CN113503197A - Marine cam-tappet pair elastohydrodynamic lubrication analysis method considering structural vibration - Google Patents

Marine cam-tappet pair elastohydrodynamic lubrication analysis method considering structural vibration Download PDF

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CN113503197A
CN113503197A CN202110783267.2A CN202110783267A CN113503197A CN 113503197 A CN113503197 A CN 113503197A CN 202110783267 A CN202110783267 A CN 202110783267A CN 113503197 A CN113503197 A CN 113503197A
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valve
cam
tappet
mass
force
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CN113503197B (en
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华德良
史修江
孙文
冯彦
邱卓一
李仁泽
卢熙群
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Harbin Engineering University
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    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F01—MACHINES OR ENGINES IN GENERAL; ENGINE PLANTS IN GENERAL; STEAM ENGINES
    • F01L—CYCLICALLY OPERATING VALVES FOR MACHINES OR ENGINES
    • F01L1/00—Valve-gear or valve arrangements, e.g. lift-valve gear
    • F01L1/12—Transmitting gear between valve drive and valve
    • F01L1/14—Tappets; Push rods
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F01—MACHINES OR ENGINES IN GENERAL; ENGINE PLANTS IN GENERAL; STEAM ENGINES
    • F01L—CYCLICALLY OPERATING VALVES FOR MACHINES OR ENGINES
    • F01L1/00—Valve-gear or valve arrangements, e.g. lift-valve gear
    • F01L1/02—Valve drive
    • F01L1/04—Valve drive by means of cams, camshafts, cam discs, eccentrics or the like
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F01—MACHINES OR ENGINES IN GENERAL; ENGINE PLANTS IN GENERAL; STEAM ENGINES
    • F01L—CYCLICALLY OPERATING VALVES FOR MACHINES OR ENGINES
    • F01L1/00—Valve-gear or valve arrangements, e.g. lift-valve gear
    • F01L1/46—Component parts, details, or accessories, not provided for in preceding subgroups
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F01—MACHINES OR ENGINES IN GENERAL; ENGINE PLANTS IN GENERAL; STEAM ENGINES
    • F01M—LUBRICATING OF MACHINES OR ENGINES IN GENERAL; LUBRICATING INTERNAL COMBUSTION ENGINES; CRANKCASE VENTILATING
    • F01M9/00—Lubrication means having pertinent characteristics not provided for in, or of interest apart from, groups F01M1/00 - F01M7/00
    • F01M9/10—Lubrication of valve gear or auxiliaries
    • F01M9/101—Lubrication of valve gear or auxiliaries of cam surfaces
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F01—MACHINES OR ENGINES IN GENERAL; ENGINE PLANTS IN GENERAL; STEAM ENGINES
    • F01M—LUBRICATING OF MACHINES OR ENGINES IN GENERAL; LUBRICATING INTERNAL COMBUSTION ENGINES; CRANKCASE VENTILATING
    • F01M9/00—Lubrication means having pertinent characteristics not provided for in, or of interest apart from, groups F01M1/00 - F01M7/00
    • F01M9/10—Lubrication of valve gear or auxiliaries
    • F01M9/104—Lubrication of valve gear or auxiliaries of tappets
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
    • Y02T90/00—Enabling technologies or technologies with a potential or indirect contribution to GHG emissions mitigation

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  • General Engineering & Computer Science (AREA)
  • Mechanical Engineering (AREA)
  • Physics & Mathematics (AREA)
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  • Geometry (AREA)
  • General Physics & Mathematics (AREA)
  • Valve-Gear Or Valve Arrangements (AREA)

Abstract

The invention aims to provide a marine cam-tappet pair elastohydrodynamic lubrication analysis method considering structural vibration, which comprises the following steps: establishing a single-mass dynamic model of the valve train, simplifying the tappet, the rocker arm and the air valve into concentrated mass, and deducing a dynamic differential equation to obtain the dynamic characteristics of parts of the valve train; establishing a cam-tappet contact analysis model, and solving the fluctuating contact load in the operation process; and establishing a cam-tappet pair elastohydrodynamic lubrication analysis model, coupling the obtained fluctuating contact load, and analyzing the oil film state including oil film pressure and oil film thickness under the fluctuating load, thereby providing a new method for the elastohydrodynamic lubrication analysis of the valve train. The cam-tappet internal contact load optimization method adopts a single mass dynamics model, optimizes the cam-tappet internal contact load, and can provide an idea for improving the cam-tappet internal contact condition. An elastohydrodynamic lubrication analysis model is adopted, and the fluctuation contact load is coupled, so that the lubrication state between the cam and the tappet is analyzed, and a new method is provided for the elastohydrodynamic lubrication analysis of the valve train.

Description

Marine cam-tappet pair elastohydrodynamic lubrication analysis method considering structural vibration
Technical Field
The invention relates to a method for analyzing the elastohydrodynamic lubrication of a distribution cam-tappet pair, in particular to a method for analyzing the elastolubrication of a distribution cam-tappet pair of a marine diesel engine.
Background
The cam-tappet pair is a core friction pair of a valve mechanism of a marine diesel engine, and the reliability and the stability of the diesel engine are directly influenced by the quality of the lubricating state of the cam-tappet pair. The diesel engine distribution cam bears periodic load, the thickness fluctuation of a lubricating oil film is large in the working process of the diesel engine distribution cam, and the existing cam-tappet elastohydrodynamic lubrication analysis usually adopts a simplified dynamic model and cannot reflect the actual working condition. Therefore, the method has important significance for researching the elastohydrodynamic lubrication performance of the distribution cam-tappet pair of the marine diesel engine and predicting the wear failure of the distribution cam-tappet pair by considering the vibration characteristic of the distribution mechanism and optimizing the cam-tappet indirect touch mechanical model. Aiming at the problem of elastohydrodynamic lubrication of the cam-tappet pair, scholars at home and abroad make a great deal of research. Ai et al [ Ai X, Yu H.A Numerical Analysis for the Transient EHL Process of a Cam-Tappet Pair in I.C. Engine [ J ] ASME Journal of Tribology,1989,111:413-416 ] first solved for a complete Numerical solution of the Cam-Tappet secondary Elastohydrodynamic Lubrication of an internal combustion engine under isothermal conditions, Kushwah et al [ Kushwaha M, Rahnejat H.transient Elastohydrodynamic Lubrication of Cam Follower coupled [ J ] Journal of Physics D: Applied physics.2002,35:2872-2890 ] combined with multi-body dynamics found that Transient Elastohydrodynamic Contact would generate unavoidable heat in Cam-Tappet Analysis. If the vibration characteristics of all parts of the valve train can be considered and the lubrication analysis of the cam-tappet pair is carried out, the valve train lubricating system has great promotion effect on the work such as valve train design, wear prediction and the like.
Disclosure of Invention
The invention aims to provide a marine cam-tappet pair elastohydrodynamic lubrication analysis method which can analyze the dynamic characteristics of a valve train and the state of a lubricating oil film between a cam and a tappet and provides convenience and reference for lubricating analysis and wear prediction of the valve train of a marine diesel engine and considers structural vibration.
The purpose of the invention is realized as follows:
the invention relates to a marine cam-tappet pair elastohydrodynamic lubrication analysis method considering structural vibration, which is characterized by comprising the following steps of:
(1) establishing a single-mass dynamic model of the valve train, simplifying a tappet, a rocker arm and an air valve into concentrated mass, deriving a dynamic differential equation, considering initial spring force and gas acting force, and solving the equation by using a Runge-Kutta method to obtain the dynamic characteristics of parts of the valve train, such as the speed of the air valve and the tappet;
(2) establishing a cam-tappet contact analysis model, solving a fluctuating contact load in the operation process, considering structural vibration to optimize a contact load equation, and obtaining working condition change conditions in a contact micro-area, including entrainment speed and curvature radius, so as to provide a basis for subsequent elastohydrodynamic lubrication analysis;
(3) and establishing a cam-tappet pair elastohydrodynamic lubrication analysis model, coupling the obtained fluctuating contact load, and analyzing the oil film state including oil film pressure and oil film thickness under the fluctuating load, thereby providing a new method for the elastohydrodynamic lubrication analysis of the valve train.
The present invention may further comprise:
1. the process of establishing the single-mass dynamic model comprises the following steps:
simplifying the valve actuating mechanism into a single-degree-of-freedom dynamic model, describing the motion of the valve by the motion of a concentrated mass, assuming the push rod as a spring without mass, and concentrating the mass of parts behind the push rod to one side of the valve end through conversion;
assuming that the spring is located at the push rod position, the push rod mass is converted by halfOn the mass M of the end system of the air valve, the mass of the push rod is set to be M1With a conversion mass of m1When the air distribution system moves, the motion speed of the rocker arm at the end of the push rod is vTThe motion speed of the rocker arm at the valve end is vGThe mass m of the push rod at the valve end1Comprises the following steps:
Figure BDA0003158034520000021
due to the fact that
Figure BDA0003158034520000022
Thus, it is possible to provide
Figure BDA0003158034520000023
Assuming that the rotary inertia of the rocker arm is I and the distance from the valve to the center of the rocker arm shaft is l, the mass M of the rocker arm is converted to the mass M of the valve end system2Comprises the following steps:
Figure BDA0003158034520000024
the moment of inertia I is obtained by actual measurement, one end of the valve spring moves along with the valve, the other end is fixed, and the mass m of the valve spring isVOnly 1/3 is switched to M, thereby obtaining
Figure BDA0003158034520000031
Adding damping elements and valve seat parameters to obtain a single-degree-of-freedom dynamic model;
after simplifying the valve actuating mechanism into a single-degree-of-freedom dynamic model, describing the motion of the valve by utilizing the motion of a concentrated mass M, wherein one end of the M has rigidity KSThe valve spring is connected with the cylinder cover, and the other end is connected with a hypothetical stiffness KTThe upper end of the spring is directly driven by the cam at the moment, and the motion rule of the springIt is known that:
x＝x(α)＝k·h(α)-δ；
k is a rocker ratio, delta is a valve clearance, h (alpha) is a tappet lift function, and x (alpha) is a valve lift function when the valve train is used as complete rigidity;
the displacement y of the concentrated mass M depends on an expression y (alpha) of a cam angle, and a differential equation and an initial condition thereof which are met by the y (alpha) are established;
assuming that the sum of the external forces acting on the lumped mass M is F, then
Figure BDA0003158034520000032
Wherein M is the concentrated mass and ω is the cam angular velocity;
the external force comprises the following parts:
elastic restoring force K of valve trainTJ, wherein
Figure BDA0003158034520000033
Spring force-K of valve springS·y(α)；
Valve spring pretightening force-F0；
Acting force-F of gas in cylinder to air valveg(α) acting force F on gasg(alpha) setting the pressure of gas in the cylinder as P and the pressure of the air passage on the back of the air valve as P0The area of the valve base plate is A1Radius r1The valve back is subjected to P0Area of action is A2Then, then
Fg(α)＝A1·P(α)-A2P0；
Aiming at the air valve structure, the air valve head is simplified into a round table, wherein r2The radius of the air valve rod is shown, the inclination angle of the air valve head is 30 degrees, and then
A1＝π·r1 2；
Figure BDA0003158034520000041
The gas valve structure is known, so that the magnitude of gas acting force borne by the gas valve can be obtained;
internal damping force CS·ω·JvWherein
Figure BDA0003158034520000042
External damping force
Figure BDA0003158034520000043
By substituting the sum of the above forces into F, the product is obtained
Figure BDA0003158034520000044
In order to obtain a specific valve lift function y, two initial conditions are additionally provided, namely, α is equal to α at the moment corresponding to the valve opening start0Is provided with
Figure BDA0003158034520000045
In the actual motion process of the valve train, all parts can be separated, the coefficient of a kinetic equation is correspondingly changed according to the contact state of all parts, and the equivalent compression amount is defined as z (alpha) -x (alpha) -y (alpha), so that when the z (alpha) is less than or equal to 0, the equivalent cam is separated from the valve;
at this time, the initial conditions are changed as follows:
Figure BDA0003158034520000046
Figure BDA0003158034520000047
in the formula: alpha is alpha0The cam shaft rotation angle when the valve is opened;
for internal damping CSThe formula is adopted:
Figure BDA0003158034520000048
when the rocker arm contacts with the valve, the valve mechanism is compressed to deform and overcome the pretightening force of the valve spring gradually, and when the resultant force of the elastic deformation force and the internal damping force of the valve mechanism is equal to the pretightening force of the valve spring, the valve starts to move to combine the resultant force F of the elastic deformation force and the internal damping force of the valve mechanism with the pretightening force F of the valve spring0When the valve is equal in size, the valve is taken as the starting point of the valve motion;
calculating the resultant force F of the elastic deformation force and the internal damping force of the valve actuating mechanism once per step length:
Figure BDA0003158034520000051
when it occurs
Figure BDA0003158034520000052
When the solution is needed, the solution is started;
considering the elastic deformation of a high-speed or high-flexibility internal combustion engine valve actuating mechanism, calculating the acting force F between a cam and a tappet by using a single-degree-of-freedom dynamic model, considering a valve and the tappet separately, and establishing the dynamic model at the cam end, namely the cam driving mass m is the mass of the tappet plus the mass of a half push rod;
the forces experienced by the cam include:
valve spring pretightening force F02 gas pressure FgInertial force F of mass mN，
Figure BDA0003158034520000053
At this time
Figure BDA0003158034520000054
Wherein M is2The tappet mass;
elastic restoring force F of valve trainCConverted to tappet end k2·KSConverted to z (alpha)/k at the end of the tappet, so that the elastic restoring force is
Figure BDA0003158034520000055
Damping force FbIf the damping coefficient measured at the valve end is CSTaking damping force as
Figure BDA0003158034520000056
The synthesis is carried out to obtain the product,
Figure BDA0003158034520000057
2. establishing a kinematic analysis model of the cam-tappet pair;
the two surfaces, namely the cam surface speed and the tappet surface speed are obtained as follows:
Figure BDA0003158034520000058
in the formula uaIs the cam surface speed; u. ofbThe tappet surface velocity; omega is the cam angular velocity; r is the comprehensive curvature radius of the cam; h ″)αIs the geometric acceleration;
the entrainment speed between the two surfaces is:
u＝(u1+u2)/2
establishing a cam-tappet pair line contact equivalent model, and simplifying the cam-tappet pair line contact equivalent model into a cylinder-to-plane line contact geometric structure, wherein the calculation formula of the comprehensive curvature radius R of the cam is as follows:
R＝R0+hα+h″α
in the formula, R is the comprehensive curvature radius of the cam; r0Is the cam base circle radius; h isαThe tappet lift motion rule is obtained;
the contact stress is:
Figure BDA0003158034520000061
the contact width is:
Figure BDA0003158034520000062
in the formula, p0Is the cam-tappet contact stress; b is the contact half width between the cam and the tappet; e' is the material equivalent elastic modulus; b is0Is the cam width;
equivalent elastic modulus E' for the contact zone:
Figure BDA0003158034520000063
in the formula, E1、E2The modulus of elasticity of the corresponding material; mu.s1、μ2Is the poisson's ratio of the corresponding material;
in the operation process of the cam-tappet, simplifying a generalized Reynolds equation to obtain a linear contact Reynolds equation under the transient condition as follows:
Figure BDA0003158034520000064
in the formula, p is oil film pressure distribution; h is the oil film thickness distribution; eta is the viscosity of the lubricating oil; rho is the density of the lubricating oil; u is the entrainment speed of the two surfaces;
the boundary conditions required to solve the Reynolds equation are:
Figure BDA0003158034520000071
in the formula, xinAnd xoutTo calculate the entrance and exit coordinates of the domain, b is the contact half-width;
the equation for the film thickness of a smooth surface line contact lubricating film considering elastic deformation is as follows:
Figure BDA0003158034520000072
in the formula, h0V (x, y, t) is an elastic deformation term for the initial film thickness;
the load capacity of the lubricating film obtained by integrating the pressure p is balanced with the contact load per unit length between the cam and the tappet in the whole range of the lubricating film:
Figure BDA0003158034520000073
in the formula, wloadCalculating the load for the dynamics analysis;
for lubrication status analysis, the Roelands pressure-viscosity equation and the Dowson-Higginson pressure-density equation were used:
Figure BDA0003158034520000074
wherein α is a lubricating oil viscosity-pressure coefficient, η0Is the ambient viscosity of the lubricating oil;
Figure BDA0003158034520000075
in the formula, ρ0Is the density at normal pressure.
The invention has the advantages that:
(1) a single mass dynamics model is adopted, the contact load between the cam and the tappet is optimized, and an idea can be provided for improving the contact condition between the cam and the tappet.
(2) An elastohydrodynamic lubrication analysis model is adopted, and the fluctuation contact load is coupled, so that the lubrication state between the cam and the tappet is analyzed, and a new method is provided for the elastohydrodynamic lubrication analysis of the valve train.
Drawings
FIG. 1 is a simplified block diagram of a valve train;
FIG. 2 is a diagram of a single degree of freedom dynamic model of a valve train;
FIG. 3 is a simplified representation of cam-lifter dynamics;
FIG. 4 is a view of a kinematic model of a cam-tappet pair;
FIG. 5 is a simplified diagram of a line contact model;
FIG. 6 is a flow chart of cam-tappet pair elastohydrodynamic lubrication numerical analysis;
FIG. 7 is a graph of cam-lifter pair dynamics;
FIG. 8a shows the change of the center pressure of the oil film of the cam-tappet pair, and FIG. 8b shows the change of the center film thickness of the oil film of the cam-tappet pair.
Detailed Description
The invention will now be described in more detail by way of example with reference to the accompanying drawings in which:
the invention provides a dynamics-tribology coupling analysis method aiming at a distribution cam-tappet pair of a marine diesel engine by combining with figures 1-8 b. During dynamic analysis, a single mass dynamic model is adopted to obtain the vibration characteristics of parts, so that optimized cam-tappet indirect contact loads are obtained, then a cam-tappet pair elastohydrodynamic lubrication analysis model is established, the obtained contact loads are coupled to an elastohydrodynamic lubrication equation, and finally the marine cam-tappet pair elastolubrication analysis method considering structural vibration is obtained. By adopting the analysis method, the dynamic characteristics of parts of the valve train can be obtained, the elastohydrodynamic lubrication state of the cam-tappet pair under fluctuating load can be obtained, and guidance can be provided for the structural design of the marine diesel engine. The specific technical scheme is as follows:
the first step is as follows: and establishing a single-mass dynamic model of the valve train, and simplifying the tappet, the rocker arm, the air valve and the like into centralized mass. And deriving a dynamic differential equation, considering the initial spring force, the gas acting force and the like, and solving the equation by using a Runge-Kutta method to obtain the dynamic characteristics of parts of the valve train, such as the speed of an air valve and a tappet.
The second step is that: and establishing a cam-tappet contact analysis model, mainly solving the fluctuating contact load in the operation process. According to the dynamics analysis result, the structural vibration is considered to optimize a contact load equation, the working condition change conditions in the contact micro-area, such as entrainment speed, curvature radius and the like, are obtained, and a foundation is provided for subsequent elastohydrodynamic lubrication analysis.
The third step: a cam-tappet pair elastohydrodynamic lubrication analysis model is established, the obtained fluctuating contact load is coupled, the oil film state under the fluctuating load, such as oil film pressure, oil film thickness and the like, is analyzed, and a new method is provided for the elastohydrodynamic lubrication analysis of the valve train.
Single mass kinetic model
Firstly, the valve train is simplified into a single degree of freedom dynamic model, and the motion of a valve is described by the motion of a concentrated mass. However, since the push rod is too long and long to be a main source of deformation, the push rod can be assumed to be a spring without mass, and the mass of the parts behind the push rod is converted and concentrated to the valve end side, as shown in fig. 1.
If the spring is placed on the push rod, half of the mass of the push rod is converted to the mass M of the valve end system, and the mass of the push rod is set to be M1With a conversion mass of m1. When the air distribution system moves, the movement speed of the rocker arm at the end of the push rod is set as vTAnd the motion speed of the rocker arm at the valve end is vGThe switching mass m of the push rod at the valve end1Comprises the following steps:
Figure BDA0003158034520000091
due to the fact that
Figure BDA0003158034520000092
Thus, it is possible to provide
Figure BDA0003158034520000093
Assuming that the rotary inertia of the rocker arm is I and the distance from the valve to the center of the rocker arm shaft is l, the mass M of the rocker arm is converted to the mass M of the valve end system2Comprises the following steps:
Figure BDA0003158034520000094
the method for calculating the moment of inertia I can be obtained by an actual measurement method. Since both the valve and the valve spring fastener are in motion, their masses (m, respectively)GAnd mP) All should be switched to M. One end of the valve spring follows the valve and the other end is fixed, so its mass (set to m)V) Only 1/3 is switched to M. Thus, can obtain
Figure BDA0003158034520000095
Then, a damping element and a valve seat parameter are added to the model of fig. 1, and a single degree of freedom dynamic model is obtained, as shown in fig. 2.
After the valve mechanism is simplified into a single-degree-of-freedom dynamic model, the motion of the valve can be described by utilizing the motion of the concentrated mass M. One end of M has a pass stiffness of KSThe valve spring is connected with the cylinder cover, and the other end is connected with a hypothetical stiffness KTThe upper end of the spring is directly driven by the cam, and the motion law of the spring is known:
x＝x(α)＝k·h(α)-δ (5)
where k is the rocker ratio, δ is the valve clearance, and h (α) is the lifter lift function. It is readily apparent that x (α) is actually the valve lift function when the valve train is considered to be fully rigid.
Our main objective is to determine the variation of the valve lift in the spring case, i.e. the displacement y of the lumped mass M, in dependence on the expression y (α) of the cam angle. For this purpose, first, a differential equation and its initial conditions are established, which y (α) satisfies.
Assuming that the sum of the external forces acting on the lumped mass M is F, then
Figure BDA0003158034520000101
Where M is the lumped mass and ω is the cam angular velocity.
The external force comprises the following parts:
1 elastic restoring force K of valve trainTJ, wherein
Figure BDA0003158034520000102
This occurs because when x (α) ≦ y (α), the mechanism is pulled, which immediately causes disengagement, and the elastic restoring force disappears.
2 valve spring elastic force-KS·y(α)
3 valve spring pretightening force-F0
4 acting force-F of gas in cylinder to air valveg(α) acting force F on gasg(alpha) setting the pressure of gas in the cylinder as P and the pressure of the air passage on the back of the air valve as P0(it may sometimes be considered to be approximately 1 atmosphere) and the valve chassis area is A1Radius r1The valve back is subjected to P0Area of action is A2Then, then
Fg(α)＝A1·P(α)-A2P0 (8)
Aiming at the structure of the air valve, in order to solve the problem, the air valve head is simplified into a circular table, wherein r2The valve head inclination, representing the valve stem radius, is 30. Then
A1＝π·r1 2 (9)
Figure BDA0003158034520000103
The gas valve structure is known, and the magnitude of the gas acting force borne by the gas valve can be obtained.
5 internal damping force CS·ω·JvWherein
Figure BDA0003158034520000111
6 external damping force
Figure BDA0003158034520000112
The sum of the above forces is brought into formula (6) to obtain
Figure BDA0003158034520000113
Wherein, J and JvDetermined by equations (7) and (11).
Equation (12) is a second order ordinary differential equation with infinite solution for the unknown function y. In order to obtain a specific valve lift function y, two initial conditions need to be given in addition, namely, α - α at the moment corresponding to the valve opening start0Is provided with
Figure BDA0003158034520000114
In the actual motion process of the valve train, all parts can be separated, and the coefficient of the dynamic equation needs to be correspondingly changed according to the contact state of each part. When z (α) ≦ 0, it indicates that the equivalent cam has disengaged from the valve.
The initial conditions should now be changed to:
Figure BDA0003158034520000115
Figure BDA0003158034520000116
in the formula: alpha is alpha0The camshaft angle at which the valve is open.
The method for determining the damping coefficient is complex and is generally estimated or tried and found according to an empirical formula. For internal damping CSThe formula is adopted:
Figure BDA0003158034520000117
when the rocker arm contacts with the valve, the valve mechanism is compressed to deform and overcome the pretightening force of the valve spring gradually. When the resultant force of the elastic deformation force and the internal damping force of the valve train is equal to the pretightening force of the valve spring, the valve starts to move. Therefore, the resultant force F of the elastic deformation force and the internal damping force of the valve train and the pretightening force F of the valve spring are combined0And when the valve motion is equal in size, the valve motion is taken as the starting point of the valve motion.
During calculation, calculating the resultant force F of the elastic deformation force and the internal damping force of the valve actuating mechanism once every step length:
Figure BDA0003158034520000121
when it occurs
Figure BDA0003158034520000122
At that time, the solution is started.
For a high-speed or high-flexibility internal combustion engine valve actuating mechanism, the elastic deformation of the valve actuating mechanism is considered, and a single-degree-of-freedom dynamic model is used for calculating the acting force F between a cam and a tappet. Since the currently considered objects are the cam and the tappet, the valve and the tappet need to be considered separately, and a dynamic model is built at the cam end, that is, the cam driving mass m should be the tappet mass plus half the push rod mass, as shown in fig. 3.
Thus, the forces to which the cam is subjected include
1 valve spring pretightening force F0
2 gas pressure Fg
Inertial force F of 3 mass mN
Figure BDA0003158034520000123
Note that at this time
Figure BDA0003158034520000124
Wherein M is2The tappet mass is given.
Elastic restoring force F of 4 valve mechanismCIt should be equal to the product of the mechanical stiffness and the deformation, due to the mechanical stiffness K given previouslySMeasured at the valve end, and should be k converted to the tappet end2·KS(ii) a The deformation is also obtained by valve timing dynamics calculation at the valve end, and is converted to the tappet end and is required to be z (alpha)/k, so that the elastic restoring force is
Figure BDA0003158034520000125
5 damping force FbIf the damping coefficient measured at the valve end is CSPreferably the damping force is
Figure BDA0003158034520000126
The analysis can be combined to obtain the product,
Figure BDA0003158034520000127
elastohydrodynamic lubrication numerical analysis model
And establishing a kinematic analysis model of the cam-tappet pair, and simplifying the operation condition of the cam-tappet pair as shown in figure 4. When the internal combustion engine for the ship runs, the cam-tappet pair is one of friction pairs with severe working conditions, and the working conditions of the cam-tappet pair are complex, namely the entrainment speed, the curvature radius of the contact surface and the contact load are all changed violently.
The two surfaces, namely the cam surface speed and the tappet surface speed are obtained as follows:
Figure BDA0003158034520000131
in the formula uaCam surface velocity (m/s); u. ofbIs the tappet surface velocity (m/s); ω is cam angular velocity (rad/s); r is the comprehensive curvature radius (m) of the cam; h ″)αIs geometric acceleration (mm/rad)2)。
The entrainment speed between the two surfaces is:
u＝(u1+u2)/2 (23)
as shown in fig. 5, a cam-tappet pair line contact equivalent model is established and simplified into a cylinder-to-plane line contact geometric structure, wherein the calculation formula of the comprehensive curvature radius R of the cam is as follows:
R＝R0+hα+h″α (24)
in the formula, R is the comprehensive curvature radius (m) of the cam; r0Is the cam base radius (m); h isαThe motion law (m) of the tappet lift is shown.
The contact stress calculation formula is as follows:
Figure BDA0003158034520000132
the contact width calculation formula is:
Figure BDA0003158034520000133
in the formula, p0Is the cam-tappet contact stress (Pa); b is the contact half width (m) between the cam and the tappet; e' is the material equivalent elastic modulus (Pa); b is0Is the cam width (m).
Calculation of the equivalent elastic modulus E' for the contact zone:
Figure BDA0003158034520000134
in the formula, E1、E2Is the modulus of elasticity (Pa) of the respective material; mu.s1、μ2Is the poisson's ratio of the corresponding material.
In the operation process of the cam-tappet, the entrainment speed changes violently, the generalized Reynolds equation is simplified, and the line contact Reynolds equation under the transient condition is obtained as follows:
Figure BDA0003158034520000141
wherein p is oil film pressure distribution (Pa); h is oil film thickness distribution (m); η is the viscosity (Pa · s) of the lubricating oil; rho is the lubricating oil density (kg/m)3) (ii) a u is the suction velocity (m/s) of both surfaces.
The boundary conditions required to solve the Reynolds equation are:
Figure BDA0003158034520000142
in the formula, xinAnd xoutTo calculate the entry and exit coordinates of a domain, take xin2.5b and xout1.5 b. Wherein b is the contact half width (m).
The influence of the curvature radius of the cam on the film thickness is large, and then the equation of the film thickness of the smooth surface line contact lubricating film considering the elastic deformation is as follows:
Figure BDA0003158034520000143
in the formula, h0V (x, y, t) is an elastic deformation term for the initial film thickness (m).
The load capacity of the lubricating film obtained by integrating the pressure p in the whole lubricating film range is balanced with the contact load of the cam-tappet on a unit length:
Figure BDA0003158034520000144
in the formula, wloadThe load (N) is calculated for the kinetic analysis.
For lubrication status analysis, the Roelands pressure-viscosity equation and the Dowson-Higginson pressure-density equation were used.
Figure BDA0003158034520000145
In the formula, A1＝ln(η0)+9.67；A2＝5.1×10-9(ii) a Alpha is lubricating oil viscosity-pressure coefficient (Pa)-1)；η0The ambient viscosity (Pa · s) of the lubricating oil.
Figure BDA0003158034520000151
In the formula, C1＝0.6×10-9；C2＝1.7×10-9；ρ0Is the density (kg/m) at normal pressure3)。
Numerical analysis method
FIG. 6 is a flow chart of cam-tappet pair elastohydrodynamic lubrication numerical analysis. In dynamic contact analysis, the stress state and the contact condition of the cam-tappet are obtained through the established single mass dynamic model. And after the working condition of the contact area is obtained, analyzing the elastohydrodynamic lubrication numerical value to obtain the lubrication state of the cam-tappet. During elastohydrodynamic lubrication analysis, a lubrication equation needs to be subjected to non-dimensionalization and discretization, and the grid number in the x direction and the grid number in the y direction are both 128 during iterative solution. When the lubrication analysis calculation is carried out, the pressure and the load reach the required convergence precision 10-4When so, the calculation is considered to be ended. And finally outputting dynamic contact characteristics, oil film pressure distribution and lubricating state conditions of the cam-tappet pair in the operation period.
The cam-tappet pair of the valve train of a marine diesel engine is used as a research object, and the running parameters and the material parameters of the valve train are shown in table 1.
TABLE 1 valve train operating parameters
Figure BDA0003158034520000152
The dynamic parameter change condition can be obtained by the dynamic and dynamic contact analysis of the cam-tappet pair, as shown in fig. 7. The contact load and the contact stress are obviously fluctuated in the operation process, and the curvature radius reaches a minimum value at the cam lobe position, so that the contact pressure is more than 0.6GPa, and the abrasion degree is aggravated.
Parameters such as contact stress, velocity vector, contact geometry and the like are obtained through contact analysis of the cam-tappet pair and then input into an elastohydrodynamic lubrication analysis model, wherein the viscosity of lubricating oil is 0.8 Pa.s, and the density is 875 kg.m-3Coefficient of viscous pressure 2.2e- 8Pa-1And further the lubrication state of the cam-tappet pair is obtained.
In the operation period, the contact load between the cam and the tappet obviously fluctuates, so that the pressure and the thickness of a lubricating oil film are unstable in the operation period of the cam, the fluctuation condition occurs, the lubricating oil film is easy to be unstable, the lubricating oil film is broken, and the lubricating effect is lost; the pressure of the oil film between the cam and the tappet is the largest at the cam nose, the corresponding oil film thickness is the smallest at the cam nose, and the lubricating effect is poor, so that elastohydrodynamic lubrication analysis considering the structural vibration characteristics is necessary.

Claims (3)

1. A ship cam-tappet pair elastohydrodynamic lubrication analysis method considering structural vibration is characterized by comprising the following steps:
(1) establishing a single-mass dynamic model of the valve train, simplifying a tappet, a rocker arm and an air valve into concentrated mass, deriving a dynamic differential equation, considering initial spring force and gas acting force, and solving the equation by using a Runge-Kutta method to obtain the dynamic characteristics of parts of the valve train, including the speeds of the air valve and the tappet;
(2) establishing a cam-tappet contact analysis model, solving a fluctuating contact load in the operation process, considering structural vibration to optimize a contact load equation, and obtaining working condition change conditions in a contact micro-area, including entrainment speed and curvature radius, so as to provide a basis for subsequent elastohydrodynamic lubrication analysis;
(3) and establishing a cam-tappet pair elastohydrodynamic lubrication analysis model, coupling the obtained fluctuating contact load, and analyzing the oil film state including oil film pressure and oil film thickness under the fluctuating load, thereby providing a new method for the elastohydrodynamic lubrication analysis of the valve train.
2. The method for analyzing elastohydrodynamic lubrication of a marine cam-tappet pair considering structural vibration as claimed in claim 1, wherein: the process of establishing the single-mass dynamic model comprises the following steps:
simplifying the valve actuating mechanism into a single-degree-of-freedom dynamic model, describing the motion of the valve by the motion of a concentrated mass, assuming the push rod as a spring without mass, and concentrating the mass of parts behind the push rod to one side of the valve end through conversion;
assuming that the spring is arranged at the position of the push rod, half of the mass of the push rod is converted to the mass M of the valve end system, and the mass of the push rod is set to be M1With a conversion mass of m1When the air distribution system moves, the motion speed of the rocker arm at the end of the push rod is vTThe motion speed of the rocker arm at the valve end is vGThe mass m of the push rod at the valve end1Comprises the following steps:
Figure FDA0003158034510000011
due to the fact that
Figure FDA0003158034510000012
Thus, it is possible to provide
Figure FDA0003158034510000013
Assuming that the rotary inertia of the rocker arm is I and the distance from the air valve to the center of the rocker arm shaft is l, the rocker arm is switchedMass M to valve end system mass M2Comprises the following steps:
Figure FDA0003158034510000021
the moment of inertia I is obtained by actual measurement, one end of the valve spring moves along with the valve, the other end is fixed, and the mass m of the valve spring isVOnly 1/3 is switched to M, thereby obtaining
Figure FDA0003158034510000022
Adding damping elements and valve seat parameters to obtain a single-degree-of-freedom dynamic model;
after simplifying the valve actuating mechanism into a single-degree-of-freedom dynamic model, describing the motion of the valve by utilizing the motion of a concentrated mass M, wherein one end of the M has rigidity KSThe valve spring is connected with the cylinder cover, and the other end is connected with a hypothetical stiffness KTThe upper end of the spring is directly driven by the cam, and the motion law of the spring is known:
x＝x(α)＝k·h(α)-δ；
k is a rocker ratio, delta is a valve clearance, h (alpha) is a tappet lift function, and x (alpha) is a valve lift function when the valve train is used as complete rigidity;
the displacement y of the concentrated mass M depends on an expression y (alpha) of a cam angle, and a differential equation and an initial condition thereof which are met by the y (alpha) are established;
assuming that the sum of the external forces acting on the lumped mass M is F, then
Figure FDA0003158034510000023
Wherein M is the concentrated mass and ω is the cam angular velocity;
the external force comprises the following parts:
elastic restoring force K of valve trainTJ, wherein
Figure FDA0003158034510000024
Spring force-K of valve springS·y(α)；
Valve spring pretightening force-F0；
Acting force-F of gas in cylinder to air valveg(α) acting force F on gasg(alpha) setting the pressure of gas in the cylinder as P and the pressure of the air passage on the back of the air valve as P0The area of the valve base plate is A1Radius r1The valve back is subjected to P0Area of action is A2Then, then
Fg(α)＝A1·P(α)-A2P0；
Aiming at the air valve structure, the air valve head is simplified into a round table, wherein r2The radius of the air valve rod is shown, the inclination angle of the air valve head is 30 degrees, and then
A1＝π·r1 2；
Figure FDA0003158034510000031
The gas valve structure is known, so that the magnitude of gas acting force borne by the gas valve can be obtained;
internal damping force CS·ω·JvWherein
Figure FDA0003158034510000032
External damping force
Figure FDA0003158034510000033
By substituting the sum of the above forces into F, the product is obtained
Figure FDA0003158034510000034
In order to obtain a specific valve lift function y, two initial conditions are additionally provided, namely, α is equal to α at the moment corresponding to the valve opening start0Is provided with
Figure FDA0003158034510000035
In the actual motion process of the valve train, all parts can be separated, the coefficient of a kinetic equation is correspondingly changed according to the contact state of all parts, and the equivalent compression amount is defined as z (alpha) -x (alpha) -y (alpha), so that when the z (alpha) is less than or equal to 0, the equivalent cam is separated from the valve;
at this time, the initial conditions are changed as follows:
Figure FDA0003158034510000037
Figure FDA0003158034510000036
in the formula: alpha is alpha0The cam shaft rotation angle when the valve is opened;
for internal damping CSThe formula is adopted:
Figure FDA0003158034510000041
when the rocker arm contacts with the valve, the valve mechanism is compressed to deform and overcome the pretightening force of the valve spring gradually, and when the resultant force of the elastic deformation force and the internal damping force of the valve mechanism is equal to the pretightening force of the valve spring, the valve starts to move to combine the resultant force F of the elastic deformation force and the internal damping force of the valve mechanism with the pretightening force F of the valve spring0When the valve is equal in size, the valve is taken as the starting point of the valve motion;
calculating the resultant force F of the elastic deformation force and the internal damping force of the valve actuating mechanism once per step length:
Figure FDA0003158034510000042
when it occurs
Figure FDA0003158034510000043
When the solution is needed, the solution is started;
considering the elastic deformation of a high-speed or high-flexibility internal combustion engine valve actuating mechanism, calculating the acting force F between a cam and a tappet by using a single-degree-of-freedom dynamic model, considering a valve and the tappet separately, and establishing the dynamic model at the cam end, namely the cam driving mass m is the mass of the tappet plus the mass of a half push rod;
the forces experienced by the cam include:
valve spring pretightening force F02 gas pressure FgInertial force F of mass mN，
Figure FDA0003158034510000044
At this time
Figure FDA0003158034510000045
Wherein M is2The tappet mass;
elastic restoring force F of valve trainCConverted to tappet end k2·KSConverted to z (alpha)/k at the end of the tappet, so that the elastic restoring force is
Figure FDA0003158034510000046
Damping force FbIf the damping coefficient measured at the valve end is CSTaking damping force as
Figure FDA0003158034510000047
The synthesis is carried out to obtain the product,
Figure FDA0003158034510000048
3. the method for analyzing elastohydrodynamic lubrication of a marine cam-tappet pair considering structural vibration as claimed in claim 1, wherein: establishing a kinematic analysis model of the cam-tappet pair;
the two surfaces, namely the cam surface speed and the tappet surface speed are obtained as follows:
Figure FDA0003158034510000051
in the formula uaIs the cam surface speed; u. ofbThe tappet surface velocity; omega is the cam angular velocity; r is the comprehensive curvature radius of the cam; h ″)αIs the geometric acceleration;
the entrainment speed between the two surfaces is:
u＝(u1+u2)/2
establishing a cam-tappet pair line contact equivalent model, and simplifying the cam-tappet pair line contact equivalent model into a cylinder-to-plane line contact geometric structure, wherein the calculation formula of the comprehensive curvature radius R of the cam is as follows:
R＝R0+hα+h″α
in the formula, R is the comprehensive curvature radius of the cam; r0Is the cam base circle radius; h isαThe tappet lift motion rule is obtained;
the contact stress is:
Figure FDA0003158034510000052
the contact width is:
Figure FDA0003158034510000053
in the formula, p0Is the cam-tappet contact stress; b is the contact half width between the cam and the tappet; e' is the material equivalent elastic modulus; b is0Is the cam width;
equivalent elastic modulus E' for the contact zone:
Figure FDA0003158034510000054
in the formula, E1、E2The modulus of elasticity of the corresponding material; mu.s1、μ2Is the poisson's ratio of the corresponding material;
in the operation process of the cam-tappet, simplifying a generalized Reynolds equation to obtain a linear contact Reynolds equation under the transient condition as follows:
Figure FDA0003158034510000061
in the formula, p is oil film pressure distribution; h is the oil film thickness distribution; eta is the viscosity of the lubricating oil; rho is the density of the lubricating oil; u is the entrainment speed of the two surfaces;
the boundary conditions required to solve the Reynolds equation are:
Figure FDA0003158034510000062
in the formula, xinAnd xoutTo calculate the entrance and exit coordinates of the domain, b is the contact half-width;
the equation for the film thickness of a smooth surface line contact lubricating film considering elastic deformation is as follows:
Figure FDA0003158034510000063
in the formula, h0V (x, y, t) is an elastic deformation term for the initial film thickness;
the load capacity of the lubricating film obtained by integrating the pressure p is balanced with the contact load per unit length between the cam and the tappet in the whole range of the lubricating film:
Figure FDA0003158034510000064
in the formula, wloadCalculating the load for the dynamics analysis;
for lubrication status analysis, the Roelands pressure-viscosity equation and the Dowson-Higginson pressure-density equation were used:
Figure FDA0003158034510000065
wherein α is a lubricating oil viscosity-pressure coefficient, η0Is the ambient viscosity of the lubricating oil;
Figure FDA0003158034510000066
in the formula, ρ0Is the density at normal pressure.
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