CN115600367A - Marine gas turbine bearing pair wear analysis method based on real machining surface - Google Patents
Marine gas turbine bearing pair wear analysis method based on real machining surface Download PDFInfo
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Abstract
The invention aims to provide a wear analysis method for a marine gas turbine bearing pair based on a real machined surface, which is characterized in that under the condition of considering the micro-topography parameters of the real machined surface, based on a three-dimensional point contact mixed lubrication model, the physical and topography, rheology, contact mechanics, lubrication mechanics and the like of the coupled surface are coupled, the excitation, geometrical characteristics and the micro-topography parameters of the machined surface under the typical working condition of the bearing pair are comprehensively considered, the calculation convergence and efficiency are improved by utilizing a quasi-system numerical analysis method and three-dimensional fast Fourier transform, the stable oil film pressure is quickly obtained, the real-time lubrication state of the bearing contact pair is coupled by means of an Archard wear theory model, the wear quantity of the bearing contact pair is predicted, and the surface topography of the contact pair is updated. The method can be used for revealing the influence rule of working condition parameters, geometrical structures and micro-topography on the wear profile of the contact pair, and provides theoretical guidance for prediction of the wear profile of the bearing pair of the marine gas turbine and design of bearing tribology.
Description
Technical Field
The invention relates to a friction analysis method, in particular to a wear analysis method for a bearing pair of a marine gas turbine.
Background
The working environment of the gas turbine bearing is harsh, particularly under the working condition of low speed and heavy load, full film lubrication is difficult to establish, local rough peak contact abrasion is brought, the surface appearance change is influenced after the bearing is abraded, and the tribological characteristics of the bearing are influenced by reacting on the lubricating state. At present, the research on the coupling between the mixed lubrication characteristic and the interface wear effect is still rarely carried out for the ship gas turbine rolling bearing, and related research work needs to be continuously and deeply carried out.
Disclosure of Invention
The invention aims to provide a method for analyzing the bearing pair wear of a marine gas turbine based on a real machined surface, which can accurately, efficiently and quantitatively simulate the lubrication characteristics and the wear profile change rule of a marine gas turbine bearing under typical load excitation and severe environment conditions.
The purpose of the invention is realized as follows:
the invention relates to a method for analyzing the wear of a bearing pair of a marine gas turbine based on a real machining surface, which is characterized by comprising the following steps of:
(1) Establishing a geometric model of the marine bearing:
establishing a ball bearing inner ring-rolling body contact geometric model, setting the circumferential direction, the radial direction and the direction vertical to the circumferential direction, the radial direction and the direction as x, z and y axes respectively, and obtaining the x, z and y axes of the rolling body for the rolling body 2j o 2j z 2j And y 2j o 2j z 2j The radius of curvature of the plane is such that,
in the same way, the inner raceway edge x is obtained 2j o 2j z 2j Radius of curvature of plane
And y 2j o 2j z 2j Radius of curvature of plane
The following equations are solved respectively:
in the formula, D W Is the diameter of the rolling element, D m Is the pitch diameter of the ball bearing, equal to the mean diameter of the inner and outer raceways, i.e. D m ＝0.5(D r1 +D r2 ) (ii) a Respectively solving the rolling body and the inner raceway along x 2j And y 2j Equivalent radius of curvature R in the direction x2j And R y2j B, carrying out the following steps of; the rolling body and the inner raceway are converted into an ellipsoid to be contacted with a semi-infinite plane:
(2) Solving the Reynolds equation considering the instantaneous velocity:
after the equivalent work of the contact model is completed, the rotating speed n of the inner ring is known, and the sliding-rolling ratio s of the rolling body to the inner raceway is assumed to be given x2j =0.2, calculating the linear velocity of the rolling body
Linear velocity of inner track
And lubricant along x 2j Direction entrainment velocity u x2j ：
Considering the entrainment speed in the bearing pair operation process, the following three-dimensional point contact mixed lubrication Reynolds equation is adopted to solve the pressure distribution,
in the formula, p 2j Oil film pressure, h 2j Is the oil film thickness, eta is the lubricating oil viscosity, and rho is the lubricating oil density;
(3) Solving the film thickness equation considering the bearing wear:
the abrasion loss generated in the service process of the rolling body and the inner roller way is taken as an additional item of an oil film thickness solving equation to be incorporated into a film thickness equation, the calculation process takes the thickness distribution of a non-abrasion oil film as an initial value to carry out the calculation work of the oil film thickness trend after the bearing abrasion occurs, in addition, the material characteristics of the two surfaces are different to cause different abrasion behaviors, the abrasion loss is calculated separately, the specific form is shown as follows,
w 1 (x 2j ,y 2j t) and w 2 (x 2j ,y 2j And t) is the abrasion loss of the two surfaces of the rolling body and the inner roller way. The solving method follows the Archard law of wear,
w(x 2j ,y 2j ,t)＝k|Δu|/H∫p 2j (x 2j ,y 2j ,t)dt
in the formula, k is a material wear coefficient and is an empirical value, and H is the hardness of the bearing auxiliary material;
(4) Solving a lubrication basis equation considering bearing wear:
when the pressure on the lubricating oil film changes, the intermolecular acting force and the intermolecular distance of the oil film change, the viscosity and the density of the oil film change along with the change, the viscosity and the density of the oil film are regarded as a pressure correlation equation, and the concrete solution is as follows,
the pressure change in the whole ellipse solving domain is integrated to obtain the total load,
(5) Solving the friction coefficient equation considering the non-Newtonian fluid effect:
the friction of the bearing under the mixed lubrication condition comprises fluid shear friction and rough peak contact friction, and the friction force calculation of a fluid lubrication area is carried out by means of a viscoelastic Bair-Winer non-Newtonian fluid rheological model:
in the formula, τ L (Pa) To limit shear stress, G ∞ (Pa) ultimate shear modulus, G is estimated using the Dyson empirical formula ∞ And τ L ：
G ∞ (p 2j ,T 2j )＝1.2p 2j /(2.52+0.024T 2j )-10 -9
τ L (p 2j ,T 2j )＝0.25G ∞
Typical mineral oil shear rates are
And brought into
In the method, a nonlinear equation for solving and calculating the shear stress distribution on any node in the domain is obtained:
the calculation of the interface flash temperature of the rolling body and the inner raceway is based on the theoretical calculation of the heat source rapidly moving on the semi-infinite solid, and a rolling body-inner raceway surface temperature calculation model is established by combining the theory, and is shown as the following formula:
in the formula, T 1 、T 2 Surface temperatures, T, of the rolling body and inner race, respectively b1 、T b2 Initial temperatures of both surfaces, c 1 、c 2 Is the specific heat capacity of the solid, k 1 、k 2 Is the solid heat transfer coefficient, K f Represents the heat conduction coefficient of the lubricating oil, q is the heat generated between the rolling element and the inner raceway in the contact area due to the friction of the roughness peaks or the shearing effect of the lubricant;
the friction force distribution of the bearing contact pair is obtained by integrating the shearing stress in the calculated domain, and the friction coefficient between the rolling body and the contact surface of the inner roller way is obtained by the ratio of the friction force to the contact load:
the material contact of the bearing simulates real working conditions on a friction and wear testing machine to measure the dry friction coefficient, and the shear stress at the dry friction position is solved as follows:
τ＝f contact ·p x2j 。
the invention has the advantages that:
(1) The method for predicting the wear profile of the bearing pair of the gas turbine is established by considering the typical working condition and the geometric characteristics of the bearing of the gas turbine and coupling a three-dimensional mixed lubrication analysis model and an Archard interface wear analysis theory.
(2) The pressure of a lubricating film is increased rapidly and the film thickness is reduced rapidly due to the frequent starting and stopping working conditions of the bearing pair, the severe high-pressure heavy-load working conditions and other factors, and the convergence of the conventional lubricating equation solving method is difficult. The method adopts a quasi-system numerical analysis method to successfully overcome the problems and becomes a potential effective means for analyzing the mixed lubrication performance of the marine bearing pair under the severe contact working condition.
(3) The bearing pair is used as a high-pair part, the oil film shearing stress and the shearing rate are not in direct proportion due to the working condition characteristics of the bearing pair, the error of the friction force is higher by adopting a traditional Newtonian fluid model to solve, and the method is combined with a Bair-Winer non-Newtonian fluid model, so that the problem of the accuracy of the friction force solving caused by the time-varying effect of the heavy load and the roughness of the marine bearing can be effectively solved.
Drawings
Fig. 1a is a contact model of a rolling element and an inner ring, fig. 1b is an equivalent model of the rolling element and the inner ring, fig. 1c is a schematic view of a contact between the rolling element and a concave surface of the inner ring, and fig. 1d is a schematic view of a contact between the rolling element and a convex surface of the inner ring;
FIG. 2 is a schematic diagram of true surface roughness;
FIG. 3a is a friction wear testing machine and a test specimen, FIG. 3b is a friction coefficient verification diagram at different speeds, and FIG. 3c is a friction coefficient verification diagram at different loads;
FIG. 4a is a topograph, FIG. 4b is a schematic diagram of two-dimensional topography sampling of a worn lower test piece, FIG. 4c is a theoretical settlement result of surface evolution of the worn lower test piece, and FIG. 4d is a schematic diagram of a theoretical calculated value of two-dimensional profile distribution after wear;
fig. 5a is a surface contour evolution rule when S =0.2, fig. 5b is a surface contour evolution rule when S =0.4, fig. 5c is a surface contour evolution rule when S =0.6, and fig. 5d is a surface contour evolution rule when S = 0.8.
Detailed Description
The invention is described in more detail below by way of example with reference to the accompanying drawings:
with reference to fig. 1 a-5 d, the invention develops a wear profile prediction method comprehensively considering influence factors such as contact interface wear, elastic deformation, actually measured mechanical surface roughness and the like by taking a certain type of gas turbine ball bearing as a research object and taking a three-dimensional point contact mixed lubrication model as a basis, can realize mixed lubrication and friction-wear state prediction in a service period of a bearing pair, and provides theoretical guidance for gas turbine bearing pair wear profile prediction and bearing tribology optimization design.
The method specifically comprises the following steps:
(1) Marine bearing geometric model establishment
FIG. 1 is a geometric equivalent model of a bearing set, which is formed by taking the contact between a rolling element and an inner raceway as an example, and converting the contact into an ellipsoid and a semi-infinite plane contact model, wherein the rolling element is respectively arranged along x 2j o 2j z 2j Plane and y 2j o 2j z 2j Planar projection, obtained at x 2j o 2j z 2j Radius of curvature R of plane x2j And y 2j o 2j z 2j Radius of curvature R of plane y2j As shown in fig. 1c and d, the solution formula is as follows,
because the inner raceway of the bearing is provided with grooves in shape, the bearing has the advantages thatTo be at x 2j And y 2j The radius of curvature in the direction is different at x 2j o 2j z 2j Radius of curvature of plane
And y 2j o 2j z 2j Radius of curvature of plane
Respectively solving through formulas (2) and (3),
in the formula, D W Is the diameter of the rolling element, D m Is the pitch diameter of the ball bearing, equal to the mean diameter of the inner and outer raceways, i.e. D m ＝0.5(D r1 +D r2 ). Respectively solving the rolling body and the inner raceway along x 2j And y 2j Equivalent radius of curvature R in direction x2j And R y2j So that the rolling elements and inner races are transformed into ellipsoids as shown in fig. 1 (b) to be in contact with semi-infinite plane.
(2) Reynolds equation taking into account instantaneous velocity
After the equivalent work of the contact model is finished, the rotating speed n of the inner ring is known, and the sliding-rolling ratio s of the rolling body to the inner raceway is assumed to be given x2j And =0.2. That is to obtain the rolling element
Linear velocity of inner track
With lubricant along x 2j Direction entrainment velocity u x2j 。
The entrainment speed in the bearing pair operation process is considered, the following three-dimensional point contact mixed lubrication Reynolds equation is adopted,
in the formula, p 2j Oil film pressure, h 2j Is the oil film thickness, η is the lubricant viscosity, and ρ is the lubricant density.
(3) Film thickness equation taking bearing wear into account
And taking the abrasion loss generated in the service process of the rolling body and the inner roller way as an additional term of an oil film thickness solving equation to be incorporated into a film thickness equation. In the calculation process, the thickness distribution of the non-wear oil film is used as an initial value, and the calculation work of the oil film thickness trend after the bearing wear occurs is carried out. Furthermore, the amount of wear of the two surfaces needs to be calculated separately, since the difference in their material properties leads to different wear behaviour, in the following manner,
w 1 (x 2j ,y 2j t) and w 2 (x 2j ,y 2j And t) is the abrasion loss of the two surfaces of the rolling body and the inner roller way. The solving method follows the Archard law of wear,
w(x 2j ,y 2j ,t)＝k|Δu|/H∫p 2j (x 2j ,y 2j ,t)dt (11)
in the formula, k is a material wear coefficient and is an empirical value. H is the hardness of the bearing auxiliary material.
(4) Lubrication foundation equation considering bearing wear
When the pressure on the lubricating oil film changes, the intermolecular force and the intermolecular distance of the oil film change. The viscosity and density of the oil film change accordingly. The calculation model considers the oil film viscosity and the density as a pressure correlation equation, and concretely solves the following,
finally, the pressure change in the whole ellipse solving domain is integrated to obtain the total load,
(5) Friction coefficient equation considering non-Newtonian fluid effects
The bearing friction under the mixed lubrication condition mainly comprises fluid shear friction and rough peak contact friction, wherein the friction force calculation of a fluid lubrication area is realized by means of a viscoelastic Bair-Winer non-Newtonian fluid rheological model.
In the formula, τ L (Pa) is ultimate shear stress, G ∞ (Pa) is the ultimate shear modulus, both of which depend on the rheological properties of the lubricating oil as a function of pressure and temperature, and the lubricating oils used in the calculations herein are typical of mineral oils, so the Dyson's empirical formula can be used to estimate G ∞ And τ L ：
G ∞ (p 2j ,T 2j )＝1.2p 2j /(2.52+0.024T 2j )-10 -9 (16)
τ L (p 2j ,T 2j )＝0.25G ∞ (17)
Typical mineral oil shear rates are
And the obtained solution is brought into the step (15), so that a nonlinear equation for solving the shear stress distribution on any node in the calculated domain can be obtained.
The calculation of the interface flash temperature of the rolling body and the inner raceway is based on the theoretical calculation of the heat source rapidly moving on the semi-infinite solid, and a rolling body-inner raceway surface temperature calculation model is established by combining the theory, and is shown as the following formula:
in the formula, T 1 ，T 2 Surface temperatures, T, of the rolling body and inner race, respectively b1 ，T b2 Initial temperatures of both surfaces, c 1 ，c 2 Is the specific heat capacity of the solid, k 1 ，k 2 Is the solid heat transfer coefficient, K f Representing the heat transfer coefficient of the lubricating oil, q is the heat generated between the rolling elements and the inner race in the contact area due to the friction of the asperities or the shearing effect of the lubricant.
And obtaining the friction force distribution of the bearing contact pair by integrating the shearing stress in the calculated domain, and obtaining the friction coefficient between the rolling body and the contact surface of the inner raceway by the ratio of the friction force to the contact load.
The friction coefficient generated by the contact of the rough peaks is easier to measure, the dry friction coefficient generally fluctuates in a smaller range in engineering practice, and the dry friction coefficient f is common contact The dry friction coefficient can be measured by simulating real working conditions on a friction and wear tester by the material contact of a specific bearing floating in the range of 0.07-0.15, and the shear stress at the dry friction position is solved as follows:
τ＝f contact ·p x2j (21)
examples
In this study, ball-disc tribology characteristic tests were performed to verify the accuracy of the method of the invention, and table 1 gives the relevant parameters for the test verification.
TABLE 1 parameters for the verification of the frictional wear test
Fig. 3b is a graph showing the comparison result between the test and theoretical calculation of the friction coefficient of the surface of the test piece at different rotating speeds under the condition that the load working condition is 20N, the test value and the friction coefficient calculated theoretically both show a decreasing trend along with the increase of the rotating speed, and the theoretical value is smaller than the test value and the error is smaller than 20%. Fig. 3c is a comparison between the test and theoretical results of the surface friction coefficient under different load conditions when the rotation speed condition of the lower test piece tray is 143r/min, and it can be seen from the figure that, with the increase of the load, the friction coefficients of the theoretical calculation and the test show an increasing trend, and a certain error exists between the test value and the theoretical value, which causes the error mainly because: although the influence of the real surface roughness and the mixed lubrication performance on the friction coefficient is comprehensively considered in the calculation method, errors are generated due to the thermal effect of the lubricating oil in an actual test, a sampling interval in the test and the like, the errors are within an allowable range and do not exceed 20%, and the core theoretical model is proved to be feasible.
The topography instrument of FIG. 4a was used to measure the two-dimensional profile of the surface at the sampling location of FIG. 4 b. And analyzed in comparison to FIG. 4d obtained by the simulation method. The maximum error between the two-dimensional maximum wear depth measured by the test and the result obtained by theoretical simulation is within 16%, the theoretical value is slightly smaller than the result measured by the test, and the two-dimensional profile distribution variation trends of the two-dimensional maximum wear depth and the result obtained by theoretical simulation are kept consistent.
In this study, a bearing set of a gas turbine for a ship was studied, and table 2 shows the calculated wear parameters of the bearing set.
TABLE 2 bearing wear calculation parameters
As can be seen from fig. 5, as the slip ratio increases, the amount of material removed from the inner raceway surface increases, and the surface wear marks become more pronounced. The initial stage of abrasion is a running-in abrasion stage, the rough peak shows up-and-down vibration, the running-in abrasion time is shorter along with the increase of the sliding-rolling ratio, and the root mean square deviation of the surface profile is increased along with the increase of the sliding-rolling ratio when the stable abrasion stage is reached. Meanwhile, the increase of the sliding-rolling ratio can shorten the running-in abrasion time of the bearing, so that the bearing enters a stable abrasion stage in advance. The wear channel is gradually deepened, so that the root mean square value of the surface profile of the inner roller way is gradually increased.
Claims (1)
1. A method for analyzing wear of a marine gas turbine bearing pair based on a real machining surface is characterized by comprising the following steps:
(1) Establishing a geometric model of the marine bearing:
establishing a ball bearing inner ring-rolling body contact geometric model, setting the circumferential direction, the radial direction and the direction vertical to the circumferential direction, the radial direction and the direction as x, z and y axes respectively, and obtaining the x, z and y axes of the rolling body for the rolling body 2j o 2j z 2j And y 2j o 2j z 2j The radius of curvature of the plane is,
in the same way, the inner raceway edge x is obtained 2j o 2j z 2j Radius of curvature of plane
And y 2j o 2j z 2j Radius of curvature of plane
The following equations are solved respectively:
in the formula, D W Is the diameter of the rolling element, D m Is the pitch diameter of the ball bearing, equal to the mean diameter of the inner and outer raceways, i.e. D m ＝0.5(D r1 +D r2 ) (ii) a Respectively solving the rolling body and the inner raceway along x 2j And y 2j Equivalent radius of curvature R in direction x2j And R y2j B, carrying out the following steps of; the rolling body and the inner raceway are converted into an ellipsoid to be contacted with a semi-infinite plane:
(2) Solving the Reynolds equation considering the instantaneous velocity:
after the equivalent work of the contact model is finished, the rotating speed n of the inner ring is known, and the sliding of the rolling body and the inner raceway is supposed to be givenRoll ratio s x2j =0.2, calculating the linear velocity of the rolling body
Linear velocity of inner track
And lubricant along x 2j Directional entrainment velocity u x2j ：
Considering the entrainment speed in the bearing pair operation process, the following three-dimensional point contact mixed lubrication Reynolds equation is adopted to solve the pressure distribution,
in the formula, p 2j Oil film pressure, h 2j Is the oil film thickness, eta is the lubricating oil viscosity, and rho is the lubricating oil density;
(3) Solving an equation of film thickness taking bearing wear into account:
the abrasion loss generated in the service process of the rolling body and the inner roller way is taken as an additional item of an oil film thickness solving equation to be incorporated into a film thickness equation, the calculation process takes the thickness distribution of a non-abrasion oil film as an initial value to carry out the calculation work of the oil film thickness trend after the bearing abrasion occurs, in addition, the material characteristics of the two surfaces are different to cause different abrasion behaviors, the abrasion loss is calculated separately, the specific form is shown as follows,
w 1 (x 2j ,y 2j t) and w 2 (x 2j ,y 2j And t) is the abrasion loss of the two surfaces of the rolling body and the inner roller way. The solving method follows the Archard law of wear,
w(x 2j ,y 2j ,t)＝k|Δu|/H∫p 2j (x 2j ,y 2j ,t)dt
in the formula, k is a material wear coefficient and is an empirical value, and H is the hardness of the bearing auxiliary material;
(4) Solving a lubrication basis equation considering bearing wear:
when the pressure of the lubricating oil film changes, the intermolecular acting force and the intermolecular distance of the oil film change, the viscosity and the density of the oil film change along with the change, the viscosity and the density of the oil film are regarded as a pressure correlation equation, and the concrete solution is as follows,
the pressure change in the whole ellipse solving domain is integrated to obtain the total load,
(5) Solving the friction coefficient equation considering the non-Newtonian fluid effect:
the friction of the bearing under the mixed lubrication condition comprises fluid shear friction and rough peak contact friction, and the friction force in a fluid lubrication area is calculated by means of a viscoelastic Bair-Winer non-Newtonian fluid rheological model:
in the formula, τ L (Pa) is ultimate shear stress, G ∞ (Pa) ultimate shear modulus, estimated by the Dyson empirical formula ∞ And τ L ：
G ∞ (p 2j ,T 2j )＝1.2p 2j /(2.52+0.024T 2j )-10 -9
τ L (p 2j ,T 2j )＝0.25G ∞
Typical mineral oil shear rates are
And brought into
In the method, a nonlinear equation for solving the shear stress distribution on any node in the calculated domain is obtained:
the calculation of the interface flash temperature of the rolling body and the inner raceway is based on the theoretical calculation of the heat source rapidly moving on the semi-infinite solid, and a rolling body-inner raceway surface temperature calculation model is established by combining the theory, and is shown as the following formula:
in the formula, T 1 、T 2 Surface temperatures, T, of the rolling bodies and inner race, respectively b1 、T b2 Initial temperatures of both surfaces, c 1 、c 2 Is the specific heat capacity of the solid, k 1 、k 2 Is the solid heat transfer coefficient, K f Denotes the heat conductivity of the lubricating oil, and q is the rolling element and the inner rollerHeat generated between lanes in the contact zone due to asperity friction or lubricant shear effects;
the friction force distribution of the bearing contact pair is obtained by integrating the shearing stress in the calculated domain, and the friction coefficient between the rolling body and the contact surface of the inner roller way is obtained by the ratio of the friction force to the contact load:
the material contact of the bearing simulates real working conditions on a friction and wear testing machine to measure the dry friction coefficient, and the shear stress at the dry friction position is solved as follows:
τ＝f contact ·p x2j 。
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| CN116933510A (en) * | 2023-07-10 | 2023-10-24 | 哈尔滨工业大学 | Prediction analysis method for bearing slip scratch failure behavior |
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