An elastohydrodynamic lubrication analysis method for the fuel supply cam-roller pair of a marine diesel engine

Abstract

The present invention provides an elastohydrodynamic lubrication analysis method for a fuel supply cam-roller pair for a marine diesel engine. Taking into account the actual interface transient contact dynamics and based on an advanced three-dimensional line contact mixed lubrication model, the cam-roller pair is coupled with transient mutation working conditions, geometric changes and non-Newtonian fluid action of the lubricating oil. A quasi-systematic numerical analysis method with good stability and fast convergence speed is adopted to form an elastohydrodynamic lubrication analysis method for a fuel supply cam-roller pair for a marine diesel engine. The method also reveals the influence of working condition changes on the lubrication state characteristics, and provides theoretical guidance for the lubrication prediction and low-friction design of the fuel supply cam-roller pair for a marine diesel engine.

Description

Technical Field

[0001] The invention belongs to the field of tribology of ship power devices, and in particular relates to an elastohydrodynamic lubrication analysis method for a fuel supply cam-roller pair of a ship diesel engine. Background Art

[0002] The cam-roller pair is the core friction pair in the diesel engine fuel supply mechanism. Since the cam and the roller are rolling friction, the friction loss is small and the power can be transmitted well. It is widely used in the diesel engine fuel supply system. During the operation of the marine diesel engine, the working conditions of the fuel supply cam-roller pair show a complex change trend. The contact interface not only has to withstand instantaneous heavy load pressure, but also the curvature radius and suction speed change dramatically, causing the cam-roller pair to be in an unstable lubrication state, resulting in contact fatigue damage and wear on the cam surface, reducing the transmission accuracy of the cam mechanism, and in severe cases, causing the diesel engine to be unable to work.

[0003] At present, most of the research is mainly aimed at the lubrication problem of the cam-roller pair in the valve train, but there is little research on the fuel supply cam-roller type motion pair, especially for the cam-roller pair with high reliability and high precision such as the fuel supply mechanism of diesel engines. Summary of the invention

[0004] The purpose of the present invention is to solve the difficulty in predicting the lubrication state of a fuel supply cam-roller pair of a marine diesel engine and to provide an elastohydrodynamic lubrication analysis method for a fuel supply cam-roller pair of a marine diesel engine.

[0005] A method for analyzing elastohydrodynamic lubrication of a fuel supply cam-roller pair for a marine diesel engine, characterized in that it comprises the following steps:

[0006] Step 1: Establish a single mass dynamics model to obtain the force state and motion conditions in the cam-roller contact micro-area;

[0007] Step 2: After obtaining the working conditions of the contact area, carry out elastohydrodynamic lubrication numerical analysis to obtain the cam-roller lubrication state;

[0008] Step 3: Output the dynamic contact characteristics and lubrication status of the oil supply cam-roller pair during the operation cycle.

[0009] Furthermore, the step 1 is specifically as follows:

[0010] Assuming the cam mechanism is a rigid body, the normal contact load F between the cam and the roller is:

[0011]

[0012] Spring force F T Determined by the following formula:

[0013] F T=F0+k·s(α)

[0014] Where F0 is the spring preload (N), k is the spring stiffness (N / m), and the force between the cam and the roller is F z is the force between the cam and the roller, F T is the spring force, F N is the inertia force of the part, F P is the oil pressure, is the pressure angle;

[0015] Part inertia force:

[0016]

[0017] Where M is the cam drive mass (kg), and its calculation formula is:

[0018]

[0019] Among them, M s is the plunger spring mass (kg), M t M is the mass of the plunger (kg), M2 is the mass of the roller (kg).

[0020] Plunger oil pressure F P , can be obtained by linear interpolation:

[0021]

[0022] Where, d is the plunger diameter (m), s max is the maximum cam lift (m), p1 is the minimum oil pressure (MPa), and p2 is the maximum oil pressure (MPa).

[0023] The pressure angle is:

[0024]

[0025] Where, e is the eccentricity (m) and R0 is the cam base circle radius (m).

[0026] Furthermore, the step 2 is specifically as follows:

[0027] Point P is the instantaneous contact point, and the velocity relationship between the two surfaces is:

[0028]

[0029] Among them, u1 is the cam surface speed (m / s), u2 is the roller surface speed (m / s), α0 is the oil supply stroke angle (°), is the pressure angle (°);

[0030] Knowing the cam curvature radius and rotation speed, the speed of the two surfaces can be obtained as:

[0031]

[0032] Where, ω is the cam angular velocity (rad / s);

[0033] The entrainment speed u is:

[0034]

[0035] Calculate the curvature radius of the oil supply cam:

[0036]

[0037] Where: g(α)=R0+R2+s(α), R1 is the cam curvature radius (m), R2 is the roller radius (m), s(α) is the roller lift (m);

[0038] Calculate the combined curvature radius of the cam-roller pair:

[0039]

[0040] The maximum contact stress is:

[0041]

[0042] Wherein, E' is the cam-roller equivalent elastic modulus (Pa); B0 is the contact line width (m), that is, the cam width.

[0043] During the operation of the cam-roller, the entrainment velocity changes dramatically. The generalized Reynolds equation is simplified to obtain the linear contact Reynolds equation under transient conditions:

[0044]

[0045] Where p is the oil film pressure distribution (Pa); h is the oil film thickness distribution (m); η is the lubricating oil viscosity (Pa·s); ρ is the lubricating oil density (kg / m 3 );

[0046] The boundary conditions required to solve the Reynolds equation are:

[0047]

[0048] Among them, x in and x out For the inlet and outlet coordinates of the computational domain, take x in = -4.5b and x out =1.5b.

[0049] The cam curvature radius has a great influence on the film thickness. The film thickness equation for line contact lubrication of a smooth surface considering elastic deformation is:

[0050]

[0051] Among them, h0(t) is the rigid center film thickness (m); R is the comprehensive curvature radius (m); the third term in the film thickness equation is the elastic deformation term.

[0052] The lubricating film load obtained by integrating the pressure p over the entire lubricating film range should be balanced with the normal contact load per unit length between the cam and roller:

[0053]

[0054] Among them, w load is the unit normal load between the oil supply cam and roller (N / m).

[0055] The beneficial effects of the present invention are:

[0056] (1) A method for predicting the elastohydrodynamic lubrication state of the fuel supply cam-roller pair of a marine diesel engine. By coupling the three-dimensional elastohydrodynamic lubrication analysis theory, a method for predicting the transient lubrication state of the fuel supply cam-roller pair of a marine diesel engine is established. This method has good practicality and can predict the oil film thickness and oil film pressure of the fuel supply cam-roller pair under any extreme working conditions and design conditions.

[0057] (2) A method for solving the friction and lubrication equations that takes into account the combined effects of multiple factors. Considering the transient mutation conditions and sudden geometry of the oil supply cam pair, the lubrication film pressure increases sharply and the film thickness decreases sharply, and the conventional lubrication equation solution method has difficulty in converging. This method successfully overcomes the above difficulties by using a quasi-system numerical analysis method, and becomes a potential effective means for analyzing the elastohydrodynamic lubrication performance under the contact mutation conditions of the oil supply cam pair. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 It is a simplified diagram of the cam-roller pair dynamic model adopted by the present invention;

[0059] Figure 2 It is a kinematic analysis diagram of the cam-roller pair used in the present invention;

[0060] Figure 3 It is a numerical analysis flow chart of cam-roller pair elastohydrodynamic lubrication adopted by the present invention;

[0061] FIG4( a ) is a diagram showing the kinematic parameter changes of the marine oil supply cam-roller pair used in the present invention;

[0062] FIG4( b ) is a diagram showing the changes in dynamic parameters of the marine oil supply cam-roller pair used in the present invention;

[0063] FIG5( a ) is a diagram showing the variation of the oil film thickness of the working section of the marine oil supply cam used in the present invention;

[0064] FIG5( b ) is a diagram showing the oil film pressure variation of the working section of the marine oil supply cam used in the present invention;

[0065] FIG. 6( a ) is a diagram showing the effect of the operating condition change on the oil film thickness of the marine oil supply cam-roller pair cam speed adopted by the present invention;

[0066] FIG. 6( b ) is a diagram showing the influence of the operating condition change adopted by the present invention on the rotation speed of the marine oil supply cam-roller pair cam, the initial load and the oil film pressure. DETAILED DESCRIPTION

[0067] The present invention is further described below in conjunction with the accompanying drawings.

[0068] The present invention takes a fuel supply cam mechanism of a marine diesel engine as the research object, and establishes an elastohydrodynamic lubrication state prediction method which takes into account the influencing factors such as the transient mutation working condition and geometric change of the cam-roller pair based on the kinematic model, the Hertz contact model and the line contact isothermal-elastohydrodynamic model. The method can realize the numerical analysis of the dynamic contact and elastohydrodynamic lubrication performance of the cam-roller pair within the working stroke, and reveal the influence of working condition changes (rotation speed, load) on its lubrication state, providing theoretical guidance for the lubrication prediction and low friction design of the fuel supply cam-roller pair of a marine diesel engine.

[0069] The specific steps include:

[0070] During the operation of the oil supply cam-roller pair, the motion forms of each component are relatively complex, and the calculation amount of the multi-mass dynamic model is too large. Therefore, this paper adopts a single-mass dynamic model with better practicality and higher calculation accuracy. The simplified dynamic model is shown in Figure 1 The plunger and other accessories such as plunger spring are simplified to mass M1 and combined with the roller mass M2 to form a single mass M. At this time, the mass of the connected roller is zero, mainly to facilitate the subsequent analysis of the normal contact load between the cam and the roller. The force F between the cam and the roller z Mainly includes the spring force F T , part inertia force F N and oil pressure F P , but the contact position involves the pressure angle That is, the normal contact load F is composed of the force F z and pressure angle The specific solution is as follows.

[0071] Assuming the cam mechanism is a rigid body, the normal contact load F between the cam and the roller can be obtained:

[0072]

[0073] Spring force F T Determined by the following formula:

[0074] F T =F0+k·s(α) (2)

[0075] Where F0 is the spring preload (N) and k is the spring stiffness (N / m).

[0076] Part inertia force F N Determined by the following formula:

[0077]

[0078] Where M is the cam drive mass (kg), and its calculation formula is:

[0079]

[0080] Among them, M s is the plunger spring mass (kg), M t M is the mass of the plunger (kg), M2 is the mass of the roller (kg).

[0081] Plunger oil pressure F P , can be obtained by linear interpolation:

[0082]

[0083] Where, d is the plunger diameter (m), s max is the maximum cam lift (m), p1 is the minimum oil pressure (MPa), and p2 is the maximum oil pressure (MPa).

[0084] The following formula can be used to calculate the pressure angle:

[0085]

[0086] Where, e is the eccentricity (m) and R0 is the cam base circle radius (m).

[0087] At present, the surface velocity analysis between cam and roller is considered to be pure rolling. However, experimental research has found that there is slippage between the cam and the roller, but its theoretical derivation is relatively complicated. Therefore, this paper combines the kinematic relationship of the particle point to establish a kinematic analysis model of the cam-roller pair, such as Figure 2 shown.

[0088] Point P is the instantaneous contact point, and the velocity relationship between the two surfaces is derived as:

[0089]

[0090] Where, u1 is the cam surface speed (m / s), u2 is the roller surface speed (m / s), α0 is the oil supply stroke angle (°), is the pressure angle (°).

[0091] Given the cam curvature radius and rotation speed, the speeds of the two surfaces can be obtained as

[0092]

[0093] Where ω is the cam angular velocity (rad / s).

[0094] The entrainment speed u is:

[0095]

[0096] For the curvature radius of the oil supply cam, the calculation formula is:

[0097]

[0098] Wherein: g(α)=R0+R2+s(α), R1 is the cam curvature radius (m), R2 is the roller radius (m), and s(α) is the roller lift (m).

[0099] The calculation formula for the comprehensive curvature radius of the cam-roller pair is:

[0100]

[0101] The maximum contact stress is calculated as follows:

[0102]

[0103] Wherein, E' is the cam-roller equivalent elastic modulus (Pa); B0 is the contact line width (m), that is, the cam width.

[0104] During the operation of the cam-roller, the entrainment velocity changes dramatically. The generalized Reynolds equation is simplified to obtain the linear contact Reynolds equation under transient conditions:

[0105]

[0106] Where p is the oil film pressure distribution (Pa); h is the oil film thickness distribution (m); η is the lubricating oil viscosity (Pa·s); ρ is the lubricating oil density (kg / m 3 ).

[0107] The boundary conditions required to solve the Reynolds equation are:

[0108]

[0109] Among them, x in and xout For the inlet and outlet coordinates of the computational domain, take x in = -4.5b and x out =1.5b.

[0110] The cam curvature radius has a great influence on the film thickness. The film thickness equation for line contact lubrication of a smooth surface considering elastic deformation is:

[0111]

[0112] Among them, h0(t) is the rigid center film thickness (m); R is the comprehensive curvature radius (m); the third term in the film thickness equation is the elastic deformation term.

[0113] The lubricating film load obtained by integrating the pressure p over the entire lubricating film range should be balanced with the normal contact load per unit length between the cam and roller:

[0114]

[0115] Among them, w load is the unit normal load between the oil supply cam and roller (N / m).

[0116] By establishing a single mass dynamics model, the force state (contact load, contact stress, etc.) and motion conditions (entrainment velocity, curvature radius, etc.) in the cam-roller contact micro-area are obtained. After obtaining the working conditions of the contact area, the elastohydrodynamic lubrication numerical analysis is carried out to obtain the cam-roller lubrication state. After the lubrication equation is dimensionless and discretized, the quasi-system numerical analysis method is used for iterative solution, in which the densest grid number and the number of grid nodes in the x and y directions are both 128. When the pressure and load reach a convergence accuracy of 10 -4 When required, the calculation is completed, and the dynamic contact characteristics and lubrication status of the oil supply cam-roller pair during the operation cycle are finally output. The numerical analysis flow chart of the elastohydrodynamic lubrication of the cam-roller pair based on transient dynamics is shown in Figure 3 shown.

[0117] The present invention takes a certain marine diesel engine fuel supply cam-roller pair as the research object, and conducts interface dynamic contact and elastohydrodynamic lubrication analysis. The analysis is based on the corresponding structural parameters in Table 1, the lubricating oil viscosity is 0.075Pa·s, the density is 875kg·m -3 , viscosity pressure coefficient 2.2e -8 Pa -1 The oil pressure in the plunger oil chamber is 0.7MPa when the oil pressure valve is just opened, and 2.3MPa when the valve displacement reaches the maximum. The plunger spring preload is 544N, the plunger spring stiffness is 24.3N / mm, and the mass of the roller and follower is 143g.

[0118] Table 1 Main parameters of the oil supply cam mechanism

[0119]

[0120] The change of contact characteristics of the marine fuel supply cam-roller pair is shown in Figure 4. As can be seen from the figure, although the cam lift increases slowly, its curvature radius fluctuates greatly; the contact load of the marine diesel engine fuel supply mechanism fluctuates significantly, and the instantaneous load reaches 150kN / m, causing the contact pressure to be greater than 1.0GPa, which is bound to bring fatigue damage risks and aggravate its wear.

[0121] The lubrication state changes of the working section of the marine oil supply cam are shown in Figure 5. From the analysis results, it can be seen that the oil film thickness is the smallest at the end of the oil supply section, mainly because the entrainment speed is small and the entrainment effect is poor; the oil film pressure gradually increases in the oil supply section and is the largest at the end angle, so the curvature radius is small and the contact load is large.

[0122] Figure 6 shows the influence of working condition changes on the lubrication state of the marine oil supply cam-roller pair. As can be seen from the figure, with the increase of speed, the lubrication film thickness between the cam and the roller increases, which is due to the increase of the suction speed between the cam and the roller; the increase of the load between the cam and the roller can significantly increase the oil film pressure, which brings the hidden danger of stress concentration and is not conducive to lubrication.

[0123] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for analyzing the elastohydrodynamic lubrication of a fuel supply cam-roller pair for a marine diesel engine, characterized in that: The following steps are involved: Step 1: Establish a single mass dynamics model to obtain the force state and motion conditions in the cam-roller contact micro-area; Assuming the cam mechanism is a rigid body, the normal contact load F between the cam and the roller is: Spring force F T Determined by the following formula: F T =F0+k·s(α) Among them, F0 is the spring preload N, k is the spring stiffness N / m, and the force between the cam and the roller is F z is the force between the cam and the roller, F T is the spring force, F N is the inertia force of the part, F P is the oil pressure, is the pressure angle, s(α) is the lift of the fuel supply cam; Part inertia force: Where M is the cam drive mass kg, and its calculation formula is: Among them, M s is the plunger spring mass kg, M t is the mass of the plunger (kg), M2 is the mass of the roller (kg); Plunger oil pressure F P , can be obtained by linear interpolation: Where, d is the plunger diameter m, s max is the maximum cam lift m, p1 is the minimum oil pressure MPa, p2 is the maximum oil pressure MPa; The pressure angle is: Among them, e is the eccentricity m, R0 is the cam base circle radius m; Step 2: After obtaining the working conditions of the contact area, carry out elastohydrodynamic lubrication numerical analysis to obtain the cam-roller lubrication state; Point P is the instantaneous contact point, and the velocity relationship between the two surfaces is: Among them, u1 is the cam surface speed m / s, u2 is the roller surface speed m / s, α0 is the oil supply stroke angle (°), is the pressure angle (°); Knowing the cam curvature radius and rotation speed, the speed of the two surfaces can be obtained as: Where, ω is the cam angular velocity rad / s; The entrainment speed u is: Calculate the curvature radius of the oil supply cam: Where: g(α)=R0+R2+s(α), R1 is the cam curvature radius m, R2 is the roller radius m, s(α) is the oil supply cam lift; Calculate the combined curvature radius of the cam-roller pair: The maximum contact stress is: Where, E' is the cam-roller equivalent elastic modulus Pa; B0 is the contact line width m, that is, the cam width; During the operation of the cam-roller, the entrainment velocity changes dramatically. The generalized Reynolds equation is simplified to obtain the linear contact Reynolds equation under transient conditions: Where p is the oil film pressure distribution Pa; h is the oil film thickness distribution m; η is the lubricating oil viscosity Pa·s; ρ is the lubricating oil density kg / m 3 ; The boundary conditions required to solve the Reynolds equation are: Among them, x in and x out For the inlet and outlet coordinates of the computational domain, take x in = -4.5b and x out =1.5b; The cam curvature radius has a great influence on the film thickness. The film thickness equation for line contact lubrication of a smooth surface considering elastic deformation is: Where h0(t) is the rigid center film thickness m; R is the integrated curvature radius m; the third term in the film thickness equation is the elastic deformation term; within the entire lubricating film range, the lubricating film load obtained by integrating the pressure p should be balanced with the normal contact load per unit length between the cam and the roller: Among them, w load is the unit normal load between the oil supply cam and roller N / m; Step 3: Output the dynamic contact characteristics and lubrication status of the oil supply cam-roller pair during the operation cycle.

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