CN115270360B - Parameter optimization method and device for turbomachine blade - Google Patents

Parameter optimization method and device for turbomachine blade Download PDF

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CN115270360B
CN115270360B CN202211201463.5A CN202211201463A CN115270360B CN 115270360 B CN115270360 B CN 115270360B CN 202211201463 A CN202211201463 A CN 202211201463A CN 115270360 B CN115270360 B CN 115270360B
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blade
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target
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particles
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CN115270360A (en
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宫伟力
韩添翼
刘佳
刘宇
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Beijing Xietong Innovation Food Technology Co ltd
China University of Mining and Technology Beijing CUMTB
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China University of Mining and Technology Beijing CUMTB
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Abstract

The application relates to a parameter optimization method and device for a turbine mechanical blade. According to the method and the device, the particle acceleration model under the two-dimensional rectangular coordinate system is established, so that the speeds of the particles at different positions and the blades with known blade shapes on the turbine can be accurately solved. The ideal leaf profile can be optimized through the model, the reasonable initial leaf profile can be selected from the positive problems more accurately, the problems existing in many manual experiences are reduced, and the technical problem that the solution conditions of given inverse problems in the leaf profile design are unreasonable or the subjective factors of designers are relied on is solved.

Description

Parameter optimization method and device for turbomachine blade
Technical Field
The application relates to the technical field of turbomachine blade design, in particular to a method and a device for optimizing parameters of a turbomachine blade.
Background
The turbomachinery has the characteristics of high rotation speed, complex movement, narrow channel and the like, the attention degree of how to improve the working efficiency of the turbomachinery in the technical field of energy conservation is gradually improved, and correspondingly, higher requirements are provided for the design technology of components including blade profiles.
Today the mainstream leaf-type design is divided into two categories: one type is given to the speed distribution of the surface of the blade, the blade profile is calculated through an inverse problem, and then the final turbine blade profile is obtained by optimizing the target position through an experimental result. This method is relatively computationally inexpensive, but if the given inverse problem solution conditions are not reasonable, which can lead to unreasonable geometries, the velocity profile needs to be re-selected for redesign. And the other type is that starting from the initial blade profile of the selected turbine, each parameter of the blade profile is continuously optimized on the premise of ensuring the reasonable geometric shape of the blade profile through a given positive problem algorithm and according to the finite element analysis and numerical analysis principles, so that the blade profile has ideal speed distribution, and the required turbine blade profile structure is finally obtained. This method is labor intensive and the initial profile determination is based on the experience of the designer.
At present, no solution capable of effectively solving the given inverse problem solution condition in the leaf profile design is unreasonable or depends on subjective factors of designers is provided.
Disclosure of Invention
The application provides a parameter optimization method and device for a turbine mechanical blade, and aims to solve the technical problem that given inverse problem solution conditions are unreasonable or the subjective factors of designers are relied on in blade profile design.
According to an aspect of an embodiment of the present application, there is provided a method for optimizing parameters of a turbomachine blade, including:
taking a connecting point of an impact mill and a target blade as an origin, taking the tangential direction of the target blade at the connecting point as the x-axis direction, and taking the normal direction of the target blade at the connecting point as the y-axis direction to create a planar rectangular coordinate system XOY;
determining a radius on the planar rectangular coordinate system as
Figure 91418DEST_PATH_IMAGE001
The center of the circle of the impact mill
Figure 939288DEST_PATH_IMAGE002
Shape obey function
Figure DEST_PATH_IMAGE003
And the curve of the target blade at the grinding disc and the angular velocity
Figure 864519DEST_PATH_IMAGE004
The mass of the rad/s rotating anticlockwise around the circle center is
Figure DEST_PATH_IMAGE005
In said planeMoving point on rectangular coordinate system
Figure 151144DEST_PATH_IMAGE006
；
Using the grinding disc and the target blade as a dynamic reference system, determining a plurality of mechanical parameters under the dynamic reference system by using the circle center of the impact mill, the curve of the target blade and the moving point, wherein the plurality of mechanical parameters comprise the relative displacement of the moving point on the dynamic reference system
Figure DEST_PATH_IMAGE007
Dynamic friction factor on the target blade
Figure 478220DEST_PATH_IMAGE008
The vector diameter of a connecting line of the moving point and the circle center of the impact mill
Figure DEST_PATH_IMAGE009
The relative speed of the moving point with respect to the moving reference system
Figure 824888DEST_PATH_IMAGE010
The absolute speed of the moving point relative to a fixed reference frame XOY
Figure DEST_PATH_IMAGE011
The speed of involvement of the moving reference system with respect to the fixed reference system XOY
Figure 237415DEST_PATH_IMAGE012
And taking the intersection point of the reverse extension line of the speed direction at the moving point and the X axis
Figure DEST_PATH_IMAGE013
When the temperature of the water is higher than the set temperature,
Figure 65081DEST_PATH_IMAGE014
and with
Figure DEST_PATH_IMAGE015
Angle (d) of
Figure 246664DEST_PATH_IMAGE016
、
Figure DEST_PATH_IMAGE017
And with
Figure 701916DEST_PATH_IMAGE018
Angle of (2)
Figure DEST_PATH_IMAGE019
、
Figure 664055DEST_PATH_IMAGE020
And
Figure DEST_PATH_IMAGE021
angle of (2)
Figure 230166DEST_PATH_IMAGE022
；
Determining Coriolis force, centrifugal force, sliding friction force and reaction force of the target blade to the moving point when the moving point moves in the dynamic reference system based on a plurality of the mechanical parameters;
constructing a target acceleration model of the particles in the impact mill under a plane rectangular coordinate system by using the Coriolis force, the centrifugal force, the sliding friction force, the reaction force and the resultant force of the four forces, so as to represent the association relation between the velocity displacement component of the particles along the X coordinate axis in the dynamic reference system and the shape function and the dynamic friction factor of the blades;
substituting the function of the target blade of the selected type into the target acceleration model to obtain an analytic solution of the displacement and the speed of the particles in the impact mill;
and optimizing the parameters of the target blade of the corresponding type by using the analytic solution.
Optionally, determining the coriolis force experienced by the moving point while moving in the frame of motion reference comprises:
determining Coriolis acceleration
Figure DEST_PATH_IMAGE023
Wherein the Coriolis acceleration direction is perpendicular to the relative speed of the moving point and points to the positive direction of the Y axis;
the mass of the moving point is measured
Figure 266255DEST_PATH_IMAGE024
Multiplying the Coriolis acceleration to obtain the Coriolis force:
Figure DEST_PATH_IMAGE025
(1)。
optionally, determining the centrifugal force to which the moving point is subjected when moving in the kinetic reference system comprises:
determining the tangential acceleration of the point of motion
Figure 954725DEST_PATH_IMAGE026
And normal acceleration
Figure DEST_PATH_IMAGE027
Wherein the direction and vector of the normal acceleration
Figure 341844DEST_PATH_IMAGE028
In the same direction;
by
Figure DEST_PATH_IMAGE029
To obtain
Figure 508384DEST_PATH_IMAGE030
Obtaining the centrifugal force:
Figure DEST_PATH_IMAGE031
(2)。
optionally, determining the sliding friction force to which the moving point is subjected when moving in the moving reference frame and the reaction force of the target blade to the moving point comprises:
setting the target leafThe reaction force of the sheet on the moving point is
Figure 664558DEST_PATH_IMAGE032
Then the sliding friction is
Figure DEST_PATH_IMAGE033
。
Optionally, constructing a target acceleration model of the particle in the impact mill in a plane rectangular coordinate system by using the coriolis force, the centrifugal force, the sliding friction force, the reaction force, and a resultant force of the four forces includes:
adding the Coriolis force, the centrifugal force, the sliding friction force and the reaction force to obtain a resultant force:
Figure 461613DEST_PATH_IMAGE034
(3)；
projecting the above formula to the tangential direction of the blade at the moving point to obtain:
Figure DEST_PATH_IMAGE035
Figure 132766DEST_PATH_IMAGE036
(4)；
taking and relative velocity
Figure DEST_PATH_IMAGE037
In the vertical direction of
Figure 306258DEST_PATH_IMAGE038
Then the force of the resultant force is directed
Figure DEST_PATH_IMAGE039
Direction and
Figure 379256DEST_PATH_IMAGE040
and (3) projecting the direction to obtain:
Figure DEST_PATH_IMAGE041
Figure 347212DEST_PATH_IMAGE042
；
substituting the above formula into (4) yields:
Figure DEST_PATH_IMAGE043
(a)；
substituting (1) and (2) into (a) to obtain a second-order differential equation between the relative displacement of the particles on the blade and the blade inclination angle:
Figure 443344DEST_PATH_IMAGE044
(5)；
based on straight lines
Figure DEST_PATH_IMAGE045
And a straight line
Figure 951686DEST_PATH_IMAGE046
The expression (c) expresses the blade pitch angle in terms of coordinate parameters as:
Figure DEST_PATH_IMAGE047
(6)
Figure 82453DEST_PATH_IMAGE048
(7)
Figure DEST_PATH_IMAGE049
(8)；
by
Figure 283627DEST_PATH_IMAGE050
In formula (5):
Figure DEST_PATH_IMAGE051
(9)
Figure 867055DEST_PATH_IMAGE052
Figure DEST_PATH_IMAGE053
(10)；
determining the sagittal diameter of formula (5) by Pythagorean theorem
Figure 116771DEST_PATH_IMAGE054
The following steps of (1):
Figure DEST_PATH_IMAGE055
(11)；
substituting (6), (8), (9), (10) and (11) into (5) to obtain the target acceleration model of the particles in the impact mill under a plane rectangular coordinate system:
Figure 102045DEST_PATH_IMAGE056
Figure DEST_PATH_IMAGE057
Figure 471191DEST_PATH_IMAGE058
(12)。
optionally, substituting a function of the target blade of the selected type into the target acceleration model to obtain an analytical solution of displacement and velocity of particles in the impact mill comprises:
in the case that the target blade is a linear blade, the shape function of the target blade is determined
Figure DEST_PATH_IMAGE059
Substituting the target acceleration model (12) to obtain:
Figure 541915DEST_PATH_IMAGE060
(13)；
calculating the analytical solution of equation (13) yields:
Figure DEST_PATH_IMAGE061
(14)
Figure 595321DEST_PATH_IMAGE062
Figure DEST_PATH_IMAGE063
(15)；
wherein,
Figure 497418DEST_PATH_IMAGE064
，
Figure DEST_PATH_IMAGE065
and
Figure 978078DEST_PATH_IMAGE066
is the undetermined constant of the differential equation;
taking the boundary condition as
Figure DEST_PATH_IMAGE067
，
Figure 270519DEST_PATH_IMAGE068
Substituting into (14) and (15) to obtain
Figure 189934DEST_PATH_IMAGE065
And
Figure 884220DEST_PATH_IMAGE066
：
Figure DEST_PATH_IMAGE069
Figure 535782DEST_PATH_IMAGE070
；
will be provided with
Figure 581098DEST_PATH_IMAGE065
And
Figure 38624DEST_PATH_IMAGE066
substituting expressions (14) and (15) into said analytical solution for displacement and velocity of particles in said impact mill:
Figure DEST_PATH_IMAGE071
Figure 587417DEST_PATH_IMAGE072
(16)
Figure DEST_PATH_IMAGE073
(17)。
optionally, optimizing the parameter of the target blade of the corresponding type using the analytic solution includes:
the following treatments were carried out for (16) and (17):
Figure 675459DEST_PATH_IMAGE074
Figure DEST_PATH_IMAGE075
Figure 4809DEST_PATH_IMAGE076
；
get
Figure DEST_PATH_IMAGE077
The above formula is simplified to obtain the speed
Figure 938130DEST_PATH_IMAGE078
About displacement
Figure 607009DEST_PATH_IMAGE079
The expression of (c):
Figure DEST_PATH_IMAGE080
(18)；
relating equation (18) to the slope
Figure 928269DEST_PATH_IMAGE081
And (4) solving a partial derivative to obtain:
Figure DEST_PATH_IMAGE082
；
order to
Figure 417019DEST_PATH_IMAGE083
Then obtain the slope
Figure DEST_PATH_IMAGE084
The optimization interval of (2):
Figure 481927DEST_PATH_IMAGE085
or
Figure DEST_PATH_IMAGE086
。
According to another aspect of the embodiments of the present application, there is provided a parameter optimization apparatus for a turbomachine blade, including:
the system comprises a coordinate system establishing module, a data processing module and a data processing module, wherein the coordinate system establishing module is used for taking a connecting point of an impact mill and a target blade as an origin, taking the tangential direction of the target blade at the connecting point as the x-axis direction, and taking the normal direction of the target blade at the connecting point as the y-axis direction to establish a plane rectangular coordinate system XOY;
a data model establishing module for determining the radius on the plane rectangular coordinate system
Figure 5312DEST_PATH_IMAGE001
The center of the circle of the impact mill
Figure 169577DEST_PATH_IMAGE002
Shape obey function
Figure 411202DEST_PATH_IMAGE087
And the curve of the target blade at the grinding disc and the angular velocity
Figure DEST_PATH_IMAGE088
The mass of the rad/s rotating anticlockwise around the circle center is
Figure 14222DEST_PATH_IMAGE005
The moving point of the particles on the plane rectangular coordinate system
Figure 392114DEST_PATH_IMAGE089
；
A mechanical parameter determining module, configured to determine, using the grinding disc and the target blade as a dynamic reference system, a plurality of mechanical parameters in the dynamic reference system by using the center of the impact mill, the curve of the target blade, and the motion point, where the plurality of mechanical parameters include a relative displacement of the motion point on the dynamic reference system
Figure DEST_PATH_IMAGE090
Motion on the target bladeCoefficient of friction
Figure 992859DEST_PATH_IMAGE008
The radius of the connecting line of the moving point and the circle center of the impact mill
Figure 456202DEST_PATH_IMAGE009
The relative speed of the moving point with respect to the moving reference system
Figure 865842DEST_PATH_IMAGE091
Absolute speed of the moving point with respect to a fixed reference frame XOY
Figure 363820DEST_PATH_IMAGE011
The velocity of involvement of the dynamic reference frame with respect to the fixed reference frame XOY
Figure DEST_PATH_IMAGE092
And taking the intersection point of the reverse extension line of the speed direction at the moving point and the X axis
Figure 869887DEST_PATH_IMAGE013
When the temperature of the water is higher than the set temperature,
Figure 148422DEST_PATH_IMAGE014
and
Figure 30927DEST_PATH_IMAGE015
angle of (2)
Figure 383411DEST_PATH_IMAGE016
、
Figure 60380DEST_PATH_IMAGE093
And
Figure 498315DEST_PATH_IMAGE018
angle of (2)
Figure DEST_PATH_IMAGE094
、
Figure 246828DEST_PATH_IMAGE020
And with
Figure 453818DEST_PATH_IMAGE021
Angle of (2)
Figure 567268DEST_PATH_IMAGE022
；
The force analysis module is used for determining the Coriolis force, the centrifugal force, the sliding friction force and the reaction force of the target blade to the moving point when the moving point moves in the moving reference system based on a plurality of mechanical parameters;
the particle acceleration model building module is used for building a target acceleration model of the particles in the impact mill under a plane rectangular coordinate system by utilizing the Coriolis force, the centrifugal force, the sliding friction force, the reaction force and the resultant force of the four forces, and is used for representing the incidence relation between the velocity displacement component of the particles along the X coordinate axis in the dynamic reference system and the blade shape function and the blade dynamic friction factor;
the analytical solution calculation module is used for substituting the function of the target blade of the selected type into the target acceleration model to obtain an analytical solution of the displacement and the speed of the particles in the impact mill;
and the parameter optimization module is used for optimizing the parameters of the target blade of the corresponding type by utilizing the analytic solution.
According to another aspect of the embodiments of the present application, there is provided an electronic device, including a memory, a processor, a communication interface, and a communication bus, where the memory stores a computer program executable on the processor, and the memory and the processor communicate with each other through the communication bus and the communication interface, and the processor implements the steps of the method when executing the computer program.
According to another aspect of embodiments of the present application, there is also provided a computer readable medium having non-volatile program code executable by a processor, the program code causing the processor to perform the above-mentioned method.
Compared with the related art, the technical scheme provided by the embodiment of the application has the following advantages:
the technical scheme of the application is as follows: taking a connecting point of an impact mill and a target blade as an origin, taking the tangential direction of the target blade at the connecting point as the x-axis direction, and taking the normal direction of the target blade at the connecting point as the y-axis direction to create a planar rectangular coordinate system XOY;
determining a radius on the planar rectangular coordinate system as
Figure 492498DEST_PATH_IMAGE001
The center of the circle of the impact mill
Figure 779123DEST_PATH_IMAGE002
Shape obey function
Figure 106199DEST_PATH_IMAGE003
And the curve of the target blade at the grinding disc and the angular velocity
Figure 390550DEST_PATH_IMAGE004
The mass of the rad/s rotating anticlockwise around the circle center is
Figure 537498DEST_PATH_IMAGE005
The moving point of the particles on the plane rectangular coordinate system
Figure 565497DEST_PATH_IMAGE006
；
Using the grinding disc and the target blade as a dynamic reference system, determining a plurality of mechanical parameters under the dynamic reference system by using the circle center of the impact mill, the curve of the target blade and the moving point, wherein the plurality of mechanical parameters comprise the relative displacement of the moving point on the dynamic reference system
Figure 809396DEST_PATH_IMAGE007
Dynamic friction factor on the target blade
Figure 264648DEST_PATH_IMAGE008
The radius of the connecting line of the moving point and the circle center of the impact mill
Figure 164471DEST_PATH_IMAGE009
The relative speed of the moving point with respect to the moving reference system
Figure 730582DEST_PATH_IMAGE010
The absolute speed of the moving point relative to a fixed reference frame XOY
Figure 766671DEST_PATH_IMAGE011
The speed of involvement of the moving reference system with respect to the fixed reference system XOY
Figure 392824DEST_PATH_IMAGE012
And taking the intersection point of the reverse extension line of the speed direction at the moving point and the X axis
Figure 576681DEST_PATH_IMAGE013
When the utility model is used, the water is discharged,
Figure 946482DEST_PATH_IMAGE014
and with
Figure 102657DEST_PATH_IMAGE015
Angle of (2)
Figure 899712DEST_PATH_IMAGE016
、
Figure 508548DEST_PATH_IMAGE017
And with
Figure 478778DEST_PATH_IMAGE018
Angle of (2)
Figure 489459DEST_PATH_IMAGE019
、
Figure 457415DEST_PATH_IMAGE020
And
Figure 553547DEST_PATH_IMAGE021
angle of (2)
Figure 265151DEST_PATH_IMAGE022
(ii) a Determining Coriolis force, centrifugal force, sliding friction force and reaction force of the target blade to the moving point when the moving point moves in the dynamic reference system based on a plurality of the mechanical parameters; constructing a target acceleration model of the particles in the impact mill under a plane rectangular coordinate system by using the Coriolis force, the centrifugal force, the sliding friction force, the reaction force and the resultant force of the four forces, so as to represent the association relation between the velocity displacement component of the particles along the X coordinate axis in the dynamic reference system and the shape function and the dynamic friction factor of the blades; substituting the function of the target blade of the selected type into the target acceleration model to obtain an analytic solution of the displacement and the speed of the particles in the impact mill; and optimizing the parameters of the target blade of the corresponding type by using the analytic solution. According to the method and the device, the particle acceleration model under the two-dimensional rectangular coordinate system is established, so that the speeds of the particles at different positions and blades with known blade shapes on the turbine can be accurately solved. The ideal leaf profile can be optimized through the model, the reasonable initial leaf profile can be selected from the positive problems more accurately, the problems existing in many manual experiences are reduced, and the technical problem that the solution conditions of given inverse problems in the leaf profile design are unreasonable or the subjective factors of designers are relied on is solved.
Drawings
The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments consistent with the present application and together with the description, serve to explain the principles of the application.
In order to more clearly illustrate the technical solutions in the embodiments or related technologies of the present application, the drawings needed to be used in the description of the embodiments or related technologies will be briefly described below, and it is obvious for those skilled in the art to obtain other drawings without any creative effort.
FIG. 1 is a schematic cross-sectional view of an alternative turbomachinery impact mill provided in accordance with an embodiment of the present application;
FIG. 2 is a schematic diagram of an alternative hardware environment for a method for optimizing parameters of a turbomachine blade according to an embodiment of the present disclosure;
FIG. 3 is a flow chart illustrating an alternative method for optimizing parameters of a turbomachine blade according to an embodiment of the present disclosure;
FIG. 4 is a schematic diagram of a data model of a turbine blade in an alternative planar rectangular coordinate system according to an embodiment of the present application;
FIG. 5 is a schematic diagram of an alternative speed versus slope curve provided in accordance with an embodiment of the present application;
FIG. 6 is a block diagram of an alternative apparatus for optimizing parameters of a turbomachine blade according to an embodiment of the present application;
fig. 7 is a schematic structural diagram of an alternative electronic device according to an embodiment of the present application.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application, and it is obvious that the described embodiments are some embodiments of the present application, but not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present application.
In the following description, suffixes such as "module", "component", or "unit" used to denote elements are used only for the convenience of description of the present application, and have no specific meaning in themselves. Thus, "module" and "component" may be used in a mixture.
In the related art, the mainstream leaf profile design is divided into two categories: one type is given to the speed distribution of the surface of the blade, the blade profile is calculated through an inverse problem, and then the final turbine blade profile is obtained by optimizing the target position through an experimental result. This method is relatively computationally inexpensive, but if the given inverse problem solution conditions are not reasonable, which can lead to unreasonable geometries, the velocity profile needs to be re-selected for redesign. And the other type is that starting from the initial blade profile of the selected turbine, each parameter of the blade profile is continuously optimized on the premise of ensuring the reasonable geometric shape of the blade profile through a given positive problem algorithm and according to the finite element analysis and numerical analysis principles, so that the blade profile has ideal speed distribution, and the required turbine blade profile structure is finally obtained. This method is labor intensive and the initial leaf profile determination is based on the experience of the designer.
In order to address the problems mentioned in the background, according to an aspect of embodiments of the present application, an embodiment of a method for parameter optimization of a turbomachine blade is provided. Taking an example of an impact grit particle acceleration model commonly used in engineering, fig. 1 shows a cross-sectional view of an impact mill, where particles are injected into the impact mill through a central coaxial hole, dispersed into the blades at the edge of the grinding disc as the disc rotates (since the disc is small, the initial velocity and initial displacement on the disc are negligible). The particles are accelerated by the blades and finally collide with the peripheral wall surface to be pulverized. What we need to research is to optimize the profile and material properties of the blade so that when the particles collide with the peripheral wall surface of the blade, a larger particle speed is obtained, thereby improving the crushing efficiency of the impact mill. The turbine blade and the turbine optimized by the technical scheme can be applied to the industries of aerospace, energy mining, food processing and the like.
Alternatively, in the embodiment of the present application, the parameter optimization method for the turbomachine blade may be applied to a hardware environment formed by the terminal 201 and the server 203 as shown in fig. 2. As shown in fig. 2, a server 203 is connected to a terminal 201 through a network, which may be used to provide services for the terminal or a client installed on the terminal, and a database 205 may be provided on the server or separately from the server, and is used to provide data storage services for the server 203, and the network includes but is not limited to: wide area network, metropolitan area network, or local area network, and the terminal 201 includes but is not limited to a PC, a cell phone, a tablet computer, and the like.
The parameter optimization method for the turbomachine blade in the embodiment of the present application may be executed by the server 203, and may also be executed by the server 203 and the terminal 201 together, as shown in fig. 3, where the method may include the following steps:
step S302, a connecting point of an impact mill and a target blade is taken as an origin, the tangential direction of the target blade at the connecting point is taken as the x-axis direction, and the normal direction of the target blade at the connecting point is taken as the y-axis direction to create a plane rectangular coordinate system XOY;
step S304, determining the radius on the plane rectangular coordinate system as
Figure 458235DEST_PATH_IMAGE001
The center of the circle of the impact mill
Figure 597093DEST_PATH_IMAGE002
Shape obey function
Figure 914941DEST_PATH_IMAGE003
And the curve of the target blade at the grinding disc and the angular velocity
Figure 430236DEST_PATH_IMAGE095
The mass of the rad/s rotating anticlockwise around the circle center is
Figure 415510DEST_PATH_IMAGE005
The moving point of the particles on the plane rectangular coordinate system
Figure 784656DEST_PATH_IMAGE006
；
Step S306, using the grinding disc and the target blade as a dynamic reference system, and determining a plurality of mechanical parameters under the dynamic reference system by using the circle center of the impact mill, the curve of the target blade and the moving point, wherein the plurality of mechanical parameters comprise the relative displacement of the moving point on the dynamic reference system
Figure 589801DEST_PATH_IMAGE007
Dynamic friction factor on the target blade
Figure 643207DEST_PATH_IMAGE008
The moving point is connected with the circle center of the impact millRadial of line
Figure 482987DEST_PATH_IMAGE009
The relative speed of the moving point with respect to the moving reference system
Figure 963647DEST_PATH_IMAGE091
The absolute speed of the moving point relative to a fixed reference frame XOY
Figure 583984DEST_PATH_IMAGE011
The velocity of involvement of the dynamic reference frame with respect to the fixed reference frame XOY
Figure 175503DEST_PATH_IMAGE012
And taking the intersection point of the reverse extension line of the speed direction at the moving point and the X axis
Figure 135369DEST_PATH_IMAGE013
When the temperature of the water is higher than the set temperature,
Figure 786930DEST_PATH_IMAGE014
and
Figure 566667DEST_PATH_IMAGE015
angle of (2)
Figure 24193DEST_PATH_IMAGE016
、
Figure 838565DEST_PATH_IMAGE093
And
Figure 661028DEST_PATH_IMAGE018
angle of (2)
Figure 928061DEST_PATH_IMAGE094
、
Figure 126961DEST_PATH_IMAGE020
And with
Figure 858157DEST_PATH_IMAGE021
Angle of (2)
Figure 851521DEST_PATH_IMAGE022
；
Step S308, determining the Coriolis force, the centrifugal force, the sliding friction force and the reaction force of the target blade to the moving point when the moving point moves in the moving reference system based on the plurality of mechanical parameters;
step S310, constructing a target acceleration model of the particles in the impact mill in a plane rectangular coordinate system by using the Coriolis force, the centrifugal force, the sliding friction force, the reaction force and the resultant force of the four forces, and representing the association relationship between the velocity displacement component of the particles along the X coordinate axis in the dynamic reference system and the blade shape function and the blade dynamic friction factor;
step S312, substituting the function of the target blade of the selected type into the target acceleration model to obtain an analytic solution of the displacement and the speed of the particles in the impact mill;
and step S314, optimizing the parameters of the target blade of the corresponding type by using the analytic solution.
Through the steps S302 to S314, the present application can accurately solve the speed of particles at different positions on the known blade shape of the turbine by establishing the particle acceleration model in the two-dimensional rectangular coordinate system. The ideal leaf profile can be optimized through the model, the reasonable initial leaf profile can be selected from the positive problems more accurately, the problems existing in many manual experiences are reduced, and the technical problem that the solution conditions of given inverse problems in the leaf profile design are unreasonable or the subjective factors of designers are relied on is solved.
According to the technical scheme, the turbine blade is abstracted into a mathematical model to construct a particle acceleration model and optimize blade parameters, so that the problem is solved based on the following assumptions according to engineering background and reasonable mechanical simplification:
1) Neglecting the interaction force among the particles;
2) Particle gravity is not considered;
3) The particles only slide on the blade without rolling;
4) The particles are small enough that the air resistance acting on the particles is negligible.
The following is a detailed description of the technical solution.
In steps S302 to S306, a rectangular plane coordinate system as shown in FIG. 2 is established
Figure DEST_PATH_IMAGE096
Radius of
Figure 605850DEST_PATH_IMAGE097
The center coordinates of the impact mill are
Figure DEST_PATH_IMAGE098
Taking a blade on the grinding disc for analysis, wherein one end of the blade is positioned at the origin
Figure 670758DEST_PATH_IMAGE099
Where its shape follows a function
Figure DEST_PATH_IMAGE100
At angular speed of the grinding disc
Figure 194143DEST_PATH_IMAGE101
The rad/s rotates anticlockwise around the circle center, and the mass is taken as
Figure DEST_PATH_IMAGE102
Particles of (2)
Figure 358408DEST_PATH_IMAGE103
The grinding disc and the blades are in a dynamic reference system as a moving point, and the relative displacement of the moving point on the dynamic system is set as
Figure DEST_PATH_IMAGE104
Dynamic friction factor on the blade of
Figure 662351DEST_PATH_IMAGE105
The vector diameter of the connecting line of the moving point and the circle center is
Figure DEST_PATH_IMAGE106
The relative speed of the moving point with respect to the motion reference system is
Figure 203053DEST_PATH_IMAGE107
The absolute velocity of the moving point relative to the fixed reference frame is
Figure DEST_PATH_IMAGE110
The velocity of the linkage between the dynamic reference system and the fixed reference system is
Figure 244008DEST_PATH_IMAGE111
. A reverse extension line of the speed direction at the pickup point and
Figure DEST_PATH_IMAGE112
axis intersects at a point
Figure 707350DEST_PATH_IMAGE113
，
Figure 51744DEST_PATH_IMAGE114
And
Figure 346459DEST_PATH_IMAGE115
is taken as
Figure 118106DEST_PATH_IMAGE116
，
Figure 68744DEST_PATH_IMAGE117
And
Figure 951250DEST_PATH_IMAGE118
is taken as
Figure 303734DEST_PATH_IMAGE119
，
Figure 311528DEST_PATH_IMAGE120
And
Figure 749463DEST_PATH_IMAGE121
is taken as
Figure 435659DEST_PATH_IMAGE122
。
In step S308, optionally, determining the coriolis force to which the moving point is subjected when moving in the motion-reference system comprises:
determining Coriolis acceleration
Figure 642650DEST_PATH_IMAGE123
Wherein the Coriolis acceleration direction is perpendicular to the relative speed of the moving point and points to the positive direction of the Y axis;
the mass of the moving point
Figure 818416DEST_PATH_IMAGE124
Multiplying the Coriolis acceleration to obtain the Coriolis force:
Figure 743647DEST_PATH_IMAGE125
(1)。
in the embodiment of the present application, the reference is made around the center of the circle
Figure 967955DEST_PATH_IMAGE126
As an angular velocity of
Figure 295031DEST_PATH_IMAGE127
The fixed shaft of the moving point has Coriolis acceleration due to the mutual influence of the traction motion and the relative motion
Figure 313802DEST_PATH_IMAGE128
Therefore, it is
Figure 726329DEST_PATH_IMAGE129
Direction perpendicular to the relative speed of the moving point, pointing
Figure 816645DEST_PATH_IMAGE130
The positive direction of the axis. From the darlinger principle of particles: "active force, restraining force and its inertia force acting on mass pointThe equilibrium force system is formed by the above formula, so that the moving point receives an inertial force opposite to the direction of the Coriolis acceleration, which is called Coriolis force.
In step S308, optionally, determining the centrifugal force to which the moving point is subjected when moving in the kinetic reference system comprises:
determining the tangential acceleration of the point of motion
Figure 998228DEST_PATH_IMAGE131
And normal acceleration
Figure 453480DEST_PATH_IMAGE132
Wherein the direction and vector of the normal acceleration
Figure 87723DEST_PATH_IMAGE133
In the same direction;
by
Figure 653834DEST_PATH_IMAGE134
To obtain
Figure 17819DEST_PATH_IMAGE135
Obtaining the centrifugal force:
Figure 643973DEST_PATH_IMAGE136
(2)。
in the embodiment of the present application, it can be known from rigid body kinematics that the tangential acceleration of any point in the rotating rigid body is equal to the vector product of the angular acceleration vector of the rigid body and the vector diameter of the point, and the normal acceleration is equal to the vector product of the angular velocity vector of the rigid body and the velocity vector of the point, that is, the vector product of the angular velocity vector of the rigid body and the velocity vector of the point
Figure 765512DEST_PATH_IMAGE137
，
Figure 135314DEST_PATH_IMAGE138
. In this model, the rigid body is at an angular velocity
Figure 291489DEST_PATH_IMAGE139
A counterclockwise constant-speed rotating dynamic reference system, therefore
Figure 150860DEST_PATH_IMAGE140
Thus, therefore, it is
Figure 759696DEST_PATH_IMAGE141
Direction and vector
Figure 667609DEST_PATH_IMAGE142
In the same direction. Because of the fact that
Figure 678291DEST_PATH_IMAGE143
Therefore, it is made
Figure 646247DEST_PATH_IMAGE144
. From the darbeyer principle of particles: since the principal force, the constraining force, and the inertial force thereof acting on the mass point form a balance force system, it is known that the moving point receives an inertial force in the direction opposite to the coriolis acceleration, which is called a centrifugal force.
In step S308, optionally, determining the sliding friction force to which the moving point is subjected when moving in the moving reference frame and the reaction force of the target blade to the moving point comprises:
setting the reaction force of the target blade to the moving point to be
Figure 804695DEST_PATH_IMAGE145
Then the sliding friction is
Figure 516299DEST_PATH_IMAGE146
。
In the embodiment of the application, the dynamic reference system generates Coriolis force in the rotating process
Figure 381487DEST_PATH_IMAGE147
Against centrifugal force
Figure 520345DEST_PATH_IMAGE148
All having a component in the direction perpendicular to the relative velocity, i.e. movementThe point will exert a pressure on the blade, which is determined by the law of action and reaction: "acting force and reacting force always exist at the same time, the two forces are equal in magnitude and opposite in direction, and act on two interacting objects respectively along the same straight line", reacting force exists at the opposite moving point of the blade
Figure 103773DEST_PATH_IMAGE149
。
From basic assumption 3: "the particles only slide on the blade without rolling", so that there is a sliding friction force proportional to the positive pressure and opposite to the relative sliding direction
Figure 681385DEST_PATH_IMAGE150
Wherein
Figure 401079DEST_PATH_IMAGE151
Is the dynamic friction factor.
In step S310, optionally, constructing a target acceleration model of the particle in the impact mill in a plane rectangular coordinate system by using the coriolis force, the centrifugal force, the sliding friction force, the reaction force, and a resultant force of the four forces includes:
adding the Coriolis force, the centrifugal force, the sliding friction force and the reaction force to obtain a resultant force:
Figure 710837DEST_PATH_IMAGE152
(3)；
projecting the above formula to the tangential direction of the blade at the moving point to obtain:
Figure 781562DEST_PATH_IMAGE153
(4)；
taking and relative velocity
Figure 834968DEST_PATH_IMAGE154
In the vertical direction of
Figure 737065DEST_PATH_IMAGE155
Then the force of the resultant force is directed
Figure 217725DEST_PATH_IMAGE156
Direction and
Figure 775745DEST_PATH_IMAGE157
and (3) projecting the direction to obtain:
Figure 367264DEST_PATH_IMAGE158
；
substituting the above equation into (4) yields:
Figure 61550DEST_PATH_IMAGE159
(a)；
and (1) and (2) are substituted into (a) to obtain a second-order differential equation between the relative displacement of the particles on the blade and the blade inclination angle:
Figure 38078DEST_PATH_IMAGE160
(5)；
based on straight lines
Figure 817815DEST_PATH_IMAGE161
And a straight line
Figure 213024DEST_PATH_IMAGE162
The expression (c) expresses the blade pitch angle in terms of coordinate parameters as:
Figure 27397DEST_PATH_IMAGE163
(6)
Figure 849859DEST_PATH_IMAGE164
(7)
Figure 179209DEST_PATH_IMAGE165
(8)；
by
Figure 378109DEST_PATH_IMAGE166
In formula (5):
Figure 46988DEST_PATH_IMAGE167
(9)
Figure 40352DEST_PATH_IMAGE168
Figure 794681DEST_PATH_IMAGE169
(10)；
determining the sagittal diameter of formula (5) by Pythagorean theorem
Figure 594010DEST_PATH_IMAGE170
The following steps of (1):
Figure 117395DEST_PATH_IMAGE171
(11)；
substituting (6), (8), (9), (10) and (11) into (5) to obtain the target acceleration model of the particles in the impact mill under a plane rectangular coordinate system:
Figure 547240DEST_PATH_IMAGE172
Figure 788865DEST_PATH_IMAGE057
Figure 63989DEST_PATH_IMAGE173
(12)。
specifically, the relationship law of particle dynamics force and acceleration is as follows: "the product of mass and acceleration of a mass point is equal to the magnitude of the action and mass point, and the direction of acceleration is the same as the direction of force", so we can deduce:
Figure 769777DEST_PATH_IMAGE174
(3)
the projection of the particle position on the tangential direction of the blade can be obtained:
Figure 104943DEST_PATH_IMAGE175
(4)；
taking and relative velocity
Figure 833865DEST_PATH_IMAGE176
In the vertical direction of
Figure 912679DEST_PATH_IMAGE177
Since the particles cannot leave the blade, they are in the direction
Figure 410656DEST_PATH_IMAGE178
The upper forces are balanced, so that the forces are tied to
Figure 244620DEST_PATH_IMAGE179
Directions and
Figure 195259DEST_PATH_IMAGE178
the directional projection can be obtained as follows:
Figure 77764DEST_PATH_IMAGE180
substituting the above formula into (4) yields:
Figure 430248DEST_PATH_IMAGE181
(a)；
substituting (1) and (2) into (a) to obtain a second-order differential equation between the relative displacement of the particles on the blade and the blade inclination angle:
Figure 372796DEST_PATH_IMAGE182
(5)。
the pitch angle of the blade is then expressed in terms of a coordinate parameter.
The coordinates of the particles are
Figure 873048DEST_PATH_IMAGE183
The shape of the blade conforming to a function
Figure 293665DEST_PATH_IMAGE184
Due to a straight line
Figure 766234DEST_PATH_IMAGE185
For the vanes at points
Figure 879684DEST_PATH_IMAGE186
Is tangent to, so its expression is
Figure 804915DEST_PATH_IMAGE187
. Get
Figure 91539DEST_PATH_IMAGE188
When the temperature of the water is higher than the set temperature,
Figure 153036DEST_PATH_IMAGE189
therefore, it is made
Figure 437387DEST_PATH_IMAGE190
Point coordinates of
Figure 849914DEST_PATH_IMAGE191
. Because the centre of a circle is ground by impact
Figure 877913DEST_PATH_IMAGE192
The coordinates are
Figure 121812DEST_PATH_IMAGE193
Therefore, can obtain
Figure 311485DEST_PATH_IMAGE194
，
Figure 211308DEST_PATH_IMAGE195
。
From the vector dot product equation:
Figure 777419DEST_PATH_IMAGE196
therefore, the following can be obtained:
Figure 79087DEST_PATH_IMAGE197
Figure 439661DEST_PATH_IMAGE198
(6)
because of the fact that
Figure 892027DEST_PATH_IMAGE199
，
Figure 261828DEST_PATH_IMAGE200
Therefore, it is
Figure 152424DEST_PATH_IMAGE201
The tangent of (A) may be defined by a point
Figure 949479DEST_PATH_IMAGE202
And point
Figure 558314DEST_PATH_IMAGE203
The coordinates of (a) to (b) are determined,
Figure 794124DEST_PATH_IMAGE204
has a tangent of a straight line
Figure 804805DEST_PATH_IMAGE205
Of (2) i.e.
Figure 772761DEST_PATH_IMAGE206
Figure 868893DEST_PATH_IMAGE207
. Due to the angle
Figure 580497DEST_PATH_IMAGE208
Is that
Figure 508002DEST_PATH_IMAGE209
About
Figure 646859DEST_PATH_IMAGE210
Outer corner of, therefore
Figure 230287DEST_PATH_IMAGE211
Thus, the angle can be obtained by trigonometric sum and difference formula
Figure 480003DEST_PATH_IMAGE212
Sine value of (c):
Figure 465276DEST_PATH_IMAGE213
Figure 837352DEST_PATH_IMAGE214
(7)；
due to the fact that
Figure 908076DEST_PATH_IMAGE215
Substituting (6) and (7) may result in:
Figure 961483DEST_PATH_IMAGE216
Figure 801263DEST_PATH_IMAGE217
(8)。
vector
Figure 281923DEST_PATH_IMAGE218
Is the relative displacement of the moving point on the moving system, so the mold
Figure 636681DEST_PATH_IMAGE219
The distance that the particle moves on the blade can be obtained by a curve integral calculation method of the arc length in a two-dimensional plane:
Figure 493778DEST_PATH_IMAGE220
because the derivation formula of the variable limit integral function is:
Figure 188065DEST_PATH_IMAGE221
therefore, it is right
Figure 839626DEST_PATH_IMAGE222
About
Figure 884942DEST_PATH_IMAGE223
The derivation can be:
Figure 342469DEST_PATH_IMAGE224
(9)
Figure 891262DEST_PATH_IMAGE052
Figure 979303DEST_PATH_IMAGE053
(10)；
due to the shape of the blade
Figure 246337DEST_PATH_IMAGE225
Therefore, the following are:
Figure 445237DEST_PATH_IMAGE226
Figure 910853DEST_PATH_IMAGE227
due to the fact that
Figure 232113DEST_PATH_IMAGE228
The vector is obtained by the Pythagorean theorem
Figure 986442DEST_PATH_IMAGE229
The following steps of (1):
Figure 723454DEST_PATH_IMAGE230
(11)；
finally, (6), (8), (9), (10) and (11) are substituted into (5), and the target acceleration model of the particles in the impact mill under a plane rectangular coordinate system is obtained:
Figure 329664DEST_PATH_IMAGE231
Figure 759508DEST_PATH_IMAGE057
Figure 735555DEST_PATH_IMAGE058
(12)。
in the embodiment of the application, through the relation, the speed of the particle target displacement position under different blade profiles can be accurately solved, so that the blade profile parameters are adjusted, and the blade profile is optimized.
Alternatively, in (12), there is a second derivative to the blade shape function, and from the knowledge about the curvature, in a planar rectangular coordinate system, the curvature of the curve
Figure 276258DEST_PATH_IMAGE232
From this, we can presume that in the formula (12)
Figure 919728DEST_PATH_IMAGE233
In relation to the curvature of the blade.
In a natural coordinate system of mass point kinematics, the acceleration of a mass point can be expressed as:
Figure 317212DEST_PATH_IMAGE234
wherein
Figure 46133DEST_PATH_IMAGE235
Is the tangential direction of the particle motion trajectory,
Figure 124948DEST_PATH_IMAGE236
is the normal direction of the particle motion track and points to the concave side of the curve.
When the above formula is substituted into the dynamic reference system of the model, the particles are mass points, the blades are the motion tracks of the mass points, and the non-linear blades have curvatures
Figure 622925DEST_PATH_IMAGE237
It is believed that the acceleration of the particle due to the change in curvature in the non-inertial system is not taken as the curvature acceleration
Figure 128993DEST_PATH_IMAGE238
。
In step S312, the straight blade is taken as the target blade of the selected type. Optionally, substituting a function of the target blade of the selected type into the target acceleration model to obtain an analytical solution of displacement and velocity of particles in the impact mill comprises:
in the case that the target blade is a linear blade, the shape function of the target blade is determined
Figure 407528DEST_PATH_IMAGE239
Substituting the target acceleration model (12) to obtain:
Figure 290033DEST_PATH_IMAGE240
(13)；
calculating the analytical solution of equation (13) yields:
Figure 642517DEST_PATH_IMAGE241
(14)
Figure 585065DEST_PATH_IMAGE242
(15)；
wherein,
Figure 23000DEST_PATH_IMAGE243
，
Figure 505934DEST_PATH_IMAGE244
and
Figure 978503DEST_PATH_IMAGE245
is the undetermined constant of the differential equation;
taking the boundary condition as
Figure 826373DEST_PATH_IMAGE246
，
Figure 751604DEST_PATH_IMAGE247
Substituting into (14) and (15) to obtain
Figure 975912DEST_PATH_IMAGE248
And
Figure 365305DEST_PATH_IMAGE249
：
Figure 649656DEST_PATH_IMAGE250
Figure 62183DEST_PATH_IMAGE251
；
will be provided with
Figure 824602DEST_PATH_IMAGE252
And
Figure 6185DEST_PATH_IMAGE253
substituting expressions (14) and (15) into said analytical solution for displacement and velocity of particles in said impact mill:
Figure 523754DEST_PATH_IMAGE071
Figure 423577DEST_PATH_IMAGE254
(16)
Figure 989687DEST_PATH_IMAGE255
(17)。
in the embodiment of the application, in the linear type blade, the shape function of the blade is taken as
Figure 25777DEST_PATH_IMAGE256
Wherein
Figure 714247DEST_PATH_IMAGE257
Is the slope of the line, and substituting (12) can obtain:
Figure 101366DEST_PATH_IMAGE258
(13)。
since (13) is a second order Chang Jishu non-homogeneous linear differential equation, the equation consists of one general solution and one special solution.
The characteristic equation of differential equation (13) is:
Figure 205588DEST_PATH_IMAGE259
get the
Figure 361763DEST_PATH_IMAGE260
Then the feature root can be written as:
Figure 158818DEST_PATH_IMAGE261
the general solution of the equation is:
Figure 829970DEST_PATH_IMAGE262
because the constant part of the differential equation does not contain independent variable
Figure 3463DEST_PATH_IMAGE263
Of the form of (1), so if you solve
Figure 14144DEST_PATH_IMAGE264
Presence of independent variable
Figure 982100DEST_PATH_IMAGE265
It is partially contrary to the equation constants, so that the solution is known as containing no independent variables
Figure 78232DEST_PATH_IMAGE265
In the form of (1).
Will be constant
Figure 524257DEST_PATH_IMAGE266
Substituting into differential equation (13), the particular solution of the equation can be solved as:
Figure 720271DEST_PATH_IMAGE267
will be used to relieve
Figure 859128DEST_PATH_IMAGE268
And special solution
Figure 442556DEST_PATH_IMAGE269
By addition, an analytical solution of the equation is obtained as:
Figure 692272DEST_PATH_IMAGE270
(14)
Figure 739862DEST_PATH_IMAGE271
(15)；
wherein,
Figure 49621DEST_PATH_IMAGE272
，
Figure 120345DEST_PATH_IMAGE273
and
Figure 173752DEST_PATH_IMAGE274
is the undetermined constant of the differential equation;
taking the boundary condition as
Figure 13532DEST_PATH_IMAGE275
，
Figure 556508DEST_PATH_IMAGE276
Substituting into (14) and (15) to obtain
Figure 848949DEST_PATH_IMAGE277
And
Figure 706047DEST_PATH_IMAGE278
：
Figure 400334DEST_PATH_IMAGE279
Figure 51895DEST_PATH_IMAGE280
；
will be provided with
Figure 159528DEST_PATH_IMAGE281
And
Figure 554737DEST_PATH_IMAGE282
substituting the expressions (14) and (15) into the analytical solution of displacement and velocity of particles in the impact mill:
Figure 103530DEST_PATH_IMAGE283
Figure 191572DEST_PATH_IMAGE284
(16)
Figure 458605DEST_PATH_IMAGE285
(17)。
in the embodiment of the present application, the expressions (16) and (17) are analytical solutions of the displacement and velocity of the particles in the impact mill under the linear blade. Due to the fact that
Figure 454243DEST_PATH_IMAGE286
And
Figure 123122DEST_PATH_IMAGE287
are all constant with the known quantity of the carbon,
Figure 382065DEST_PATH_IMAGE288
and
Figure 870815DEST_PATH_IMAGE289
slope and dynamic friction factor, displacement, respectively, of a linear blade
Figure 873406DEST_PATH_IMAGE290
And velocity
Figure 459108DEST_PATH_IMAGE291
Is with respect to time
Figure 623373DEST_PATH_IMAGE292
As a function of (c). So theoretically, at the target displacement
Figure 864999DEST_PATH_IMAGE293
Can obtain the time
Figure 405702DEST_PATH_IMAGE294
Substituting it into the velocity
Figure 783593DEST_PATH_IMAGE295
When the speed is about
Figure 384339DEST_PATH_IMAGE296
And
Figure 909998DEST_PATH_IMAGE297
the speed limit value can be obtained by the binary function of (2).
In practice, since the particles need to move in the positive direction of the coordinate axis when they are accelerated in the blade, there cannot be a phenomenon of "backflow", i.e.
Figure 254392DEST_PATH_IMAGE298
，
Figure 752369DEST_PATH_IMAGE299
The following solves the requirement for satisfying the above expression.
Velocity of
Figure 258437DEST_PATH_IMAGE300
Due to the fact that
Figure 474655DEST_PATH_IMAGE301
，
Figure 419477DEST_PATH_IMAGE302
，
Figure 771961DEST_PATH_IMAGE303
Always on, therefore, it is required
Figure 448930DEST_PATH_IMAGE304
And
Figure 886864DEST_PATH_IMAGE305
the same number. Due to the fact that
Figure 573061DEST_PATH_IMAGE306
And a function of
Figure 839438DEST_PATH_IMAGE307
Is about
Figure 952888DEST_PATH_IMAGE308
Is a monotonically increasing function of
Figure 878119DEST_PATH_IMAGE309
Namely, it is
Figure 102427DEST_PATH_IMAGE310
This is always true and can be derived from this.
Due to the displacement satisfy
Figure 429503DEST_PATH_IMAGE311
Speed is satisfied
Figure 776170DEST_PATH_IMAGE312
Therefore, it can be derived from
Figure 923118DEST_PATH_IMAGE313
When the temperature of the water is higher than the set temperature,
Figure 951117DEST_PATH_IMAGE314
this is always true.
In summary, if the displacement or the velocity of the wall surface particle is negative, the slope and the dynamic friction factor need to satisfy the relationship
Figure 132699DEST_PATH_IMAGE315
。
The influence of different parameters on the result is intuitively analyzed through the numerical solution corresponding to the analytic solution.
Since in formula (13), the rotational speed
Figure 650268DEST_PATH_IMAGE316
And radius
Figure 550091DEST_PATH_IMAGE317
Are all constants, therefore, take
Figure 116202DEST_PATH_IMAGE318
=1000rad/s，
Figure 152291DEST_PATH_IMAGE319
=1m. And the pitch of the blade
Figure 778444DEST_PATH_IMAGE320
Coefficient of kinetic friction
Figure 899984DEST_PATH_IMAGE321
To be evaluated, the result is influenced. In order to quantitatively analyze results under different parameters, differential equations under different parameters are solved by using an ode function in MATLAB software, and the differential equations under different parameters are compared
Figure 332103DEST_PATH_IMAGE322
And (= 3 m), particle velocity.
From Table 1, when
Figure 488277DEST_PATH_IMAGE323
When =0.5At a speed of
Figure 285332DEST_PATH_IMAGE324
A peak appears near = -0.2. From table 2, it can be seen that when the slope is constant, the speed decreases as the kinetic friction factor increases, which is also consistent with our life experience.
TABLE 1 Effect of slope on acceleration
Figure 894168DEST_PATH_IMAGE325
TABLE 2 Effect of Friction on acceleration Effect
Figure 802081DEST_PATH_IMAGE326
Note: due to the solving precision, the accurate positioning can not be realized
Figure 875079DEST_PATH_IMAGE327
Data of =3m, so take
Figure 843035DEST_PATH_IMAGE327
At position of = (3 ± 0.1) m, corresponding velocity
Figure 939167DEST_PATH_IMAGE295
And (4) carrying out analysis.
From this we can conclude that for a linear blade of a given material, the coefficient of dynamic friction is determined to have an optimum slope to maximize its acceleration effect, and therefore we need to find a relation of sum, an optimization method is given below.
In step S314, optionally, optimizing the parameters of the target blade of the corresponding type using the analytic solution includes:
the following treatments were carried out for (16) and (17):
Figure 650771DEST_PATH_IMAGE328
Figure 781538DEST_PATH_IMAGE075
Figure 982713DEST_PATH_IMAGE076
；
get
Figure 300561DEST_PATH_IMAGE329
The above formula is simplified to obtain the speed
Figure 815856DEST_PATH_IMAGE295
About displacement
Figure 801130DEST_PATH_IMAGE327
Expression (c):
Figure 110889DEST_PATH_IMAGE330
(18)；
relating equation (18) to the slope
Figure 978350DEST_PATH_IMAGE331
And (4) solving a partial derivative to obtain:
Figure 31757DEST_PATH_IMAGE332
；
order to
Figure 871537DEST_PATH_IMAGE333
Then obtain the slope
Figure 352197DEST_PATH_IMAGE334
The optimization interval of (2):
Figure 910217DEST_PATH_IMAGE085
or
Figure 564053DEST_PATH_IMAGE086
。
In the embodiment of the application:
the following processes may be performed for (16) and (17):
Figure 523918DEST_PATH_IMAGE328
Figure 175480DEST_PATH_IMAGE075
Figure 955217DEST_PATH_IMAGE076
；
get under different parameters
Figure 350426DEST_PATH_IMAGE327
Time corresponding to =3m
Figure 230045DEST_PATH_IMAGE335
[2.5×10 -3 ,3×10 -3 ]. Get
Figure 52507DEST_PATH_IMAGE336
=1000rad/s, therefore
Figure 319541DEST_PATH_IMAGE337
[-6,-5]. Due to dynamic friction factor
Figure 518441DEST_PATH_IMAGE338
(0,1), therefore
Figure 187319DEST_PATH_IMAGE339
(1,1.41), therefore
Figure 243000DEST_PATH_IMAGE340
-5，
Figure 997330DEST_PATH_IMAGE341
Therefore:
Figure 999921DEST_PATH_IMAGE342
it is thus advisable:
Figure 523306DEST_PATH_IMAGE077
from which the speed can be derived
Figure 687571DEST_PATH_IMAGE343
About displacement
Figure 991513DEST_PATH_IMAGE344
The expression of (c):
Figure 532216DEST_PATH_IMAGE080
(18)；
wherein,
Figure 910108DEST_PATH_IMAGE345
。
the speed is observed (18)
Figure 510853DEST_PATH_IMAGE346
Is about
Figure 36513DEST_PATH_IMAGE347
And
Figure 380906DEST_PATH_IMAGE348
with respect to which
Figure 613305DEST_PATH_IMAGE349
Calculating a partial derivative:
Figure 384951DEST_PATH_IMAGE350
wherein,
Figure 335590DEST_PATH_IMAGE351
。
since in the above formula, no parameters appear
Figure 280412DEST_PATH_IMAGE348
So that the speed can be determined
Figure 632896DEST_PATH_IMAGE346
About a parameter
Figure 575444DEST_PATH_IMAGE352
Monotonicity of and
Figure 13379DEST_PATH_IMAGE348
irrelevant, order
Figure 761892DEST_PATH_IMAGE083
Then obtain the slope
Figure 968883DEST_PATH_IMAGE349
The optimization interval of (2):
Figure 82332DEST_PATH_IMAGE085
or
Figure 7563DEST_PATH_IMAGE086
。
The schematic diagram is made by MATLAB software as shown in FIG. 5, so when
Figure 231871DEST_PATH_IMAGE353
Time, speed
Figure 621264DEST_PATH_IMAGE346
Take a maximum value because
Figure 640035DEST_PATH_IMAGE354
，
Figure 52562DEST_PATH_IMAGE355
Therefore speed of
Figure 80561DEST_PATH_IMAGE346
Can not get the extreme point
Figure 262144DEST_PATH_IMAGE356
。
As can be seen from the solution process of (18), the error of the formula is derived from the pair
Figure 779713DEST_PATH_IMAGE357
So that the magnitude of the error depends on
Figure 413956DEST_PATH_IMAGE358
And
Figure 980067DEST_PATH_IMAGE359
the value range of (a). Dynamic friction factor
Figure 281735DEST_PATH_IMAGE360
The smaller, the time
Figure 907889DEST_PATH_IMAGE361
The smaller the formula error. Is taken from below
Figure 88816DEST_PATH_IMAGE349
=0.5，
Figure 458617DEST_PATH_IMAGE362
=1000rad/s，
Figure 614792DEST_PATH_IMAGE363
=1m authentication respectively
Figure 411847DEST_PATH_IMAGE364
=0.1，
Figure 20682DEST_PATH_IMAGE364
=0.3，
Figure 990912DEST_PATH_IMAGE364
Relative error of speed at different positions when = 0.5:
TABLE 3
Figure 1594DEST_PATH_IMAGE365
Relative error at 0.1
Displacement of True value Calculated value Relative error
0.001 12.42 687.88 5438.39%
0.07 307.04 744.63 142.52%
1.00 1558.32 1674.52 7.46%
3.00 3319.63 3367.64 1.45%
6.00 6890.76 6910.60 0.29%
TABLE 4
Figure 969550DEST_PATH_IMAGE366
Relative error at 0.3
Displacement of True value Calculated value Relative error
0.001 36.73 506.69 1279.42%
0.07 281.56 551.17 97.17%
1.00 1270.17 1311.85 3.28%
3.00 2722.41 2733.28 0.40%
6.80 5620.55 5623.50 0.05%
TABLE 5
Figure 65682DEST_PATH_IMAGE366
Relative error at 0.5
Displacement of True value Calculated value Relative error
0.001 36.21 371.52 926.08%
0.07 247.53 411.69 66.32%
1.00 1039.90 1050.39 1.01%
3.00 2198.00 2199.50 0.07%
6.80 4596.21 4596.44 0.00%
As shown in tables 3, 4 and 5, the time course was changed
Figure 777286DEST_PATH_IMAGE367
Increase or displacement of
Figure 704791DEST_PATH_IMAGE368
And the relative error is gradually reduced when the error is increased. Coefficient of kinetic friction
Figure 843648DEST_PATH_IMAGE369
The relative error at different displacement is continuously reduced in an increasing way, and the relative error is continuously reduced along with the time
Figure 427076DEST_PATH_IMAGE370
The relative error is also reduced. The error of (18) is time dependent on the dynamic friction factor. Multiplying a harmonic coefficient before the formula
Figure 942371DEST_PATH_IMAGE371
Wherein
Figure 662065DEST_PATH_IMAGE372
Is about
Figure 34141DEST_PATH_IMAGE373
So as to reduce the error due to the friction factor, thus obtaining:
Figure 104865DEST_PATH_IMAGE374
wherein,
Figure 158272DEST_PATH_IMAGE375
。
through the analysis, we find that the above optimization method is
Figure 998052DEST_PATH_IMAGE376
[0,2×10-3]There is also an optimization space for errors within the range of (1), and the following is to verify the utility of the formula in this section.
Boundary condition
Figure 478711DEST_PATH_IMAGE377
The corresponding values can be obtained by substituting (14) and (15)
Figure 99049DEST_PATH_IMAGE378
And with
Figure 690567DEST_PATH_IMAGE379
：
Figure 384854DEST_PATH_IMAGE380
(19)
Figure 301994DEST_PATH_IMAGE381
(20)
The following treatments were carried out for (14) and (15):
Figure 81731DEST_PATH_IMAGE382
Figure 539257DEST_PATH_IMAGE383
Figure 353630DEST_PATH_IMAGE384
(21)
will be provided with
Figure 176092DEST_PATH_IMAGE385
Is taken as an error adjustment coefficient
Figure 443125DEST_PATH_IMAGE386
Due to the fact that
Figure 642025DEST_PATH_IMAGE387
[0,2×10-3]Therefore, it is
Figure 373221DEST_PATH_IMAGE388
. Bringing (19), (20) into (21) yields:
Figure 366585DEST_PATH_IMAGE389
(22)
wherein:
Figure 120914DEST_PATH_IMAGE390
due to the fact that
Figure 857926DEST_PATH_IMAGE387
[0,2×10-3]So at this stage, over time
Figure 381311DEST_PATH_IMAGE391
Increase, displacement increment
Figure 873473DEST_PATH_IMAGE392
Is very small and tends to 0, so it can be considered that
Figure 115098DEST_PATH_IMAGE393
. In the step (22), the first step is carried out,
Figure 390222DEST_PATH_IMAGE394
is about
Figure 33693DEST_PATH_IMAGE395
And
Figure 368859DEST_PATH_IMAGE396
a multiple function of
Figure 163027DEST_PATH_IMAGE397
About
Figure 241842DEST_PATH_IMAGE398
After the partial derivative is calculated, the value at the extreme point is the same as
Figure 739819DEST_PATH_IMAGE399
Is related to, but due to
Figure 511466DEST_PATH_IMAGE400
So that it is possible to directly use
Figure 462104DEST_PATH_IMAGE401
Change to
Figure 406927DEST_PATH_IMAGE402
But has no influence, so:
Figure 759411DEST_PATH_IMAGE403
(22)
wherein
Figure 701959DEST_PATH_IMAGE404
。
To (2)2) About
Figure 139893DEST_PATH_IMAGE405
The partial derivatives are obtained:
Figure 560510DEST_PATH_IMAGE406
the formula is solved by a quadratic equation of a unary to obtain:
Figure 33080DEST_PATH_IMAGE407
(23)
due to the following:
Figure 208846DEST_PATH_IMAGE408
Figure 134077DEST_PATH_IMAGE409
so it is easy to prove:
Figure 358385DEST_PATH_IMAGE410
(24)
and because of
Figure 419882DEST_PATH_IMAGE411
Therefore, the following can be obtained:
Figure 766550DEST_PATH_IMAGE412
it can thus be deduced that:
Figure 179076DEST_PATH_IMAGE413
(25)
by the relationship between (24) and (25), the properties of the one-dimensional quadratic equation are combined to obtain:
Figure 207075DEST_PATH_IMAGE414
hence speed
Figure 388658DEST_PATH_IMAGE415
Is about
Figure 578331DEST_PATH_IMAGE416
Because of the monotonously increasing function of
Figure 540471DEST_PATH_IMAGE417
Therefore, it is when
Figure 106581DEST_PATH_IMAGE418
When taking the maximum value, the speed
Figure 408250DEST_PATH_IMAGE419
And maximum. This is consistent with the optimization results described above, so equation (18) applies across the whole segment.
In the shape of
Figure 768824DEST_PATH_IMAGE420
The linear blade is also one of the polynomial function blades which can be easily found by the above solving process. Through previous research on the problems, the blades with different curvatures can accelerate particles more, so that the curvatures of the blades need to be optimized, and a polynomial function just can meet the requirements. The optimization idea of the polynomial function blade is given as follows:
using a quadratic polynomial function of
Figure 155943DEST_PATH_IMAGE421
For example. Since the model requires the blade to intersect the origin, it
Figure 588061DEST_PATH_IMAGE422
。
The blade is arranged at
Figure 478657DEST_PATH_IMAGE423
Projection on axis being equally divided into
Figure 275711DEST_PATH_IMAGE424
Segments, each segment having a length of
Figure 884547DEST_PATH_IMAGE425
Therefore, it is first
Figure 58040DEST_PATH_IMAGE426
The end point coordinate of the segment blade is
Figure 131038DEST_PATH_IMAGE427
. We take the first stage blade when
Figure 98994DEST_PATH_IMAGE428
When the slope is very large, the section of the blade can be approximately seen as a linear blade, and the slope of the section of the blade is equal to the slope of the linear blade according to the optimization result of the linear blade
Figure 195126DEST_PATH_IMAGE429
When the particle velocity is at a maximum, i.e.
Figure 906730DEST_PATH_IMAGE430
From this it can be derived:
Figure 771918DEST_PATH_IMAGE431
will be provided with
Figure 910775DEST_PATH_IMAGE432
Substituting (12), and optimizing to maximize the particle velocity by numerical solution and analytic solution
Figure 556520DEST_PATH_IMAGE433
。
Repeat the above steps againStep of converting the known size
Figure 806236DEST_PATH_IMAGE434
，
Figure 791509DEST_PATH_IMAGE435
，
Figure 101268DEST_PATH_IMAGE436
Substituting cubic function
Figure 171992DEST_PATH_IMAGE437
Then, the solution is substituted into (12), and the particle velocity is optimized to be the maximum by numerical solution and analytic solution
Figure 284786DEST_PATH_IMAGE438
。
By analogy, through the method, the parameters of the polynomial function blade are continuously optimized, and the shape of the blade can be continuously close to the optimal shape theoretically.
According to the method and the device, the particle acceleration model under the two-dimensional rectangular coordinate system is established, so that the speeds of the particles at different positions and the blades with known blade shapes on the turbine can be accurately solved. The ideal leaf profile can be optimized through the model, the reasonable initial leaf profile can be selected from the positive problems more accurately, the problems of many manual experiences are reduced, and the technical problem that the solution conditions of given inverse problems in the leaf profile design are unreasonable or the solution conditions depend on subjective factors of designers is solved.
According to still another aspect of an embodiment of the present application, as shown in fig. 6, there is provided a parameter optimizing device for a turbomachine blade, including:
a coordinate system establishing module 601, configured to take a connection point of the impact mill and the target blade as an origin, use a tangential direction of the target blade at the connection point as an x-axis direction, and use a normal direction of the target blade at the connection point as a y-axis direction to establish a planar rectangular coordinate system XOY;
a data model establishing module 603 for determining a radius on the plane rectangular coordinate system
Figure 124566DEST_PATH_IMAGE001
The center of the circle of the impact mill
Figure 605226DEST_PATH_IMAGE002
Shape obey function
Figure 897667DEST_PATH_IMAGE439
And the curve of the target blade at the grinding disc and the angular velocity
Figure 754765DEST_PATH_IMAGE095
When rad/s rotates anticlockwise around the circle center, the mass is
Figure 511368DEST_PATH_IMAGE005
The moving point of the particles on the plane rectangular coordinate system
Figure 162929DEST_PATH_IMAGE089
；
A mechanical parameter determining module 605, configured to determine, using the grinding disc and the target blade as a dynamic reference system, a plurality of mechanical parameters in the dynamic reference system by using the center of the impact mill, the curve of the target blade, and the moving point, where the plurality of mechanical parameters include a relative displacement of the moving point on the dynamic reference system
Figure 208246DEST_PATH_IMAGE090
Dynamic friction factor on the target blade
Figure 603455DEST_PATH_IMAGE008
The radius of the connecting line of the moving point and the circle center of the impact mill
Figure 152248DEST_PATH_IMAGE009
The relative speed of the moving point with respect to the moving reference system
Figure 302606DEST_PATH_IMAGE091
The moving point is relative to a fixed referenceAbsolute velocity of system XOY
Figure 569640DEST_PATH_IMAGE011
The velocity of involvement of the dynamic reference frame with respect to the fixed reference frame XOY
Figure 768540DEST_PATH_IMAGE092
And taking the intersection point of the reverse extension line of the speed direction at the moving point and the X axis
Figure 171839DEST_PATH_IMAGE013
When the utility model is used, the water is discharged,
Figure 430782DEST_PATH_IMAGE014
and with
Figure 247429DEST_PATH_IMAGE015
Angle of (2)
Figure 984441DEST_PATH_IMAGE016
、
Figure 507826DEST_PATH_IMAGE093
And
Figure 937670DEST_PATH_IMAGE018
angle of (2)
Figure 913716DEST_PATH_IMAGE094
、
Figure 516736DEST_PATH_IMAGE440
And with
Figure 160207DEST_PATH_IMAGE021
Angle (d) of
Figure 495373DEST_PATH_IMAGE022
；
A force analysis module 607 for determining, based on a plurality of the mechanical parameters, a coriolis force, a centrifugal force, a sliding friction force, and a reaction force of the target blade to the moving point, which are applied to the moving point when the moving point moves in the dynamic reference system;
a particle acceleration model building module 609, configured to build a target acceleration model of the particle in the impact mill in a planar rectangular coordinate system by using the coriolis force, the centrifugal force, the sliding friction force, the reaction force, and a resultant force of the four forces, so as to represent an association relationship between a velocity displacement component of the particle in the dynamic reference system along an X coordinate axis and a blade shape function and a blade dynamic friction factor;
an analytic solution calculation module 611, configured to substitute a function of the target blade of the selected type into the target acceleration model to obtain an analytic solution of displacement and velocity of the particle in the impact mill;
a parameter optimization module 613, configured to optimize a parameter of the target blade of the corresponding type using the analytic solution.
It should be noted that the coordinate system establishing module 601 in this embodiment may be configured to execute step S202 in this embodiment, the data model establishing module 603 in this embodiment may be configured to execute step S204 in this embodiment, the mechanical parameter determining module 605 in this embodiment may be configured to execute step S206 in this embodiment, the stress analyzing module 607 in this embodiment may be configured to execute step S208 in this embodiment, the particle acceleration model constructing module 609 in this embodiment may be configured to execute step S210 in this embodiment, the analytic solution calculating module 611 in this embodiment may be configured to execute step S212 in this embodiment, and the parameter optimizing module 613 in this embodiment may be configured to execute step S14 in this embodiment.
It should be noted here that the modules described above are the same as the examples and application scenarios implemented by the corresponding steps, but are not limited to the disclosure of the above embodiments. It should be noted that the modules described above as a part of the apparatus may operate in a hardware environment as shown in fig. 1, and may be implemented by software or hardware.
Optionally, the mechanical parameter determining module is specifically configured to:
determining Coriolis acceleration
Figure 224295DEST_PATH_IMAGE023
Wherein the Coriolis acceleration direction is perpendicular to the relative speed of the moving point and points to the positive direction of the Y axis;
the mass of the moving point
Figure 303109DEST_PATH_IMAGE024
Multiplying the Coriolis acceleration to obtain the Coriolis force:
Figure 863404DEST_PATH_IMAGE025
(1)。
optionally, the mechanical parameter determining module is specifically configured to:
determining the tangential acceleration of the point of motion
Figure 369471DEST_PATH_IMAGE026
And normal acceleration
Figure 585689DEST_PATH_IMAGE027
Wherein the direction and vector of the normal acceleration
Figure 468194DEST_PATH_IMAGE028
In the same direction;
by
Figure 820678DEST_PATH_IMAGE029
To obtain
Figure 825544DEST_PATH_IMAGE030
Obtaining the centrifugal force:
Figure 263478DEST_PATH_IMAGE031
(2)。
optionally, the mechanical parameter determining module is specifically configured to:
setting the reaction force of the target blade to the moving point to be
Figure 684095DEST_PATH_IMAGE032
Then the sliding friction is
Figure 156665DEST_PATH_IMAGE033
。
Optionally, the particle acceleration model building module is specifically configured to:
adding the Coriolis force, the centrifugal force, the sliding friction force and the reaction force to obtain a resultant force:
Figure 4535DEST_PATH_IMAGE034
(3)；
projecting the above formula to the tangential direction of the blade at the moving point to obtain:
Figure 992083DEST_PATH_IMAGE441
Figure 216391DEST_PATH_IMAGE442
(4)；
taking and relative velocity
Figure 543467DEST_PATH_IMAGE037
In the vertical direction of
Figure 827818DEST_PATH_IMAGE038
Then the force of the resultant force is directed
Figure 240344DEST_PATH_IMAGE443
Direction and
Figure 68011DEST_PATH_IMAGE040
and (3) projecting the direction to obtain:
Figure 249593DEST_PATH_IMAGE444
Figure 704845DEST_PATH_IMAGE445
；
substituting the above formula into (4) yields:
Figure 604668DEST_PATH_IMAGE446
(a)；
substituting (1) and (2) into (a) to obtain a second-order differential equation between the relative displacement of the particles on the blade and the blade inclination angle:
Figure 170779DEST_PATH_IMAGE447
(5)；
based on straight lines
Figure 269185DEST_PATH_IMAGE448
And a straight line
Figure 895338DEST_PATH_IMAGE449
The expression (c) expresses the blade pitch angle in terms of coordinate parameters as:
Figure 282457DEST_PATH_IMAGE450
(6)
Figure 386679DEST_PATH_IMAGE451
(7)
Figure 542854DEST_PATH_IMAGE452
(8)；
by
Figure 339909DEST_PATH_IMAGE453
In a manner of(5) The method comprises the following steps:
Figure 11062DEST_PATH_IMAGE454
(9)
Figure 184554DEST_PATH_IMAGE455
Figure 195235DEST_PATH_IMAGE456
(10)；
determining the sagittal diameter of formula (5) by Pythagorean theorem
Figure 163191DEST_PATH_IMAGE457
The following steps of (1):
Figure 259323DEST_PATH_IMAGE458
(11)；
substituting (6), (8), (9), (10) and (11) into (5) to obtain the target acceleration model of the particles in the impact mill under a plane rectangular coordinate system:
Figure 767665DEST_PATH_IMAGE231
Figure 898432DEST_PATH_IMAGE057
Figure 37290DEST_PATH_IMAGE173
(12)。
optionally, the analytic solution calculating module is specifically configured to:
in the case that the target blade is a linear blade, the shape function of the target blade is determined
Figure 620718DEST_PATH_IMAGE059
Substituting the target acceleration model (12) to obtain:
Figure 932750DEST_PATH_IMAGE459
(13)；
calculating the analytical solution of equation (13) yields:
Figure 918024DEST_PATH_IMAGE061
(14)
Figure 227782DEST_PATH_IMAGE460
Figure 298507DEST_PATH_IMAGE461
(15)；
wherein,
Figure 351913DEST_PATH_IMAGE462
，
Figure 254010DEST_PATH_IMAGE065
and
Figure 734670DEST_PATH_IMAGE066
is the undetermined constant of the differential equation;
taking the boundary condition as
Figure 27111DEST_PATH_IMAGE067
，
Figure 884209DEST_PATH_IMAGE463
Substituting into (14) and (15) to obtain
Figure 578495DEST_PATH_IMAGE065
And
Figure 292373DEST_PATH_IMAGE066
：
Figure 337690DEST_PATH_IMAGE464
Figure 732899DEST_PATH_IMAGE465
；
will be provided with
Figure 281692DEST_PATH_IMAGE466
And
Figure 369734DEST_PATH_IMAGE467
substituting the expressions (14) and (15) into the analytical solution of displacement and velocity of particles in the impact mill:
Figure 699084DEST_PATH_IMAGE071
Figure 632405DEST_PATH_IMAGE254
(16)
Figure 301284DEST_PATH_IMAGE468
(17)。
optionally, the parameter optimization module is specifically configured to:
the following treatments were carried out for (16) and (17):
Figure 560227DEST_PATH_IMAGE469
Figure 48977DEST_PATH_IMAGE075
Figure 134392DEST_PATH_IMAGE076
；
get the
Figure 657778DEST_PATH_IMAGE077
The above formula is simplified to obtain the speed
Figure 822043DEST_PATH_IMAGE470
About displacement
Figure 63668DEST_PATH_IMAGE471
Expression (c):
Figure 604371DEST_PATH_IMAGE080
(18)；
relating equation (18) to the slope
Figure 44580DEST_PATH_IMAGE472
And (4) solving a partial derivative to obtain:
Figure 645325DEST_PATH_IMAGE473
；
order to
Figure 108668DEST_PATH_IMAGE474
Then obtain the slope
Figure 453061DEST_PATH_IMAGE475
The optimization interval of (2):
Figure 13356DEST_PATH_IMAGE476
or
Figure 519423DEST_PATH_IMAGE477
。
According to another aspect of the embodiments of the present application, an electronic device is provided, as shown in fig. 7, and includes a memory 701, a processor 703, a communication interface 705, and a communication bus 707, where the memory 701 stores a computer program that is executable on the processor 703, the memory 701 and the processor 703 communicate with each other through the communication interface 705 and the communication bus 707, and the processor 703 implements the steps of the method when executing the computer program.
The memory and the processor in the electronic equipment are communicated with the communication interface through the communication bus. The communication bus may be a Peripheral Component Interconnect (PCI) bus, an Extended Industry Standard Architecture (EISA) bus, or the like. The communication bus may be divided into an address bus, a data bus, a control bus, etc.
The Memory may include a Random Access Memory (RAM) or a non-volatile Memory (non-volatile Memory), such as at least one disk Memory. Optionally, the memory may also be at least one memory device located remotely from the processor.
The Processor may be a general-purpose Processor, and includes a Central Processing Unit (CPU), a Network Processor (NP), and the like; the Integrated Circuit may also be a Digital Signal Processor (DSP), an Application Specific Integrated Circuit (ASIC), a Field Programmable Gate Array (FPGA) or other Programmable logic device, a discrete Gate or transistor logic device, or a discrete hardware component.
There is also provided, in accordance with yet another aspect of an embodiment of the present application, a computer program product or computer program comprising computer instructions stored in a computer-readable storage medium. The processor of the computer device reads the computer instructions from the computer-readable storage medium, and the processor executes the computer instructions to cause the computer device to perform the steps of any of the embodiments described above.
Optionally, in an embodiment of the present application, a computer readable medium is configured to store program code for the processor to perform the above steps.
Optionally, for a specific example in this embodiment, reference may be made to the example described in the foregoing embodiment, and this embodiment is not described herein again.
When the embodiments of the present application are specifically implemented, reference may be made to the above embodiments, and corresponding technical effects are achieved.
It is to be understood that the embodiments described herein may be implemented in hardware, software, firmware, middleware, microcode, or any combination thereof. For a hardware implementation, the Processing units may be implemented within one or more Application Specific Integrated Circuits (ASICs), digital Signal Processors (DSPs), digital Signal Processing Devices (DSPDs), programmable Logic Devices (PLDs), field Programmable Gate Arrays (FPGAs), general purpose processors, controllers, micro-controllers, microprocessors, other electronic units configured to perform the functions described herein, or a combination thereof.
For a software implementation, the techniques described herein may be implemented by means of units performing the functions described herein. The software codes may be stored in a memory and executed by a processor. The memory may be implemented within the processor or external to the processor.
Those of ordinary skill in the art will appreciate that the various illustrative elements and algorithm steps described in connection with the embodiments disclosed herein may be implemented as electronic hardware or combinations of computer software and electronic hardware. Whether such functionality is implemented as hardware or software depends upon the particular application and design constraints imposed on the implementation. Skilled artisans may implement the described functionality in varying ways for each particular application, but such implementation decisions should not be interpreted as causing a departure from the scope of the present application.
It is clear to those skilled in the art that, for convenience and brevity of description, the specific working processes of the above-described systems, apparatuses and units may refer to the corresponding processes in the foregoing method embodiments, and are not described herein again.
In the embodiments provided in the present application, it should be understood that the disclosed apparatus and method may be implemented in other ways. For example, the above-described apparatus embodiments are merely illustrative, and for example, the division of the modules is merely a logical division, and in actual implementation, there may be other divisions, for example, multiple modules or components may be combined or integrated into another system, or some features may be omitted, or not implemented. In addition, the shown or discussed mutual coupling or direct coupling or communication connection may be an indirect coupling or communication connection through some interfaces, devices or units, and may be in an electrical, mechanical or other form.
The units described as separate parts may or may not be physically separate, and parts displayed as units may or may not be physical units, may be located in one place, or may be distributed on a plurality of network units. Some or all of the units can be selected according to actual needs to achieve the purpose of the solution of the embodiment.
In addition, functional units in the embodiments of the present application may be integrated into one processing unit, or each unit may exist alone physically, or two or more units are integrated into one unit.
The functions, if implemented in the form of software functional units and sold or used as a stand-alone product, may be stored in a computer readable storage medium. Based on such understanding, the technical solutions of the embodiments of the present application, which are essential or part of the technical solutions contributing to the prior art, may be embodied in the form of a software product, which is stored in a storage medium and includes several instructions for causing a computer device (which may be a personal computer, a server, or a network device) to execute all or part of the steps of the methods described in the embodiments of the present application. And the aforementioned storage medium includes: various media capable of storing program codes, such as a U disk, a removable hard disk, a ROM, a RAM, a magnetic disk, or an optical disk. It is noted that, in this document, relational terms such as "first" and "second," and the like, may be used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Also, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising a … …" does not exclude the presence of another identical element in a process, method, article, or apparatus that comprises the element.
The above description is merely exemplary of the present application and is presented to enable those skilled in the art to understand and practice the present application. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the application. Thus, the present application is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims (9)

1. A method of optimizing parameters of a turbomachine blade, comprising:
taking a connecting point of an impact mill and a target blade as an origin, taking the tangential direction of the target blade at the connecting point as the x-axis direction, and taking the normal direction of the target blade at the connecting point as the y-axis direction to create a plane rectangular coordinate system XOY;
determining a radius on the planar rectangular coordinate system as
Figure 516995DEST_PATH_IMAGE002
The center of the circle of the impact mill
Figure 434135DEST_PATH_IMAGE004
Shape obey function
Figure 213872DEST_PATH_IMAGE006
And the curve of the target blade at the grinding disc and the angular velocity
Figure 546765DEST_PATH_IMAGE008
The mass of the rad/s rotating anticlockwise around the circle center is
Figure 361137DEST_PATH_IMAGE010
The moving point of the particles on the plane rectangular coordinate system
Figure 183599DEST_PATH_IMAGE012
；
Using the grinding disc and the target blade as a dynamic reference system, determining a plurality of mechanical parameters under the dynamic reference system by using the circle center of the impact mill, the curve of the target blade and the moving point, wherein the plurality of mechanical parameters comprise the relative displacement of the moving point on the dynamic reference system
Figure 637583DEST_PATH_IMAGE014
Dynamic friction factor on the target blade
Figure 836483DEST_PATH_IMAGE016
The radius of the connecting line of the moving point and the circle center of the impact mill
Figure 505362DEST_PATH_IMAGE018
The relative speed of the moving point with respect to the moving reference system
Figure 436409DEST_PATH_IMAGE020
The absolute speed of the moving point relative to a fixed reference frame XOY
Figure 190738DEST_PATH_IMAGE022
The velocity of involvement of the dynamic reference frame with respect to the fixed reference frame XOY
Figure 927750DEST_PATH_IMAGE024
And taking the intersection point of the reverse extension line of the speed direction at the moving point and the X axis
Figure 629297DEST_PATH_IMAGE026
When the temperature of the water is higher than the set temperature,
Figure 59142DEST_PATH_IMAGE028
and
Figure 238450DEST_PATH_IMAGE030
angle of (2)
Figure 513574DEST_PATH_IMAGE032
、
Figure 157045DEST_PATH_IMAGE034
And
Figure 679162DEST_PATH_IMAGE036
angle of (2)
Figure 408083DEST_PATH_IMAGE038
、
Figure 486898DEST_PATH_IMAGE040
And
Figure 922558DEST_PATH_IMAGE042
angle of (2)
Figure 694205DEST_PATH_IMAGE044
；
Determining Coriolis force, centrifugal force, sliding friction force and reaction force of the target blade to the moving point when the moving point moves in the dynamic reference system based on a plurality of the mechanical parameters;
constructing a target acceleration model of the particles in the impact mill under a plane rectangular coordinate system by using the Coriolis force, the centrifugal force, the sliding friction force, the reaction force and the resultant force of the four forces, so as to represent the association relation between the velocity displacement component of the particles along the X coordinate axis in the moving reference system and the blade shape function and the blade sliding friction factor;
substituting the function of the target blade of the selected type into the target acceleration model to obtain an analytic solution of the displacement and the speed of the particles in the impact mill;
optimizing parameters of the target blade of the corresponding type by using the analytic solution;
constructing a target acceleration model of the particles in the impact mill in a plane rectangular coordinate system by using the Coriolis force, the centrifugal force, the sliding friction force, the reaction force and the resultant force of the four forces, wherein the target acceleration model comprises the following steps:
adding the Coriolis force, the centrifugal force, the sliding friction force and the reaction force to obtain a resultant force:
Figure 644844DEST_PATH_IMAGE046
(3)；
wherein:
Figure 714300DEST_PATH_IMAGE048
(1)；
Figure 66784DEST_PATH_IMAGE050
is the Coriolis acceleration;
Figure 9332DEST_PATH_IMAGE052
(2)；
Figure 384950DEST_PATH_IMAGE054
is the normal acceleration;
projecting the formula (3) to the tangential direction of the blade at the moving point to obtain:
Figure 805567DEST_PATH_IMAGE056
(4)；
taking and relative velocity
Figure 278136DEST_PATH_IMAGE058
In the vertical direction of
Figure 578536DEST_PATH_IMAGE060
Then the force of the resultant force is directed
Figure 503767DEST_PATH_IMAGE062
Direction and
Figure 728075DEST_PATH_IMAGE064
and (3) projecting the direction to obtain:
Figure 727255DEST_PATH_IMAGE066
；
substituting the above formula into (4) yields:
Figure 11606DEST_PATH_IMAGE068
(a)；
substituting (1) and (2) into (a) to obtain a second-order differential equation between the relative displacement of the particles on the blade and the blade inclination angle:
Figure 424133DEST_PATH_IMAGE070
(5)；
based on straight lines
Figure 452132DEST_PATH_IMAGE072
And a straight line
Figure 823595DEST_PATH_IMAGE074
The expression (c) expresses the blade pitch angle in terms of coordinate parameters as:
Figure 13267DEST_PATH_IMAGE076
(6)
Figure 913090DEST_PATH_IMAGE078
(7)
Figure 416884DEST_PATH_IMAGE080
(8)；
by
Figure 718552DEST_PATH_IMAGE082
In formula (5):
Figure 79126DEST_PATH_IMAGE084
(9)
Figure 653196DEST_PATH_IMAGE086
(10)；
determining the sagittal diameter of formula (5) by Pythagorean theorem
Figure 22998DEST_PATH_IMAGE088
The following steps of (1):
Figure 913593DEST_PATH_IMAGE090
(11)；
substituting (6), (8), (9), (10) and (11) into (5) to obtain the target acceleration model of the particles in the impact mill under a plane rectangular coordinate system:
Figure 648331DEST_PATH_IMAGE092
(12)。
2. the method of claim 1, wherein determining the coriolis force experienced by the motion point while moving in the motion reference frame comprises:
determining Coriolis acceleration
Figure 257167DEST_PATH_IMAGE094
Wherein the Coriolis acceleration direction is perpendicular to the relative speed of the moving point and points to the positive direction of the Y axis;
the mass of the moving point
Figure 430659DEST_PATH_IMAGE096
Multiplying the Coriolis acceleration to obtain the Coriolis force:
Figure 628291DEST_PATH_IMAGE048
(1)。
3. the method of claim 2, wherein determining a centrifugal force to which the moving point is subjected when moving in the kinetic reference frame comprises:
determining the tangential acceleration of the point of motion
Figure 596247DEST_PATH_IMAGE098
And normal acceleration
Figure 692379DEST_PATH_IMAGE099
Wherein v is the linear velocity of the circular motion of the particles, and the direction and the vector of the normal acceleration
Figure 341666DEST_PATH_IMAGE101
In the same direction;
by
Figure 206854DEST_PATH_IMAGE103
To obtain
Figure 345712DEST_PATH_IMAGE105
Obtaining the centrifugal force:
Figure 116090DEST_PATH_IMAGE052
(2)；
wherein t is time.
4. The method of claim 3, wherein determining a sliding friction force experienced by the moving point while moving in the kinetic reference frame and a reaction force of the target blade to the moving point comprises:
setting the reaction force of the target blade to the moving point to be
Figure 365806DEST_PATH_IMAGE107
Then the sliding friction is
Figure 288763DEST_PATH_IMAGE109
。
5. The method of claim 1, wherein substituting a function of the target blade of the selected type into the target acceleration model to obtain an analytical solution of displacement and velocity of particles in the impact mill comprises:
in the case where the target blade is a linear blade, the shape of the target blade is determinedFunction(s)
Figure 598521DEST_PATH_IMAGE111
Substituting the target acceleration model (12) to obtain:
Figure 669246DEST_PATH_IMAGE113
(13)；
wherein k is the slope of the shape function of the linear blade;
calculating the analytical solution of equation (13) yields:
Figure 912533DEST_PATH_IMAGE115
(14)
Figure 752313DEST_PATH_IMAGE117
(15)；
wherein,
Figure 232973DEST_PATH_IMAGE119
，
Figure 463097DEST_PATH_IMAGE121
and
Figure 320194DEST_PATH_IMAGE123
is the undetermined constant of the differential equation;
taking the boundary condition as
Figure 14481DEST_PATH_IMAGE125
，
Figure 852993DEST_PATH_IMAGE127
Substituting into (14) and (15) to obtain
Figure 898309DEST_PATH_IMAGE129
And
Figure 293518DEST_PATH_IMAGE131
：
Figure DEST_PATH_IMAGE133
Figure DEST_PATH_IMAGE135
；
will be provided with
Figure DEST_PATH_IMAGE137
And
Figure DEST_PATH_IMAGE139
substituting the expressions (14) and (15) into the analytical solution of displacement and velocity of particles in the impact mill:
Figure DEST_PATH_IMAGE141
(16)
Figure DEST_PATH_IMAGE143
(17)。
6. the method of claim 5, wherein optimizing parameters of the corresponding type of the target blade using the analytic solution comprises:
the following treatments were carried out for (16) and (17):
Figure 904628DEST_PATH_IMAGE144
；
get
Figure 992670DEST_PATH_IMAGE146
The above formula is simplified to obtain the speed
Figure 259703DEST_PATH_IMAGE148
About displacement
Figure 645554DEST_PATH_IMAGE150
Expression (c):
Figure 48854DEST_PATH_IMAGE152
(18)；
relating equation (18) to the slope
Figure 307797DEST_PATH_IMAGE154
And (3) calculating a partial derivative to obtain:
Figure 999809DEST_PATH_IMAGE156
；
order to
Figure 736821DEST_PATH_IMAGE158
Then obtain the slope
Figure 260206DEST_PATH_IMAGE160
The optimization interval of (2):
Figure 879931DEST_PATH_IMAGE162
or
Figure 855977DEST_PATH_IMAGE164
。
7. A parameter optimization device for a turbomachine blade, comprising:
the coordinate system establishing module is used for taking a connecting point of the impact mill and a target blade as an origin, taking the tangential direction of the target blade at the connecting point as the x-axis direction, and taking the normal direction of the target blade at the connecting point as the y-axis direction to establish a planar rectangular coordinate system XOY;
a data model establishing module for determining the radius on the plane rectangular coordinate system
Figure 396680DEST_PATH_IMAGE166
The center of the circle of the impact mill
Figure 977834DEST_PATH_IMAGE168
Shape obey function
Figure 313000DEST_PATH_IMAGE170
And the curve of the target blade at the grinding disc and the angular velocity
Figure 41922DEST_PATH_IMAGE172
The mass of the rad/s rotating anticlockwise around the circle center is
Figure 307687DEST_PATH_IMAGE174
The moving point of the particles on the plane rectangular coordinate system
Figure 805664DEST_PATH_IMAGE176
；
A mechanical parameter determining module, configured to determine, using the grinding disc and the target blade as a dynamic reference system, a plurality of mechanical parameters in the dynamic reference system by using the center of the impact mill, the curve of the target blade, and the motion point, where the plurality of mechanical parameters include a relative displacement of the motion point on the dynamic reference system
Figure 311732DEST_PATH_IMAGE178
Dynamic friction factor on the target blade
Figure 465633DEST_PATH_IMAGE180
The moving point and the stationRadius of circle center connecting line of impact mill
Figure 348138DEST_PATH_IMAGE182
The relative speed of the moving point with respect to the moving reference system
Figure 700622DEST_PATH_IMAGE184
The absolute speed of the moving point relative to a fixed reference frame XOY
Figure 830121DEST_PATH_IMAGE186
The velocity of involvement of the dynamic reference frame with respect to the fixed reference frame XOY
Figure 268056DEST_PATH_IMAGE188
And taking the intersection point of the reverse extension line of the speed direction at the moving point and the X axis
Figure 688673DEST_PATH_IMAGE190
When the temperature of the water is higher than the set temperature,
Figure 98926DEST_PATH_IMAGE192
and
Figure 946796DEST_PATH_IMAGE194
angle of (2)
Figure 872027DEST_PATH_IMAGE196
、
Figure 283285DEST_PATH_IMAGE198
And
Figure 610361DEST_PATH_IMAGE200
angle of (2)
Figure 894712DEST_PATH_IMAGE202
、
Figure 244922DEST_PATH_IMAGE204
And
Figure 7342DEST_PATH_IMAGE206
angle of (2)
Figure 188924DEST_PATH_IMAGE208
；
The force analysis module is used for determining the Coriolis force, the centrifugal force, the sliding friction force and the reaction force of the target blade to the moving point when the moving point moves in the moving reference system based on a plurality of mechanical parameters;
the particle acceleration model building module is used for building a target acceleration model of the particles in the impact mill in a plane rectangular coordinate system by utilizing the Coriolis force, the centrifugal force, the sliding friction force, the reaction force and the resultant force of the four forces, and is used for representing the association relation between the velocity displacement component of the particles in the moving reference system along the X coordinate axis and the blade shape function and the blade dynamic friction factor;
the analytic solution calculation module is used for substituting the function of the target blade of the selected type into the target acceleration model to obtain an analytic solution of the displacement and the speed of the particles in the impact mill;
a parameter optimization module for optimizing parameters of the target blade of the corresponding type using the analytic solution;
the particle acceleration model construction module is specifically configured to:
adding the Coriolis force, the centrifugal force, the sliding friction force and the reaction force to obtain a resultant force:
Figure 845775DEST_PATH_IMAGE046
(3)；
wherein:
Figure 745598DEST_PATH_IMAGE048
(1)；
Figure 249392DEST_PATH_IMAGE050
is the Coriolis acceleration;
Figure 285481DEST_PATH_IMAGE052
(2)；
Figure 911635DEST_PATH_IMAGE054
is the normal acceleration;
projecting the formula (3) to the tangential direction of the blade at the moving point to obtain:
Figure 485704DEST_PATH_IMAGE056
(4)；
taking and relative velocity
Figure 589926DEST_PATH_IMAGE058
In the vertical direction of
Figure 746101DEST_PATH_IMAGE060
Then the force of the resultant force is directed
Figure 480839DEST_PATH_IMAGE062
Direction and
Figure 89675DEST_PATH_IMAGE064
and (3) projecting the direction to obtain:
Figure 450118DEST_PATH_IMAGE066
；
substituting the above formula into (4) yields:
Figure 460799DEST_PATH_IMAGE068
(a)；
substituting (1) and (2) into (a) to obtain a second-order differential equation between the relative displacement of the particles on the blade and the blade inclination angle:
Figure 428755DEST_PATH_IMAGE070
(5)；
based on straight lines
Figure 462570DEST_PATH_IMAGE072
And a straight line
Figure 908595DEST_PATH_IMAGE074
The expression (c) expresses the blade pitch angle in terms of coordinate parameters as:
Figure 39362DEST_PATH_IMAGE076
(6)
Figure 178220DEST_PATH_IMAGE078
(7)
Figure 948598DEST_PATH_IMAGE080
(8)；
by
Figure 198314DEST_PATH_IMAGE082
In formula (5):
Figure 121271DEST_PATH_IMAGE084
(9)
Figure 431029DEST_PATH_IMAGE086
(10)；
determining the sagittal diameter of formula (5) by Pythagorean theorem
Figure 501754DEST_PATH_IMAGE088
The following steps of (1):
Figure 745041DEST_PATH_IMAGE090
(11)；
substituting (6), (8), (9), (10) and (11) into (5) to obtain the target acceleration model of the particles in the impact mill under a plane rectangular coordinate system:
Figure 584821DEST_PATH_IMAGE092
(12)。
8. an electronic device comprising a memory, a processor, a communication interface and a communication bus, wherein the memory stores a computer program operable on the processor, and the memory and the processor communicate via the communication bus and the communication interface, wherein the processor implements the steps of the method according to any of the claims 1 to 6 when executing the computer program.
9. A computer-readable medium having non-volatile program code executable by a processor, wherein the program code causes the processor to perform the method of any of claims 1 to 6.
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CN111894681A (en) * 2020-08-06 2020-11-06 长江大学 Turbine blade parametric modeling design method of high-speed turbine drilling tool
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