CN113503197B - 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 PDFInfo
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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
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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
- F01L1/02—Valve drive
- F01L1/04—Valve drive by means of cams, camshafts, cam discs, eccentrics or the like
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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
- F01L1/46—Component parts, details, or accessories, not provided for in preceding subgroups
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- 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
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- 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
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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; a cam-tappet pair elastohydrodynamic lubrication analysis model is established, the obtained fluctuating contact load is coupled, the oil film state including oil film pressure and oil film thickness under the fluctuating load is analyzed, and a new method is provided for elastohydrodynamic lubrication analysis of the valve mechanism. 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
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 distribution cam of the diesel engine bears periodic load, the thickness fluctuation of a lubricating oil film is large in the working process of the 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-tapper Pair in I.C. Engine [ J ]. ASME Journal of Tribology,1989, 111-416 ] 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 to feeder controlled act [ J ]. Journal of Physics D: applied Physics.2002, 35-2872-2890 ] combined with the multi-body dynamic Cam-limited Contact to find that the Cam-Tappet Lubrication will generate unavoidable heat in the 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 lubrication 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 kinetic 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 M 1 With a conversion mass of m 1 When the air distribution system moves, the motion speed of the rocker arm at the end of the push rod is v T The motion speed of the rocker arm at the valve end is v G The mass m of the push rod at the valve end 1 Comprises the following steps:
due to the fact that
Thus, the device
Assuming that the moment of inertia of the rocker arm is I, the valve goes to the rocker shaftThe distance of the center is l, the rocker arm is switched to the mass M on the valve end system mass M 2 Comprises the following steps:
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 is V Only 1/3 of the conversion to M, thereby obtaining
Adding damping elements and valve seat parameters to obtain a single-degree-of-freedom dynamic model;
after simplifying a valve mechanism into a single-degree-of-freedom dynamic model, describing the motion of a valve by utilizing the motion of a concentrated mass M, wherein one end of the mass M has rigidity K S The valve spring is connected with the cylinder cover, and the other end of the valve spring is connected with a hypothetical rigidity K T The 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 lumped mass M depends on the expression y = y (alpha) of the cam rotation angle, and a differential equation satisfied by y = y (alpha) and an initial condition thereof are established;
assuming that the sum of the external forces acting on the lumped mass M is F, then
Wherein M is a concentrated mass, and omega is a cam angular velocity;
the external force comprises the following parts:
elastic restoring force K of valve train T J, wherein
Valve spring elastic force-K S ·y(α)；
Valve spring pretightening force-F 0 ；
Acting force-F of gas in cylinder to air valve g (α) force F against gas g (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 P 0 The area of the valve base plate is A 1 Radius r 1 Valve back receiving P 0 Area of action is A 2 Then, then
F g (α)＝A 1 ·P(α)-A 2 P 0 ；
Aiming at the air valve structure, the air valve head is simplified into a round table, wherein r 2 The radius of the valve rod is shown, the inclination angle of the valve head is 30 degrees, and then
A 1 ＝π·r 1 2 ；
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 C S ·ω·J v Wherein
External damping force
By substituting the sum of the above forces into F, the product is obtained
In order to obtain a specific valve lift function y, two initial conditions are additionally provided, namely, α = α at the moment corresponding to the valve opening start 0 Is provided with
In the actual motion process of the valve mechanism, parts can be separated, the coefficient of a dynamic equation is changed correspondingly according to the contact state of the parts, the equivalent compression amount is defined as z (alpha) = x (alpha) -y (alpha), and when z (alpha) is less than or equal to 0, the equivalent cam is indicated to be separated from the valve;
at this time, the initial conditions are changed as follows:
in the formula: alpha (alpha) ("alpha") 0 The cam shaft rotation angle when the valve is opened;
for internal damping C S The formula is adopted:
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 spring 0 When 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:
when it occurs
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 to which the cam is subjected include:
valve spring pretightening force F 0 2 gas pressure F g Inertial force F of mass m N ，
At this time
Wherein M is 2 The tappet mass;
elastic restoring force F of valve train C Converted to tappet end k 2 ·K S Converted to z (α)/k at the end of the tappet, so that the elastic restoring force is
Damping force F b If the damping coefficient measured at the valve end is C S Taking damping force as
The synthesis is carried out to obtain the product,
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:
in the formula u a Is the cam surface speed; u. of b The tappet surface velocity; omega is the cam angular velocity; r is the comprehensive curvature radius of the cam; h α Is the geometric acceleration;
the entrainment rate between the two surfaces was:
u＝(u 1 +u 2 )/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＝R 0 +h α +h″ α
in the formula, R is the comprehensive curvature radius of the cam; r is 0 Is the cam base circle radius; h is a total of α The tappet lift motion rule is obtained;
the contact stress is:
the contact width is:
in the formula, p 0 Is 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 is 0 Is the cam width;
equivalent elastic modulus E' for the contact zone:
in the formula, E 1 、E 2 The modulus of elasticity of the corresponding material; mu.s 1 、μ 2 Is 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:
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:
in the formula, x in And x out To 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 lubrication film considering elastic deformation is:
in the formula, h 0 V (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:
in the formula, w load Calculating the load for the dynamics analysis;
for lubrication status analysis, the Roelands pressure-viscosity equation and the Dowson-Higginson pressure-density equation were used:
wherein α is a viscosity-pressure coefficient of lubricating oil, η 0 Is the ambient viscosity of the lubricating oil;
in the formula, ρ 0 Is the density at atmospheric 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 gas distribution cam-tappet pair of a marine diesel engine by combining figures 1-8 b. During dynamic analysis, a single mass dynamic model is adopted to obtain 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 elastolubrication 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: 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, and the oil film state under the fluctuating load, such as oil film pressure, oil film thickness and the like, is analyzed, so that a new method is provided for elastohydrodynamic lubrication analysis of a valve mechanism.
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 M 1 With a conversion mass of m 1 . When the air distribution system moves, the movement speed of the rocker arm at the end of the push rod is set as v T And the motion speed of the rocker arm at the valve end is v G The switching mass m of the push rod at the valve end 1 Comprises the following steps:
due to the fact that
Thus, it is possible to provide
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 system 2 Comprises the following steps:
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 (set m, respectively) G And m P ) All transitions should be to M. One end of the valve spring follows the valve and the other end is fixed, so its mass (set as m) V ) Only 1/3 is switched to M. Thereby obtaining
Then, a damping element and a valve seat parameter are added to the model of fig. 1, so as to obtain a single-degree-of-freedom dynamic model, 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 K S The valve spring is connected with the cylinder cover, and the other end of the valve spring is connected with a hypothetical rigidity K T The 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 known that x (α) is actually the valve lift function when the valve train is considered to be fully rigid.
Our main aim is to determine the variation of the lift of the valve in the elastic case, i.e. the displacement y of the lumped mass M, in dependence on the expression y = y (α) of the cam angle. For this purpose, first, a differential equation satisfied by y = y (α) and its initial conditions are established.
Assuming that the sum of the external forces acting on the lumped mass M is F, then
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 train T J, wherein
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-K S ·y(α)
3 valve spring pretightening force-F 0
4 acting force-F of gas in cylinder to air valve g (α) acting force F on gas g (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 P 0 (it may be considered that the pressure is approximately 1 atmosphere) and the valve base area is A 1 Radius r of 1 The valve back is subjected to P 0 Area of action is A 2 Then, then
F g (α)＝A 1 ·P(α)-A 2 P 0 (8)
Aiming at the air valve structure, in order to solve the problem, the air valve head is simplified into a circular table, wherein r 2 The valve head inclination is 30 deg. representing the valve stem radius. Then
A 1 ＝π·r 1 2 (9)
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 C S ·ω·J v In which
6 external damping force
The sum of the above forces is brought into formula (6) to obtain
Wherein, J and J v Is represented by the formula (7) and(11) And (4) determining.
Equation (12) is a second order ordinary differential equation with infinite solution for the unknown function y. In order to obtain a certain valve lift function y, two initial conditions need to be given in addition, namely, a = a at the moment corresponding to the valve opening start 0 Is provided with
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. An equivalent compression amount is defined as z (α) = x (α) -y (α), and when z (α) ≦ 0, it indicates that the equivalent cam has disengaged from the valve.
The initial conditions should now be changed to:
in the formula: alpha is alpha 0 The camshaft angle at which the valve is open.
The method for determining the damping coefficient is complex and is generally estimated or tried according to an empirical formula. For internal damping C S The formula is adopted:
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 combined 0 When the sizes are equalAs the starting point of the valve movement.
During calculation, the resultant force F of the elastic deformation force and the internal damping force of the valve actuating mechanism is calculated once every step length:
when it occurs
When this happens, the solution is started.
For a high-speed or high-flexibility internal combustion engine valve actuating mechanism, elastic deformation of the valve actuating mechanism is considered, and a single-degree-of-freedom dynamic model is used for calculating an acting force F between a cam and a tappet. Since the objects considered at present are the cam and the tappet, the valve and the tappet need to be considered separately, and a dynamic model is established at the cam end, namely the cam driving mass m should be the tappet mass plus half the push rod mass at the moment, as shown in fig. 3.
Thus, the forces to which the cam is subjected include
1 valve spring pretightening force F 0
2 gas pressure F g
Inertial force F of 3 mass m N
Note that at this time
Wherein M is 2 The tappet mass is given.
4 elastic restoring force F of valve mechanism C It should be equal to the product of the mechanical stiffness and the deformation, due to the mechanical stiffness K given previously S Measured at the valve end, and should be k converted to the tappet end 2 ·K S (ii) a The deformation is also obtained by valve timing dynamics calculation at the valve end, and is converted to the tappet end and should be z (alpha)/k, so the elastic restoring forceIs composed of
5 damping force F b If the damping coefficient measured at the valve end is C S Preferably the damping force is
The analysis is combined to obtain the product,
elastohydrodynamic lubrication numerical analysis model
And (3) 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.
Two surfaces, namely the cam surface speed and the tappet surface speed are obtained as follows:
in the formula u a Cam surface speed (m/s); u. of b Is the tappet surface velocity (m/s); omega is cam angular velocity (rad/s); r is the comprehensive curvature radius (m) of the cam; h ″) α Is geometric acceleration (mm/rad) 2 )。
The entrainment rate between the two surfaces was:
u＝(u 1 +u 2 )/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＝R 0 +h α +h″ α (24)
in the formula, R is the comprehensive curvature radius (m) of the cam; r 0 Is the cam base radius (m); h is a total of α The motion law (m) of the tappet lift is shown.
The contact stress calculation formula is:
the contact width calculation formula is:
in the formula, p 0 Is 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 is 0 Is the cam width (m).
Calculation of the equivalent elastic modulus E' for the contact zone:
in the formula, E 1 、E 2 Is the modulus of elasticity (Pa) of the respective material; mu.s 1 、μ 2 Is 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:
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 density (kg/m) of lubricating oil 3 ) (ii) a u is two surfacesThe sucking speed (m/s).
The boundary conditions required to solve the Reynolds equation are:
in the formula, x in And x out To calculate the entry and exit coordinates of a domain, take x in = 2.5b and x out =1.5b. Wherein b is a 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:
in the formula, h 0 V (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:
in the formula, w load The 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.
In the formula, A 1 ＝ln(η 0 )+9.67；A 2 ＝5.1×10 -9 (ii) a Alpha is lubricating oil viscosity-pressure coefficient (Pa) -1 )；η 0 The ambient viscosity (Pa · s) of the lubricating oil.
In the formula, C 1 ＝0.6×10 -9 ；C 2 ＝1.7×10 -9 ；ρ 0 Is the density (kg/m) at normal pressure 3 )。
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 value to obtain the lubrication state of the cam-tappet. During elastohydrodynamic lubrication analysis, a lubrication equation needs to be subjected to dimensionless and discretization, and the grid numbers in the x direction and the y direction are both 128 during iterative solution. When the lubrication analysis and calculation are carried out, the pressure and the load reach the required convergence precision 10 -4 When so, the calculation is considered to be ended. And finally outputting the dynamic contact characteristics, oil film pressure distribution and lubrication 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
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 fluctuate obviously in the operation process, and when the cam is at the cam nose, the curvature radius reaches a minimum value, so that the contact pressure is greater than 0.6GPa, and the abrasion degree is increased.
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 0.8Pa s, and the density is 875kg m -3 Coefficient of viscosity pressure 2.2e - 8 Pa -1 And then obtainCam-tappet pair lubrication status.
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 peach point, the corresponding oil film thickness is the smallest at the cam peach point, and the lubricating effect is worse, so that elastohydrodynamic lubrication analysis considering the structural vibration characteristic is necessary.
Claims (2)
1. A marine 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) Establishing a cam-tappet pair elastohydrodynamic lubrication analysis model, coupling the obtained fluctuating contact load, and analyzing the oil film state under the fluctuating load, including oil film pressure and oil film thickness, so as to provide a new method for the elastohydrodynamic lubrication analysis of the valve train;
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 M 1 With a conversion mass of m 1 When the air distribution system moves, the movement speed of the rocker arm at the end of the push rod is v T The velocity of motion of the rocker arm at the valve end is v G The mass m of the push rod at the valve end 1 Comprises the following steps:
due to the fact that
Thus, it is possible to provide
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 system 2 Comprises the following steps:
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 is V Only 1/3 of the conversion to M, thereby obtaining
Adding damping elements and valve seat parameters to obtain a single-degree-of-freedom dynamic model;
after simplifying a valve mechanism into a single-degree-of-freedom dynamic model, describing the motion of a valve by utilizing the motion of a concentrated mass M, wherein one end of the mass M has rigidity K S The valve spring is connected with the cylinder cover, and the other end of the valve spring is connected with a hypothetical rigidity K T The upper end of the spring is directly driven by the cam, and the moving gauge thereofThe law is known as follows:
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 mechanism is completely rigid;
the displacement y of the lumped mass M depends on the expression y = y (alpha) of the cam rotation angle, and a differential equation and an initial condition thereof which are met by y = y (alpha) are established;
assuming that the sum of the external forces acting on the lumped mass M is F, then
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 train T J, wherein
Spring force-K of valve spring S ·y(α)；
Valve spring pretightening force-F 0 ；
Acting force-F of gas in cylinder to air valve g (α) acting force F on gas g (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 P 0 The area of the valve chassis is A 1 Radius r of 1 Valve back receiving P 0 Area of action is A 2 Then, then
F g (α)＝A 1 ·P(α)-A 2 P 0 ；
Aiming at the air valve structure, the air valve head is simplified into a round table, wherein r 2 The radius of the air valve rod is shown, the inclination angle of the air valve head is 30 degrees, and then
A 1 ＝π·r 1 2 ；
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 C S ·ω·J v Wherein
External damping force
By substituting the sum of the above forces into F, the product can be obtained
In order to obtain a specific valve lift function y, two initial conditions are additionally provided, namely, a = a at the moment corresponding to the valve opening start 0 Is provided with
In the actual motion process of the valve mechanism, parts can be separated, the coefficient of a dynamic equation is changed correspondingly according to the contact state of the parts, the equivalent compression amount is defined as z (alpha) = x (alpha) -y (alpha), and when z (alpha) is less than or equal to 0, the equivalent cam is indicated to be separated from the valve;
at this time, the initial conditions are changed as follows:
in the formula: alpha is alpha 0 The cam shaft rotation angle when the valve is opened;
for internal damping C S The formula is adopted:
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 spring 0 When 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:
when it occurs
When the solution is needed, the solution is started;
for a high-speed or high-flexibility internal combustion engine valve actuating mechanism, considering elastic deformation, calculating an 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 building the dynamic model at the end of the cam, namely the cam driving mass m is the mass of the tappet plus the mass of a half of a push rod;
the forces experienced by the cam include:
valve spring pretightening force F 0 2 gas pressure F g Inertial force F of mass m N ，
At this time
Wherein M is 2 The tappet mass;
elastic restoring force F of valve train C Converted to tappet end k 2 ·K S Converted to z (alpha)/k at the end of the tappet, so that the elastic restoring force is
Damping force F b If the damping coefficient measured at the valve end is C S Taking the damping force as
The synthesis is carried out to obtain the product,
2. 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:
in the formula u a Is the cam surface speed; u. of b Is the tappet surface velocity; omega is the cam angular velocity; r is the comprehensive curvature radius of the cam；h″ α Is the geometric acceleration;
the entrainment speed between the two surfaces is:
u＝(u 1 +u 2 )/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＝R 0 +h α +h' α '
in the formula, R is the comprehensive curvature radius of the cam; r is 0 Is the cam base radius; h is α The tappet lift motion rule is obtained;
the contact stress is:
the contact width is:
in the formula, p 0 Is 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 0 Is the cam width;
equivalent elastic modulus E' for the contact zone:
in the formula, E 1 、E 2 The modulus of elasticity of the corresponding material; mu.s 1 、μ 2 Is 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:
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 velocity of both surfaces;
the boundary conditions required to solve the Reynolds equation are:
in the formula, x in And x out To 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:
in the formula, h 0 V (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 over the whole lubricating film range:
in the formula, w load Calculating the load for the dynamics analysis;
for lubrication status analysis, the Roelands pressure-viscosity equation and the Dowson-Higginson pressure-density equation were used:
wherein α is a lubricating oil viscosity-pressure coefficient, η 0 Is the ambient viscosity of the lubricating oil;
in the formula, ρ 0 Is the density at normal pressure.
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