechanism for a flanging machine and a flanging beam displacement solving method. Meanwhile, the bending die is high in rigidity, and the load of the moving pair is small; when the first connecting rod is hinged with the first folding beam, the folding load is directly transmitted to the rack through the crank-connecting rod mechanism, and the kinematic pair only needs to bear a small load (only needs to bear the overturning load caused by the fact that the load center and the hinge center are not on the same straight line, and actually the load is far smaller than the folding working load), so that the transmission rigidity is high, and the service life of the transmission guide component is longer; the automatic control device can also realize the accurate control of the tool nose track, has high control precision, can automatically complete the calculation of a correction value through accurate mathematical calculation when angle correction is carried out in the bending process, has high efficiency, and can realize the intelligent control of the bending angle.
In order to solve the technical problems, the invention adopts the technical scheme that:
a high-speed and high-precision numerical control flanging machine comprises a machine frame, a flanging beam, a flanging die, a flanging beam, an inclined plane slide rail, a driving seat, a first crank-link mechanism and a second crank-link mechanism.
The blank holder beam is used for pressing the plate.
The driving seat is provided with a first inclined surface and a second inclined surface, and the plane where the first inclined surface is located is intersected with the plane where the second inclined surface is located.
The first inclined plane is connected to the inclined plane slide rail in a sliding mode, and the inclined plane slide rail is fixed to the rack.
And the second inclined plane is in sliding fit with a flanging beam of the flanging machine.
One end of the first crank connecting rod mechanism is hinged on the frame, and the other end of the first crank connecting rod mechanism is hinged with the driving seat or the folding beam.
One end of the second crank connecting rod mechanism is hinged on the driving seat, and the other end of the second crank connecting rod mechanism is hinged with the flanging beam.
And the flanging beam realizes displacement in the vertical direction and the horizontal direction under the common coupling action of the first crank connecting rod mechanism and the second crank connecting rod mechanism.
The folding beam is provided with a sliding inclined plane matched with the inclined plane.
The device also comprises a grating ruler used for detecting the coordinates of the edge folding beam.
The grating ruler comprises a scale grating, a reading head and a displacement connecting rod. The scale grating is installed on frame or hem roof beam, and reading head sliding connection is in the scale grating, and the displacement connecting rod is used for connecting reading head and hem roof beam or frame. Through the synthesis and operation of the readings of the two groups of grating rulers, the horizontal and vertical movement displacements of the edge folding beam are indirectly fed back.
The driving seat is triangular, trapezoidal, wedge-shaped, L-shaped, quadrilateral or rectangular.
The link transmission of the first crank link mechanism is driven by a toggle link mechanism, and the toggle link mechanism is a third crank link mechanism or a screw rod transmission mechanism.
The first crank-link mechanism comprises a first crank and a first connecting rod which are hinged with each other. The tail end of the first crank is hinged to the rack, and the other end of the first connecting rod is hinged to the driving seat or the flanging beam.
The second crank connecting rod mechanism comprises a second crank and a second connecting rod which are hinged with each other. The tail end of the second crank is hinged to the driving seat, and the other end of the second connecting rod is hinged to the flanging beam.
The included angle between the first inclined plane and the horizontal plane is-75 degrees, and the included angle between the second inclined plane and the vertical plane is-75 degrees.
A method for solving displacement of a folded edge beam solves the displacement of the folded edge beam by two sets of grating rulers, and specifically comprises the following steps:
step 1, establishing a coordinate system and a linear equation of a grating ruler, comprising the following steps:
step 11, establishing a coordinate system: the two sets of grating scales are respectively a first grating scale and a second grating scale. The first grating ruler comprises a first ruler grating, a first reading head and a first displacement connecting rod. The second grating ruler comprises a second ruler grating, a second reading head and a second displacement connecting rod. The first scale grating and the second scale grating are fixed in position, the first reading head is connected to the first scale grating in a sliding mode, and the second reading head is connected to the second scale grating in a sliding mode. The other ends of the first reading head and the second reading head are hinged to the folding edge beam. And establishing an XOY coordinate system by taking the horizontal direction as the X direction, the vertical direction as the Y direction and the intersection point of the two scale gratings as an origin O.
Step 12, establishing a linear equation 1 where the first scale grating is located:
y=K1x
K1=tan(a1)
wherein a1 is the angle between the first scale grating and the X direction. The coordinate of the point of the reading head I on the straight line equation 1 is P1 (x)p1,yP1) Then the distance from the point P1 to the origin O is R1。xp1、yP1The value of (c) is read automatically by the reading head, as a known value.
Step 13, establishing a linear equation 2 where the second scale grating is located:
y=K2x
K2=tan(a2)
wherein a2 is the angle between the second scale grating and the X direction. The point coordinate of the second reading head on the straight line equation 2 is P2 (x)p2,yP2) Then the distance from the point P2 to the origin O is R2。xp2、yP2The value of (A) is automatically read by the reading head two, and is knownThe value is obtained.
Step 2, establishing the radius as R1Circle 1 of (a): with point P1 as the center, establish radius R1Circle 1, then the equation for circle 1 is:
the equation of circle 1 is expanded as:
step 3, establishing the radius as R2Circle 2 of (a): with point P2 as the center, establish radius R2Circle 2, then the equation for circle 2 is:
the equation of circle 2 is expanded as:
step 4, solving the point coordinate P (x) of the edge folding beamp,yP): point coordinate P (x) of the hemming beamp,yP) And is the intersection of circle 1 and circle 2. By solving for xpAnd yPThereby obtaining the displacement of the hemming beams in the horizontal direction and the vertical direction.
In step 4, xpAnd yPThe solving process is as follows:
in step 4, xpAnd yPThe solving process is as follows: subtracting the formula (3) from the formula (4) to obtain the following difference intersection equation:
order:
then, equation (5) is simplified as:
y=Kx+b (6)
bringing formula (6) into formula (1) and finishing to obtain:
order:
A=K2+1
B=2(Kb-Kyp1-xp1)
after the formula (7) is finished, the product can be obtained:
Ax2+Bx+C=0 (8)
solving the solution of the unitary quadratic function of equation (8) can yield a display solution of the X coordinate of the intersection:
then, the display solution of the Y coordinate of the intersection can be obtained by bringing equation (9) into equation (6):
yp=Kxp+b (10)
at this point, all solutions x are completedpAnd yP。
The invention has the following beneficial effects:
1. the hemming die and the hemming beam are complete rigid X, Y-direction movement translation without additional swing, the degree of freedom is simple, the accurate control of the tool nose track can be realized, the rolling of the tool nose on the plate can be realized without relative sliding, and the indentation on the surface of the plate is avoided, so that the hemming die and the hemming beam can be applied to the strict requirements on the indentation on the surface of the plate in the industries of household appliances, elevators and the like.
2. The linear guide rail is adopted for guiding, so that the manufacturing difficulty is small, the precision is high, the precision is easy to control, and the device is durable. The hinge point of the invention is only used for driving, and the ' guiding ' of the folding beam, or the function called freedom degree limiting ', is realized by the moving pair (guide rail), the precision of the hinge point is far better than that of the hinge mode, and the manufacturing difficulty is lower.
3. Because no additional swing exists, linear displacement feedback measuring devices such as a grating ruler and the like can be adopted to feed back the displacement of the flanging beam in real time, and closed-loop control is formed. Through grating chi feedback, can compensate transmission part error, temperature deformation, the elastic deformation of structure, the precision promotes by a wide margin.
4. The automatic control device has the advantages that the accurate control of the tool nose track can be realized, the control precision is high, the calculation of a correction value can be automatically completed through accurate mathematical calculation when the angle is corrected in the bending process, the efficiency is high, and the intelligent control of the bending angle can be realized.
5. The invention is suitable for bending equipment with small tonnage requirement and high bending precision, such as bending equipment with the bending tonnage below 50 tons.
6. When the connecting rod of the crank-link mechanism I is hinged with the folded edge beam, the inverse kinematics solution of the folded edge beam driving mechanism is simpler, the analytic inverse solution is easier to realize, and the high-speed and high-precision control is facilitated. The bending angle of the invention can reach +/-0.1 DEG, the speed is high, the single-pass bending time can be less than-0.3S, the bending size precision is +/-0.02 mm, and the parallelism is +/-0.05 mm.
7. Bending load is directly transmitted to the rack through the crank-link mechanism, the kinematic pair only needs to bear small load (only needs to bear overturning load caused by the fact that a load center and a hinge center are not on the same line, and actually the load is far smaller than the bending working load), so that the transmission rigidity is high, and the service life of the transmission guide component is longer.
Drawings
FIG. 1 shows a structural diagram of a high-speed and high-precision numerical control flanging machine of the invention when a first connecting rod is connected with a driving seat.
FIG. 2 shows a structural diagram of a high-speed and high-precision numerical control flanging machine of the invention when a first connecting rod is connected with a flanging beam.
FIG. 3 is a schematic view showing the structure of the hem beam and the driving seat; fig. 3a and 3b show enlarged schematic structural views of the hemming beam and the driving seat in fig. 1 and 2, respectively.
FIG. 4 shows a working schematic diagram of a high-speed and high-precision numerical control flanging machine of the invention; fig. 4a and 4b show the working principle of the structure shown in fig. 1 and 2, respectively.
FIG. 5 is a schematic diagram showing the position change of the hemming die when driven by two crank link mechanisms with any degree of freedom according to the present invention; fig. 5a and 5b are schematic views showing the position change of the hemming die when the structure shown in fig. 1 and 2 is adopted.
FIG. 6 is a schematic diagram showing the position change of the hemming die driven by two crank-link mechanisms according to the present invention in a vertical translation; fig. 6a and 6b are schematic diagrams showing the position change of the hemming die in vertical translation when the structure shown in fig. 1 and 2 is adopted.
FIG. 7 is a schematic diagram showing the position change of the hemming die driven by two crank-link mechanisms according to the present invention in the horizontal translation; fig. 7a and 7b are views showing the position change of the hemming die in the horizontal translation when the structure shown in fig. 1 and 2 is adopted.
FIG. 8 shows a structure diagram of the installation of a grating ruler in a high-speed and high-precision numerical control flanging machine.
FIG. 9 is a schematic diagram showing the combined horizontal displacement and vertical variation of two linear scales according to the present invention; FIG. 9a is a schematic diagram showing the combined horizontal displacement variation of two grating scales; fig. 9b shows a schematic diagram of the resultant vertical displacement change of two grating scales.
Fig. 10 shows a schematic diagram of the displacement solving process of the grating ruler.
Fig. 11 shows a schematic diagram of the rolling trajectory of the nose in the hemming die during bending.
FIG. 12 shows the stress deformation of the lead screw under heavy load when the lead screw is used in the transmission mechanism of the present invention.
FIG. 13 shows a speed versus position graph for the transmission of the present invention.
FIG. 14 shows a force versus position graph for the transmission of the present invention.
Fig. 15 shows a schematic view of the crank mechanism of the present invention moved to a specific position.
Fig. 16 shows a schematic view of a first embodiment of the toggle mechanism.
Fig. 17 shows a schematic view of a second embodiment of the toggle mechanism.
Fig. 18 shows a schematic view of a third embodiment of the toggle mechanism.
Among them are:
10. a frame; 11. an upper slide plate; 111. an upper die; 12. a lower fixing plate; 121. a lower die;
20. a plate material;
30. folding a die; 31. a flanging beam; 311, C-shaped groove; 312. a horizontal cross beam; 313. a sliding ramp; 32. upward flanging dies; 33. downward flanging dies; 34. a knife tip; 35. a nose trajectory;
41. an inclined slide rail; 42. a driving seat; 421. a first inclined plane; 422. a second inclined plane;
43. a first crank link mechanism; 431. a rack fixing seat; 432. a first crank; 433. a first connecting rod;
44. a second crank link mechanism; 441. a crank II; 442. a second connecting rod;
50. a hemming die displacement detection mechanism; 51. a first scale grating; 52. reading a first reading head; 53. a first displacement connecting rod; 54. a second scale grating; 55. a second reading head; 56. and a second displacement connecting rod.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings and specific preferred embodiments.
In the description of the present invention, it is to be understood that the terms "left side", "right side", "upper part", "lower part", etc., indicate orientations or positional relationships based on those shown in the drawings, and are only for convenience of describing the present invention and simplifying the description, but do not indicate or imply that the referred device or element must have a specific orientation, be constructed in a specific orientation, and be operated, and that "first", "second", etc., do not represent an important degree of the component parts, and thus are not to be construed as limiting the present invention. The specific dimensions used in the present example are only for illustrating the technical solution and do not limit the scope of protection of the present invention.
As shown in fig. 1 and 2, a high-speed and high-precision numerical control flanging machine comprises a frame 10, a flanging beam, a flanging die 30, a flanging beam 31, an inclined slide rail 41, a driving seat 42, a first crank-link mechanism 43, a second crank-link mechanism 44 and a flanging die displacement detection mechanism.
The frame comprises an upper sliding plate 11, a lower fixing plate 12 and side plates.
The upper and lower fixing plates 11 and 12 constitute an edge pressing beam for pressing a plate 20 to be flanged.
The lower fixing plate is fixed in position and is preferably connected with the side plate or not. The upper fixing plate is located right above the lower fixing plate and is preferably in sliding connection with the side plates, and the height of the upper fixing plate can be lifted.
The upper fixing plate and the side plate are not limited to be installed in a sliding mode, and other connection modes in the prior art such as swinging installation can be adopted, so long as the plate can be pressed.
A lower die 121 is provided on the upper surface of the lower fixing plate, and an upper die 111 is provided on the lower surface of the upper slide plate.
As shown in fig. 2, the hemming die includes an upper hemming die 32 and a lower hemming die 33, and is mounted on the hemming beam 31.
The hem beam includes a C-shaped notch 311 and a horizontal cross member 312.
The hemming dies are preferably installed at the notches of the C-shaped notches, and the upper hemming die 32 and the lower hemming die 33 are installed at the opposite upper and lower sides of the C-shaped notches, respectively.
One end of the horizontal beam is connected with the C-shaped notch, and the other end of the horizontal beam is provided with a sliding inclined surface 313.
The inclined slide rail is obliquely arranged on a rack of numerical control bending equipment adjacent to the flanging die, namely the upper surface of the plate supporting seat adjacent to the lower die. That is, an inclined smooth surface is arranged on the upper surface of the plate supporting seat adjacent to the lower die and is used as an inclined slide rail. The inclined slide rail is used as an organic component of the frame, so that the support rigidity is high, and the folding device is suitable for folding requirements of large-tonnage metal plates.
As shown in fig. 2, the driving seat has two non-parallel inclined planes, i.e. an inclined plane one 421 and an inclined plane two 422.
The first inclined plane is slidably mounted on the inclined slide rail, and a first moving pair is formed between the first inclined plane and the inclined slide rail. The second inclined plane is in sliding fit with the sliding inclined plane of the folded beam, and a second sliding pair is formed between the second inclined plane and the sliding inclined plane of the folded beam.
In this embodiment, the driving seat is preferably triangular, more preferably acute-angled triangular, and still more preferably isosceles acute-angled triangular. But may also be right triangular.
Alternatively, the driving seat may be in the shape of other polygon such as L-shape, trapezoid, wedge, L-shape, quadrangle or rectangle, but in the case of trapezoid, the two unparallel slopes are respectively two legs of the trapezoid.
The first inclined surface 421 and the second inclined surface 422 are preferably acute angles, but may be right angles.
The specific preferred settings are as follows: the included angle between the first sliding pair and the horizontal plane is preferably within +/-75 degrees. The included angle between the second sliding pair and the vertical plane is preferably within +/-75 degrees. For example, when the included angle between the first sliding pair and the horizontal plane is 0 °, the included angle between the second sliding pair and the vertical plane may be any acute angle of 0 ° or 75 °. And may be any acute angle between 0 ° or up to 75 °. The special embodiment that the first moving pair is 0 degree to the horizontal plane and the second moving pair is 0 degree to the vertical plane is also included.
The two crank-link mechanisms are a first crank-link mechanism 43 and a second crank-link mechanism 44, respectively.
The first crank-link mechanism comprises a crank I432 and a link I433 which are hinged with each other.
The tail end of the first crank is preferably hinged and mounted on the frame through a first fixing seat 431, and the hinge mounting point of the first connecting rod has the following two preferred embodiments:
example 1: as shown in figures 1 and 3a, one end of the first connecting rod is hinged with the first crank, and the other end of the first connecting rod is hinged with the driving seat.
Example 2: as shown in fig. 2 and 3b, one end of the first connecting rod is hinged with the first crank, and the other end of the first connecting rod is hinged with the hemming beam. In the embodiment, the inverse kinematics solution is simpler, and the load of the guided sliding pair is smaller.
In the present invention, the link transmission of the first crank link mechanism preferably has the following two driving methods.
The first driving mode: the rack is preferably provided with a first servo motor for driving the first crank to rotate.
A second driving mode: the connecting rod transmission of the first crank connecting rod mechanism driven by the toggle rod mechanism has the following specific setting modes: the toggle rod mechanism is hinged and installed at a hinge point of the crank, which is hinged with the connecting rod, and the hinge point is called a driving hinge point.
Wherein, the toggle mechanism has two preferred embodiments as follows:
1. as shown in fig. 16, the toggle link mechanism is a third crank connecting mechanism, the third crank connecting mechanism includes a third crank and a third connecting rod, one end of the third connecting rod is hinged to the third crank, and the other end of the third connecting rod is hinged to the driving hinge point. The other end of the crank III is hinged on the rack and is connected with a servo motor I installed on the rack.
2. As shown in fig. 17, the toggle mechanism is a screw transmission mechanism, one end of the screw is hinged to the driving hinge point, the other end of the screw is connected to the screw seat through a screw pair, and the other end of the screw seat is hinged to the frame and is driven to rotate by a servo motor mounted on the frame.
3. As shown in fig. 18, the toggle link mechanism is a third crank connecting mechanism, the third crank connecting mechanism includes a third crank and a third connecting rod, one end of the third connecting rod is hinged to the third crank, and the other end of the third connecting rod is hinged to the driving hinge point. The other end of the crank III is hinged on the driving seat and is connected with a servo motor I installed on the driving seat.
Alternatively, the link transmission of the first crank-link mechanism may also adopt a mode that a servo motor drives a link to move.
The second crank-link mechanism comprises a second crank 442 and a second connecting rod 443 which are hinged with each other. The tail end of the second crank is preferably hinged to the driving seat through a second fixing seat 441, and the rack is preferably provided with a second servo motor for driving the second crank to rotate.
The other end of the second connecting rod is preferably hinged with the horizontal cross beam of the hemming beam.
In the present invention, the link transmission of the second crank link mechanism may have two driving modes such as the first crank link mechanism. Alternatively, a servo motor can be used to drive the second link to move.
The hemming die displacement detection mechanism is used for detecting the coordinates of the hemming die, preferably two sets of grating rulers, and indirectly feeds back the horizontal and vertical movement displacement of the hemming beam through the synthesis and operation of the readings of the two sets of grating rulers.
Each group of grating rulers comprises a ruler grating, a reading head and a displacement connecting rod.
The two sets of grating scales are a first grating scale and a second grating scale respectively, and as shown in fig. 8, the first grating scale includes a first scale grating 51, a first reading head 52 and a first displacement connecting rod 53. The second grating ruler comprises a second ruler grating 54, a second reading head 55 and a second displacement connecting rod 56.
The first scale grating and the second scale grating are both installed on the rack, the first reading head is slidably connected into the first scale grating, the second reading head is slidably connected into the second scale grating, the first displacement connecting rod is used for connecting the first reading head and the flanging die, and the second displacement connecting rod is used for connecting the second reading head and the flanging die.
Alternatively, the first scale grating and the second scale grating can be arranged on the edge folding beam, and the other ends of the two displacement connecting rods are connected with the frame.
According to the invention, the precision and the rigidity of the flanging die can be improved and the loads of the first movable pair and the second movable pair are reduced by optimizing the inclination angles of the two inclined planes in the driving seat, the position of a hinge point in the crank-link mechanism, the supporting position and the length of the link.
The two groups of crank link mechanisms in the invention can drive the hemming beams and the hemming dies to realize multi-degree-of-freedom movement, and the driving principle is shown in figure 4.
The present invention will be described in detail by taking the following three specific driving examples as examples.
Example 1 Simultaneous movement in the horizontal (X) and vertical (Y) directions
By the nonlinear coupling driving (composite driving) of the first crank driving mechanism and the second crank driving mechanism, the driving process is as shown in fig. 5, and the simultaneous movement in the horizontal direction and the vertical direction can be realized.
In the process, no additional swing exists, so that as shown in fig. 11, the accurate control of the movement track 35 of the tool nose in the hemming die on the XOY plane can be realized, and when the tool nose 34 of the hemming die is contacted with the sheet material, the tool nose does not slide relative to the sheet material and only rolls in the bending process, so that the indentation on the sheet material is avoided, and particularly, the indentation on the surface of the sheet material in the industries of household appliances, elevators and the like has strict requirements.
In the actual bending process, the angle error cannot be avoided, the motion displacement in the horizontal direction and the vertical direction of the folding beam required by angle compensation can be calculated according to accurate mathematical operation for compensation and correction, and then the corresponding rotation angles of the crank I and the crank II are calculated through inverse kinematics solution, so that the compensation of the bending precision is realized. The whole process can realize automatic control, namely intelligent angle precision compensation through closed-loop control of angle measurement, displacement calculation of the folding beam, calculation of first and second driving angles of a crank and real-time correction.
And a linear displacement feedback measuring device such as a grating ruler is adopted to feed back the displacement of the folded beam in real time to form closed-loop control. Through grating chi feedback, can compensate transmission part error, temperature deformation, the elastic deformation of structure, the precision promotes by a wide margin.
Example 2 vertical movement
Through the nonlinear coupling driving (composite driving) of the first crank driving mechanism and the second crank driving mechanism, the driving process is as shown in fig. 6, and then the vertical translation motion can be realized.
In the vertical translation process, the displacement X and the displacement Y of the folded beam can be solved by an analytical method through the real-time reading of the two grating scales. The displacement movement of the two scales is shown in fig. 9 b.
Example 3 horizontal motion
By the nonlinear coupling driving (composite driving) of the first crank driving mechanism and the second crank driving mechanism, the driving process is as shown in fig. 7, and then the horizontal translation motion can be realized.
In the horizontal translation process, the displacement X and the displacement Y of the folded beam can be solved by an analytical method through the real-time reading of the two grating rulers. The displacement movement of the two optical scales is as shown in fig. 9 a.
As shown in fig. 10, a method for solving displacement of a hem beam, in which the hem beam performs a solution of its own displacement through two sets of grating scales, specifically includes the following steps.
Step 1, establishing a coordinate system and a linear equation of a grating ruler, comprising the following steps.
Step 11, establishing a coordinate system: the two sets of grating scales are respectively a first grating scale and a second grating scale. The first grating ruler comprises a first ruler grating, a first reading head and a first displacement connecting rod. The second grating ruler comprises a second ruler grating, a second reading head and a second displacement connecting rod. The first scale grating and the second scale grating are fixed in position, the first reading head is connected to the first scale grating in a sliding mode, and the second reading head is connected to the second scale grating in a sliding mode. The other ends of the first reading head and the second reading head are hinged to the folding edge beam. And establishing an XOY coordinate system by taking the horizontal direction as the X direction, the vertical direction as the Y direction and the intersection point of the two scale gratings as an origin O.
Step 12, establishing a linear equation 1 where the first scale grating is located:
y=K1x
K1=tan(a1)
wherein a1 is the angle between the first scale grating and the X direction. The coordinate of the point of the reading head I on the straight line equation 1 is P1 (x)p1,yP1) Then the distance from the point P1 to the origin O is R1。xp1、yP1The value of (c) is read automatically by the reading head, as a known value.
Step 13, establishing a linear equation 2 where the second scale grating is located:
y=K2x
K2=tan(a2)
wherein a2 is the angle between the second scale grating and the X direction. The second reading head is in a straight linePoint coordinate on Range 2 is P2 (x)p2,yP2) Then the distance from the point P2 to the origin O is R2。xp2、yP2The value of (2) is automatically read by the reading head two and is a known value.
Step 2, establishing the radius as R1Circle 1 of (a): with point P1 as the center, establish radius R1Circle 1, then the equation for circle 1 is:
the equation of circle 1 is expanded as:
step 3, establishing the radius as R2Circle 2 of (a): with point P2 as the center, establish radius R2Circle 2, then the equation for circle 2 is:
the equation of circle 2 is expanded as:
step 4, solving the point coordinate P (x) of the edge folding beamp,yP): point coordinate P (x) of the hemming beamp,yP) And is the intersection of circle 1 and circle 2. By solving for xpAnd yPThereby obtaining the displacement of the hemming beams in the horizontal direction and the vertical direction.
X is abovepAnd yPThe solving process is as follows:
in step 4, xpAnd yPThe solving process is as follows: subtracting the formula (3) from the formula (4) to obtain the following difference intersection equation:
order:
then, equation (5) is simplified as:
y=Kx+b (6)
bringing formula (6) into formula (1) and finishing to obtain:
order:
A=K2+1
B=2(Kb-Kyp1-xp1)
after the formula (7) is finished, the product can be obtained:
Ax2+Bx+C=0 (8)
solving the solution of the unitary quadratic function of equation (8) can yield a display solution of the X coordinate of the intersection:
then, the display solution of the Y coordinate of the intersection can be obtained by bringing equation (9) into equation (6):
yp=Kxp+b (10)
at this point, all solutions x are completedpAnd yP。
Compared with the traditional lead screw transmission, the arrangement of the two crank connecting rod mechanisms has the following advantages:
1. the screw transmission is linear transmission, inverse kinematics solution is easy to obtain, motion control is simple, however, the difficulty of mechanical structure design and manufacture is increased, mechanical design and manufacture cannot be realized, and the overall performance of the mechanism is reduced. However, the invention is nonlinear coupling, the solution of the inverse kinematics is relatively complex, but once the solution is obtained, the design and manufacturing difficulty of the mechanical structure can be greatly reduced, and the performance of the mechanism can be improved.
2. For the screw nut transmission mode, the matching precision between the central line of the hinge revolute pair of the screw and the central line of the thread transmission pair is required to be very high, and generally the matching precision needs to be controlled to be about 0.02mm, which is difficult to achieve in actual production. The non-linear crank connecting rod mechanism is common and conventional hinged constraint, is small in manufacturing difficulty and easy to realize industrialization.
3. Due to the nonlinear characteristic of the mechanism, the output is fast carried out at low load in a non-working stroke, and the output is carried out at low load in a working stroke, so that the pressure maintaining is favorably realized at the tail end of the bending working stroke, the bending machining precision is improved, and the pressure maintaining can be realized only by smaller motor torque. And the linear mechanism of the screw rod can maintain pressure by the peak torque of the motor, so that the motor can generate heat.
4. When the lead screw bears heavy load, the hinge point and the thread pair of the lead screw are not strictly symmetrical structures, and the connection rigidity of the lead screw and the structural part is poor, so that the lead screw can generate bending deformation as shown in figure 12 under stress, and the service life of the lead screw is influenced. The present invention does not have this problem.
5. The invention has nonlinear characteristic, which is very suitable for bending working condition, and can output fast low load in non-working stroke and output fast large load in working stroke.
6. When the first connecting rod of the first crank connecting rod mechanism is hinged with the flanging beam, the bending load is directly transmitted to the rack through the first crank connecting rod mechanism, and the kinematic pair only needs to bear a small load (only needs to bear the overturning load caused by the fact that the load center and the hinge center are not on the same straight line, and actually the load is far smaller than the bending working load), so that heavy-load and large-tonnage bending can be realized.
When the connecting rod of the crank-link mechanism I is hinged with the folded edge beam, the inverse kinematics solution of the folded edge beam driving mechanism is simpler, the analytic inverse solution is easier to realize, and the high-speed and high-precision control is facilitated.
Assuming that the speed of the total stroke is about 200mm/s, the idle stroke is 190mm, the bending stroke is 5mm (upper and lower ends), the bending speed is 8mm (not much affecting the efficiency), and the maximum speed is 200 mm/s: assuming a required bending load of 150000N, the time for both mechanisms to travel full stroke at the highest speed is equal, 1 s.
For a linear transmission mechanism of a ball screw, the power required by a motor is as follows: p is 0.2 m/s.150000N is 30000W is 30 kW.
After the nonlinear crank-link transmission mechanism is adopted, the speed-position curve, the force-position curve and the schematic diagram when the crank-link mechanism moves to a certain specific position are respectively shown in fig. 13, fig. 14 and fig. 15.
In the crank-link mechanism, assuming that a hinge point between the crank and the frame is a, a hinge point between the crank and the link is B, and a hinge point between the link and the driving seat or the hem beam is C, a schematic diagram when the crank-link mechanism moves to a certain specific position is shown in fig. 17. Wherein α is 17 ° and β is 2 ° and R is 100m and is crank length, 750mm is link length, and 5mm represents the distance of the bending stroke.
The output torque of the servo motor I or the servo motor II is as follows:
M=F·R·sin(α+β)=150000·0.1·sin(19°)=4883.5Nm
where F is the bending load and R is the length of the crank 100mm, i.e. 0.1 m.
The angular velocity is:
the output power of the servo motor I or the servo motor II is as follows: and P is 4883.5 Nm.3.14 rad/s is 15334W and is approximately equal to 15 kW.
Therefore, compared with a linear transmission mode of a ball screw, the linear transmission device has the advantages that the motor driving power is reduced by about 50%, and the energy-saving and cost-reducing effects are very obvious.
Although the preferred embodiments of the present invention have been described in detail, the present invention is not limited to the details of the embodiments, and various equivalent modifications can be made within the technical spirit of the present invention, and the scope of the present invention is also within the scope of the present invention.