CN116484655B - Multi-objective optimization design method for die clamping mechanism of extrusion casting equipment - Google Patents
Multi-objective optimization design method for die clamping mechanism of extrusion casting equipment Download PDFInfo
- Publication number
- CN116484655B CN116484655B CN202310738277.3A CN202310738277A CN116484655B CN 116484655 B CN116484655 B CN 116484655B CN 202310738277 A CN202310738277 A CN 202310738277A CN 116484655 B CN116484655 B CN 116484655B
- Authority
- CN
- China
- Prior art keywords
- rod
- objective
- clamping mechanism
- ratio
- length
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
- 230000007246 mechanism Effects 0.000 title claims abstract description 85
- 238000000034 method Methods 0.000 title claims abstract description 81
- 238000013461 design Methods 0.000 title claims abstract description 60
- 238000005457 optimization Methods 0.000 title claims abstract description 50
- 238000005266 casting Methods 0.000 title claims abstract description 13
- 238000001125 extrusion Methods 0.000 title claims abstract description 13
- 230000008569 process Effects 0.000 claims abstract description 21
- 230000008094 contradictory effect Effects 0.000 claims abstract description 11
- 238000013178 mathematical model Methods 0.000 claims abstract description 9
- 230000014509 gene expression Effects 0.000 claims description 25
- 230000001133 acceleration Effects 0.000 claims description 21
- 230000002265 prevention Effects 0.000 claims description 4
- 238000012360 testing method Methods 0.000 claims description 3
- 238000004519 manufacturing process Methods 0.000 abstract description 3
- 230000009286 beneficial effect Effects 0.000 abstract description 2
- 238000013433 optimization analysis Methods 0.000 abstract description 2
- 238000010586 diagram Methods 0.000 description 9
- 238000004458 analytical method Methods 0.000 description 8
- 230000002829 reductive effect Effects 0.000 description 7
- 230000002787 reinforcement Effects 0.000 description 6
- 239000003921 oil Substances 0.000 description 5
- 238000004364 calculation method Methods 0.000 description 2
- 238000006243 chemical reaction Methods 0.000 description 2
- 238000005516 engineering process Methods 0.000 description 2
- 230000036961 partial effect Effects 0.000 description 2
- 238000003825 pressing Methods 0.000 description 2
- 230000009471 action Effects 0.000 description 1
- 230000003321 amplification Effects 0.000 description 1
- 230000015556 catabolic process Effects 0.000 description 1
- 230000008859 change Effects 0.000 description 1
- 230000007547 defect Effects 0.000 description 1
- 238000006731 degradation reaction Methods 0.000 description 1
- 230000001419 dependent effect Effects 0.000 description 1
- 238000004512 die casting Methods 0.000 description 1
- 238000006073 displacement reaction Methods 0.000 description 1
- 238000005265 energy consumption Methods 0.000 description 1
- 238000002474 experimental method Methods 0.000 description 1
- 239000010720 hydraulic oil Substances 0.000 description 1
- 230000002452 interceptive effect Effects 0.000 description 1
- 230000000670 limiting effect Effects 0.000 description 1
- 238000013507 mapping Methods 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
- 210000000633 nuclear envelope Anatomy 0.000 description 1
- 238000003199 nucleic acid amplification method Methods 0.000 description 1
- 238000012545 processing Methods 0.000 description 1
- 230000004044 response Effects 0.000 description 1
- 238000009716 squeeze casting Methods 0.000 description 1
- 230000003068 static effect Effects 0.000 description 1
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
-
- B—PERFORMING OPERATIONS; TRANSPORTING
- B22—CASTING; POWDER METALLURGY
- B22D—CASTING OF METALS; CASTING OF OTHER SUBSTANCES BY THE SAME PROCESSES OR DEVICES
- B22D18/00—Pressure casting; Vacuum casting
- B22D18/02—Pressure casting making use of mechanical pressure devices, e.g. cast-forging
-
- B—PERFORMING OPERATIONS; TRANSPORTING
- B22—CASTING; POWDER METALLURGY
- B22D—CASTING OF METALS; CASTING OF OTHER SUBSTANCES BY THE SAME PROCESSES OR DEVICES
- B22D18/00—Pressure casting; Vacuum casting
- B22D18/08—Controlling, supervising, e.g. for safety reasons
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F2111/00—Details relating to CAD techniques
- G06F2111/04—Constraint-based CAD
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F2111/00—Details relating to CAD techniques
- G06F2111/06—Multi-objective optimisation, e.g. Pareto optimisation using simulated annealing [SA], ant colony algorithms or genetic algorithms [GA]
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
- G06F2119/14—Force analysis or force optimisation, e.g. static or dynamic forces
-
- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02P—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN THE PRODUCTION OR PROCESSING OF GOODS
- Y02P90/00—Enabling technologies with a potential contribution to greenhouse gas [GHG] emissions mitigation
- Y02P90/30—Computing systems specially adapted for manufacturing
Landscapes
- Engineering & Computer Science (AREA)
- Physics & Mathematics (AREA)
- Theoretical Computer Science (AREA)
- Mechanical Engineering (AREA)
- Computer Hardware Design (AREA)
- Evolutionary Computation (AREA)
- Geometry (AREA)
- General Engineering & Computer Science (AREA)
- General Physics & Mathematics (AREA)
- Moulds For Moulding Plastics Or The Like (AREA)
Abstract
The application discloses a multi-objective optimization design method of a die clamping mechanism of extrusion casting equipment, which comprises the following steps: setting a plurality of objective functions to be optimized, and determining design variables; applying constraint conditions to the design variables to establish a mathematical model of the clamping mechanism; solving the objective function, and solving the contradictory objective functions through a coordination curve method and a tolerant sequence layering method if the contradictory objective functions exist in the solving process; and selecting an optimal design scheme of the die clamping mechanism according to the solved result. The application has the beneficial effects that: when the optimization design is carried out, corresponding to the objective functions with the contradiction of the design, the coordination relation between the contradiction objective functions can be determined by combining a coordination curve method and a tolerance layering sequence method, and then the tolerance optimization analysis is carried out on a plurality of contradiction targets, so that the optimization result can more accord with the actual production requirement.
Description
Technical Field
The application relates to the technical field of die casting machines, in particular to a multi-objective optimization design method for a die clamping mechanism of extrusion casting equipment.
Background
The mold clamping mechanism is one of key mechanisms of extrusion casting equipment and is used for ensuring the reliable closing of a forming mold and realizing the opening action of the forming mold, namely ejecting a product, and the performance of the forming mold directly influences the quality of the formed product. The existing mould closing mechanism is mainly divided into a hydraulic type and a crank connecting rod type, wherein the double-crank structure has the characteristics of compact structure, reliable mould locking, good movement characteristic, high strength and rigidity of the mechanism and the like, is widely applied, and well meets the production requirements of extrusion casting.
The structure of the conventional clamping mechanism is shown in fig. 1, and when designing, the parameters of the mechanism obtained by mapping, analogy and experience design methods are difficult to be optimally combined, and the performance requirements of a plurality of targets cannot be met, so that the practical value of the clamping mechanism is reduced to a certain extent. Therefore, the design of the mold closing mechanism at the present stage generally adopts the CAE technology, and the CAE technology can greatly improve the accuracy of an optimization algorithm and obviously improve the scientificity and the design efficiency of the product design in face of the multi-objective optimization requirement of the mold closing mechanism.
However, when the existing optimization method is used for optimizing and solving the objective function, a simple linear weighting method or multiplication and division method is mainly adopted to convert the multi-objective function into a single objective function, and the method for converting the interval optimization problem into the deterministic optimization problem for solving has the following defects:
(1) In the conversion process, the selection and mixing of parameters such as the probability level, the weight coefficient, the penalty factor and the like have larger subjective randomness, the values of the parameters have direct and important influence on the optimization result, and the feasibility and the effectiveness of the design scheme obtained by single-day standard unconstrained deterministic optimization solution after conversion in actual engineering are difficult to ensure due to the inappropriate values of the parameters;
(2) In the process of converting the interval optimization problem into the deterministic optimization problem for solving, uncertainty information described in the uncertainty modeling is lost, which also breaks against the original purpose of truly reflecting the objective uncertainty essence when establishing an interval optimization model to solve the size optimization problem of the high-speed press slide block mechanism;
(3) Because of the contradictory relation between reinforcement and acceleration in the die assembly mechanism, a simple linear weighting method or multiplication and division method is adopted to convert the multi-objective function into a single-objective function, and the difference of the magnitude of each objective before and after unified processing is easily ignored, so that the calculation result is not converged.
Therefore, how to perform multi-objective optimization on the structure of the conventional clamping mechanism is a technical problem to be solved by those skilled in the art.
Disclosure of Invention
One of the objects of the present application is to provide a design method that enables multi-scheme optimization of multiple objectives of a die closing mechanism.
In order to achieve the purpose, the application adopts the following technical scheme: a multi-objective optimization design method for a die clamping mechanism of extrusion casting equipment comprises the following steps:
s100: setting a plurality of objective functions to be optimized; determining a design variable;
s200: applying constraint conditions to the design variables to establish a mathematical model of the clamping mechanism;
s300: solving the objective function, wherein in the process of solving, if a plurality of objective functions are contradictory, the objective functions are solved by a coordination curve method and a tolerant sequence layering method;
s400: and selecting an optimal design scheme of the die clamping mechanism according to the solved result.
Preferably, for objective functions where there are multiple contradictions, step S300 includes the following solving steps:
s310: dividing the importance degrees of a plurality of objective functions;
s320: firstly, solving an optimal solution for an important objective function, and setting a given tolerance according to the optimal solution;
s330: solving an optimal solution for the next objective function within the given tolerance of the previous objective function, and setting the given width tolerance of the current objective function according to the optimal solution;
s340: step S330 is repeated until all objective functions are solved.
Preferably, in step S300, the objective function is solved by an interior point penalty function method for nonlinear programming.
Preferably, in step S100, the objective function includes a clamping mechanism force increasing ratio M p Stroke ratio R S Speed ratio R v And the acceleration value a of the movable template m And the sum of the rod masses.
Preferably, in the mold closing mechanism, the hinge point of the bent toggle rod and the tail plate is A, the hinge point of the bent toggle rod and the large connecting rod is B, and the hinge point of the bent toggle rod and the small connecting rod is D; the design variables in step S100 include the length L of the connection AB of the hinge point A, B 1 Length L of large link 2 Length L of small link 4 Length L of line AD of hinge point A, D 5 Included angle θ between connecting line AD and horizontal direction at die closing limit, included angle γ between connecting line AB and AD, and maximum toggle angle α max And the vertical distance H of the crosshead to position A b 。
Preferably, the power-up ratio M p The expression of (2) is:
；
stroke ratio R S The expression of (2) is:
；
speed ratio R v The expression of (2) is:
；
acceleration a of movable template m The expression of (2) is:
；
the rod mass assembly is suitable for passing through the total length L of the rod And performing equivalent representation; l (L) And =L 1 + L 2 + L 3 + L 4 + L 5 ；
wherein L is 3 The length of the connecting line BD between the hinge points B, D is the elbow angle, the included angle between the large connecting rod and the horizontal direction is beta,is the included angle of the horizontal direction of the small connecting rod, +.>Angular acceleration, ω, of a curved toggle lever 1 To bend the angular velocity of the toggle lever omega 2 Is the angular velocity of the large connecting rod.
Preferably, in step S200, the constraints include interference prevention and self-locking constraints, rod length constraints, angle constraints, domain constraints, and design variable boundary constraints.
Preferably, for the constraint of the length of the rod, the length ratio of the rod is takenThe value range of (5) is [0.7,0.85 ]]The method comprises the steps of carrying out a first treatment on the surface of the The rod length constraint is expressed as follows:
；
。
preferably, for defining domain constraints, if the increase ratio M is to be made p And stroke ratio R S Meaning, the following conditions need to be satisfied:
；
。
preferably, boundary constraints for the design variables; wherein L is 1 、L 2 、L 4 And L 5 The specific value boundary of (1) is suitable for passing H b Is obtained by repeated test; then θ ε [4×Pi/180,6 ×Pi/180 ]]，γ∈[18×Pi/180，25×Pi/180]，α max ∈[90×Pi/180，110×Pi/180]。
Compared with the prior art, the application has the beneficial effects that:
(1) When the optimization design is carried out, the coordination relation between the contradictory objective functions can be determined by combining the coordination curve method and the tolerant hierarchical sequence method corresponding to the objective functions with the contradictory design, and then the tolerant optimization analysis is carried out on a plurality of contradictory targets, so that the optimization result can be more in line with the actual production requirement.
(2) The method avoids converting the interval optimization problem into the deterministic optimization problem, explores a direct solving method of the interval optimization problem different from the traditional indirect solving method, and determines the optimal design scheme of the size parameters of the clamping mechanism through direct comparison of the merits of the interval objective function values.
Drawings
Fig. 1 is a schematic structural view of a conventional double-toggle clamping mechanism.
FIG. 2 is a schematic diagram of a design flow in the present application.
FIG. 3 is a schematic flow chart of the coordinated solution when the objective function contradiction occurs in the present application.
FIG. 4 is a schematic diagram showing the motion principle analysis of the clamping mechanism in the application.
FIG. 5 is a schematic diagram showing a speed analysis of a clamping mechanism according to the present application.
FIG. 6 is a schematic diagram of a mechanical analysis of a clamping mechanism in accordance with the present application.
FIG. 7 is a graph showing the coordination of the stroke ratio and the increasing ratio according to the present application.
FIG. 8 is a graph showing the variation of the speed ratio parameters according to the present application.
FIG. 9 is a graph showing the difference between the peak and the valley of the velocity according to the present application.
FIG. 10 is a graph showing comparison of the results of the performance parameters before and after the optimization of the clamping mechanism in the application.
FIG. 11 is a schematic diagram showing the comparison of the design variable optimization values of the clamping mechanism in the present application.
In the figure: the device comprises a die closing cylinder 1, a tail plate 2, a crank rod 3, a small connecting rod 4, a cross head 5, a large connecting rod 6, a movable die plate 7, a tie rod 8 and a head plate 9.
Detailed Description
The present application will be further described with reference to the following specific embodiments, and it should be noted that, on the premise of no conflict, new embodiments may be formed by any combination of the embodiments or technical features described below.
In the description of the present application, it should be noted that, for the azimuth words such as terms "center", "lateral", "longitudinal", "length", "width", "thickness", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", "clockwise", "counterclockwise", etc., the azimuth and positional relationships are based on the azimuth or positional relationships shown in the drawings, it is merely for convenience of describing the present application and simplifying the description, and it is not to be construed as limiting the specific scope of protection of the present application that the device or element referred to must have a specific azimuth configuration and operation.
It should be noted that the terms "first," "second," and the like in the description and in the claims are used for distinguishing between similar objects and not necessarily for describing a particular sequential or chronological order.
FIG. 1 is a schematic diagram of a conventional double-toggle clamping mechanism; the die assembly mechanism comprises a die assembly oil cylinder 1, a tail plate 2, a pair of toggle rods 3, a pair of small connecting rods 4, a cross head 5, a pair of large connecting rods 6, a movable die plate 7, a plurality of tie bars 8 and a head plate 9. The tail plate 2 and the head plate 9 are fixedly arranged on the frame, the number of the tie bars 8 is four generally, the tie bars are fixedly arranged between the tail plate 2 and the head plate 9, and the movable mould plate 7 is slidably arranged on the tie bars 8. The output end of the die closing cylinder 1 is arranged on the tail plate 2 in a sliding way, and the cross head 5 is fixedly arranged at the output end of the die closing cylinder 1. Two sides of the non-die-combining surface of the movable die plate 7 are respectively hinged with a large connecting rod 6; meanwhile, the other end of the large connecting rod 6 is hinged with one side of the tail plate 2 through bent toggle rods 3, and each bent toggle rod 3 is also hinged with the cross head 5 through a small connecting rod 4. Therefore, the die closing oil cylinder 1 can drive the cross head 5 to move through the axial direction, and further drive the small connecting rod 4, the bent toggle rod 3 and the large connecting rod 6 to do connecting rod movement so as to drive the movable die plate 7 to slide along the tie bar 8 in the axial direction, so that die opening and die closing of the die are realized.
In the design of the clamping mechanism, structural parameters and position parameters among the tail plate 2, the toggle rod 3, the small connecting rod 4, the cross head 5, the large connecting rod 6 and the movable die plate 7 need to be designed and considered, and contradictory interference exists among part of the parameters, so that the design optimization of the clamping mechanism is difficult.
In order to solve the above-mentioned technical problems, according to one preferred embodiment of the present application, as shown in fig. 2, a multi-objective optimization design method for a mold clamping mechanism of an extrusion casting apparatus includes the steps of:
s100: setting a plurality of objective functions to be optimized; design variables are determined.
S200: constraints are imposed on the design variables to build a mathematical model of the clamping mechanism.
S300: and solving the objective function, wherein in the process of solving, if the objective functions are contradictory, the objective functions are solved by a coordination curve method and a tolerant sequence layering method.
S400: and selecting an optimal design scheme of the die clamping mechanism according to the solved result.
It should be noted that the optimization process of the clamping mechanism is the optimization of the parameters, so that a mathematical model needs to be built for the clamping mechanism, and the building of the mathematical model needs to depend on the problem to be solved, i.e. the objective function, and the parameters affecting the objective function, i.e. the design variables. After the design variable is selected, constraint is needed for the variable value of the design variable, otherwise, there are countless choices for the design variable, the operation amount can be greatly reduced by constraining the design variable, and the direction can be provided for optimization so as to improve the accuracy of optimization.
In this embodiment, the objective function is dependent on a primary parameter affecting the performance of the clamping mechanism, such as the clamping mechanism force increasing ratio M p Stroke ratio R S Speed ratio R v And the acceleration value a of the movable template m And the sum of rod masses, etc. Wherein the boosting ratio M p The size of the clamping force generated by the clamping mechanism under the driving of the same clamping cylinder 1 is determined, and the boosting ratio M p The larger the generated clamping force is, the larger the clamping force is; stroke ratio R S The size of the movable mold plate 7 determines the stroke of the movable mold plate 7 which can be generated by the mold clamping mechanism under the driving stroke of the same mold clamping oil cylinder 1; speed ratio R v And the acceleration value a of the movable template m The response performance of the die clamping mechanism is determined; the total mass of the clamping mechanism is determined by the total mass of the rod pieces.
For easy understanding, the mathematical model building process of each objective function may be described in detail below; for ease of understanding, the schematic structural diagram of the clamping mechanism shown in fig. 1 may be simplified to a schematic diagram of the principle of motion analysis as shown in fig. 4.
As shown in fig. 4, the hinge point of the crank lever 3 and the tail plate 2 is a, the hinge point of the crank lever 3 and the large connecting rod 6 is B, the hinge point of the large connecting rod 6 and the movable template 7 is C, the hinge point of the crank lever 3 and the small connecting rod 4 is D, and the hinge point of the cross head 5 and the small connecting rod 4 is E; the length of the connection line AB between the hinge points A, B can be set to L 1 The length of the large connecting rod 6 is L 2 The length of the connecting line BD between the hinge points B, D on the toggle rod 3 is L 3 The length of the small connecting rod 4 is L 4 The length of the connecting line AD of the hinge point A, D is L 5 The method comprises the steps of carrying out a first treatment on the surface of the The included angle between the connecting line AD and the horizontal direction is theta, the included angle between the connecting line AB and AD is gamma, the rotation angle of the bent toggle rod 3 is a bent toggle angle alpha, the included angle between the large connecting rod 6 and the horizontal direction is beta, and the small connecting rod is4 with the horizontal direction isThe method comprises the steps of carrying out a first treatment on the surface of the The stroke of the die closing cylinder 1 is S o The motion travel of the movable template 7 is S m Vertical distance H from hinge point E to hinge point A b 。
The working principle of the die closing mechanism is as follows: when the die assembly starts, the die assembly oil cylinder 1 pushes the cross head 5 to move, and the small connecting rod 4 is connected in parallel to drive the bent toggle rod 3 to rotate around the hinge point A at the same angular speed, so that the hinge assembly is gradually straightened, and the movable die plate 7 is pushed to move until the movable die plate contacts the die. Then, the mold clamping cylinder 1 continues to drive the cross head 5 to force the mold clamping mechanism parts to elastically deform, so that the mold clamping mechanism generates a pressing force (mold clamping force) to be in a self-locking state, and the mold clamping force still exists even if the cylinder pushing force is removed. At this time, the corresponding positions of the hinge points B, C, D and E at the mold closing position are shown as B ', C', D ', and E' in fig. 4.
Wherein, the stroke S of the die closing cylinder 1 o I.e. the movement stroke of the crosshead 5 (hinge point E); taking the hinge point A as the origin of coordinates, the projection length of the hinge point E on the x axis at the initial position and any position can be deduced according to the geometric relationship of the mechanism in FIG. 4, and the projection length is shown in the following expressions (1) and (2):
（1）。
（2）。
the projection length of the small link 4 on the x-axis at the initial position and at an arbitrary position is as shown in the following expressions (3) and (4):
（3）。
（4）。
motion stroke S of the crosshead 5 in any state o The expression (5) can be used for the illustration.
（5）。
The specific formula of expression (5) can be obtained by taking the above-described expressions (3) and (4) into expressions (1) and (2), respectively; the above-mentioned carrying-in process is a well-known technique for those skilled in the art, and is not described in detail herein.
Travel S of moving die plate 7 m Namely the motion travel of the hinge point C; from the geometric relationship, it is possible to derive the following expressions (6) and (7) of the projection length of the hinge point C on the x-axis at the initial position as well as at any position.
（6）。
（7）。
From the projected position relationship of the large link 6 on the y-axis, it can be deduced that:
(8) The method comprises the steps of carrying out a first treatment on the surface of the Thus, there are:
（9）。
finally, the stroke S of the movable die plate 7 can be obtained m The expression of (2) is:
（10）。
by taking the above expression (9) into the expressions (6) and (7), the stroke S with respect to the movable die plate 7 can be obtained m Is described. The above-mentioned carrying-in process is a well-known technique for those skilled in the art, and is not described in detail herein.
The ratio of the displacement of the movable die plate 7 to the cross head 5 is:
（11）。
when the clamping mechanism operates to the clamping limit, the maximum stroke S of the movable platen 7 can be defined m And the maximum movement stroke S of the cross head 5 o Is the stroke ratio R S I.e., α=0; the stroke ratio R can be obtained S The expression of (2) is:
（12）。
FIG. 5 is a schematic diagram showing the movement analysis of the clamping mechanism. Half of the die closing mechanism is regarded as a crank connecting rod structure, and the speed ratio of the hinge point C on the movable die plate 7 to the hinge point E of the cross head 5 can be obtained by adopting a speed instantaneous center method.
Firstly, two instantaneous centers of the mechanism are found out, wherein the connecting line AB on the crank rod 3 and the speed instantaneous center of the large connecting rod 6 are G, and the connecting line AD on the crank rod 3 and the speed instantaneous center of the small connecting rod 4 are F; obtaining the speed relation between the hinge point C and the hinge point B on the movable template 7, between the hinge point D and the hinge point E on the cross head 5, and finally converting to obtain the ratio R of the movement speed of the movable template 7 to the movement speed of the cross head 5 v As shown in the following expression (13):
（13）。
wherein V is m Indicating the instantaneous speed, V, of the moving platen 7 o Indicating the instantaneous speed, V, of the clamp cylinder 1 B Representing the instantaneous speed, V, of the hinge point B C Representing the instantaneous speed, V, of the hinge point C D Representing the instantaneous speed, V, of the hinge point C E Representing the instantaneous speed of the hinge point E.
Instantaneous movement of the moving platen 7Time speed V m Deriving the time t, the acceleration a of the movable die plate 7 with the toggle angle alpha of the toggle lever as a variable can be obtained m Is represented by the expression:
（14）。
wherein the angular acceleration of the line AB on the toggle lever 3The method comprises the following steps:
（15）。
angular velocity ω of the line AB on the toggle lever 3 1 The method comprises the following steps:
（16）。
angular velocity ω of small connecting rod 4 4 The method comprises the following steps:
（17）。
angular velocity ω of large connecting rod 6 2 The method comprises the following steps:
（18）。
from the above expressions (4) and (8), the angle β and the angle β can be obtainedIs brought into expression (14) to obtain a relational expression of the acceleration of the movable platen 7.
When the die assembly starts, the die assembly oil cylinder 1 pushes the cross head 5 to do linear motion and moves the small connecting rod 4 in parallel, so that the machine hinge assembly is gradually straightened, and the movable die plate 7 is pushed to move until the movable die plate contacts the die. Then the mold clamping cylinder 1 continues to drive the cross head 5 to force the mold clamping mechanism parts to elastically deform,thereby generating a pressing force P on the die m (mold clamping force) to bring the clamping mechanism into a self-locking state. As shown in fig. 6, in the process of mold closing, the stress analysis of the mechanism under neglecting friction force is schematically shown, and the stress analysis of the mold closing mechanism is performed by combining the static force balance theory and the moment balance theory, wherein the stress analysis of the small connecting rod 4, the large connecting rod 6 and the toggle rod 3 is as follows:
。
P m /2=P 2 ×cosβ（20）。
。
wherein P is o Represents the thrust force, P, of the mold clamping cylinder 1 2 Shows the thrust force, P, of the movable die plate 7 and the toggle rod 3 respectively applied to the two ends of the large connecting rod 6 4 The thrust force received by the small connecting rod 4 is shown; h is a 2 Representing the thrust P 2 Arm length between the hinge point A and the arm, h 4 Representing the thrust P 4 The length of the arm of force between the hinge point A.
By combining the stress relationship, the mode locking force P can be obtained m Thrust P with mold clamping cylinder 1 o Is the mathematical relationship of (i.e. the force-increasing ratio M) p The expression of (2) is as follows:
（22）。
to facilitate subsequent optimization, the boost ratio M is performed p The value of expression (22) at α=2.5° can be selected as the optimization target. At the same time, the speed ratio R is being carried out v And the acceleration value a of the movable template m In order to meet the requirements of a rapid mold opening and closing process and better acceleration performance and deceleration performance of the movable mold plate, the difference between the peak value and the valley value of the speed ratio, the starting value of the speed ratio and the difference between the peak value and the valley value of the acceleration can be used as optimization targets. While the total mass of the rod members is not convenient to calculate, so thatBy optimizing the length of the bars instead of the mass of the bars, i.e. by the total length L of the bars And instead of the total mass of the rod, the function expression is L And =L 1 + L 2 + L 3 + L 4 + L 5 。
thus, the above-described objective function establishment procedure can be known: in step S100, the main parameter affecting the objective function, i.e. the design variable, includes the length L of the connection AB of the hinge point A, B 1 Length L of large connecting rod 6 2 Length L of small link 4 4 Length L of line AD of hinge point A, D 5 Included angle θ between connecting line AD and horizontal direction at die closing limit, included angle γ between connecting line AB and AD, and maximum toggle angle α max And the vertical distance H of the crosshead 5 to the hinge point a b 。
After the design variables are determined, constraint conditions are required to be applied to the design variables to reduce the optimization range of the design variables so as to improve the solving speed and the solving precision of the objective functions in order to ensure that the solving process of the objective functions can be accurate and rapid.
In this embodiment, the constraints to be added in step S200 include interference prevention and self-locking constraints, rod length constraints, angle constraints, domain constraints, and design variable boundary constraints.
Wherein, for the interference prevention and self-locking constraint conditions:
(1) As known from the working principle of the toggle type clamping mechanism, the clamping mechanism is of an up-down symmetrical structure, and the upper and lower toggle levers 3 are prevented from interfering in the process of opening and closing the mold, so that the following conditions are required to be satisfied in the optimization process of the clamping mechanism:
（23）。
（24）。
wherein d B 、d D Is the rotation diameter of the hinge point B, D, H S Is the center distance between the upper hinge point and the lower hinge point of the cross head 5.
(2) The self-locking phenomenon is avoided in the mold closing and opening stage, and the angle EDB=180°; meanwhile, the friction circle theory of the bent toggle rod 3 is considered, and the EDB is required to be less than 160 degrees; there are the following constraints:
（25）。
wherein, for the rod length constraint:
(1) For compact structure and improved system rigidity, according to design experience, the length ratio of the rodGenerally in interval [0.7,0.85 ]]In the inner, the following constraint exists:
（26）。
（27）。
(2) Meets the rotation requirement of the rod piece, ensures that the small connecting rod 4 and the toggle rod 3 have enough length to meet the rotation condition, namely L 4 ≥（d E + d D ）/2，L 3 ≥（d B + d D ) 2; there are the following constraints:
（28）。
（29）。
wherein d E The diameter of the revolution is the hinge point E.
Wherein, for the angle constraint condition, from multiple experiments or experience in the field, in order to ensure the speed stability of the movable mould plate 7 and the mechanical property of the mould closing mechanism, the method can be adoptedMaximum apex angleThe method comprises the steps of carrying out a first treatment on the surface of the There are the following constraints:
（30）。
wherein, for a domain constraint:
(1) As is clear from the above expressions (4) and (9), if the power ratio M is to be increased p And stroke ratio R S Meaning, then the following needs to be satisfied:，/>the method comprises the steps of carrying out a first treatment on the surface of the There are the following constraints:
（31）。
（32）。
(2) Travel S of moving die plate 7 m Needs to meet a certain range, namely S m ∈[X，Y]Stroke ratio R S Satisfy not greater than Z; there are the following constraints:
（33）。
（34）。
（35）。
for easy understanding, the die assembly mechanism of the 400 ton type extrusion casting equipment in the enterprise can be taken as an example, and the movable die plate 7 of the die assembly mechanismIs of the stroke S of (2) m ∈[500，600]I.e., x=500, y=600; at the same time its stroke ratio R S No more than 1.12 is satisfied, i.e., z=1.12.
Wherein, for the design variable boundary constraint:
the boundary conditions are reasonably set, so that the optimization efficiency can be improved, and the calculated amount can be reduced. Taking the mold clamping mechanism of the 400-ton extrusion casting equipment as an example. The inclination angle theta is 4-6 degrees, so that under the condition of slightly increasing the size of the tail plate 2, a larger stroke of the movable die plate 7 can be obtained, and the characteristics of force amplification and die moving speed cannot be changed obviously. From the economic standpoint, the size of the tail plate 2 should not be too large, and the distance H between the joint E of the cross head 5 and the small connecting rod 4 and the hinge point A is set b The upper boundary is 250mm. Under the condition of not affecting the convergence of the optimal solution, the boundary condition of each design variable is obtained by repeated test
L 1 ∈[320，410]；L 2 ∈[415，505]；L 4 ∈[100，150]；L 5 ∈[280，330]；θ∈[4×Pi/180，6×Pi/180]，γ∈[18×Pi/180，25×Pi/180]，α max ∈[90×Pi/180，110×Pi/180]；H b ∈[210，250]。
It can be appreciated that through the above process, a mathematical model of the nuclear membrane mechanism can be established, and then the mathematical model is led to solving software, and Matlab software is generally adopted to solve the objective function through the software. In the process of solving the objective function, contradiction may occur in the solution between the plurality of objective functions; for example, the force and stroke ratios in a clamping mechanism are a pair of contradictory objective functions; during the optimization process, degradation of the remaining objective function will occur when the objective function of the increase ratio is optimized. Therefore, the existing single objective function optimization design method for the force increasing ratio, the stroke ratio, the rod piece mass sum and the speed ratio of the die closing mechanism is not reasonable enough. Therefore, the optimization design of the modular mechanism is required to be carried out by combining a coordination curve method and a tolerance layering sequence method.
In the optimization process, the coordination curve method coordinates the function values of each partial target of the die closing mechanism, and gives some yield to each other so as to finally obtain a most reasonable scheme which is acceptable to each partial target from the engineering practical point of view. The tolerance sequence layering method can optimize the objective functions of the increasing ratio, the stroke ratio and the rod piece mass sum in the optimization process of the die assembly mechanism one by one according to the importance degree, firstly, the important objective functions are solved with the optimal solution, the given wide capacity is taken out of the optimal value, and then the next objective is optimized, so that the poor calculation result caused by different dimensions and orders of objective function values is avoided.
In this embodiment, as shown in fig. 3, for the objective function with a plurality of contradictions, the optimization of the modeling mechanism by using the coordination curve method and the tolerant hierarchical sequence method in step S300 includes the following specific steps:
s310: the importance of multiple objective functions is divided.
S320: the optimal solution is firstly solved for the important objective function, and the given latitude is set according to the optimal solution.
S330: and solving an optimal solution for the next objective function within the given tolerance of the previous objective function, and setting the given width tolerance of the current objective function according to the optimal solution.
S340: step S330 is repeated until all objective functions are solved.
It is understood that in step S300, the objective function may be solved by an interior point penalty function method for nonlinear programming. The principles of the interior point penalty function are well known to those skilled in the art and will not be described in detail herein.
For easy understanding, a specific process of optimizing the die closing mechanism by using the coordination curve method and the tolerant layering sequence method can be described below with respect to an example of a die closing mechanism of an extrusion casting device of 400 ton type in an enterprise.
(1) And determining a coordination curve relation between the increasing force ratio and the stroke ratio, and collecting all non-inferior solutions meeting the K-T condition. The fMincon function for solving the nonlinear multi-constraint optimization problem in the Matlab optimization tool box is adopted to optimize the objective function of the reinforcement ratio of the modular mechanism, the maximum value of the reinforcement ratio is 26.55 in the constraint condition limit, the stroke ratio is divided into 13 groups from 1.0 to 1.12, the corresponding optimal value of the reinforcement ratio is calculated again, and the obtained coordination curve relationship is shown in figure 7.
(2) And (5) making an allowable deviation of the corresponding target optimal value, and solving the minimum rod mass sum value. According to the model design experience, the stroke ratio is controlled in the interval [1, 1.12], namely the force increasing ratio is positioned in the interval [21.8, 26.55], so that 13 groups of optimization schemes are obtained. The optimal value of the force ratio and the stroke ratio in the 13 groups of schemes is given with a wide capacity, and then the target of the division of the total rod mass is optimized, so that the optimal value of the rod mass and the corresponding force ratio and the stroke ratio are finally obtained as shown in the figure 7.
(3) And analyzing parameters such as the difference between the speed ratio peak and the valley values, the speed ratio starting value and the difference between the acceleration peak and the valley values of different schemes by considering the optimal speed ratio curve and the acceleration value. For a small 400-ton squeeze casting device, the operating efficiency of a mechanism is more important, so that the speed ratio and the acceleration value are very important parameters, and the change curves of the speed ratio and the acceleration parameter in different schemes are made according to the scheme parameters obtained in the steps. The speed ratio parameter variation curve and the acceleration peak-to-valley parameter variation curve are shown in fig. 8 and 9.
(4) The resulting optimized performance parameter pairs for the 13 sets of data are optimized according to the method described above, such as shown in fig. 10. In combination with the objective function values, scheme 4 can be found to be a better design. When the force increasing ratio is larger than 23.1 and the stroke ratio is smaller than 1.09, the performance of the speed ratio peak-valley value, the stroke ratio and other parameters is rapidly reduced, the speed increasing and reducing performance of the movable mould plate 7 is linearly reduced, and the operation efficiency of the mould clamping mechanism is reduced. Meanwhile, the mechanism rod is long and long, the mass is large, and the occupied space of the die clamping mechanism is increased; if the power-up ratio is less than 23.1 and the stroke ratio is greater than 1.09, the power-up performance and the speed ratio start-up value are poor. The values of the specific design variables thus obtained according to scheme 4 are shown in fig. 11.
It should be noted that, as compared with the original design, in the scheme 4, under the condition that the total of the length, the floor area and the rod piece mass of the machine is basically unchanged, the reinforcement ratio is increased from 20.2 to 23.1, and the reinforcement ratio is increased by 14.4%, so that the energy consumption of the hydraulic oil pump can be effectively reduced; the stroke ratio is improved from 1.02 to 1.09, and the stroke ratio is improved by 6.9 percent. Meanwhile, the speed ratio and the acceleration are effectively improved, and the working efficiency is improved.
The foregoing has outlined the basic principles, features, and advantages of the present application. It will be understood by those skilled in the art that the present application is not limited to the embodiments described above, and that the above embodiments and descriptions are merely illustrative of the principles of the present application, and various changes and modifications may be made therein without departing from the spirit and scope of the application, which is defined by the appended claims. The scope of the application is defined by the appended claims and equivalents thereof.
Claims (2)
1. The multi-objective optimization design method of the die clamping mechanism of the extrusion casting equipment is characterized by comprising the following steps of:
s100: setting a plurality of objective functions to be optimized, and determining design variables;
s200: applying constraint conditions to the design variables to establish a mathematical model of the clamping mechanism;
s300: solving the objective function, wherein in the process of solving, if a plurality of objective functions are contradictory, the objective functions are solved by a coordination curve method and a tolerant sequence layering method;
s400: selecting an optimal design scheme of the mold closing mechanism according to the solved result;
for objective functions where there are multiple contradictions, step S300 includes the following solving steps:
s310: dividing the importance degrees of a plurality of objective functions;
s320: firstly, solving an optimal solution for an important objective function, and setting a given tolerance according to the optimal solution;
s330: solving an optimal solution for the next objective function within the given tolerance of the previous objective function, and setting the given width tolerance of the current objective function according to the optimal solution;
s340: repeating the step S330 until all objective functions are solved;
in step S300, the objective function is solved by an interior point penalty function method for nonlinear programming;
in step S100, the objective function includes a force-increasing ratio M of the clamping mechanism p Stroke ratio R S Speed ratio R v And the acceleration value a of the movable template m Sum of rod piece mass;
in the mold closing mechanism, the hinge point of the bent toggle rod and the tail plate is set as A, the hinge point of the bent toggle rod and the large connecting rod is set as B, and the hinge point of the bent toggle rod and the small connecting rod is set as D; the design variables in step S100 include the length L of the connection AB of the hinge point A, B 1 Length L of large link 2 Length L of small link 4 Length L of line AD of hinge point A, D 5 Included angle θ between connecting line AD and horizontal direction at die closing limit, included angle γ between connecting line AB and AD, and maximum toggle angle α max And the vertical distance H of the crosshead to position A b ；
In step S200, constraints include interference prevention and self-locking constraints, rod length constraints, angle constraints, domain constraints, and design variable boundary constraints;
for the rod length constraint, the rod length ratio λ=l is taken 1 /L 2 The value range of (5) is [0.7,0.85 ]]The method comprises the steps of carrying out a first treatment on the surface of the The rod length constraint is expressed as follows:
；
；
for the definition of domain constraints, if the increase ratio M p And stroke ratio R S Meaning, the following conditions need to be satisfied:
；
；
boundary constraints for design variables; wherein L is 1 、L 2 、L 4 And L 5 The specific value boundary of (1) is suitable for passing H b Is obtained by repeated test; then θ ε [4×Pi/180,6 ×Pi/180 ]]，γ∈[18×Pi/180，25×Pi/180]，α max ∈[90×Pi/180，110×Pi/180]。
2. The multi-objective optimization design method of a mold clamping mechanism of an extrusion casting device according to claim 1, wherein: the sum of the rod masses is suitable for passing through the total length L of the rod And performing equivalent representation; the boosting ratio M p Stroke ratio R S Speed ratio R v Acceleration value a of movable template m Total length L of rod And the expressions of (2) are respectively:
；
；
；
；
L and =L 1 + L 2 + L 3 + L 4 + L 5 ；
wherein L is 3 The length of the connecting line BD between the hinge points B, D is the crank angle, the included angle between the large connecting rod and the horizontal direction is beta, the included angle between the small connecting rod and the horizontal direction is phi,angular acceleration, ω, of a curved toggle lever 1 To bend the angular velocity of the toggle lever omega 2 Is the angular velocity of the large connecting rod.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202310738277.3A CN116484655B (en) | 2023-06-21 | 2023-06-21 | Multi-objective optimization design method for die clamping mechanism of extrusion casting equipment |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202310738277.3A CN116484655B (en) | 2023-06-21 | 2023-06-21 | Multi-objective optimization design method for die clamping mechanism of extrusion casting equipment |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN116484655A CN116484655A (en) | 2023-07-25 |
| CN116484655B true CN116484655B (en) | 2023-08-25 |
Family
ID=87227220
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202310738277.3A Active CN116484655B (en) | 2023-06-21 | 2023-06-21 | Multi-objective optimization design method for die clamping mechanism of extrusion casting equipment |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN116484655B (en) |
Citations (12)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| FR652162A (en) * | 1927-02-08 | 1929-03-05 | Atlantic Prec Company | Improvements to the means used to measure the characteristics of materials |
| WO1999007543A1 (en) * | 1997-08-08 | 1999-02-18 | Bridgestone Corporation | Method of designing tire, optimization analyzer and storage medium on which optimization analysis program is recorded |
| CN101947840A (en) * | 2010-08-05 | 2011-01-19 | 华南理工大学 | Servo motor control system of all-electric injection molding machine and control method thereof |
| CN201832981U (en) * | 2010-11-02 | 2011-05-18 | 宁波力劲科技有限公司 | Mold closing device of mold casting machine |
| CN102867083A (en) * | 2012-08-30 | 2013-01-09 | 浙江大学 | High-rigidity and light-weight design method considering uncertainty of slide block mechanism of press machine |
| CN103286297A (en) * | 2012-03-02 | 2013-09-11 | 宁波力劲科技有限公司 | Optimization design method for die-clamping mechanism of horizontal die-casting machine |
| CN106774162A (en) * | 2016-12-06 | 2017-05-31 | 天津商业大学 | A kind of digital control processing parameter Multipurpose Optimal Method |
| CN107423512A (en) * | 2017-07-28 | 2017-12-01 | 广东省智能制造研究所 | A kind of light-weight design method of large-scale die-casting machine tailgate |
| CN107958103A (en) * | 2017-11-07 | 2018-04-24 | 北京理工大学 | Design of part method of topological optimization design based on compromise decision-making |
| CN114154371A (en) * | 2021-11-19 | 2022-03-08 | 哈尔滨工程大学 | Multi-objective optimization method for reinforced gearbox based on response surface method |
| WO2022188001A1 (en) * | 2021-03-08 | 2022-09-15 | 浙江大学 | Reliability-based topology optimization design method for part structure by considering bounded hybrid uncertainty |
| CN116088457A (en) * | 2023-04-10 | 2023-05-09 | 清华大学 | Steelmaking continuous casting scheduling method and device of distributed robust joint opportunity constraint model |
-
2023
- 2023-06-21 CN CN202310738277.3A patent/CN116484655B/en active Active
Patent Citations (12)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| FR652162A (en) * | 1927-02-08 | 1929-03-05 | Atlantic Prec Company | Improvements to the means used to measure the characteristics of materials |
| WO1999007543A1 (en) * | 1997-08-08 | 1999-02-18 | Bridgestone Corporation | Method of designing tire, optimization analyzer and storage medium on which optimization analysis program is recorded |
| CN101947840A (en) * | 2010-08-05 | 2011-01-19 | 华南理工大学 | Servo motor control system of all-electric injection molding machine and control method thereof |
| CN201832981U (en) * | 2010-11-02 | 2011-05-18 | 宁波力劲科技有限公司 | Mold closing device of mold casting machine |
| CN103286297A (en) * | 2012-03-02 | 2013-09-11 | 宁波力劲科技有限公司 | Optimization design method for die-clamping mechanism of horizontal die-casting machine |
| CN102867083A (en) * | 2012-08-30 | 2013-01-09 | 浙江大学 | High-rigidity and light-weight design method considering uncertainty of slide block mechanism of press machine |
| CN106774162A (en) * | 2016-12-06 | 2017-05-31 | 天津商业大学 | A kind of digital control processing parameter Multipurpose Optimal Method |
| CN107423512A (en) * | 2017-07-28 | 2017-12-01 | 广东省智能制造研究所 | A kind of light-weight design method of large-scale die-casting machine tailgate |
| CN107958103A (en) * | 2017-11-07 | 2018-04-24 | 北京理工大学 | Design of part method of topological optimization design based on compromise decision-making |
| WO2022188001A1 (en) * | 2021-03-08 | 2022-09-15 | 浙江大学 | Reliability-based topology optimization design method for part structure by considering bounded hybrid uncertainty |
| CN114154371A (en) * | 2021-11-19 | 2022-03-08 | 哈尔滨工程大学 | Multi-objective optimization method for reinforced gearbox based on response surface method |
| CN116088457A (en) * | 2023-04-10 | 2023-05-09 | 清华大学 | Steelmaking continuous casting scheduling method and device of distributed robust joint opportunity constraint model |
Non-Patent Citations (1)
| Title |
|---|
| 空间网格结构优化设计的模糊判决方法研究;郦亮, 孙仁范, 葛心, 牟在根;空间结构(第01期);全文 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN116484655A (en) | 2023-07-25 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN111191378B (en) | Nonlinear constitutive relation analysis method, system and device of negative poisson ratio structure | |
| CN101559511B (en) | Method for analog calculation of welding value by taking temperature as control variable | |
| CN107563066A (en) | A kind of springback process model compensatation method based on numerical simulation | |
| CN108108582A (en) | A kind of method for numerical simulation of curved-surface piece flexible rolling forming process | |
| CN112096696B (en) | Self-adaptive inversion control method for pump-controlled asymmetric hydraulic position system | |
| CN1300649C (en) | Combined modeling method and system for complex industrial process | |
| CN108228925A (en) | A kind of method for numerical simulation of complex shapes extrusion process | |
| CN111177906A (en) | Method for accurately compensating discrete die profile | |
| CN116484655B (en) | Multi-objective optimization design method for die clamping mechanism of extrusion casting equipment | |
| CN115374670A (en) | Powder pressing process technological parameter optimization method based on digital twinning | |
| CN112380650A (en) | Method for designing structural member of working device | |
| CN115705443A (en) | Method for manufacturing steel pipe cold-drawing die | |
| CN109255141A (en) | A kind of body of a motor car forward direction conceptual design cross sectional shape optimization method | |
| CN109214100B (en) | Sheet material rapid forming prediction method | |
| CN116187074A (en) | Multi-scale topological optimization method of anisotropic periodic structure material based on isogeometry | |
| CN110609468A (en) | Consistency control method of PI-based nonlinear time-lag multi-agent system | |
| Ramadan et al. | A parallel two mesh method for speeding-up processes with localized deformations: application to cogging | |
| Chang et al. | Forging preform design using a reverse simulation approach with the upper bound finite element procedure | |
| CN108229054B (en) | Symmetrical tensioning integral structure shape finding method based on group theory | |
| Kloppenborg et al. | Accurate welding line prediction in extrusion processes | |
| Elie-dit-Cosaque et al. | Analysis and design of hydroformed thin-walled tubes using enhanced one-step method | |
| CN114863063B (en) | Springback prediction method for single-point gradual change surface topography forming | |
| CN117034474B (en) | Quick design and optimization method for pre-forging die based on isothermal surface method | |
| CN113102515B (en) | Control method for residual strain in rolling process of titanium steel composite plate | |
| Kridli et al. | Two dimensional plane strain modeling of tube hydroforming |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant | ||
| TR01 | Transfer of patent right | ||
| TR01 | Transfer of patent right |
Effective date of registration: 20240419 Address after: Room 903-3, Building 1, Baoshan Road 527, Xinqi Street, Beilun District, Ningbo City, Zhejiang Province, 315800 Patentee after: Ningbo Lijin Intelligent Casting Research Institute Co.,Ltd. Country or region after: China Address before: 315800 No. 18, yanshanhe North Road, Beilun District, Ningbo City, Zhejiang Province Patentee before: NINGBO L.K. TECHNOLOGY Co.,Ltd. Country or region before: China |