Shafting vibration characteristic analysis method and system based on elastohydrodynamic lubrication

Abstract

The invention discloses a shafting vibration characteristic analysis method and system based on elastohydrodynamic lubrication, and relates to the technical field of mechanical engineering.The method comprises the steps that the entrainment speed, the time-varying curvature radius and the contact load at a contact point in a gas distribution-oil supply cam pair are determined; respectively inputting the entrainment speed, the time-varying curvature radius and the contact load at the contact point into a friction analysis model in an elastohydrodynamic lubrication state, and calculating a time-varying curve of the total interfacial friction force of the gas distribution-oil supply cam pair in the whole working cycle; based on time-varying friction excitation corresponding to any moment in the change curve, determining a system excitation vector of the gas distribution-oil supply cam pair by using interface friction as a key connection quantity through experimental testing and simulation modeling technologies; according to the system excitation vector and the structure parameters of the camshaft system, establishing a camshaft system torsional vibration characteristic coupling analysis model considering the interface elastohydrodynamic state; and solving the shaft system torsional vibration differential equation set to obtain the influence rule of the time-varying friction on the instantaneous vibration characteristics of the camshaft system.

Description

TECHNICAL FIELD

[0001] The application relates to the technical field of mechanical engineering, in particular to a shaft system vibration characteristic analysis method and system based on elastohydrodynamic lubrication. BACKGROUND

[0002] The lubricating oil of the working interface of the valve gear-oil supply cam pair can form an oil film on the contact surface due to the fluid dynamic pressure, viscous pressure characteristics and elastic deformation effect, thereby reducing friction and wear and prolonging the service life of the parts. The friction excitation generated by the contact of the viscous lubricating oil with the surface presents nonlinear time-varying characteristics, and also causes the change of the comprehensive excitation of the interface, thereby affecting the multi-degree-of-freedom coupling vibration performance of the slender cam shaft system. In addition, the fluctuating speed caused by the system vibration also has a feedback effect on the contact interface, thereby affecting the changes of the lubricating film thickness and the friction coefficient and other parameters. Therefore, it is of great significance to explore the relationship between the elastohydrodynamic state of the cam shaft system interface and the system vibration effect. SUMMARY

[0003] The application aims to provide a shaft system vibration characteristic analysis method and system based on elastohydrodynamic lubrication, which can effectively analyze the vibration characteristics of the valve gear-oil supply cam pair under the elastohydrodynamic lubrication state.

[0004] To achieve the above-mentioned purpose, the application provides the following solutions:

[0005] In a first aspect, the application provides a shaft system vibration characteristic analysis method based on elastohydrodynamic lubrication, comprising:

[0006] According to the actual working parameters of the valve gear-oil supply cam pair, the entrainment speed, time-varying curvature radius and contact load at the contact point in the valve gear-oil supply cam pair are determined;

[0007] Based on the linear contact elastohydrodynamic lubrication theory, a friction analysis model under the elastohydrodynamic lubrication state is established; the friction analysis model under the elastohydrodynamic lubrication state is composed of a linear contact Reynolds equation, a contact lubricating film thickness equation, a contact load equation, a Bair-Winer rheological model and a flash temperature model;

[0008] The entrainment speed, time-varying curvature radius and contact load at the contact point are respectively input into the friction analysis model under the elastohydrodynamic lubrication state, and the change curve of the total friction force of the valve gear-oil supply cam pair with time in the entire working cycle is calculated; the change curve is used to reflect the change of the time-varying friction excitation;

[0009] Based on the time-varying friction excitation corresponding to any moment in the change curve, the system excitation vector of the valve gear-oil supply cam pair is determined by experimental testing and simulation modeling technology, with the interface friction as the key connection quantity;

[0010] Based on the system excitation vector and the structural parameters of the camshaft system, a coupled analysis model of the torsional vibration characteristics of the camshaft system considering the interfacial elastohydrodynamic state is established; the camshaft system is a shaft structure including the valve train-fuel supply cam pair; the coupled analysis model of the torsional vibration characteristics of the camshaft system includes a set of differential equations for the torsional vibration of the shaft system.

[0011] Based on the Newmark-β integral algorithm, the differential equations of shaft torsional vibration are solved to obtain the influence law of time-varying friction on the instantaneous vibration characteristics of the camshaft system.

[0012] Optionally, the formula for the line contact Reynolds equation is:

[0013]

[0014] Where p represents the fluid pressure distribution in the solution domain; h represents the oil film thickness distribution; η * ρ is the viscosity of the lubricating oil; u is the entrainment speed.

[0015] Optionally, the formula for the contact lubrication film thickness equation is:

[0016]

[0017] Where h0(t) is the normal approximation; x 2 / 2R represents the contact geometry before deformation; R(t) represents the time-varying radius of curvature of the cam pair; v e (x,y,t) represents the surface elastic deformation.

[0018] Optionally, the formula for the contact load equation is:

[0019]

[0020] Where F is the contact load obtained in the single-mass dynamic analysis, and y out The calculation area is the exit point along the y-direction; y in x is the entrance to the computational region along the y-direction; out Let x be the exit point of the calculation region along the x-direction; in This is the entry point of the computation region along the x-direction.

[0021] Optionally, the formula expression of the Bair-Winer rheological model is:

[0022]

[0023] in, τ is the shear rate. f For the oil film shear stress, τ L For the ultimate shear stress, G ∞ η is the limiting shear modulus, and η is the effective viscosity.

[0024] Optionally, the formula expression of the flash temperature model is:

[0025]

[0026] wherein, T b1 and T b2 is the initial surface temperature, ρ1, ρ2 is the density of the contact material, c1, c2 is the specific heat capacity of the contact material, k1, k2 is the thermal conductivity of the contact material, k f is the thermal conductivity of the lubricating oil, q is the heat generated in the lubricating contact area, is the contact interface temperature of the object 1, is the contact interface temperature of the object 2, ξ is the coordinate of the target point of the calculated temperature field, λ is the contact surface of the calculated temperature field, u2 is the sliding speed of the object 2 relative to the contact area, and u1 is the sliding speed of the object 1 relative to the contact area.

[0027] Optionally, based on the time-varying friction excitation corresponding to any moment in the change curve, the system excitation vector of the valve train-oil supply cam pair is determined by experimental testing and simulation modeling technology, with the interface friction as the key connection quantity, specifically including:

[0028] Based on the normal force F1 between the cam and the tappet and its arm L obtained by dynamic analysis, and the time-varying friction excitation corresponding to any moment in the change curve, the load torque T1 of a single valve train or oil supply cam pair is calculated according to the formula T1 = F1L + F f1 (R 11 +h α1 ); wherein, F f1 is the friction force, R 11 +h α1 is the arm of the friction force.

[0029] According to the number of cylinders, the firing order, the valve timing phase and the oil supply phase, the load torques T1 of the valve train and oil supply cam pairs of each cylinder are superimposed in time sequence, and based on the transmission relationship of the timing gear system, the system excitation vector of the valve train-oil supply cam pair is obtained.

[0030] Optionally, according to the system excitation vector and the structural parameters of the camshaft system, a coupling analysis model of the torsional vibration characteristics of the camshaft system considering the interface elastohydrodynamic state is established, specifically including:

[0031] The structure of the valve train-oil supply cam pair is discretized into 44 concentrated inertias;

[0032] Based on the load torque excitation condition of the valve train-oil supply cam, the differential equation set of the shaft system torsional vibration is established:

[0033] wherein, is an angular acceleration column vector, is an angular velocity column vector, {θ}=[θ1, θ2, …, θn]T 44 ] T is an angular displacement column vector, [J] is a camshaft system concentrated inertia matrix, [C] is a camshaft system damping matrix, [K] is a camshaft system stiffness matrix, and {T} is a system excitation vector.

[0034] Optionally, based on the Newmark-β integration algorithm, the shaft system torsional vibration differential equation set is solved to obtain the influence law of time-varying friction on the instantaneous vibration characteristics of the camshaft system, specifically including:

[0035] Based on the Newmark-β integration algorithm, the shaft system torsional vibration differential equation set is solved to obtain the response data of the instantaneous angular displacement, instantaneous angular velocity and instantaneous angular acceleration of each concentrated inertia varying with time;

[0036] The response data obtained under the conditions of considering and not considering the interface friction excitation are compared and analyzed to determine the influence law of time-varying friction on the instantaneous vibration characteristics of the camshaft system.

[0037] In a second aspect, the application provides a shaft system vibration characteristic analysis system based on elastohydrodynamic lubrication, comprising:

[0038] A calculation module is configured to determine the entrainment velocity, time-varying curvature radius and contact load at the contact point of the valve oil supply cam pair according to the actual working parameters of the valve oil supply cam pair.

[0039] A first analysis model construction module is configured to establish a friction analysis model in an elastohydrodynamic lubrication state based on the theory of linear contact elastohydrodynamic lubrication; the friction analysis model in the elastohydrodynamic lubrication state is composed of a linear contact Reynolds equation, a contact lubrication film thickness equation, a contact load equation, a Bair-Winer rheological model and a flash temperature model.

[0040] A curve drawing module is configured to input the entrainment velocity, time-varying curvature radius and contact load at the contact point into the friction analysis model in the elastohydrodynamic lubrication state respectively, and calculate the variation curve of the interface total friction of the valve oil supply cam pair over time within the entire working cycle; the variation curve is used to reflect the variation of the time-varying friction excitation.

[0041] An excitation vector calculation module is configured to determine the system excitation vector of the valve oil supply cam pair by experimental testing and simulation modeling technology based on the time-varying friction excitation corresponding to any time in the variation curve, with the interface friction as the key connection quantity.

[0042] a second analysis model construction module, configured to construct a torsional vibration characteristic coupling analysis model of the camshaft system considering the elastohydrodynamic state of the interface according to the system excitation vector and the structural parameters of the camshaft system; the camshaft system is a shaft structure comprising a valve distribution-oil supply cam pair; the torsional vibration characteristic coupling analysis model of the camshaft system comprises a shaft system torsional vibration differential equation set;

[0043] a law solving module, configured to solve the shaft system torsional vibration differential equation set based on a Newmark-β integration algorithm to obtain an influence law of the time-varying friction on the instantaneous vibration characteristics of the camshaft system.

[0044] According to the specific embodiments provided in the application, the following technical effects are disclosed:

[0045] The application provides an analysis method and system for vibration characteristics of a shaft system based on elastohydrodynamic lubrication. First, the actual working parameters of the valve distribution-oil supply cam pair determine the key information in the working state. The entrainment speed affects the formation and maintenance of the lubricating film, the time-varying curvature radius reflects the geometric shape change of the contact point between the cam and the follower, and the contact load directly determines the stress condition of the contact area. Then, a friction analysis model under the elastohydrodynamic lubrication state is established. The Reynolds equation of line contact describes the fluid pressure distribution and flow in the lubricating film and is the core equation for studying elastohydrodynamic lubrication, which can determine the pressure of the lubricating film to analyze the friction. The contact lubricating film thickness equation directly gives the film thickness, which is important for judging the lubrication state and calculating the friction. The appropriate film thickness can reduce the friction and vibration. The contact load equation clearly defines the stress in the contact area, which is related to the actual stress. The Bair-Winer rheological model describes the rheological properties of lubricating oil under high pressure. Since the elastohydrodynamic lubrication pressure is high, it can accurately reflect the behavior of the lubricating oil and help to accurately calculate the friction. The flash temperature model considers the instantaneous temperature change caused by friction heat in the contact. Temperature affects the performance of lubricating oil and material properties, and then affects the friction and vibration. The friction analysis model composed of these equations and models can comprehensively and accurately analyze the friction under elastohydrodynamic lubrication and provide key basis for vibration characteristic analysis. Then, the entrainment speed, time-varying curvature radius and contact load determined in the foregoing are input into the friction analysis model, and the curve of the total friction of the valve distribution-oil supply cam pair with respect to time in the entire working cycle can be obtained. The curve directly reflects the change of the time-varying friction excitation. Based on the time-varying friction excitation corresponding to any moment in the curve, the system excitation vector of the valve distribution-oil supply cam pair is determined by using experimental testing and simulation modeling technology with the interface friction as the key connection quantity. Then, a torsional vibration characteristic coupling analysis model of the camshaft system considering the elastohydrodynamic state of the interface is constructed according to the system excitation vector and the structural parameters of the camshaft system. Finally, the shaft system torsional vibration differential equation set is solved based on the Newmark-β integration algorithm, and the influence law of the time-varying friction on the instantaneous vibration characteristics of the camshaft system can be obtained. BRIEF DESCRIPTION OF DRAWINGS

[0046] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following will briefly introduce the drawings needed in the embodiments. Obviously, the drawings described below only illustrate some of the embodiments of the present application, and for those skilled in the art, other drawings can be obtained from these drawings without creative labor.

[0047] Figure 1 A flowchart of a shaft vibration characteristic analysis method based on elastohydrodynamic lubrication provided by an embodiment of the present application.

[0048] Figure 2 A kinematic analysis model schematic diagram of a valve cam-lifter pair provided by an embodiment of the present application.

[0049] Figure 3 A valve cam pair force analysis diagram provided by an embodiment of the present application.

[0050] Figure 4 An elastohydrodynamic lubrication pressure and film thickness schematic diagram provided by an embodiment of the present application.

[0051] Figure 5 A contact oil film shape and temperature distribution schematic diagram provided by an embodiment of the present application.

[0052] Figure 6 A valve oiling-cam shaft vibration analysis model schematic diagram in an elastohydrodynamic state provided by an embodiment of the present application.

[0053] Figure 7 An elastohydrodynamic state valve oiling-cam shaft torsional vibration coupling analysis flowchart provided by an embodiment of the present application.

[0054] Figure 8 A valve oiling-cam shaft instantaneous rotational speed fluctuation change schematic diagram provided by an embodiment of the present application.

[0055] Figure 9 A valve oiling-cam shaft segment additional stress change schematic diagram provided by an embodiment of the present application. DETAILED DESCRIPTION

[0056] The technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only some of the embodiments of the present application, but not all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the scope of the present application.

[0057] In order to make the above purposes, features and advantages of the present application more obvious and easy to understand, the present application will be further described in detail below with reference to the drawings and specific embodiments.

[0058] Embodiment one

[0059] As Figure 1 shown, the embodiment provides a shafting vibration characteristic analysis method based on elastohydrodynamic lubrication, comprising:

[0060] Step 101: According to the actual working parameters of the valve oil supply cam pair, the entrainment velocity, time-varying curvature radius and contact load at the contact point in the valve oil supply cam pair are determined;

[0061] Step 102: Based on the linear contact elastohydrodynamic lubrication theory, a friction analysis model under elastohydrodynamic lubrication state is established; the friction analysis model under elastohydrodynamic lubrication state is composed of linear contact Reynolds equation, contact lubrication film thickness equation, contact load equation, Bair-Winer rheological model and flash temperature model;

[0062] Step 103: The entrainment velocity, time-varying curvature radius and contact load at the contact point are input into the friction analysis model under elastohydrodynamic lubrication state respectively, and the change curve of the interface total friction force of the valve oil supply cam pair with time in the whole working cycle is calculated; the change curve is used to reflect the change of time-varying friction excitation;

[0063] Step 104: Based on the time-varying friction excitation corresponding to any time in the change curve, through experimental test and simulation modeling technology, the interface friction is determined as the key connection quantity, and the system excitation vector of the valve oil supply cam pair is determined;

[0064] Step 105: According to the system excitation vector and the structural parameters of the camshaft, a camshaft torsional vibration characteristic coupling analysis model considering the interface elastohydrodynamic state is established; the camshaft is a shafting structure containing the valve oil supply cam pair; the camshaft torsional vibration characteristic coupling analysis model includes a shafting torsional vibration differential equation set;

[0065] Step 106: Based on the Newmark-β integral algorithm, the shafting torsional vibration differential equation set is solved, and the influence law of time-varying friction on the instantaneous vibration characteristics of the camshaft is obtained.

[0066] In some embodiments, when step 101 is performed, it includes:

[0067] determining the contact point of the valve oil supply cam pair:

[0068] (1) Kinematics analysis of valve cam pair:

[0069] When the camshaft rotates, it pushes the tappet and push rod to move, and converts the rotary motion into reciprocating linear motion of the valve through the rocker arm. The surface speed of the cam-tappet pair under constant speed is calculated, so as to obtain the entrainment speed, curvature radius and other parameters between the contact surfaces, thereby providing important input parameters for analyzing the friction and lubrication state of the cam pair. The kinematic analysis model of the cam-tappet pair is established based on the kinematics of the particle, as shown in Figure 2 .

[0070] In Figure 2 , X1O1Y1 is a fixed coordinate system, and the coordinate origin is fixed at the cam center; P1 is the contact point of the cam and the tappet, which changes with the rotation of the cam; R P1 is the radius of the contact point relative to the coordinate origin O1. In the analysis, only the up-and-down reciprocating motion of the tappet along the center line is considered, and the spin and deflection of the tappet are ignored. Assuming that the cam surface speed u 11 at the contact point P1 is

[0071] u 11 = ω1R P1 (1).

[0072] The horizontal and vertical velocity components of the cam surface speed u 11 at the contact point are:

[0073]

[0074] The horizontal and vertical components of the tappet surface speed u 12 at the contact point are and In the analysis, the lateral movement of the tappet is not considered, and the cam and the tappet always maintain contact, so their sizes can be represented as:

[0075]

[0076] Assuming that the cam and the tappet do not separate during operation, we have:

[0077]

[0078] From equations (2), (3) and (4), we have

[0079]

[0080] where L is the contact offset of the cam pair, and ω1 is the angular velocity of the cam pair.

[0081] With the rotation of the camshaft, the contact point of the cam and the tappet moves along the cam profile. Let the moving speed of the contact point relative to the flat tappet be u 12 , then:

[0082]

[0083] where, is the virtual acceleration derived from cam profile, which is independent of time and rotational speed.

[0084] Since the rotation of the flat tappet is neglected, i.e. The relative velocity between the tappet and the cam in the horizontal direction is ω1(R 11 +h α1 ), then the moving velocity of the contact point relative to the cam surface is

[0085]

[0086] Let R1 be the instantaneous radius of curvature of the tappet surface at the contact point with the cam, then the instantaneous radius of curvature of the cam surface at the contact point can be expressed as:

[0087]

[0088] where, R 11 is the base circle radius of the valve cam, h α1 is the valve cam lift.

[0089] (2) Valve-cam contact force:

[0090] In the operation process of the marine diesel engine valve train, the movement of each component is relatively complex. In order to facilitate the calculation, the tappet, push rod, rocker arm and valve mass are combined into a concentrated mass M1, as shown in Figure 3 The valve movement can be described by the movement of the concentrated mass M1. One end is connected to the cylinder head through the valve spring to ensure that the valve has a reaction force during opening and closing, and the other end is directly controlled by the valve cam, whose movement state is closely related to the cam geometry and rotational speed. The concentrated mass M1 can be calculated by the following formula:

[0091]

[0092] where, k r is the rocker arm ratio, m v is the valve spring mass, m e is the sum of the mass of the valve lock and other parts, I0 is the moment of inertia of the rocker arm, l0 is the length of the rocker arm on the tappet side, m T is the tappet mass, m P is the push rod mass.

[0093] The force F1 between the cam and the tappet is mainly composed of the valve spring force F T1 , the inertia force F N1 , and the gas force FG The specific solution is as follows:

[0094] F1=F T1 +F N1 +k i F G (10).

[0095] In the formula, F T1 is the gas valve spring force, F N1 is the part inertia force, F G is the gas acting force, k i is the intake and exhaust indication, k i =0 indicates intake, and k i =1 indicates exhaust.

[0096] F T1 =k r [F 01 +k s1 h α1 ] (11).

[0097] In the formula, F 01 is the gas valve spring pre-tightening force, and k s1 is the gas valve spring stiffness.

[0098]

[0099] In the formula, M1 is the concentrated mass of the valve train, and ω1 is the cam angular velocity of the valve train.

[0100] F G is the gas acting force, the in-cylinder gas pressure p g is known, and only the gas acting on the valve bottom surface is considered, so the change of the gas acting force can be obtained as follows:

[0101]

[0102] In the formula, d v is the valve disc diameter, and p g is the in-cylinder pressure.

[0103] The modules are consistent in calculating the load torques of the intake and exhaust cam pairs, but the exhaust valve system needs to additionally consider the influence of the combustion pressure. The load torques of the intake and exhaust valve trains mainly come from the inertia force, spring force, and gas force as well as the friction force, and the valve seat elastic reaction force and damping force when the valve is seated are not considered. As can be seen from Figure 3 , the force arm of the cam-lifter interaction force F1 is L, the force arm of the friction force F f1 is R 11 +h α1 , and L=dh α1Therefore, according to the above calculation of the cam-lifter pair force and the force arm corresponding to the force, the effect of each force can be effectively quantified, and the load torque of a single valve cam pair is obtained as:

[0104] T1 = F1L + F f1 (R 11 +h α1 ) (14).

[0105] In some embodiments, when step 102 is performed, it can be specifically as follows:

[0106] A friction analysis model under elastohydrodynamic lubrication is established, as shown in Figure 4 In the high load contact area, the fluid dynamic pressure distribution is approximately the Hertz pressure distribution, and the oil film thickness distribution in the contact area is almost uniform, and the lubrication performance in the contact area is relatively stable. In addition, a secondary pressure peak appears near the outlet of the contact area, which corresponds to the position of the oil film thickness necking (minimum oil film thickness), which is a typical sign of oil film pressure and thickness distribution in elastohydrodynamic lubrication.

[0107] In the elastohydrodynamic lubrication equation set, the Reynolds equation for solving the oil film pressure, the film thickness equation for solving the film thickness distribution, the elastic deformation equation for solving the elastic deformation, and the load balance equation for determining the convergence condition are included, and the viscosity and density of the lubricating oil also change significantly with the change of pressure. Elastohydrodynamic lubrication analysis can obtain the oil film pressure and thickness distribution in the lubrication contact area, and the pressure distribution in the contact area can be solved by the Reynolds equation. However, during the operation of the valve-cylinder-lubricating cam pair, the entrainment speed changes sharply and it is one of the important parameters affecting the contact film thickness, and the linear contact Reynolds equation under transient conditions is:

[0108]

[0109] In the formula, p is the fluid pressure distribution in the solution domain, h is the oil film thickness distribution, η * is the viscosity of the lubricating oil, ρ is the density of the lubricating oil, and u is the entrainment speed, which is defined as the average value of the speed of the two surfaces.

[0110] During the operation of the cam pair, the curvature radius is transiently changed, and it is not kept at a fixed value except for the base circle segment. The cam curvature radius has a great influence on the film thickness, so the contact lubrication film thickness equation considering elastic deformation is:

[0111]

[0112] In the formula, h0(t) is the normal approach, x 2 / 2R is the contact geometry without deformation, R(t) is the time-varying curvature radius of the cam pair, and v e(x, y, t) is the elastic deformation of the surface, which can be calculated by hydrodynamic pressure.

[0113] To ensure the accuracy of numerical calculation in the whole range of lubricating film, the load of lubricating film obtained by integrating the oil film pressure should be balanced with the contact load between cam pair:

[0114]

[0115] In the formula, F is the contact load obtained in single mass dynamic analysis.

[0116] 1The lubricating oil film not only bears shear force but also is compressed, resulting in friction heat between the contact interface and temperature rise of the friction interface. The oil film morphology and temperature distribution during the contact process, such as Figure 5 , are shown.

[0117] During actual operation, a certain amount of heat will be generated due to friction between the cam pair interface, resulting in a coupling reaction between temperature change and lubricating oil properties, which may affect the viscosity and flow characteristics of the lubricating oil. The Bair-Winer model is a rheological model based on a large amount of experimental data to describe the fluid behavior in elastohydrodynamic lubrication contact, which is especially suitable for the rheological behavior of lubricating oil under high shear rate. Therefore, using the Bair-Winer rheological model to solve the oil film friction in the contact domain can more accurately reflect the flow characteristics of the lubricating oil under actual working conditions.

[0118]

[0119] In the formula, τ f is the shear stress of the oil film, is the interface temperature, τ L is the limiting shear stress, G ∞ is the limiting shear modulus, which is a pressure and temperature function of the lubricating oil performance parameter, which can be estimated using the Dyson model, and η is the effective viscosity.

[0120]

[0121] The shear rate refers to the rate of change of a layer of fluid relative to the adjacent layer. Since the oil film thickness is thin, the shear rate can be assumed as:

[0122]

[0123] In order to facilitate the solution of shear stress in the contact area, the following transformation can be made.

[0124]

[0125] Substituting formulas (20) and (21) into formula (19) can be written as:

[0126]

[0127] The shear stress at each node can be obtained by using the dichotomy method, and the shear stress distribution τ f (x,y), and then the friction force in the lubrication film can be calculated by integration, as shown in equation (23).

[0128]

[0129] The limiting shear stress of the lubricant is a function of temperature, so that the interface friction is significantly affected by the surface temperature. The change of friction directly determines the heat generated at the interface, so there is a mutual dependence between friction and flash temperature. Therefore, based on the fast moving heat source theory model, the surface heat conduction perpendicular to the heat source velocity direction is ignored, and the convex cam pair interface temperature calculation model is established by means of the second type of Volterra integral equation.

[0130]

[0131] In the formula, T b1 and T b2 are the initial temperature of the surface, ρ1, ρ2 are the density of the contact material, c1, c2 are the specific heat capacity of the contact material, k1, k2 are the thermal conductivity of the contact material, k f is the thermal conductivity of the lubricating oil, and q is the heat generated in the lubricating contact area.

[0132] In some embodiments, when steps 103-104 are performed, the following can be specifically performed:

[0133] Based on the friction analysis model under the elastohydrodynamic lubrication state, the change of the time-varying friction excitation of the convex cam pair interface is obtained.

[0134] Specifically, the numerical solution of the friction analysis model under the elastohydrodynamic lubrication state is performed, and the total friction force F f1 of the convex cam pair interface is calculated within the entire working cycle. The change of the time-varying friction excitation is specifically embodied as the friction force-time variation curve F f1 , which reflects the dynamic response characteristics of the friction under transient working conditions, and is a key excitation quantity connecting the micro-interface behavior of elastohydrodynamic lubrication and the macro-vibration of the shaft system.

[0135] Based on the friction excitation, the camshaft excitation is obtained by means of experimental testing and simulation modeling, taking the interface friction as a key connection quantity.

[0136] The normal force F1 between the cam and the tappet and the force arm L obtained in step 101 are considered, as well as the friction force F f1and its force arm R 11 + h α1 , the load torque T1 of the single valve or oil distribution cam pair is calculated:

[0137] T1 = F1L + F f1 (R 11 + h α1 ) (26).

[0138] According to the number of cylinders, the firing order, the valve timing and the oil distribution timing of the diesel engine, the load torques T1 of the valve cam pairs and the oil distribution cam pairs of each cylinder are superimposed in time sequence, and the transmission relationship of the timing gear system is considered to obtain a time-varying comprehensive driving torque excitation vector {T} acting on the entire camshaft system, that is, a system excitation vector. The excitation vector {T} is an input condition for subsequent torsional vibration analysis of the camshaft system.

[0139] In some embodiments, based on the excitation vector {T} obtained in step 104 and the structural parameters of the camshaft system, a coupling analysis model of the torsional vibration characteristics of the camshaft system considering the elastohydrodynamic state of the interface is established, which can be specifically as follows:

[0140] A lumped parameter model is used for torsional vibration analysis of the valve-oil distribution camshaft system. In the model construction process, it is assumed that all dynamic variables in the system are independent of the overall layout, and space homogenization processing is used to simplify the model. The lumped parameter model is widely used in dynamic problems where spatial variation is not the main concern because of its convenient calculation. In dynamic conditions, this model meets the ordinary differential equation and can effectively characterize the evolution of the system over time. This model is particularly suitable for engineering problems that require simplified processing and do not require high overall system behavior. Its independent variable characteristics and adaptability to different calculation conditions make the lumped parameter model an important numerical modeling tool for solving practical problems in the engineering field.

[0141] The vibration analysis model of the valve-oil distribution camshaft system under the elastohydrodynamic state is shown in FIG. 1. The valve-oil distribution camshaft system is connected by the timing gear system, so the front gear transmission system needs gear mass parameters, including moment of inertia, excitation torque and mesh stiffness, etc. in the modeling process. The modeling of the camshaft system includes the moment of inertia of the camshaft segment, the excitation of the cam pair and the contact stiffness, etc. The equivalent parameter model of the diesel engine camshaft system can be divided into 44 inertias, of which inertias 1, 2, 13 and 24 are gear inertias, inertias 3-12 and 14-23 are valve camshaft inertias, and inertias 25-44 are oil distribution camshaft inertias. The torsional lumped parameters of the camshaft system are shown in Table 1. Figure 6 Table 1 Torsional lumped parameters of the camshaft system

[0142]

[0143]

[0144] ​

[0145] The parts of the valve gear and oil supply mechanism are represented by lumped masses, the connections between the shaft segments are replaced by stiffness-damping models, and the interface friction excitation is considered in the system vibration analysis model. For a relatively regular camshaft, J i is the rotational inertia of the shaft segment, θ i is the torsion angle of the camshaft segment, T i is the total force moment of the cam. The valve gear-oil supply camshaft system involves a large number of inertias, and the influence of the valve gear and oil supply valve system is considered to establish a torsional vibration analysis model of the diesel engine valve gear-oil supply camshaft system. According to the known parameters of the stiffness, damping, and rotational inertia of each part of the camshaft system, and based on the load torque excitation conditions of the valve gear-oil supply cam, the shaft system torsional vibration differential equation set is:

[0146]

[0147] In the formula, is the angular acceleration column vector, is the angular velocity column vector, {θ} = [θ1, θ2, …, θ 44 ] T is the angular displacement column vector.

[0148] [J] is the lumped inertia matrix of the camshaft system, and the specific form is:

[0149]

[0150] In the formula, J n is the rotational inertia of each shaft segment.

[0151] [C] is the damping matrix of the camshaft system, and the specific form is:

[0152]

[0153] In the formula, c n-1,n is the damping between the n-1 inertia and the n inertia.

[0154] [K] is the stiffness matrix of the camshaft system, and the specific form is:

[0155]

[0156] In the formula, k cn-1,n is the stiffness between the n-1 inertia and the n inertia.

[0157] {T} is the excitation vector acting on the system, and the specific form is:

[0158]

[0159] In the formula, T nThe driving torque borne by each inertia.

[0160] When steps 105-106 are performed, the following can be specifically implemented:

[0161] According to the system excitation vector and the structural parameters of the camshaft system, a coupling analysis model of torsional vibration characteristics of the camshaft system considering the interface elastohydrodynamic state is established, which specifically includes:

[0162] The shaft system structure of the valve timing-camshaft phasing (VCP) system is discretized into 44 concentrated inertias.

[0163] Based on the load torque excitation condition of the VCP system, a system of differential equations of shaft system torsional vibration is established:

[0164]

[0165] In the formula, is an angular acceleration column vector, is an angular velocity column vector, and {θ}=[θ1,θ2,…,θ 44 ] T is an angular displacement column vector, [J] is a concentrated inertia matrix of the camshaft system, [C] is a damping matrix of the camshaft system, [K] is a stiffness matrix of the camshaft system, and {T} is a system excitation vector.

[0166] Based on the Newmark-β integration algorithm, the system of differential equations of shaft system torsional vibration is solved to obtain the influence law of time-varying friction on the instantaneous vibration characteristics of the camshaft system, which specifically includes:

[0167] Based on the Newmark-β integration algorithm, the system of differential equations of shaft system torsional vibration is solved to obtain the response data of the instantaneous angular displacement, instantaneous angular velocity, and instantaneous angular acceleration of each concentrated inertia varying with time;

[0168] The response data obtained under the conditions of considering and not considering the interface friction excitation are compared and analyzed to determine the influence law of time-varying friction on the instantaneous vibration characteristics of the camshaft system.

[0169] In addition, the present embodiment is also based on a diesel engine camshaft system dynamics equivalent simulation test bench, and the correctness of the numerical model is verified by comparing the instantaneous speed variation. Specifically as follows:

[0170] Based on the diesel engine camshaft system dynamics equivalent simulation test bench, the instantaneous speed signals of the key measuring points are accurately measured; the coupling analysis model of torsional vibration characteristics of the camshaft system considering the interface elastohydrodynamic state established in step 105 is used to calculate the instantaneous speed simulation signals of the same measuring points under the same working conditions.

[0171] The measured instantaneous speed change curve is compared with the curve obtained by numerical simulation in time domain waveform and frequency domain characteristics. If the two are well matched in the main characteristics, the correctness and reliability of the established camshaft torsional vibration coupling analysis model considering the elastohydrodynamic state of the interface and its calculation results are verified.

[0172] For the analysis of the torsional vibration coupling of the valve distribution-oil supply camshaft under the elastohydrodynamic state, the process is as shown in the figure. Figure 7 First, the cam pair motion and dynamics analysis model is established to determine the current motion and force state in the cam pair contact area, and then the cam pair lubrication performance and interface friction excitation are obtained based on the line contact elastohydrodynamic lubrication model. However, due to the combined effects of transient mutation working conditions and complex geometric structures of the cam pair, the lubrication film pressure will rise sharply and the film thickness will decrease, often causing convergence difficulties of the coefficient matrix diagonal non-optimization, especially under low-speed heavy-load conditions. Therefore, the quasi-system numerical analysis method is used to analyze the friction and lubrication performance of the cam pair under the contact mutation working condition.

[0173] Based on the established valve distribution and oil supply cam pair load torque calculation model, the relationship between the firing sequence of each cylinder and the valve distribution phase is considered, and the interface friction excitation is used as the key connection quantity to calculate the comprehensive torque change of the cam pair under the combined action of multi-valve system dynamic excitation. Then, the two-way coupling iteration model of camshaft friction and vibration is constructed, and combined with the gear system excitation, camshaft structure parameters, stiffness and damping parameters, and excitation torque, etc., the influence of friction excitation on the elastic dynamics of valve distribution-oil supply camshaft is obtained. The dynamics calculation of the shaft system involves multi-degree-of-freedom and nonlinear excitation, which brings difficulties to the shaft vibration analysis. Therefore, based on the Newmark integral algorithm, the nonlinear and multi-degree-of-freedom system response is processed, and the real-time speed and acceleration of the shaft system are obtained. Finally, based on the camshaft friction and vibration co-analysis, the cam pair fluctuating speed is obtained, and the current fluctuating speed is fed back to the cam pair friction lubrication calculation to realize synchronous updating, and a cross-scale dynamic coupling closed-loop analysis is formed, until all transient friction and lubrication performance calculations of the camshaft running period are completed.

[0174] For the analysis of the torsional vibration characteristics of the camshaft under the elastohydrodynamic state, the specific process is as follows:

[0175] During operation, the valve train and fuel supply camshaft system of a diesel engine is subjected to both external excitations (such as gas pressure and component loads) and internal excitations (such as interface friction), causing each camshaft end to deviate from its stable speed. This unstable velocity fluctuation then feeds back to the contact interface, affecting parameters such as lubrication film thickness and friction coefficient, and also causing unnecessary vibration noise and energy loss in the camshaft system, thus impacting the overall efficiency of the transmission system. Therefore, based on the cam pair friction lubrication and camshaft system torsional vibration analysis model established in this chapter under elastohydrodynamic conditions, a cross-scale coupled analysis of the vibration characteristics of the valve train and fuel supply camshaft system under elastohydrodynamic conditions is conducted.

[0176] The instantaneous speed fluctuation of the valve train and fuel supply camshaft, such as Figure 8 As shown. By Figure 8 Analysis shows that the speed fluctuation range is smaller near the input end, while the free end, due to its lower structural stiffness, exhibits a larger instantaneous speed fluctuation range. Because the fuel injection camshaft bears a greater driving torque, its instantaneous speed is significantly higher than that of the valve train. Considering the time-varying friction excitation at the interface, which increases the overall driving torque, the increase in instantaneous speed at each camshaft end is even more pronounced. For example, the maximum increase in speed fluctuation at the exhaust camshaft end is 10 r / min, the maximum increase at the fuel injection camshaft end is 8.5 r / min, while the maximum increase at the fuel injection camshaft end is 25 r / min.

[0177] Vibration of the camshaft system causes relative changes in the torsion angle between the camshafts, resulting in additional torque on the shaft system and thus generating corresponding additional stress. Figure 9 The variation of additional stress in the valve train and fuel injection camshafts is presented. By comparing the additional stress of the three camshafts, it is found that the additional stress level of the fuel injection camshaft is higher, and its shaft vibration characteristics are worse than those of the valve train camshaft. This is mainly due to the higher fuel injection pressure and excessive drive torque experienced by the fuel injection camshaft. Considering interfacial friction, the additional stress at the valve train camshaft end increases by approximately 1.0 MPa, while that at the fuel injection camshaft end increases by approximately 3.5 MPa. The allowable additional stress value for the camshaft section is 25 MPa. Although it does not reach the allowable shaft stress considering interfacial friction, it is still nearly 30% higher than that without considering friction, indicating that interfacial friction has a significant effect on the shaft vibration characteristics. The analysis results also show that the fuel injection camshaft not only faces higher additional shaft stress but also a significant increase in instantaneous speed fluctuations, which may negatively affect the timeliness and stability of the camshaft's fuel injection timing.

[0178] Example 2

[0179] This embodiment provides a shaft vibration characteristic analysis system based on elastohydrodynamic lubrication, including:

[0180] The computing module is configured to determine the entrainment velocity, the time-varying curvature radius and the contact load at the contact point in the valve-oil distribution cam pair according to actual working parameters of the valve-oil distribution cam pair.

[0181] The first analysis model construction module is configured to establish a friction analysis model in an elastohydrodynamic lubrication state based on a line contact elastohydrodynamic lubrication theory.

[0182] The curve drawing module is configured to input the entrainment velocity, the time-varying curvature radius and the contact load at the contact point into the friction analysis model in the elastohydrodynamic lubrication state respectively, and calculate a curve of the total interface friction force of the valve-oil distribution cam pair varying with time within the entire working cycle.

[0183] The excitation vector calculation module is configured to determine a system excitation vector of the valve-oil distribution cam pair by experimental testing and simulation modeling technology based on the time-varying friction excitation corresponding to any moment in the curve, with the interface friction as a key connection quantity.

[0184] The second analysis model construction module is configured to establish a coupling analysis model of torsional vibration characteristics of the camshaft system considering the interface elastohydrodynamic state according to the system excitation vector and structural parameters of the camshaft system.

[0185] The law solving module is configured to solve the differential equation set of the torsional vibration of the camshaft system based on a Newmark-β integral algorithm to obtain an influence law of the time-varying friction on the instantaneous vibration characteristics of the camshaft system.

[0186] In summary, the present application has the following technical effects:

[0187] The present application takes the valve-oil distribution camshaft system as the research object, comprehensively considers the influences of the non-Newtonian fluid effect of lubricating oil and thermal shear strain rate and other factors, establishes a line contact friction and lubrication analysis model considering the dynamics of the cam pair, and combines the structural stiffness of the cam pair, friction and system excitation and the like to construct a torsional vibration characteristic analysis model of the valve-oil distribution camshaft system in an elastohydrodynamic state, builds an equivalent camshaft system dynamics test bench to verify the correctness of the model, and studies the influence of the interface friction of the cam pair on the dynamic performance of the valve-oil distribution camshaft system.

[0188] Any combination of the technical features of the above embodiments can be made, and for the sake of brevity, not all possible combinations are described in the above description. However, it should be understood that the scope of the specification includes all possible combinations of the technical features.

[0189] The principles and implementations of the present application are described in the specific examples, and the above examples are only used to help understand the method and core idea of the present application; meanwhile, for those skilled in the art, according to the idea of the present application, the specific implementation and application range will be changed. In summary, the content of the specification should not be understood as a limitation of the present application.

Claims

1. A method for analyzing the vibration characteristics of shaft systems based on elastohydrodynamic lubrication, characterized in that, include: Based on the actual working parameters of the valve train-fuel supply cam pair, determine the entrainment speed, time-varying radius of curvature, and contact load at the contact point in the valve train-fuel supply cam pair; Based on the theory of line contact elastohydrodynamic lubrication, a friction analysis model under elastohydrodynamic lubrication state is established; The friction analysis model under the elastohydrodynamic lubrication state consists of the Reynolds equation for line contact, the equation for contact lubrication film thickness, the equation for contact load, the Bair-Winer rheological model, and the flash temperature model. The entrainment velocity, time-varying radius of curvature, and contact load at the contact point are respectively input into the friction analysis model under the elastohydrodynamic lubrication state to calculate the curve of the total interfacial friction force of the valve-fuel cam pair changing with time throughout the entire working cycle; the curve is used to reflect the change of time-varying friction excitation. Based on the time-varying friction excitation corresponding to any moment in the aforementioned change curve, the system excitation vector of the valve-fuel cam pair is determined through experimental testing and simulation modeling techniques, with interface friction as the key connection quantity. Based on the system excitation vector and the structural parameters of the camshaft system, a coupled analysis model of the torsional vibration characteristics of the camshaft system considering the interfacial elastohydrodynamic state is established; the camshaft system is a shaft structure including the valve train-fuel supply cam pair; the coupled analysis model of the torsional vibration characteristics of the camshaft system includes a set of differential equations for the torsional vibration of the shaft system. Based on the Newmark-β integral algorithm, the differential equations of shaft torsional vibration are solved to obtain the influence law of time-varying friction on the instantaneous vibration characteristics of the camshaft system.

2. The method for analyzing shaft vibration characteristics based on elastohydrodynamic lubrication according to claim 1, characterized in that, The formula for the Reynolds equation for line contact is: Where p represents the fluid pressure distribution in the solution domain; h represents the oil film thickness distribution; η * ρ is the viscosity of the lubricating oil; u is the entrainment speed.

3. The method for analyzing shaft vibration characteristics based on elastohydrodynamic lubrication according to claim 1, characterized in that, The formula for the contact lubrication film thickness equation is as follows: Where h0(t) is the normal approximation; x 2 / 2R represents the contact geometry before deformation; R(t) represents the time-varying radius of curvature of the cam pair; v e (x,y,t) represents the surface elastic deformation.

4. The method for analyzing shaft vibration characteristics based on elastohydrodynamic lubrication according to claim 1, characterized in that, The formula for the contact load equation is as follows: Where F is the contact load obtained in the single-mass dynamic analysis, and y out The calculation area is the exit point along the y-direction; y in x is the entrance to the computational region along the y-direction; out Let x be the exit point of the calculation region along the x-direction; in This is the entry point of the computation region along the x-direction.

5. The method for analyzing shaft vibration characteristics based on elastohydrodynamic lubrication according to claim 1, characterized in that, The formula for the Bair-Winer rheological model is as follows: in, τ is the shear rate. f For the oil film shear stress, τ L For the ultimate shear stress, G ∞ η is the limiting shear modulus, and η is the effective viscosity.

6. The method for analyzing shaft vibration characteristics based on elastohydrodynamic lubrication according to claim 1, characterized in that, The formula for the flash temperature model is as follows: In the formula, T b1 and T b2 Let ρ1 and ρ2 be the initial surface temperature, ρ1 and ρ2 be the densities of the contact materials, c1 and c2 be the specific heat capacities of the contact materials, k1 and k2 be the thermal conductivity of the contact materials, and k be the initial surface temperature. f Let q be the thermal conductivity of the lubricating oil, and q be the heat generated in the lubrication contact area. The temperature of the contact interface of object 1. Let ξ be the temperature of the contact interface of object 2, ξ be the coordinates of the target point for calculating the temperature field, λ be the contact surface for calculating the temperature field, u2 be the sliding velocity of object 2 relative to the contact area, and u1 be the sliding velocity of object 1 relative to the contact area.

7. The method for analyzing shaft vibration characteristics based on elastohydrodynamic lubrication according to claim 1, characterized in that, Based on the time-varying frictional excitation corresponding to any moment in the aforementioned variation curve, and through experimental testing and simulation modeling techniques, using interface friction as the key connectivity quantity, the system excitation vector of the valve-fuel cam pair is determined, specifically including: Based on the normal force F1 and its lever arm L between the cam and tappet obtained from the dynamic analysis, and the time-varying friction excitation corresponding to any moment in the variation curve, according to the formula T1=F1L+F f1 (R 11 +h α1 ) Calculate the load torque T1 of a single valve train or fuel injection cam pair; where, F f1 For friction, R 11 +h α1 The lever arm of the frictional force; Based on the number of cylinders, firing order, valve timing, and fuel injection phase of the diesel engine, the load torque T1 of the valve timing cam pair and fuel injection cam pair of each cylinder is superimposed in time sequence, and the system excitation vector of the valve timing cam pair is determined based on the transmission relationship of the timing gear system.

8. The method for analyzing shaft vibration characteristics based on elastohydrodynamic lubrication according to claim 1, characterized in that, Based on the system excitation vector and the structural parameters of the camshaft system, a coupled analysis model of the torsional vibration characteristics of the camshaft system considering the interfacial elastohydrodynamic state is established, specifically including: The shaft system structure of the valve train-fuel cam pair is discretized into 44 lumped inertia; Based on the excitation condition of the valve train-fuel supply cam load torque, a set of differential equations for shaft torsional vibration is established: In the formula, Let angular acceleration be the column vector. Let {θ} be the column vector of angular velocities, where {θ} = [θ1, θ2, ..., θ 44 ] T {J} is the column vector of angular displacement, [C] is the lumped inertia matrix of the camshaft system, [K] is the damping matrix of the camshaft system, [K] is the stiffness matrix of the camshaft system, and {T} is the excitation vector of the system.

9. The method for analyzing shaft vibration characteristics based on elastohydrodynamic lubrication according to claim 1, characterized in that, Based on the Newmark-β integral algorithm, the differential equations of torsional vibration of the shaft system are solved to obtain the influence law of time-varying friction on the instantaneous vibration characteristics of the camshaft system, specifically including: The torsional vibration differential equations of the shaft system were solved using the Newmark-β integral algorithm, and the response data of instantaneous angular displacement, instantaneous angular velocity and instantaneous angular acceleration of each concentrated inertia as a function of time were obtained. By comparing and analyzing the response data calculated under the two cases of considering interface friction excitation and not considering interface friction excitation, the influence law of time-varying friction on the instantaneous vibration characteristics of the camshaft system is determined.

10. A shaft vibration characteristic analysis system based on elastohydrodynamic lubrication, characterized in that, include: The calculation module is used to determine the entrainment speed, time-varying radius of curvature, and contact load at the contact point of the valve-fuel cam pair based on the actual working parameters of the valve-fuel cam pair. The first analytical model construction module is used to establish a friction analysis model under elastohydrodynamic lubrication based on the line contact elastohydrodynamic lubrication theory. The friction analysis model under elastohydrodynamic lubrication consists of the line contact Reynolds equation, the contact lubrication film thickness equation, the contact load equation, the Bair-Winer rheological model, and the flash temperature model. The curve plotting module is used to input the entrainment velocity, time-varying radius of curvature, and contact load at the contact point into the friction analysis model under the elastohydrodynamic lubrication state, and calculate the curve of the total interfacial friction force of the valve-fuel cam pair changing with time throughout the entire working cycle; the curve is used to reflect the changes in time-varying friction excitation. The excitation vector calculation module is used to determine the system excitation vector of the valve-fuel cam pair based on the time-varying friction excitation corresponding to any moment in the change curve, through experimental testing and simulation modeling techniques, with interface friction as the key connection quantity. The second analysis model construction module is used to establish a coupled analysis model of the torsional vibration characteristics of the camshaft system, considering the interfacial elastohydrodynamic state, based on the system excitation vector and the structural parameters of the camshaft system. The camshaft system is a shaft structure that includes a valve train-fuel supply cam pair. The coupled analysis model of the torsional vibration characteristics of the camshaft system includes a set of differential equations for the torsional vibration of the shaft system. The law-solving module is used to solve the differential equations of shaft torsional vibration based on the Newmark-β integral algorithm, and obtain the law of influence of time-varying friction on the instantaneous vibration characteristics of the camshaft system.

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