CN113343462B - Multi-oil-cavity dynamic and static pressure sliding bearing oil film characteristic simulation method based on high-order isosurface - Google Patents
Multi-oil-cavity dynamic and static pressure sliding bearing oil film characteristic simulation method based on high-order isosurface Download PDFInfo
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Abstract
The method comprises the steps of firstly determining an analysis model of oil film pressure distribution of a multi-oil-cavity feedback dynamic and static sliding bearing based on high-order isostoid multi-oil-cavity dynamic and static sliding bearing, then establishing the high-order isostoic analysis model of oil film pressure distribution of the multi-oil-cavity feedback dynamic and static sliding bearing, then constructing a high-order isostoic calculation model of oil film pressure distribution of the multi-oil-cavity feedback dynamic and static sliding bearing, then constructing a boundary control equation of an analysis layer and a control layer in the bearing, and finally constructing and solving global pressure field distribution information under a complex structure boundary; the invention realizes the high-efficiency analysis of the oil film pressure field of the internal feedback dynamic and static pressure sliding bearing with complex structure and boundary.
Description
Technical Field
The invention belongs to the technical field of dynamic and static pressure bearings, and particularly relates to a multi-oil-cavity dynamic and static pressure sliding bearing oil film characteristic simulation method based on high-order isogeometry.
Background
The sliding bearing is an important part in mechanical equipment, has the advantages of small friction resistance, high efficiency and good vibration absorption performance compared with the rolling bearing, and has wide application; the sliding bearing is divided into a dynamic pressure bearing, a static pressure bearing and a dynamic and static pressure bearing according to the working principle, the static pressure bearing fills viscous working medium into a relatively moving gap by means of the replenishment of an external system so as to form a supported liquid film, but the external system is complex, the control is complicated, factors of medium filtration, pressure compensation, medium and compatibility of working environment need to be considered, and the cost is quite high; the dynamic pressure bearing has poor starting characteristics, and is extremely easy to generate accidents of dry friction, damage and burnout when undergoing three stages of static friction, boundary friction and mixed friction.
The dynamic-static pressure hybrid bearing is a sliding bearing capable of simultaneously working under hydrostatic lubrication and hydrodynamic lubrication, the working principle is that the working principles of the dynamic pressure bearing and the hydrostatic bearing are mixed and overlapped in different operation periods, the bearing is started, normally works to stop swinging, dynamic pressure and static pressure act in different stages to different degrees, and through the use of a hole type oil supply and oil groove shallow cavity structure, the oil film pressure of the bearing is improved, and then the bearing capacity is improved, and the problems of main shaft drift, insufficient oil film rigidity, contact wear of the main shaft and a bearing bush and the like are respectively overcome by utilizing the dynamic-static pressure principle. The calculation of the pressure distribution of a lubricating oil film is a core key of the lubrication problem of the dynamic and static sliding bearing, and how to realize accurate and efficient pressure field solution is an important challenge of the improvement and the innovation design of the complex bearing structure.
However, because the structure and the working mechanism of the internal feedback dynamic and static pressure bearing are very complex, the lack of a high-efficiency and accurate numerical calculation means for the analysis of the coupling fields leads to the improvement of the dynamic and static pressure sliding bearing structure and the difficulty in the step lifting of innovative design, the lack of accurate physical field response leads to the unreliability and the non-optimality of structural design, and a solution method with excessive calculation cost is difficult to be in butt joint with engineering practice, so that a numerical analysis method capable of solving the boundary problem of a complex structure is highly demanded to solve the oil film pressure distribution of the internal feedback dynamic and static pressure sliding bearing efficiently and accurately.
Disclosure of Invention
In order to overcome the defects of the technology, the invention aims to provide a multi-oil-cavity dynamic and static pressure sliding bearing oil film characteristic simulation method based on high-order isogeometry, and the high-efficiency analysis of an internal feedback dynamic and static pressure sliding bearing oil film pressure field with a complex structure and a boundary is realized.
In order to achieve the purpose, the invention adopts the following technical scheme:
a multi-oil-cavity dynamic and static sliding bearing oil film characteristic simulation method based on high-order isosurface comprises the following steps:
1) Determining an analysis model of oil film pressure distribution of the feedback dynamic and static sliding bearing in the multiple oil cavities;
2) Establishing a high-order geometric analysis model of oil film pressure distribution of the feedback dynamic and static sliding bearing in the multiple oil cavities;
3) Constructing a high-order geometric calculation model of oil film pressure distribution of the feedback dynamic and static sliding bearing in the multiple oil cavities;
4) Constructing a boundary control equation of an analysis layer and a control layer in the bearing;
5) And constructing and solving global pressure field distribution information under the boundary of the complex structure.
The step 1) specifically comprises the following steps:
1.1 Importing a geometric model of an internal feedback dynamic-static sliding bearing, defining geometric control coefficients according to the shape of a solving area, realizing the complete envelope of a control point polygon to the solving area, preliminarily selecting discrete interpolation orders according to analysis precision requirements, establishing complete isogeometric analysis node vectors under a parameter coordinate system, constructing a physical field analysis layer, and defining a non-decreasing sequence xi= (ζ) based on the calculation definition of NURBS theory i I=0, 1, m) non-zero shape interpolation basis functions on m), namely, a B spline basis function, and a Cox-de Boor recurrence formula of the B spline basis function is as follows:
wherein B is i,0 And B i,q The method is characterized in that the method is a B spline curve basis function with different orders, q is the basis function order, and ζ is different nodes under a parameter coordinate system;
dividing a physical domain according to the obtained node vector and the shape control point, and obtaining the NURBS basis function expression form in the corresponding low-dimensional space based on the projection of the corresponding B-spline basis function in the high-dimensional space as follows:
wherein R is i,q As a one-dimensional NURBS basis function, B i,q And B j,q The method is characterized in that the method is a B spline curve basis function with different orders, and omega is a transmission projection weight factor;
based on the calculated one-dimensional NURBS basis function, a two-dimensional NURBS basis function is obtained through tensor product expansion, and a NURBS curved surface is constructed as follows:
wherein S is the NURBS curved surface obtained by construction, P i,j Is a coordinate matrix of a two-dimensional control point grid, R i.j As a two-dimensional NURBS basis function, B i.q And B j,w The method is characterized in that the method is a B spline curve basis function with different orders in different directions, q and w are basis function orders, ω is a transmission projection weight factor, and ζ are node vectors in two directions in a parameter domain;
1.2 Building an accurate analysis model of oil film pressure distribution of the feedback dynamic and static sliding bearing in a complex structure:
based on the analysis model initially established according to the geometric configuration in the step 1.1), according to the requirement of solving precision and the restriction of actual computing capacity of a subsequent physical field, the method of inserting or improving the order of the two-dimensional NURBS basis function by adopting the control points in a self-adaptive manner is adopted to refine the analysis model, and the accurate analysis model of the oil film pressure distribution of the feedback dynamic and static sliding bearing in the complex structure is obtained.
The step 2) is specifically as follows: according to the two-dimensional NURBS basis function, the node vector and the control point grid obtained in the step 1), based on an isoparametric transformation idea, a single sixteen-node bilinear unit is adopted to carry out high-order geometric discretization on an analysis domain, and the static pressure distribution field of the oil film of the feedback dynamic-static pressure sliding bearing in a complex structure is constructed by combining the two-dimensional NURBS basis function in the analysis model with physical field information at a corresponding control point; physical analysis Domain Ω ε And a parameter coordinate system Ω e Is interpolated by a method based on a two-dimensional NURBS basis function:
F：Ω e →Ω ε ，
wherein R is i,j Is a double third order NURBS basis function, c ij For controlling the point coordinate grid, ζ and ζ are node coordinates of two directions in the parameter coordinate system, and φ and y are coordinates of two directions in the physical analysis domain, Ω respectively e Is a parameter coordinate system omega ε For the physical analysis domain, F is the coordinate transformation based on the double third order NURBS basis function;
the complete oil film pressure distribution field is obtained by interpolation using the same double third order NURBS basis function and control point physical information:
wherein p is the static pressure distribution field of oil film, d ij Physical information grid for control points.
The step 3) is specifically as follows:
3.1 The static pressure distribution of the oil film of the internal feedback dynamic and static pressure sliding bearing is obtained by solving the Reynolds equation of the oil film, and for the radial internal feedback dynamic and static pressure sliding bearing, the Reynolds equation of the steady and unsteady incompressible oil film is in the strong form as follows:
wherein r is the radius of the journal, phi is the circumferential angular coordinate, y is the axial coordinate, h is the oil film thickness, mu is the lubricating oil viscosity, omega is the angular speed of the journal around the center of the journal, e is the eccentricity of the journal, and theta is the included angle between the eccentric direction and the vertical direction of the journal;
the equivalent integrated weak form of the constant incompressible oil film reynolds equation is derived as follows:
where v is an approximate solution function introduced by the Galerkin method, let:
then the chemical formula (10) is:
based on NURBS and other geometric analysis methods, the following steps:
ν＝R (13)
the approximate solution function is made to be a third-order NURBS basis function;
3.2 Based on the double third-order NURBS basis function and the internal feedback dynamic and static sliding bearing oil film flow weak form control equation obtained in the step 2) isogeometric analysis model, solving the weak form Reynolds equation shown in the step (12) by utilizing a high-order isogeometric analysis technology according to a space mapping Jacobian matrix, performing high-order isogeometric interpolation on the internal feedback dynamic and static sliding bearing pressure field of the complex structure, and obtaining a global borderless pressure distribution calculation linear equation set through deduction:
Kd＝U (14)
wherein K is a generalized stiffness matrix, U is an equivalent control point load vector, d is a control point physical information vector to be solved, and K and U are respectively shown as follows:
wherein JF is a spatially mapped jacobian matrix, d ij For controlling the physical information vector of the point, R l,k And R is i,j For the same set of dual third order NURBS basis functions, F is the coordinate transformation based on the dual third order NURBS basis functions.
The step 4) is specifically as follows: based on formulas (4), (5) and (6), identifying and marking physical positions applied by the boundaries in the analysis layer, and constructing a boundary control point information matrix equation corresponding to the nodes at the boundaries of the analysis layer according to nonlinear corresponding rules of the geometric control grids such as third-order NURBS and the like and the grids of the analysis layer, wherein the equation is as follows:
K (bcdof,freedof) x bcdof ＝b bcdof (17)
wherein K is (bcdof,freedof) Matrix formed by basis functions corresponding to each boundary control point information, x bcdof B, for the physical field information of the boundary control point to be solved bcdof Boundary information vectors formed for boundary conditions;
and (3) solving the boundary control equation shown in the formula (17) to obtain the physical field information of the boundary control point.
The step 5) is specifically as follows: filtering invalid boundary control points based on the boundary control equation obtained in the step 4), and updating boundary control point information vectors:
wherein K is nonzero For the matrix of the basis functions corresponding to the effective boundary control points, x bcdof,nonzero The effective boundary control point information vector;
combining the obtained boundary control point information vector with the non-boundary control point information vector to construct and obtain a global pressure field distribution information vector under the boundary of the complex structure;
wherein x is alldof Is the global pressure field distribution information vector under the boundary of a complex structure, x freedof Is a non-boundary control point information vector, x bcdof And K is a generalized stiffness matrix of the corresponding control point, and b is an equivalent load vector.
The invention has the following beneficial technical results:
the invention realizes the high-order isogeometric solution of the static pressure distribution of the oil film of the radial internal feedback dynamic and static pressure sliding bearing with a complex dynamic and static pressure structure for the first time; the invention does not use a finite element analysis method, so that the introduction error from the beginning of analysis can be eliminated from the source; because the invention uses high-order geometric analysis based on NURBS basis functions, the calculation accuracy is improved, the degree of freedom is reduced, the calculation efficiency is improved, and the solving process is more efficient and accurate; the invention provides a boundary processing method for nonlinear correspondence of an analysis layer and a control layer, so that the correct use of geometric methods such as high order and the like can be ensured, and the pressure field distribution of a complex structure can be solved more accurately.
According to the invention, the static pressure distribution of the oil film of the radial internal feedback dynamic and static pressure sliding bearing is accurately solved, the nonlinear corresponding complex boundary problem when the high-order isogeometry is used is effectively processed, a foundation is provided for continuously solving the dynamic and static characteristic solving problem of the complex radial internal feedback dynamic and static pressure sliding bearing structure, and a design foundation is provided for the high-power complex internal feedback dynamic and static pressure sliding bearing structure design which is not developed at home at present.
Drawings
FIG. 1 is a schematic illustration of an embodiment of an inward feedback hydrostatic bearing structure.
Fig. 2 is a flow chart of the present invention.
FIG. 3 is a schematic view of a portion of a control point and NURBS surface in accordance with an embodiment of the present invention.
Fig. 4 is a schematic diagram of the boundary control situation of the present invention.
Fig. 5 is a schematic diagram of the solution of the oil film thickness according to the embodiment of the invention.
Fig. 6 is a schematic diagram of a solution result of static pressure distribution of an oil film according to an embodiment of the present invention.
Detailed Description
The method can be used for solving the oil film pressure distribution of various internal feedback dynamic and static pressure sliding bearings with complex structures by combining the drawings and the embodiment, and the embodiment adopts a certain type of high-power fast reactor radial internal feedback dynamic and static pressure bearing, as shown in figure 1, wherein the type of fast reactor radial internal feedback dynamic and static pressure bearing has the diameter of 450mm, the total width of 750mm, the unilateral gap of 0.3mm, the feedback cavity wrap angle of 20 degrees, the feedback cavity width of 40mm, the working cavity wrap angle of 11.5 degrees, the working cavity width of 253mm, the rotating speed of 10000rpm, the eccentricity of 0.7 and the lubricating working medium viscosity of 0.01 Pa.s.
Referring to fig. 2, the oil film characteristic simulation method of the multi-oil-cavity dynamic and static sliding bearing based on high-order isosurface comprises the following steps:
1) Determining an analysis model of oil film pressure distribution of the feedback dynamic and static sliding bearing in the multiple oil cavities:
1.1 Importing a geometric model of the feedback dynamic-static sliding bearing in the embodiment, defining geometric control coefficients according to the shape of a solving area, realizing the complete envelope of a control point polygon on the solving area, preliminarily selecting discrete interpolation orders according to analysis precision requirements, establishing complete isogeometric analysis node vectors under a parameter coordinate system, constructing a physical field analysis layer, and defining a non-decreasing sequence xi= (ζ) based on the calculation of NURBS theory i I=0, 1,..m) a non-zero shape interpolation basis function, i.e. the B-spline basis function, the Cox-de Boor recurrence formula for the B-spline basis function is as follows:
wherein B is i,0 And B i,q The method is characterized in that the method is a B spline curve basis function with different orders, q is the basis function order, and ζ is different nodes under a parameter coordinate system;
dividing physical domains according to the node vectors and the shape control points obtained in the previous process, and obtaining NURBS basis function expression forms in the corresponding low-dimensional space based on projection of the corresponding B-spline basis functions in the high-dimensional space as follows:
wherein R is i,q As a one-dimensional NURBS basis function, B i,q And B j,q Is B spline curve basis function of different orders, q is the basis function order, omega is the transmission projection weightA factor;
based on the one-dimensional NURBS basis functions obtained by the calculation, a two-dimensional NURBS basis function is obtained by tensor product expansion and a NURBS curved surface is constructed as follows:
wherein S is the NURBS curved surface obtained by construction, P i,j Is a coordinate matrix of a two-dimensional control point grid, R i.j As a two-dimensional NURBS basis function, B i.q And B j,w The method is characterized in that the method is a B spline curve basis function with different orders in different directions, q and w are basis function orders, ω is a transmission projection weight factor, and ζ are node vectors in two directions in a parameter domain; as shown in fig. 3, it can be seen from fig. 3 that the resulting NURBS surface is enveloped by a control point polygon and is smooth with the same trend as the control point;
1.2 Building an accurate analysis model of oil film pressure distribution of the feedback dynamic and static sliding bearing in the complex structure of the embodiment:
based on the step 1.1), an analysis model of the oil film static pressure distribution of the internal feedback dynamic and static pressure sliding bearing is initially established according to the geometric configuration, and the refinement of the analysis model is realized by adopting a method of inserting control points or improving the two-dimensional NURBS basis function order in a self-adaptive manner according to the requirement of the solution precision of a subsequent physical field and the restriction of the actual computing capacity, so that an accurate analysis model of the oil film pressure distribution of the internal feedback dynamic and static pressure sliding bearing with a complex structure is obtained;
2) Establishing a high-order geometric analysis model of oil film pressure distribution of the feedback dynamic and static sliding bearing in the multiple oil cavities:
according to the two-dimensional NURBS basis function, the node vector and the control point grid obtained in the step 1), based on the principle of equal parameter conversion, a single sixteen-node bilinear unit is adopted to carry out high-order geometric discretization on an analysis domain, and an oil film static pressure distribution field of the feedback dynamic and static pressure sliding bearing in a complex structure is formed by an analysis modelThe two-dimensional NURBS basis function and the physical field information at the corresponding control point are combined and constructed; physical analysis Domain Ω ε And a parameter coordinate system Ω e Is interpolated by a method based on a two-dimensional NURBS basis function:
F：Ω e →Ω ε ，
wherein R is i,j Is a double third order NURBS basis function, c ij For controlling the point coordinate grid, ζ and ζ are node coordinates of two directions in the parameter coordinate system, and φ and y are coordinates of two directions in the physical analysis domain, Ω respectively e Is a parameter coordinate system omega ε For the physical analysis domain, F is the coordinate transformation based on the double third order NURBS basis function;
the complete oil film pressure distribution field is obtained by interpolation using the same double third order NURBS basis function and control point physical information:
wherein p is the static pressure distribution field of oil film, d ij A physical information grid for the control point;
3) Constructing a geometric calculation model of high order of oil film pressure distribution of the feedback dynamic and static sliding bearing in the multiple oil cavities:
3.1 The static pressure distribution of the oil film of the feedback dynamic and static pressure sliding bearing in the embodiment is obtained by solving the Reynolds equation of the oil film, and for the radial feedback dynamic and static pressure sliding bearing, the Reynolds equation of the steady and unsteady incompressible oil film is in the strong form as follows:
wherein r is the radius of the journal, phi is the circumferential angular coordinate, y is the axial coordinate, h is the oil film thickness, mu is the lubricating oil viscosity, omega is the angular speed of the journal around the center of the journal, e is the eccentricity of the journal, and theta is the included angle between the eccentric direction and the vertical direction of the journal;
the equivalent integrated weak form of the constant incompressible oil film reynolds equation is derived as follows:
where v is an approximate solution function introduced by the Galerkin method, let:
then the chemical formula (10) is:
based on NURBS and other geometric analysis methods, the following steps:
ν＝R (13)
the approximate solution function is made to be a third-order NURBS basis function;
3.2 Based on the double third-order NURBS basis function and the internal feedback dynamic and static sliding bearing oil film flow weak form control equation obtained in the step 2) isogeometric analysis model, solving the weak form Reynolds equation shown in the step (12) by utilizing a high-order isogeometric analysis technology according to a space mapping Jacobian matrix, performing high-order isogeometric interpolation on the internal feedback dynamic and static sliding bearing pressure field of the complex structure, and obtaining a global borderless pressure distribution calculation linear equation set through deduction:
Kd＝U (14)
wherein K is a generalized stiffness matrix, U is an equivalent control point load vector, d is a control point physical information vector to be solved, and K and U are respectively shown as follows:
wherein JF is a spatially mapped jacobian matrix, d ij For controlling the physical information vector of the point, R l,k And R is i,j For the same group of double third-order NURBS basis functions, F is coordinate conversion based on the double third-order NURBS basis functions;
4) Constructing a boundary control equation of an analysis layer and a control layer in the bearing:
based on formulas (4), (5) and (6), identifying and marking physical positions applied by the boundaries in the analysis layer, and constructing a boundary control point information matrix equation corresponding to the nodes at the boundaries of the analysis layer according to nonlinear corresponding rules of the geometric control grids such as third-order NURBS and the like and the grids of the analysis layer, wherein the equation is as follows:
K (bcdof,freedof) x bcdof ＝b bcdof (17)
wherein K is (bcdof,freedof) Matrix formed by basis functions corresponding to each boundary control point information, x bcdof B, for the physical field information of the boundary control point to be solved bcdof Boundary information vectors formed for boundary conditions;
constructing and solving the boundary control equation, wherein the schematic diagram of the boundary control situation is shown in fig. 4, and the physical field information of the boundary control point is obtained;
5) Constructing and solving global pressure field distribution information under the boundary of the complex structure of the embodiment:
filtering invalid boundary control points based on the boundary control equation obtained in the step 4), and updating boundary control point information vectors:
wherein K is nonzero For the matrix of the basis functions corresponding to the effective boundary control points, x bcdof,nonzero The effective boundary control point information vector;
combining the obtained boundary control point information vector with the non-boundary control point information vector to construct and obtain a global pressure field distribution information vector under the boundary of the complex structure of the embodiment;
wherein x is alldof Is the global pressure field distribution information vector under the boundary of a complex structure, x freedof Is a non-boundary control point information vector, x bcdof The method is characterized in that the method is a boundary control point information vector, K is a generalized stiffness matrix of a corresponding control point, and b is an equivalent load vector; referring to fig. 5, fig. 5 is a solution result of the thickness of the oil film of the feedback dynamic and static sliding bearing in the embodiment, and it can be seen from fig. 5 that the oil film thickness has a minimum value and is distributed from large to small and then is enlarged, so that the oil film thickness accords with the condition of the oil film in the actual bearing; referring to fig. 6, fig. 6 is a solution result of oil film static pressure distribution of the feedback dynamic and static pressure sliding bearing in the embodiment, and it can be seen from fig. 6 that two groups of oil cavity structures and two groups of forced boundary conditions are correctly reflected in the result, so as to meet the expected result.
Claims (2)
1. The oil film characteristic simulation method for the multi-oil-cavity dynamic and static sliding bearing based on high-order isosurface is characterized by comprising the following steps of:
1) Determining an analysis model of oil film pressure distribution of the feedback dynamic and static sliding bearing in the multiple oil cavities;
2) Establishing a high-order geometric analysis model of oil film pressure distribution of the feedback dynamic and static sliding bearing in the multiple oil cavities;
3) Constructing a high-order geometric calculation model of oil film pressure distribution of the feedback dynamic and static sliding bearing in the multiple oil cavities;
4) Constructing a boundary control equation of an analysis layer and a control layer in the bearing;
5) Constructing and solving global pressure field distribution information under the boundary of the complex structure;
the step 1) specifically comprises the following steps: 1.1 Importing a geometric model of an internal feedback dynamic-static sliding bearing, defining geometric control coefficients according to the shape of a solving area, realizing the complete envelope of a control point polygon to the solving area, preliminarily selecting discrete interpolation orders according to analysis precision requirements, establishing complete isogeometric analysis node vectors under a parameter coordinate system, constructing a physical field analysis layer, and defining a non-decreasing sequence xi= (ζ) based on the calculation definition of NURBS theory i I=0, 1,..m) a non-zero shape interpolation basis function, i.e. the B-spline basis function, the Cox-de Boor recurrence formula for the B-spline basis function is as follows:
wherein B is i,0 And B i,q The method is characterized in that the method is a B spline curve basis function with different orders, q is the basis function order, and ζ is different nodes under a parameter coordinate system;
dividing a physical domain according to the obtained node vector and the shape control point, and obtaining the NURBS basis function expression form in the corresponding low-dimensional space based on the projection of the corresponding B-spline basis function in the high-dimensional space as follows:
wherein R is i,q As a one-dimensional NURBS basis function, B i,q And B j,q The method is characterized in that the method is a B spline curve basis function with different orders, and omega is a transmission projection weight factor;
based on the calculated one-dimensional NURBS basis function, a two-dimensional NURBS basis function is obtained through tensor product expansion, and a NURBS curved surface is constructed as follows:
wherein S is the NURBS curved surface obtained by construction, P i,j Is a coordinate matrix of a two-dimensional control point grid, R i.j As a two-dimensional NURBS basis function, B i.q And B j,w The method is characterized in that the method is a B spline curve basis function with different orders in different directions, q and w are basis function orders, ω is a transmission projection weight factor, and ζ are node vectors in two directions in a parameter domain;
1.2 Building an accurate analysis model of oil film pressure distribution of the feedback dynamic and static sliding bearing in a complex structure:
based on the analysis model initially established according to the geometric configuration in the step 1.1), according to the requirement of solving precision and the restriction of actual computing capacity of a subsequent physical field, the method of inserting or improving the two-dimensional NURBS basis function order by adopting control points in a self-adaptive manner is adopted to refine the analysis model, and an accurate analysis model of the oil film pressure distribution of the feedback dynamic and static sliding bearing in a complex structure is obtained;
the step 2) is specifically as follows: according to the two-dimensional NURBS basis function, the node vector and the control point grid obtained in the step 1), based on an isoparametric transformation idea, a single sixteen-node bilinear unit is adopted to carry out high-order geometric discretization on an analysis domain, and the static pressure distribution field of the oil film of the feedback dynamic-static pressure sliding bearing in a complex structure is constructed by combining the two-dimensional NURBS basis function in the analysis model with physical field information at a corresponding control point; physical analysis Domain Ω ε And a parameter coordinate system Ω e Is interpolated by a method based on a two-dimensional NURBS basis function:
wherein R is i,j Is a double third order NURBS basis function, c ij For controlling the point coordinate grid, ζ and ζ are node coordinates of two directions in the parameter coordinate system, and φ and y are coordinates of two directions in the physical analysis domain, Ω respectively e Is a parameter coordinate system omega ε For the physical analysis domain, F is the coordinate transformation based on the double third order NURBS basis function;
the complete oil film pressure distribution field is obtained by interpolation using the same double third order NURBS basis function and control point physical information:
wherein p is the static pressure distribution field of oil film, d ij A physical information grid for the control point;
the step 3) is specifically as follows:
3.1 The static pressure distribution of the oil film of the internal feedback dynamic and static pressure sliding bearing is obtained by solving the Reynolds equation of the oil film, and for the radial internal feedback dynamic and static pressure sliding bearing, the Reynolds equation of the steady and unsteady incompressible oil film is in the strong form as follows:
wherein r is the radius of the journal, phi is the circumferential angular coordinate, y is the axial coordinate, h is the oil film thickness, mu is the lubricating oil viscosity, omega is the angular speed of the journal around the center of the journal, e is the eccentricity of the journal, and theta is the included angle between the eccentric direction and the vertical direction of the journal;
the equivalent integrated weak form of the constant incompressible oil film reynolds equation is derived as follows:
where v is an approximate solution function introduced by the Galerkin method, let:
then the chemical formula (10) is:
based on NURBS and other geometric analysis methods, the following steps:
ν＝R (13)
the approximate solution function is made to be a third-order NURBS basis function;
3.2 Based on the double third-order NURBS basis function and the internal feedback dynamic and static sliding bearing oil film flow weak form control equation obtained in the step 2) isogeometric analysis model, solving the weak form Reynolds equation shown in the step (12) by utilizing a high-order isogeometric analysis technology according to a space mapping Jacobian matrix, performing high-order isogeometric interpolation on the internal feedback dynamic and static sliding bearing pressure field of the complex structure, and obtaining a global borderless pressure distribution calculation linear equation set through deduction:
Kd＝U (14)
wherein K is a generalized stiffness matrix, U is an equivalent control point load vector, d is a control point physical information vector to be solved, and K and U are respectively shown as follows:
wherein JF is a spatially mapped jacobian matrix, d ij For controlling the physical information vector of the point, R l,k And R is i,j For the same group of double third-order NURBS basis functions, F is coordinate conversion based on the double third-order NURBS basis functions;
the step 4) is specifically as follows: based on formulas (4), (5) and (6), identifying and marking physical positions applied by the boundaries in the analysis layer, and constructing a boundary control point information matrix equation corresponding to the nodes at the boundaries of the analysis layer according to nonlinear corresponding rules of the geometric control grids such as third-order NURBS and the like and the grids of the analysis layer, wherein the equation is as follows:
K (bcdof,freedof) x bcdof ＝b bcdof (17)
wherein K is (bcdof,freedof) Matrix formed by basis functions corresponding to each boundary control point information, x bcdof B, for the physical field information of the boundary control point to be solved bcdof Boundary information vectors formed for boundary conditions;
and (3) solving the boundary control equation shown in the formula (17) to obtain the physical field information of the boundary control point.
2. The method for simulating the oil film characteristics of the multi-oil-cavity dynamic-static sliding bearing based on high-order isogeometry according to claim 1, wherein the step 5) is specifically: filtering invalid boundary control points based on the boundary control equation obtained in the step 4), and updating boundary control point information vectors:
wherein K is nonzero For the matrix of the basis functions corresponding to the effective boundary control points, x bcdof,nonzero The effective boundary control point information vector;
combining the obtained boundary control point information vector with the non-boundary control point information vector to construct and obtain a global pressure field distribution information vector under the boundary of the complex structure;
wherein x is alldof Is the global pressure field distribution information vector under the boundary of a complex structure, x freedof Is a non-boundary control point information vector, x bcdof And K is a generalized stiffness matrix of the corresponding control point, and b is an equivalent load vector.
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