CN115659490A - Gas turbine bearing gluing failure prediction method considering real surface roughness - Google Patents
Gas turbine bearing gluing failure prediction method considering real surface roughness Download PDFInfo
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Abstract
The invention provides a method for predicting the bonding failure of a gas turbine bearing by considering real surface roughness, which is characterized in that the typical working condition and the geometric characteristics of the gas turbine bearing are considered, a three-dimensional mixed lubrication analysis model and a second class Volterra integral equation are coupled, and a method for predicting the bonding failure of a gas turbine bearing pair is established; the mixed lubrication equation solving method considering the multi-factor comprehensive effect considers the real surface roughness, the non-Newtonian characteristic of lubricating oil and the specific structure and service working condition of the ship bearing, can realize the prediction of the whole lubricating state from full-film lubrication, mixed lubrication, boundary lubrication to dry contact, and can guide the optimization design of the bearing structure from the aspect of failure (abrasion, gluing and the like).
Description
Technical Field
The invention belongs to the field of tribology of ship power devices, and particularly relates to a method for predicting the gluing failure of a gas turbine bearing by considering real surface roughness.
Background
The gas turbine ball bearing is in a mixed lubrication state under severe working conditions of high speed, heavy load, high temperature and the like, a rolling body and a rolling path of the gas turbine ball bearing can generate local rough peak contact and relative slip aggravate friction phenomena under the mixed lubrication condition, heat is generated by friction, temperature distribution is influenced, even bearing high-temperature gluing failure occurs, the temperature influences shear modulus, the friction and the temperature are reacted to generate a friction-temperature mutual coupling effect, and at present, friction-flash temperature coupling research under the mixed lubrication condition is still rarely carried out on the ship gas turbine rolling bearing. By taking a Block gluing failure judgment criterion as a basis, the bearing pair gluing failure position can be predicted according to the flash temperature change rule of the bearing rolling element and the inner raceway in a lubrication-contact state, the gluing failure forming mechanism is revealed, and theoretical guidance is provided for effectively preventing the bearing from gluing failure in the service process.
Disclosure of Invention
In view of the above, the invention aims to provide a method for predicting the bonding failure of a gas turbine bearing by considering real surface roughness, which can accurately and efficiently simulate the lubricating property and the friction flash temperature change process caused by the typical harsh working conditions of a marine bearing, such as complicated load excitation, high-frequency variable working conditions, overlong service duration and the like, so as to accurately predict the bonding failure caused by the overhigh flash temperature of the contact pair interface of the bearing.
A method for predicting the gluing failure of a gas turbine bearing by considering the real surface roughness comprises the following steps:
taking the circumferential direction of the inner ring raceway as x 2j Shaft, radial of inner race 2j Axis, perpendicular to the circumferential and radial directions, y 2j The center of mass of the shaft and the bearing is the origin o of the coordinate system 2j Establishing a rectangular coordinate system; x obtained after the rolling body completes the geometric equivalence 2j o 2j z 2j Plane curveRadius of curvature
And y 2j o 2j z 2j Radius of curvature of plane
The same is that:
inner raceway by the above analysis along x 2j o 2j z 2j Radius of curvature of plane
And y 2j o 2j z 2j Radius of curvature of plane
Respectively as follows:
in the formula, D W Is the diameter of the rolling element, D m Is the pitch diameter, alpha, of the ball bearing 2j The initial contact angle of the bearing being equal to the mean diameter of the inner and outer raceways, i.e. D m ＝0.5(D r1 +D r2 )，f i The curvature coefficients of the inner and outer channels;
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 ：
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 which t represents a time variable, p 2j (x 2j ,y 2j ) Is oil film pressure, h is oil film thickness, η is lube viscosity, ρ is lube density, u is lube oil viscosity x2j Is rolling and inner raceway edge x 2j The entrainment speed in the axial direction;
the specific form of the oil film thickness equation considering the true surface roughness is as follows:
in the formula, v e (x 2j ,y 2j T) is the elastic deformation between the contact pairs, E' is the equivalent elastic modulus between the bearing pairs, delta 1 (x 2j ,y 2j T) and delta 2 (x 2j ,y 2j T) true roughness of the rolling body and inner raceway surface, h 0 (t) represents the normal approach between the rolling elements and the inner raceway,
describing the equivalent rear ellipsoid geometry of the rolling body and the inner raceway, R x2j And R y2j Through step 2, xi and
for a computing node at x 2j Axes and y 2j Coordinates of the axes, Ω denotes a solution area;
oil film viscosity and density were considered as pressure related equations:
η 0 and rho 0 Respectively representing the environmental viscosity and the environmental density, wherein alpha is the viscosity-pressure coefficient of the lubricating oil;
step 5, considering a friction-flash temperature equation of the non-Newtonian fluid effect:
the friction of the bearing under the mixed lubrication condition mainly comprises fluid shear friction and rough peak contact friction, wherein the friction force of a fluid lubrication area is calculated by means of a viscoelastic Bair-Winer non-Newtonian fluid rheological model:
in the formula, τ L In order to limit the shear stress,
as derivative of shear stress, G ∞ Is the ultimate shear modulus, both of which are a function of pressure and temperature depending on the rheological properties of the lubricating oil,
shear rate of
Wherein the linear velocity of the rolling body is
Inner raceway linear velocity is expressed as
And substituting the obtained product into a formula (12) to obtain the solution of the shear stress tau on any node in the calculated domain fluid Non-linear equation of distribution:
the shear stress at dry friction is solved as follows:
τ contact ＝f contact ·p x2j (x 2j ,y 2j ) (15)
f contact represents a dry friction coefficient;
final bearing overall shear stress τ total Comprises the following steps:
τ total ＝τ contact +τ fluid (16)
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 raceway is obtained by the ratio of the friction force to the contact load:
dividing the generated heat into two parts according to a set heat distribution coefficient A:
meanwhile, calculating the lubricating local speed distribution and the temperature change curve under the condition of sliding according to the research result of Plint, determining the heat distribution coefficient between the rolling body and the inner roller way and obtaining:
in the formula, T 1 ，T 2 Surface temperatures of the rolling elements and inner race, K f Represents the heat conduction coefficient of the lubricating oil;
the calculation of the flash temperature of the interface of the rolling body and the inner raceway is based on the theoretical calculation of the heat source which moves rapidly on the semi-infinite solid, a rolling body-inner raceway surface temperature calculation model is established by combining the theory, and based on the theory, a second class of Volterra integral equation is expressed as follows:
in the formula, T b1 ，T b2 Initial temperatures of the rolling elements and inner raceway surface, C 1 And C 2 Is the specific heat capacity of the solid, k 1 ，k 2 Coefficient of thermal conductivity, p, of rolling bodies and inner races 1 ,ρ 2 The density of the rolling body and the inner raceway is respectively, the surface of the rolling body and the surface of the inner raceway are respectively arranged along x 2j The axis is divided into grids, lambda represents any one of the grids, T 1 (lambda) and T 2 (λ) represents the temperature of the rolling elements and inner raceway surface, respectively, at the grid λ; q (λ) represents the heat at grid λ; lambda belongs to (-x) 2j Xi), xi is x corresponding to the end state temperature rise 2j Axis coordinates;
the gluing failure judgment formula is as follows:
T b +T fm ≤T sc (21)
wherein, T sc Critical temperature for gluing, temperature rise T of contact pair interface fm ＝T 1 /T 2 ；
T in the formula (21) when judging whether the rolling bodies are bonded and failed b Replacement by initial temperature T of rolling body 1b Judging whether the formula is invalid or not according to the formula; t in the formula (21) when judging whether the inner raceway is in failure of bonding b Replacement by inner race initial temperature T 2b And judging whether the failure occurs or not according to the formula.
Preferably, the following steps:
G ∞ ＝1.2p 2j (x 2j ,y 2j )/(2.52+0.024T 2 )-10 -9 (12)
τ L ＝0.25G ∞ (13)
preferably, the following steps: coefficient of dry friction f contact The value range is 0.07-0.15.
The invention has the following beneficial effects:
the invention provides a method for predicting the bonding failure of a gas turbine bearing by considering real surface roughness, which is characterized in that a three-dimensional mixed lubrication analysis model and a second class Volterra integral equation are coupled by considering the typical working conditions and the geometric characteristics of the gas turbine bearing, and a method for predicting the bonding failure of a gas turbine bearing pair is established; the mixed lubrication equation solving method considering the multi-factor comprehensive effect considers the real surface roughness, the non-Newtonian characteristic of lubricating oil and the specific structure and service working condition of the ship bearing, can realize the prediction of the whole lubricating state from full-film lubrication, mixed lubrication, boundary lubrication to dry contact, and can guide the optimization design of the bearing structure from the aspect of failure (abrasion, gluing and the like).
Drawings
FIG. 1 is an equivalent diagram of a bearing rolling element and inner raceway lubrication model adopted by the invention;
fig. 2 (a) is a temperature rise diagram of a three-dimensional inner raceway of a grinding surface, fig. 2 (b) is a temperature rise diagram of a three-dimensional inner raceway of a honing surface, fig. 2 (c) is a temperature rise diagram of a three-dimensional inner raceway of a shaving surface, and fig. 2 (d) is a temperature rise diagram of a three-dimensional inner raceway of a polishing surface;
FIG. 3 is a graph of the coefficient of friction and lubrication solution trend for a true surface roughness as employed in the present invention;
4 (a) and 4 (b) maximum temperature rise graphs of the surface of the rolling body and the surface of the inner roller under different load conditions;
fig. 5 (a) and 5 (b) are graphs of oil film pressure and oil film thickness variation trends at different entrainment speeds, respectively.
Detailed Description
The invention is described in detail below by way of example with reference to the accompanying drawings.
The invention provides a bearing interface lubrication-flash temperature coupling analysis method for a marine gas turbine, which is based on the consideration of an actually measured real surface roughness and point contact mixed lubrication model, the consideration of three-dimensional surface morphology parameters of high speed, heavy load, large size and real surface roughness of a marine bearing pair, the utilization of a second class of Volterra integral equation and a fast moving heat source theory to obtain transient temperature rise distribution between contact pairs, the Blok flash temperature criterion is used as a gluing criterion, the interface temperature rise influences the friction-lubrication characteristic of the bearing pair by influencing the ultimate shear modulus and ultimate shear stress of lubricating oil, and the heat generation of friction is reflected in the temperature between the contact pairs, so that the friction and the temperature rise influence each other. Finally, a bearing lubrication-flash temperature coupling analysis method is formed, the influence rule of parameters such as working conditions, geometry and morphology textures on friction coefficient and flash temperature distribution can be revealed, theoretical guidance is provided for transient temperature rise prediction of a marine gas turbine bearing pair and bearing structure design, and the specific technical scheme is as follows:
FIG. 1 shows an established geometric model of the inner ring-rolling element contact of a ball bearing, which can be converted into a contact model of an ellipsoid and a semi-infinite plane, taking the contact of the rolling element and an inner raceway as an example, and the contact model is x along the circumferential direction of the inner raceway 2j Shaft, radial of inner race 2j Axis, perpendicular to the circumferential and radial directions, y 2j The center of mass of the shaft and the bearing is the origin o of the coordinate system 2j Establishing a rectangular coordinate system; x obtained after the rolling body completes the geometric equivalence 2j o 2j z 2j Radius of curvature of plane
And y 2j o 2j z 2j Radius of curvature of plane
The same is that:
inner raceway is followed by the above analysis x 2j o 2j z 2j Radius of curvature of plane
And y 2j o 2j z 2j Radius of curvature of plane
Respectively as follows:
in the formula, D W Is the diameter of the rolling element, D m Is the pitch diameter, alpha, of the ball bearing 2j The initial contact angle of the bearing being equal to the mean diameter of the inner and outer raceways, i.e. D m ＝0.5(D r1 +D r2 )，f i The curvature coefficients of the inner and outer channels.
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 So that the rolling elements and inner raceway are transformed into ellipsoids shown in fig. 2 to be in contact with a semi-infinite plane:
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, t represents a time variable, p 2j (x 2j ,y 2j ) Is oil film pressure, h is oil film thickness, η is lube viscosity, ρ is lube density, u is lube oil viscosity x2j Is rolling and inner raceway edge x 2j The sucking speed in the axial direction.
For a bearing pair, transient real surface roughness is an important factor influencing the contact film thickness, and the specific form of an oil film thickness equation considering the real surface roughness is as follows:
in the formula, v e (x 2j ,y 2j T) elastic deformation between contact pairs, E' equivalent modulus of elasticity between bearing pairs, delta 1 (x 2j ,y 2j T) and delta 2 (x 2j ,y 2j T) true roughness of the rolling body and inner raceway surface, h 0 (t) represents the normal approach between the rolling elements and the inner raceway,
describing the equivalent rear ellipsoid geometry of the rolling body and the inner raceway, R x2j And R y2j Through step 2, xi and
for a computing node at x 2j Axes and y 2j The coordinates of the axes, Ω, represent the solution area.
When the pressure on the lubricating oil film changes, the intermolecular force and the intermolecular distance of the oil film change, so that the viscosity and the density of the oil film change. The calculation model of the invention considers the oil film viscosity and the density as a pressure correlation equation, and concretely solves the following steps:
η 0 and rho 0 Respectively, the environmental viscosity and the environmental density, and alpha is the viscosity-pressure coefficient of the lubricating oil.
Step 5, considering friction-flash temperature equation of non-Newtonian fluid effect
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 In order to limit the shear stress,
derivative of shear stress, G ∞ The lubricating oil used in the calculation of the invention is typically a mineral oil, so that the Dyson empirical formula can be used to estimate G, both of which depend on the rheological properties of the lubricating oil as a function of pressure and temperature ∞ And τ L ：
G ∞ ＝1.2p 2j (x 2j ,y 2j )/(2.52+0.024T 2 )-10 -9 (12)
τ L ＝0.25G ∞ (13)
Typical mineThe shear rate of the crude oil is
Wherein the linear velocity of the rolling body is
Inner raceway linear velocity is expressed as
And substituting the obtained product into a formula (12) to obtain the shear stress tau on any node in the solved and calculated domain fluid A non-linear equation of distribution.
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 contact ＝f contact ·p x2j (x 2j ,y 2j ) (15)
final bearing overall shear stress τ total Comprises the following steps:
τ total ＝τ contact +τ fluid (16)
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 roller way according to the ratio of the friction force to the contact load.
The friction and the heat are interdependent, and the heat generated in the working process of the ball bearing is mainly transferred out through the flow of lubricating oil and the heat conduction between the rolling body and the inner raceway and the environment. Based on Francis's research results, the amount of heat generated can be divided into two parts according to the heat distribution coefficient a:
meanwhile, the lubrication local speed distribution and the temperature change curve under the sliding condition are calculated according to the research result of Plint, the heat distribution coefficient between the rolling body and the inner roller way is determined, and the following results are obtained:
in the formula, T 1 ，T 2 Surface temperatures of the rolling elements and inner race, K f Represents the heat transfer coefficient of the lubricating oil.
The calculation of the flash temperature of the interface of the rolling body and the inner raceway is based on the theoretical calculation of the heat source which moves rapidly on the semi-infinite solid, a rolling body-inner raceway surface temperature calculation model is established by combining the theory, and based on the theory, a second class of Volterra integral equation is expressed as follows:
in the formula, T b1 ，T b2 Initial temperatures of the rolling elements and inner raceway surface, C 1 And C 2 Is the specific heat capacity of the solid, k 1 ，k 2 Coefficient of thermal conductivity, p, of rolling bodies and inner races 1 ,ρ 2 The density of the rolling body and the inner raceway is respectively, q is the heat generated between the rolling body and the inner raceway in a contact area due to the friction of a rough peak or the shearing effect of a lubricant, and the surfaces of the rolling body and the inner raceway are respectively arranged along x 2j The axis is divided into grids, lambda represents any one of the grids, T 1 (lambda) and T 2 (λ) represents the temperature of the rolling elements and inner raceway surface, respectively, at grid λ; q (λ) represents the heat at grid λ;λ∈(-x 2j xi), xi is x corresponding to the end state temperature rise 2j The axis coordinate, h is the oil film thickness, is found by step 2.
The instantaneous temperature criterion proposed by Blok is that the generation of the gluing is caused by the fact that the local instantaneous temperature of the surface reaches a critical value, and is the only gluing failure judgment principle which is currently subjected to ISO certification.
T b +T fm ≤T sc (21)
Wherein, T sc Critical temperature for gluing, temperature rise T of contact pair interface fm ＝T 1 /T 2 。
T in the formula (21) when judging whether the rolling bodies are bonded and failed b Replacement by initial temperature T of rolling body 1b Judging whether the formula is invalid or not according to the formula; t in the formula (21) when judging whether the inner raceway is in failure of bonding b Replacement by inner race initial temperature T 2b And judging whether the failure occurs according to the formula.
Example (b):
in the embodiment, a certain type of gas turbine ball bearing is taken as a research object, the operating parameters of a bearing pair are given in table 1, and a bearing lubrication-flash temperature prediction method comprehensively considering influence factors such as contact interface flash temperature, elastic deformation and actually measured mechanical surface roughness is developed on the basis of a three-dimensional point contact mixed lubrication model, so that mixed lubrication and rolling element and inner roller transient temperature rise state prediction in a service period of the bearing pair can be realized, and theoretical guidance is provided for gas turbine bearing pair gluing failure prediction and bearing structure optimization design.
TABLE 1 bearing set running parameters
In fig. 2, the influence of the real rough surface on the temperature rise of the gas turbine ball bearing interface under four different processing technologies is known, under the same working condition, the area of a high-temperature area and the peak value of the temperature rise generated by shaving the inner raceway of the rough surface are far larger than those of the other three rough surfaces, the maximum temperature rise of the inner raceway under the rough polishing condition is 63.6 ℃ lower than that of a flash point, and the maximum temperature rise of the inner raceway under the three processing modes of honing, grinding and shaving is respectively 183%, 247% and 793% higher than that of the polished surface. In the bearing temperature rise analysis, the temperature rise of the inner roller path of the polished rough surface is far away from the critical value of the interface gluing temperature, and the performance is the most excellent in the aspect of the gluing resistance, so that the contact surface of the bearing is polished as much as possible in order to avoid the gluing failure of the high-speed bearing of the gas turbine in service.
FIG. 3 is a graph plotting the lubrication performance under different rough surfaces. Through the comparison, it can be seen that only polishing rough surface arithmetic lower ball bearing is in the full-film lubrication state, and other three surfaces all take place coarse peak direct contact under the different degree, lead to coefficient of friction increase, and the friction loss process aggravates, and the dry friction themogenesis can't in time transmit heat energy to external environment, also causes other three contact surface interface temperature rise to be far greater than the main reason on polishing surface.
Fig. 4 (a) and fig. 4 (b) are graphs showing the influence of the load size on the maximum temperature rise distribution of the rolling element and the inner raceway of the gas turbine bearing at different moments, and it can be known from the graphs that the maximum temperature rise of the surface of the inner raceway is smaller than that of the surface of the rolling element, the maximum temperature rise of the interface changes remarkably with the gradual increase of the load, and when the contact load between the interfaces reaches 1.4GPa, the maximum temperature rise of the interface increases by 103% compared with 0.9 GPa.
Fig. 5 (a) records the oil film thickness distribution at different entrainment speeds, where an oil film thickness of 0 indicates the dry friction region. It can be seen from the figure that when the entrainment speed is high, reaching 30m/s, the two contact surfaces are completely separated by the oil film, the interface is in a full film lubrication state, the thickness of the oil film gradually decreases with the decrease of the entrainment speed, when the speed decreases to 3m/s, a partial dry friction area appears on the interface, and the dry friction area further expands with the continuous decrease of the entrainment speed. In the oil film pressure distribution of FIG. 5 (b), since the oil film thickness at the exit region is 0 in part at a velocity of 3m/s, the asperity contact is caused, resulting in a phenomenon that a higher pressure peak is generated at the exit region at 3m/s than at 30 m/s.
In summary, the above description is only a preferred embodiment of the present invention, and is not intended to limit the scope of the present invention. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (3)
1. A method for predicting the gluing failure of a gas turbine bearing by considering the real surface roughness is characterized by comprising the following steps:
step 1, establishing a geometric model:
with x in the circumferential direction of the inner race track 2j Shaft, radial of inner race 2j Axis, perpendicular to the circumferential and radial directions, y 2j The center of mass of the shaft and the bearing is the origin o of the coordinate system 2j Establishing a rectangular coordinate system; x obtained after the rolling body completes the geometric equivalence 2j o 2j z 2j Radius of curvature of plane
And y 2j o 2j z 2j Radius of curvature of plane
The same is that:
inner raceway by the above analysis along x 2j o 2j z 2j Radius of curvature of plane
And y 2j o 2j z 2j Radius of curvature of plane
Respectively as follows:
in the formula D W Is the diameter of the rolling element, D m Is the pitch diameter, alpha, of the ball bearing 2j The initial contact angle of the bearing being equal to the mean diameter of the inner and outer raceways, i.e. D m ＝0.5(D r1 +D r2 )，f i The curvature coefficients of the inner and outer channels;
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 ：
Step 2, considering the Reynolds equation of the instantaneous speed:
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 which t represents a time variable, p 2j (x 2j ,y 2j ) Is oil film pressure, h is oil film thickness, η is lube viscosity, ρ is lube density, u is lube oil viscosity x2j Is rolling and inner raceway edge x 2j Axial directionThe entrainment speed of;
step 3, establishing an oil film thickness equation:
the specific form of the oil film thickness equation considering the true surface roughness is as follows:
in the formula, v e (x 2j ,y 2j T) elastic deformation between contact pairs, E' equivalent modulus of elasticity between bearing pairs, delta 1 (x 2j ,y 2j T) and delta 2 (x 2j ,y 2j T) true roughness of the rolling body and inner raceway surface, h 0 (t) represents the normal approach between the rolling elements and the inner raceway,
describing the equivalent rear ellipsoid geometrical shape of the rolling body and the inner raceway, R x2j And R y2j Through step 2, xi and
for computing nodes at x 2j Axis and y 2j Coordinates of the axis, Ω denotes a solution area;
step 4, establishing a lubrication basic equation:
the oil film viscosity and density were considered as a pressure correlation equation:
η 0 and rho 0 Respectively representing the environmental viscosity and the environmental density, wherein alpha is the viscosity-pressure coefficient of the lubricating oil;
step 5, considering a friction-flash temperature equation of the non-Newtonian fluid effect:
the friction of the bearing under the mixed lubrication condition mainly comprises fluid shear friction and rough peak contact friction, wherein the friction force of a fluid lubrication area is calculated by means of a viscoelastic Bair-Winer non-Newtonian fluid rheological model:
in the formula, τ L In order to limit the shear stress,
derivative of shear stress, G ∞ The ultimate shear modulus, both of which are a function of pressure and temperature depending on the rheological properties of the lubricating oil,
shear rate of
Wherein the linear velocity of the rolling body is
Inner raceway linear velocity is expressed as
And substituting the obtained product into a formula (12) to obtain the solution of the shear stress tau on any node in the calculated domain fluid Non-linear equation of distribution:
the shear stress at dry friction is solved as follows:
τ contact ＝f contact ·p x2j (x 2j ,y 2j ) (15)
f contact represents a dry friction coefficient;
final bearing overall shear stress τ total Comprises the following steps:
τ total ＝τ contact +τ fluid (16)
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 raceway is obtained by the ratio of the friction force to the contact load:
dividing the generated heat into two parts according to a set heat distribution coefficient A:
meanwhile, calculating the lubricating local speed distribution and the temperature change curve under the condition of sliding according to the research result of Plint, determining the heat distribution coefficient between the rolling body and the inner roller way and obtaining:
in the formula, T 1 ，T 2 Surface temperatures of the rolling elements and inner races, K f Represents the heat transfer coefficient of the lubricating oil;
the interface flash temperature calculation of the rolling body and the inner raceway is based on the theoretical calculation of a fast moving heat source on the semi-infinite solid, a rolling body-inner raceway surface temperature calculation model is established by combining the theory, and based on the theory, a second class Volterra integral equation is expressed as follows:
in the formula, T b1 ，T b2 Initial temperatures of the rolling elements and inner raceway surface, C 1 And C 2 Is the specific heat capacity of the solid, k 1 ，k 2 Is the coefficient of thermal conductivity, rho, of the rolling bodies and the inner race 1 ,ρ 2 The density of the rolling body and the inner raceway is respectively, the surface of the rolling body and the surface of the inner raceway are respectively arranged along x 2j The axis is divided into grids, lambda represents any one of the grids, T 1 (lambda) and T 2 (λ) represents the temperature of the rolling elements and inner raceway surface, respectively, at the grid λ; q (λ) represents the heat at grid λ; lambda belongs to (-x) 2j Xi), xi is x corresponding to the end state temperature rise 2j Axis coordinates;
the formula for determining the gluing failure is as follows:
T b +T fm ≤T sc (21)
wherein, T sc Critical temperature for gluing, temperature rise T of contact pair interface fm ＝T 1 /T 2 ；
T in the formula (21) when judging whether the rolling bodies are bonded and failed b Replacement by initial temperature T of rolling body 1b Judging whether the failure occurs according to the formula; t in the formula (21) when judging whether the inner raceway is in failure of bonding b Replacement by inner race initial temperature T 2b And judging whether the failure occurs according to the formula.
2. A method of predicting the seizure failure of a bearing of a combustion engine considering the real surface roughness as set forth in claim 1, wherein:
G ∞ ＝1.2p 2j (x 2j ,y 2j )/(2.52+0.024T 2 )-10 -9 (12)
τ L ＝0.25G ∞ (13)。
3. the method of claim 1, wherein the method is used for predicting the bonding failure of the bearing of the gas turbine by considering the actual surface roughnessCharacterized in that: coefficient of dry friction f contact The value range is 0.07-0.15.
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN116933510A (en) * | 2023-07-10 | 2023-10-24 | 哈尔滨工业大学 | Prediction analysis method for bearing slip scratch failure behavior |
| CN117932823A (en) * | 2024-03-21 | 2024-04-26 | 浙江大学 | Method and system for calculating temperature of roller-plunger pair of hydraulic motor |
-
2022
- 2022-10-09 CN CN202211228492.0A patent/CN115659490A/en active Pending
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN116933510A (en) * | 2023-07-10 | 2023-10-24 | 哈尔滨工业大学 | Prediction analysis method for bearing slip scratch failure behavior |
| CN117932823A (en) * | 2024-03-21 | 2024-04-26 | 浙江大学 | Method and system for calculating temperature of roller-plunger pair of hydraulic motor |
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