CN116796451A - Dynamic bearing mixed viscoelastic flow lubricating performance calculation method under inclination of journal - Google Patents
Dynamic bearing mixed viscoelastic flow lubricating performance calculation method under inclination of journal Download PDFInfo
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Abstract
The invention discloses a method for calculating the mixed viscoelastic flow lubrication performance of a dynamic bearing under the inclination of a journal, which solves the problem that the mixed lubrication performance of the dynamic bearing is calculated by the traditional method under the inclined working condition of the journal, and the viscoelasticity deformation effect of the bearing is obvious due to the fact that the load is ignored greatly and quickly changed; according to the invention, the oil film cavitation and friction interface surface morphology effect are comprehensively considered, a mass conservation average Reynolds equation is established, then the inclined state of the bearing is represented by adopting two journal inclination angles in the horizontal and vertical directions, the bearing viscoelastic deformation under the action of dynamic load is calculated by utilizing a standard linear solid model, the oil film thickness distribution under the influence of the bearing viscoelastic deformation and the journal inclination is corrected, finally a journal motion equation is established, the journal eccentricity and the eccentric speed are updated by adopting a Newmark method, and the dynamic load bearing mixed viscoelastic flow lubrication performance parameter is calculated iteratively.
Description
Technical Field
The invention belongs to the technical field of dynamic load sliding bearing lubrication performance solving, and particularly relates to a dynamic load bearing mixed viscoelastic flow lubrication performance calculation method under the inclination of a journal.
Background
The coupling system of the shaft and the dynamic load sliding bearing is a key supporting transmission system for ensuring the performance integrity of mechanical equipment and is widely applied to various reciprocating and rotating machines. During actual operation of a dynamic bearing system, the inclination of the journal is unavoidable due to factors such as machining errors, assembly errors, deformation of the shaft under load, etc. The presence of the journal tilt changes the oil film pressure and oil film thickness distribution of the lubricating oil, increases the friction between the bearing and the journal surface, and in severe cases, can exacerbate bearing surface wear and even cause system oscillations.
The dynamic load sliding bearing has smaller eccentricity under the heavy load effect, and is in a mixed lubrication state of oil film, boundary and dry friction for a long time. According to the existing hybrid elastic hydrodynamic lubrication theory for analyzing the lubrication performance of the dynamic load sliding bearing, the thickness distribution of an oil film is corrected by the complete elastic deformation of the surface of the bearing under the action of a high-pressure oil film, and the hybrid lubrication performance of the bearing under the dynamic load is calculated. However, metallic materials have proven to be viscoelastic, and the deformation of the bearing surface upon loading exhibits a viscous and elastic mutual coupling, i.e. a viscoelastic deformation effect. The mixed lubrication performance parameters such as oil film pressure, oil film thickness, rough contact pressure, friction power consumption and end leakage flow are key keys of the lubrication problem of the dynamic sliding bearing, the complete elasticity is used as a bearing compression deformation criterion, initial knocking and rough bumping and grinding characteristics of the bearing in a journal tilting state are easily ignored, the lubrication parameters of the dynamic sliding bearing under severe working conditions are difficult to accurately calculate, the lubrication condition of the bearing is difficult to master, and further the structural optimization design improvement and lubrication performance monitoring of the dynamic sliding bearing are influenced.
Therefore, aiming at the problems that the dynamic bearing mixed viscoelastic flow lubrication characteristic under the inclination of the journal is unknown and the complex coupling physical field numerical analysis still lacks theoretical basis, the invention provides an accurate and efficient numerical calculation method for solving the dynamic bearing mixed viscoelastic flow lubrication performance under the inclination of the journal.
Disclosure of Invention
The invention aims to provide a method for calculating the mixed viscoelastic flow lubrication performance of a dynamic bearing under the inclination of a journal aiming at the viscoelastic deformation effect generated by the compression of the surface of the sliding bearing under the inclination working condition of the journal and dynamic load.
The aim of the invention is achieved by the following technical scheme:
firstly, determining geometric and material parameters of the journal and the bearing and physical parameters of lubricating oil, setting initial eccentricity of the journal, initial eccentric speed, inclination angle of the journal in horizontal direction and vertical direction, and determining oil inlet pressure.
Secondly, comprehensively considering the surface morphology effect of the oil film cavitation and friction interface, establishing a mass conservation average Reynolds equation, discretizing the Reynolds equation by using a finite difference method, and solving the oil film pressure by using an ultra-relaxation iterative algorithm.
And solving the viscoelastic deformation of the bearing surface under the high-pressure oil film by using a standard linear solid model, and constructing a sliding bearing viscoelastic deformation equation at any moment.
And secondly, characterizing the inclination state of the journal by using two journal inclination angles in the horizontal direction and the vertical direction, and establishing the oil film thickness distribution under the correction of the viscoelastic deformation and the journal inclination.
And finally, constructing a journal motion equation by combining the dynamic load, the oil film force and the rough contact force of the sliding bearing, updating the eccentricity and the eccentric speed of the journal, and iteratively calculating the lubricating performance parameters.
The method for calculating the mixed viscoelastic flow lubricating performance of the dynamic bearing under the inclination of the journal is characterized by comprising the following steps of:
first, initial parameters of the dynamic load sliding bearing system are set.
(1) Determining the radius, length, elastic modulus, poisson ratio and physical parameters of lubricating oil of a journal and a bearing of a dynamic load sliding bearing system;
(2) The initial eccentricity and eccentric speed of the journal are set. For a dynamic bearing system, the initial eccentricity is selected to be in the range of 0-c (where c is the radial clearance), and the initial eccentricity speed of the sliding bearing system is set to be 0 at the initial moment.
(3) The inclination of the journal is characterized by adopting inclination angles in the horizontal direction and the vertical direction, and oil inlet pressure is utilized to initialize oil film pressure distribution.
And secondly, establishing a lubrication control equation.
The invention statistically processes the roughness effect and utilizes the pressure flow factor and the shear flow factor to characterize the effect of surface roughness contact on lubrication characteristics. Meanwhile, in order to consider the influence of lubrication film cavitation on lubrication characteristics, a mass conservation average Reynolds equation is established by introducing a fluid fraction theta by using the mass conservation equation.
Wherein p represents oil film pressure, h represents oil film thickness, h T The average oil film thickness is expressed, x is the circumferential direction coordinate, and z is the axial direction coordinate. Phi (phi) x And phi z Respectively representing pressure flow factors in x direction and z direction, phi s Represents the shear flow factor, U represents the journal tangential velocity,is the standard deviation of the comprehensive roughness of the surface of the bearing journal, sigma j Sum sigma b Standard deviation of journal and bearing surface roughness, respectively, t represents time。
μ is the dynamic viscosity of the lubricating oil calculated by adopting a Barus viscosity-pressure equation, and the equation is as follows:
wherein mu 0 The dynamic viscosity of the lubricating oil at normal pressure is shown.
Discretizing the formula (1) by using a second-order center difference format of a finite difference method, and then solving oil film pressure and fluid fraction by using an ultra-relaxation iteration method:
wherein i and j respectively represent the sequence numbers of the circumferential grid nodes and the axial grid nodes, n represents the number of time cycle steps, k represents the number of iterative converging steps,and->Respectively representing the oil film pressure obtained by the kth and the kth-1 iteration of the node (i, j) at the nth time step +.>And->Respectively representing fluid fractions, w, obtained by the nodes (i, j) at the kth and kth-1 iterations of the nth time step p Super relaxation parameter, w, representing oil film pressure θ The superrelaxation parameter is indicative of the fluid fraction.
To ensure that the oil film pressure and fluid fraction converge in the iterative process, the convergence criterion is:
wherein N is 1 And N 2 Respectively represent the number of circumferential and axial nodes ζ p Zeta is the convergence tolerance of oil film pressure θ Is the convergence tolerance of the fluid fraction.
And thirdly, constructing a bearing viscoelasticity deformation equation.
The viscoelastic deformation mechanism of the dynamic sliding bearing under load is characterized by adopting a standard linear solid model, and the equation is as follows:
wherein, delta (x, z, t) represents the actual deformation of the bearing at the current simulation time, delta t (x, z, t) represents the total elastic deformation of the lower bearing at the current simulation time, delta l (x, z, t-Deltat) represents the time-lag deformation of the bearing at the last simulation moment,the full time-lag deformation of the bearing under the oil film pressure p at the last simulation moment is represented, tau represents the viscoelastic relaxation time of the bearing material, q represents the total step number of the simulation time, and Deltat represents the time step.
The complete elastic deformation of the sliding bearing is solved by adopting a Winkler method:
wherein v is b And E is connected with b The poisson ratio and the elastic modulus of the bearing are respectively shown, and l is the thickness of the sliding bearing.
And fourthly, solving the thickness distribution of the oil film.
The thickness of the dynamic load sliding bearing oil film considering bearing clearance, eccentricity, journal inclination and bearing viscoelasticity deformation is as follows:
h＝h 0 +h mis +h v (7)
wherein h is 0 To take into account the oil film thickness component of the radial clearance of the bearing from the journal and the eccentricity of the journal, h mis Oil film thickness component, h, corrected for journal tilt v Is a bearingThe oil film thickness component corrected for viscoelastic deformation, i.e. h v ＝δ(x,z,t)。
h 0 The equation of (2) is as follows:
wherein c is radial clearance, X is the eccentricity of the center of the shaft neck in the X direction, Y is the eccentricity of the center of the shaft neck in the Y direction, Y is the coordinate of the thickness direction of the oil film,is the journal offset angle.
The invention adopts two inclined angles gamma of a horizontal plane and a vertical plane x And gamma is equal to y The journal tilting effect is represented, and an oil film thickness component equation for correcting the journal tilting is obtained according to the geometric position relation of the journal in the bearing hole when the journal tilts.
Wherein R is b The radius of the bearing, and the width of the bearing.
As can be seen from equation (9), when γ x ＝γ y When=0, h mis =0, at which point equation (7) translates to oil film thickness in the journal untilted state.
And fifthly, establishing a journal motion equation.
The lubrication control equation (1) is to update the eccentricity and the eccentric speed iteratively by using the journal motion equation with given initial eccentricity and eccentric speed to correct the oil film thickness and the oil film pressure. The journal centroid is assumed herein to be an effective mass particle and the equation of motion of the journal in a dynamic bearing system is expressed as follows:
wherein m is j Indicating the mass of the journal,and->Respectively represent the eccentric acceleration in the x and y directions, +.>And->Representing the dynamic load acting in x and y directions of the plain bearing system, respectively,/->And->Oil film forces in x and y directions, respectively, ">And->Representing the rough contact forces in the x and y directions, respectively.
In the mixed lubrication state, the oil film pressure and the rough contact pressure respectively form the oil film force and the rough contact force of the bearing, and the oil film force and the rough contact force can be obtained by adopting a complex trapezoidal integral to the pressure:
wherein p is asp Representing the rough contact pressure.
Equation (10) is solved using the newmark method to iteratively calculate the eccentricity of the smallest difference between the outer load and the calculated support load. The convergence criteria used were:
wherein X is n And X is n-1 Respectively represent the eccentricities in the x direction calculated under the time step numbers n and n-1, Y n And Y is equal to n-1 Respectively represent the y-direction eccentricity calculated under the time step numbers n and n-1, ζ X Convergence tolerance, ζ, of X Y Is the convergence tolerance of Y.
And sixthly, calculating the mixed lubrication performance parameter.
The mixed lubrication performance of the dynamic load sliding bearing in the inclined state of the journal comprises inclination moment, friction power consumption and end leakage flow.
For a journal-tilting bearing, the oil film pressure is asymmetric on both sides of the bearing center section. In order to make the bearing work stably, corresponding moment needs to act on the bearing, and the bearing inclination moment components in the x and y directions are as follows:
the tilting moment of the combination is as follows:
friction force F in mixed lubrication state f Viscous friction caused by liquid shearFriction force of asperity contact caused by contacting with asperity peak +.>The two parts are composed of the following expressions:
wherein, κ=0.02 is the boundary friction coefficient, φ f Is the shear flow factor phi fs Is the shear stress factor and phi fp Is a friction pressure flow factor.
φ f 、φ fs And phi fp The following relation is used:
where Λ=h/σ represents the film thickness ratio, g=Λ/3 represents the film thickness judgment index, and e represents the natural constant.
For friction power consumption, equal to the product of friction and tangential velocity.
P f ＝|F f U| (22)
Wherein F is f The calculated friction force for equation (16), U, is the journal tangential velocity.
When the journal inclines, the end leakage flow Q of the front end face and the rear end face of the bearing 1 And Q is equal to 2 Can be calculated as follows:
the total end bleed flow is:
Q＝Q 1 +Q 2 (25)
drawings
FIG. 1A flow chart of the invention
FIG. 2 is a flow chart of a method for calculating the lubricating performance of a mixed viscoelastic flow of a dynamic bearing under the inclination of a journal
FIG. 3 is a schematic view of journal tilting for a dynamic bearing system
FIG. 4 is a graph showing the steady-state distribution of oil film pressure at different neck tilt angles
FIG. 5 is a graph showing the steady-state distribution of the rough contact pressure at different neck tilt angles
FIG. 6 maximum oil film pressure graph at different neck tilt angles
FIG. 7 maximum rough contact pressure graph at different neck tilt angles
FIG. 8 graph of minimum oil film thickness at different neck tilt angles
FIG. 9 is a graph of tilting moment at different neck tilt angles
FIG. 10 is a graph of friction power consumption at different neck tilt angles
FIG. 11 is a graph of lower leakage flow at different neck tilt angles
Detailed Description
For a better understanding of the technical solution of the present invention, the following detailed description of the specific embodiments of the present invention will be given with reference to the accompanying drawings.
FIG. 1 is a flow chart of the present invention. Fig. 2 is a flowchart of a method for calculating the lubrication performance of a sliding bearing, and the method for calculating the lubrication performance of a mixed viscoelastic flow of a dynamic bearing under the inclination of a journal provided by the invention comprises the following steps:
first, initial parameters of the dynamic load sliding bearing system are set.
(1) Determining the radius, length, elastic modulus, poisson ratio and physical parameters of lubricating oil of a journal and a bearing of a dynamic load sliding bearing system;
(2) The initial eccentricity and eccentric speed of the journal are set. For a dynamic bearing system, the initial eccentricity is selected to be in the range of 0-c (where c is the radial clearance), and the initial eccentricity speed of the sliding bearing system is set to be 0 at the initial moment.
(3) Journal tilt is characterized by tilt angles in both the horizontal and vertical directions. In the invention, the oil inlet pressure is 347kPa, and the oil film pressure distribution is initialized according to the oil inlet pressure. Fig. 3 is a schematic view of a journal tilt state of a dynamic bearing system.
And secondly, establishing a lubrication control equation.
The invention statistically processes the roughness effect and utilizes the pressure flow factor and the shear flow factor to characterize the effect of surface roughness contact on lubrication characteristics. Meanwhile, in order to consider the influence of lubrication film cavitation on lubrication characteristics, a mass conservation average Reynolds equation is established by introducing a fluid fraction theta by using the mass conservation equation.
Wherein p represents oil film pressure, h represents oil film thickness, h T The average oil film thickness is expressed, x is the circumferential direction coordinate, and z is the axial direction coordinate. Phi (phi) x And phi z Respectively representing pressure flow factors in x direction and z direction, phi s Represents the shear flow factor, U represents the journal tangential velocity,is the standard deviation of the comprehensive roughness of the surface of the bearing journal, sigma j Sum sigma b The standard deviation of the journal and bearing surface roughness, respectively, and t represents time.
μ is the dynamic viscosity of the lubricating oil calculated by adopting a Barus viscosity-pressure equation, and the equation is as follows:
wherein mu 0 The dynamic viscosity of the lubricating oil at normal pressure is shown.
Discretizing the formula (1) by using a second-order center difference format of a finite difference method, and then solving oil film pressure and fluid fraction by using an ultra-relaxation iteration method:
wherein i and j respectively represent the sequence numbers of the circumferential grid nodes and the axial grid nodes, n represents the number of time cycle steps, k represents the number of iterative converging steps,and->Respectively representing the oil film pressure obtained by the kth and the kth-1 iteration of the node (i, j) at the nth time step +.>And->Respectively representing fluid fractions, w, obtained by the nodes (i, j) at the kth and kth-1 iterations of the nth time step p Super relaxation parameter, w, representing oil film pressure θ The superrelaxation parameter is indicative of the fluid fraction.
To ensure that the oil film pressure and fluid fraction converge in the iterative process, the convergence criterion is:
wherein N is 1 And N 2 Respectively represent the number of circumferential and axial nodes ζ p Zeta is the convergence tolerance of oil film pressure θ Is the convergence tolerance of the fluid fraction. The steady-state distribution of oil film pressure at different neck tilt angles is shown in fig. 4.
And thirdly, constructing a bearing viscoelasticity deformation equation.
The viscoelastic deformation mechanism of the dynamic sliding bearing under load is characterized by adopting a standard linear solid model, and the equation is as follows:
wherein, delta (x, z, t) represents the actual deformation of the bearing at the current simulation time, delta t (x, z, t) represents the total elastic deformation of the lower bearing at the current simulation time, delta l (x, z, t-Deltat) represents the time-lag deformation of the bearing at the last simulation moment,the full time-lag deformation of the bearing under the oil film pressure p at the last simulation moment is represented, tau represents the viscoelastic relaxation time of the bearing material, q represents the total step number of the simulation time, and Deltat represents the time step.
The complete elastic deformation of the sliding bearing is solved by adopting a Winkler method:
wherein v is b And E is connected with b The poisson ratio and the elastic modulus of the bearing are respectively shown, and l is the thickness of the sliding bearing.
And fourthly, solving the thickness distribution of the oil film.
The thickness of the dynamic load sliding bearing oil film considering bearing clearance, eccentricity, journal inclination and bearing viscoelasticity deformation is as follows:
h＝h 0 +h mis +h v (7)
wherein h is 0 To take into account the oil film thickness component of the radial clearance of the bearing from the journal and the eccentricity of the journal, h mis Oil film thickness component, h, corrected for journal tilt v The oil film thickness component corrected for bearing viscoelastic deformation, i.e. h v ＝δ(x,z,t)。
h 0 The equation of (2) is as follows:
wherein c is radial clearance, X is the eccentricity of the center of the shaft neck in the X direction, Y is the eccentricity of the center of the shaft neck in the Y direction, Y is the coordinate of the thickness direction of the oil film,is the journal offset angle.
The invention adopts two inclined angles gamma of a horizontal plane and a vertical plane x And gamma is equal to y The journal tilting effect is represented, and an oil film thickness component equation for correcting the journal tilting is obtained according to the geometric position relation of the journal in the bearing hole when the journal tilts.
Wherein R is b The radius of the bearing, and the width of the bearing.
As can be seen from equation (9), when γ x ＝γ y When=0, h mis =0, at which point equation (7) translates to oil film thickness in the journal untilted state.
And fifthly, establishing a journal motion equation.
The lubrication control equation (1) is to update the eccentricity and the eccentric speed iteratively by using the journal motion equation with given initial eccentricity and eccentric speed to correct the oil film thickness and the oil film pressure. The journal centroid is assumed herein to be an effective mass particle and the equation of motion of the journal in a dynamic bearing system is expressed as follows:
wherein m is j Indicating the mass of the journal,and->Respectively represent the eccentric acceleration in the x and y directions, +.>And->Indicating the x and y directions acting on the plain bearing system, respectivelyDynamic load (I)>And->Oil film forces in x and y directions, respectively, ">And->Representing the rough contact forces in the x and y directions, respectively. FIG. 5 is a steady-state distribution of asperity contact pressure at different neck tilt angles.
In the mixed lubrication state, the oil film pressure and the rough contact pressure respectively form the oil film force and the rough contact force of the bearing, and the oil film force and the rough contact force can be obtained by adopting a complex trapezoidal integral to the pressure:
wherein p is asp Representing the rough contact pressure.
Equation (10) is solved using the newmark method to iteratively calculate the eccentricity of the smallest difference between the outer load and the calculated support load. The convergence criteria used were:
wherein X is n And X is n-1 Respectively represent the eccentricities in the x direction calculated under the time step numbers n and n-1, Y n And Y is equal to n-1 Respectively represent the y-direction eccentricity calculated under the time step numbers n and n-1, ζ X Convergence tolerance, ζ, of X Y Is the convergence tolerance of Y. FIG. 6 shows maximum oil film pressure curve at different neck tilt anglesA wire. Fig. 7 shows the maximum asperity contact pressure curve at different neck tilt angles. Figure 8 shows the minimum oil film thickness curve at different neck tilt angles.
And sixthly, calculating the mixed lubrication performance parameter.
The mixed lubrication performance of the dynamic load sliding bearing in the inclined state of the journal comprises inclination moment, friction power consumption and end leakage flow.
For a journal-tilting bearing, the oil film pressure is asymmetric on both sides of the bearing center section. In order to make the bearing work stably, corresponding moment needs to act on the bearing, and the bearing inclination moment components in the x and y directions are as follows:
the tilting moment is shown in formula (15), and fig. 9 is a graph of tilting moment at different neck tilt angles.
Friction force F in mixed lubrication state f Viscous friction caused by liquid shearFriction force of asperity contact caused by contacting with asperity peak +.>The two parts are composed of the following expressions:
wherein, κ=0.02 is the boundary friction coefficient, φ f Is the shear flow factor phi fs Is the shear stress factor and phi fp Is a friction pressure flow factor. FIG. 10 is a graph of friction power consumption at different neck tilt angles.
φ f 、φ fs And phi fp The following relation is used:
where Λ=h/σ represents the film thickness ratio, g=Λ/3 represents the film thickness judgment index, and e represents the natural constant.
For friction power consumption, equal to the product of friction and tangential velocity.
P f ＝|F f U| (22)
Wherein F is f The calculated friction force for equation (16), U, is the journal tangential velocity.
When the journal inclines, the end leakage flow Q of the front end face and the rear end face of the bearing 1 And Q is equal to 2 Can be calculated as follows:
the total end bleed is shown in equation (25) and fig. 11 is a graph of the lower end bleed for different neck tilt angles.
Q＝Q 1 +Q 2 (25)。
Claims (1)
1. The method for calculating the mixed viscoelastic flow lubricating performance of the dynamic bearing under the inclination of the journal is characterized by comprising the following steps of:
firstly, setting initial parameters of a dynamic load sliding bearing system;
(1) Determining the radius, length, elastic modulus, poisson ratio and physical parameters of lubricating oil of a journal and a bearing of a dynamic load sliding bearing system;
(2) Setting the initial eccentricity and the eccentric speed of the journal; the initial eccentric distance selection range of the dynamic load sliding bearing system is 0-c, wherein c is a radial clearance, and the initial eccentric speed of the sliding bearing system is set to be 0 at the initial moment;
(3) The inclination of the journal is characterized by adopting inclination angles in the horizontal direction and the vertical direction, and oil inlet pressure is utilized to initialize oil film pressure distribution;
secondly, establishing a lubrication control equation;
statistically treating the roughness effect, and characterizing the effect of the surface roughness contact on the lubrication characteristic by using the pressure flow factor and the shear flow factor; meanwhile, in order to consider the influence of lubrication film cavitation on lubrication characteristics, a mass conservation average Reynolds equation is established by introducing a fluid fraction theta by using the mass conservation equation;
wherein p represents oil film pressure, h represents oil film thickness, h T The average oil film thickness is represented, x represents the circumferential direction coordinate, and z represents the axial direction coordinate; phi (phi) x And phi z Respectively representing pressure flow factors in x direction and z direction, phi s Represents the shear flow factor, U represents the journal tangential velocity,is the standard deviation of the comprehensive roughness of the surface of the bearing journal, sigma j Sum sigma b Standard deviation of journal and bearing surface roughness, respectively, when t is expressedA compartment;
μ is the dynamic viscosity of the lubricating oil calculated by adopting a Barus viscosity-pressure equation, and the equation is as follows:
wherein mu 0 Represents the dynamic viscosity of the lubricating oil at normal pressure;
discretizing the formula (1) by using a second-order center difference format of a finite difference method, and then solving oil film pressure and fluid fraction by using an ultra-relaxation iteration method:
wherein i and j respectively represent the sequence numbers of the circumferential grid nodes and the axial grid nodes, n represents the number of time cycle steps, k represents the number of iterative converging steps,and->Respectively representing the oil film pressure obtained by the kth and the kth-1 iteration of the node (i, j) at the nth time step +.>And->Respectively representing fluid fractions, w, obtained by the nodes (i, j) at the kth and kth-1 iterations of the nth time step p Super relaxation parameter, w, representing oil film pressure θ A super relaxation parameter representing a fluid fraction;
to ensure that the oil film pressure and fluid fraction converge in the iterative process, the convergence criterion is:
wherein N is 1 And N 2 Respectively represent the number of circumferential and axial nodes ζ p Zeta is the convergence tolerance of oil film pressure θ Convergence tolerance for fluid fraction;
thirdly, constructing a bearing viscoelasticity deformation equation;
the viscoelastic deformation mechanism of the dynamic sliding bearing under load is characterized by adopting a standard linear solid model, and the equation is as follows:
wherein, delta (x, z, t) represents the actual deformation of the bearing at the current simulation time, delta t (x, z, t) represents the total elastic deformation of the lower bearing at the current simulation time, delta l (x, z, t-Deltat) represents the time-lag deformation of the bearing at the last simulation moment,the method comprises the steps that the complete time-lag deformation of a bearing under the oil film pressure p at the last simulation moment is represented, τ represents the viscoelasticity relaxation time of a bearing material, q represents the total step number of the simulation time, and Deltat represents the time step;
the complete elastic deformation of the sliding bearing is solved by adopting a Winkler method:
wherein v is b And E is connected with b Respectively representing the poisson ratio and the elastic modulus of the bearing, and l represents the thickness of the sliding bearing;
fourthly, solving the thickness distribution of the oil film;
the thickness of the dynamic load sliding bearing oil film considering bearing clearance, eccentricity, journal inclination and bearing viscoelasticity deformation is as follows:
h＝h 0 +h mis +h v (7)
wherein h is 0 To take into account the oil film thickness component of the radial clearance of the bearing from the journal and the eccentricity of the journal, h mis Oil film thickness component, h, corrected for journal tilt v The oil film thickness component corrected for bearing viscoelastic deformation, i.e. h v ＝δ(x,z,t)；
h 0 The equation of (2) is as follows:
wherein c is radial clearance, X is the eccentricity of the center of the shaft neck in the X direction, Y is the eccentricity of the center of the shaft neck in the Y direction, Y is the coordinate of the thickness direction of the oil film,is the journal offset angle;
by two inclination angles gamma of horizontal plane and vertical plane x And gamma is equal to y The journal tilting effect is represented, and an oil film thickness component equation for correcting the journal tilting is obtained according to the geometric position relationship of the journal in the bearing hole when the journal tilts;
wherein R is b The radius of the bearing is the radius of the bearing, and B is the width of the bearing;
as can be seen from equation (9), when γ x ＝γ y When=0, h mis =0, at which point equation (7) translates to oil film thickness in the journal untilted state;
fifthly, establishing a journal motion equation;
the lubrication control equation (1) is to update the eccentricity and the eccentric speed iteratively by using a journal motion equation according to a given initial eccentricity and eccentric speed so as to correct the oil film thickness and the oil film pressure; the journal centroid is assumed herein to be an effective mass particle and the equation of motion of the journal in a dynamic bearing system is expressed as follows:
wherein m is j Indicating the mass of the journal,and->Respectively represent the eccentric acceleration in the x and y directions, +.>And->Representing the dynamic load acting in x and y directions of the plain bearing system, respectively,/->And->Oil film forces in x and y directions, respectively, ">And->The rough contact forces in the x and y directions are shown, respectively;
in the mixed lubrication state, the oil film pressure and the rough contact pressure respectively form the oil film force and the rough contact force of the bearing, and the oil film force and the rough contact force can be obtained by adopting a complex trapezoidal integral to the pressure:
wherein p is asp Represents the rough contact pressure;
solving equation (10) by using a Newmark method to iteratively calculate the eccentricity of the minimum difference between the external load and the calculated support load; the convergence criteria used were:
wherein X is n And X is n-1 Respectively represent the eccentricities in the x direction calculated under the time step numbers n and n-1, Y n And Y is equal to n-1 Respectively represent the y-direction eccentricity calculated under the time step numbers n and n-1, ζ X Convergence tolerance, ζ, of X Y Convergence tolerance for Y;
step six, calculating the mixed lubrication performance parameter;
the mixed lubrication performance of the dynamic load sliding bearing in the inclined state of the journal comprises inclination moment, friction power consumption and end leakage flow;
for a bearing with an inclined journal, oil film pressure on two sides of the central section of the bearing is asymmetric; in order to make the bearing work stably, corresponding moment needs to act on the bearing, and the bearing inclination moment components in the x and y directions are as follows:
the tilting moment of the combination is as follows:
friction force F in mixed lubrication state f Viscous friction caused by liquid shearFriction force of asperity contact caused by contacting with asperity peak +.>The two parts are composed of the following expressions:
wherein, κ=0.02 is the boundary friction coefficient, φ f Is the shear flow factor phi fs Is the shear stress factor and phi fp Is a friction pressure flow factor;
φ f 、φ fs and phi fp The following relation is used:
wherein Λ=h/σ represents a film thickness ratio, g=Λ/3 represents a film thickness judgment index, and e represents a natural constant;
for friction power consumption, equal to the product of friction and tangential velocity;
P f ＝|F f U| (22)
wherein F is f The friction force calculated for equation (16), U is the journal tangential velocity;
when the journal inclines, the end leakage flow Q of the front end face and the rear end face of the bearing 1 And Q is equal to 2 Can be calculated as follows:
the total end bleed flow is:
Q＝Q 1 +Q 2 (25)。
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