WO2023236593A1 - 一种计算翻边轴承耦合润滑与动力学特性参数的方法 - Google Patents

一种计算翻边轴承耦合润滑与动力学特性参数的方法 Download PDF

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WO2023236593A1
WO2023236593A1 PCT/CN2023/078759 CN2023078759W WO2023236593A1 WO 2023236593 A1 WO2023236593 A1 WO 2023236593A1 CN 2023078759 W CN2023078759 W CN 2023078759W WO 2023236593 A1 WO2023236593 A1 WO 2023236593A1
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radial
bearing
oil film
thrust
axial
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PCT/CN2023/078759
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English (en)
French (fr)
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赵滨
施佳皓
卢熙群
李玩幽
徐含章
马旋
史修江
率志君
郭宜斌
王东华
李宏亮
董烈祎
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哈尔滨工程大学
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Priority to US18/291,586 priority Critical patent/US20240264039A1/en
Publication of WO2023236593A1 publication Critical patent/WO2023236593A1/zh

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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
    • G01M13/00—Testing of machine parts
    • G01M13/04—Bearings
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/11—Complex mathematical operations for solving equations, e.g. nonlinear equations, general mathematical optimization problems
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01L—MEASURING FORCE, STRESS, TORQUE, WORK, MECHANICAL POWER, MECHANICAL EFFICIENCY, OR FLUID PRESSURE
    • G01L5/00—Apparatus for, or methods of, measuring force, work, mechanical power, or torque, specially adapted for specific purposes
    • G01L5/0009—Force sensors associated with a bearing
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/14—Force analysis or force optimisation, e.g. static or dynamic forces
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
    • Y02T90/00—Enabling technologies or technologies with a potential or indirect contribution to GHG emissions mitigation

Definitions

  • the invention relates to the technical field of diesel engine simulation, and belongs to a method for calculating coupling lubrication and dynamic characteristic parameters of flanged bearings.
  • crankshaft-bearing system's lubrication performance will directly affect the reliability and life of the diesel engine.
  • the flange bearing is generally located at the end of the crankshaft. It is an important component that radially supports the crankshaft and prevents its axial movement. It is very easy for the oil film gap to be very small, and the lubrication conditions are relatively harsh, often accompanied by high-temperature ablation, thereby reducing the diesel engine's performance. life.
  • a method for calculating the coupled lubrication and dynamic characteristics parameters of the flanged bearing is proposed, a simulation model is established that comprehensively considers the radial thrust thermoelastohydrodynamic lubrication and dynamic characteristics of the flanged bearing, and the radial thrust of the flanged bearing is established.
  • the pressure coupling and thermal coupling relationship of the push part can more accurately explain the lubrication mechanism that causes ablation, reveal the lubrication and dynamic laws of flange bearings in the transient process, and provide information for ablation failure and instability analysis of flange bearings.
  • Theoretical support and solving the difficulties existing in the existing technology are urgent problems that those skilled in the art need to solve.
  • the present invention provides a method for calculating the coupling lubrication and dynamic characteristics parameters of a flange bearing, comprehensively considering the simulation model of the radial thrust thermoelastohydrodynamic lubrication and dynamic characteristics of the flange bearing, and establishing a simulation model of the flange bearing
  • the pressure coupling and thermal coupling relationship of the radial thrust part can more accurately explain the lubrication mechanism that causes ablation, reveal the lubrication and dynamic laws of the flange bearing in the transient process, and provide solutions for the ablation failure and failure of the flange bearing. Stability analysis provides theoretical support.
  • a method for calculating coupled lubrication and dynamic characteristic parameters of flanged bearings including the following steps:
  • the specific content of S3 is: based on the input structural parameters and operating conditions of the flanged bearing, calculate the oil film thickness of the radial part and the thrust part;
  • the average Reynolds equation considering the axial velocity is introduced, and the average Reynolds equation is solved.
  • the finite difference method is used to calculate the oil film pressure distribution in the radial and thrust parts respectively, and iterates until the pressure convergence judgment is satisfied.
  • the pressure boundary adopts Reynolds boundary conditions
  • the finite difference method is used to solve the three-dimensional energy equation of the radial part and the thrust part and the heat conduction equation of the bearing bush respectively.
  • the boundary conditions include: the oil inlet end temperature of the radial part and the thrust part is a given inlet temperature. Oil temperature; the outside of the bearing bush is subject to convection heat exchange conditions with the environment; the heat at the oil outlet end of the radial part and the inner diameter area of the thrust part is calculated through the heat flow continuity condition; updated in each cycle iteration, and the cycle continues until The temperature meets the convergence condition;
  • the elastic deformation matrix On the basis of the current pressure, use the elastic deformation matrix to calculate the elastic deformation of each node in the radial part and thrust part, substitute it into the oil film thickness equation, repeat the previous oil film pressure calculation, and add boundary conditions at this time: the radial part is close to the stop
  • the pressure on the push side end face and the oil film pressure at the inner diameter of the thrust part meet the flow and pressure continuity conditions.
  • the calculation is cyclic until the elastic deformation meets the convergence.
  • the oil film pressure is integrated to calculate the oil film bearing capacity.
  • the radial part oil film thickness equation is:
  • c is the radius gap
  • ⁇ represents the eccentricity
  • ⁇ represents the position angle of the bearing
  • ⁇ JE represents the elastic deformation of the radial part
  • ⁇ JT represents the thermal deformation of the radial part
  • the offset angle of the central section ⁇ j is the inclination angle of the journal in the main bearing shell
  • ⁇ r is the angle between the projection of the journal centerline and the eccentricity
  • ⁇ p is the circumferential inclination angle of a single tile
  • h p is the average oil film gap
  • r is the radial coordinate
  • ⁇ TE is the elastic deformation
  • ⁇ TT is the thermal deformation
  • ⁇ x , ⁇ y , ⁇ s , and ⁇ c are respectively the x-direction and y-direction pressure flow factors, shear flow factor and contact factor introduced when considering roughness, h J is the radial part of the oil film thickness, eta is Lubricating medium viscosity, p J is the oil film pressure distribution in the radial part, ⁇ is the relative rotation speed of the journal and the bearing bush, V is the axial speed of the journal, r is the inner diameter of the bearing, x is the x-direction position of the bearing, y is the y-direction position of the bearing , t is time.
  • ⁇ ⁇ and ⁇ r are respectively the circumferential and radial pressure flow factors introduced when considering roughness
  • r T represents the radial position of the thrust surface
  • h T is the oil film thickness of the thrust part
  • p T is the radial part
  • ⁇ is the circumferential position of the bearing, and the others are the same as the radial part.
  • the heat flow continuity condition is:
  • T j,m is the oil film temperature at the interface between the radial part and the thrust part
  • j is the circumferential position
  • m corresponds to the axial position of the radial part and the radial position of the thrust part
  • U r The radial flow velocity of the oil film
  • v is the axial flow velocity of the oil film in the radial part
  • ⁇ z is the axial unit length of the radial part
  • ⁇ r is the radial unit length of the thrust part
  • the deformation matrix method to calculate thermal and elastic deformation is expressed as:
  • COL is the number of meshes in the circumferential direction
  • ROW is the number of meshes in the axial direction, corresponding to the number of radial meshes in the thrust part
  • Elastic deformation produced by ( ⁇ ,z) nodes is the thermal deformation matrix, the thermal deformation produced at the ( ⁇ ,z) node due to unit temperature rise at the ( ⁇ ′,z′) node of the bearing material
  • ⁇ is the length of the circumferential unit
  • ⁇ z is the length of the axial unit corresponding to the thrust part Radial element length;
  • the flow and pressure continuity conditions are:
  • P j,m is the oil film pressure at the interface between the radial part and the thrust part
  • j is the circumferential position
  • m corresponds to the axial position of the radial part and the radial position of the thrust part
  • h T is the Oil film thickness
  • h J is the oil film thickness of the radial part
  • ⁇ z is the axial unit length of the radial part
  • ⁇ r is the radial unit length of the thrust part.
  • the perturbation Reynolds equation used to calculate the coupling disturbance force is:
  • ⁇ J corresponds to the micro-perturbation term of the radial part
  • ⁇ T corresponds to the micro-perturbation term of the thrust part, when ⁇ is x, y, z, it corresponds to the horizontal, vertical and axial displacement perturbation terms, when ⁇ is corresponds to the horizontal, vertical and axial velocity disturbance terms;
  • the disturbance pressure is calculated through the above disturbance equation, the disturbance pressure is integrated to determine the coupling oil film stiffness and damping value of each part.
  • the specific expression is as follows:
  • K J and K T correspond to the radial and axial stiffness respectively
  • C J and C T correspond to the radial and axial damping respectively.
  • the above method optionally, in S6, use the three-dimensional motion equation to calculate the relative position of the crankshaft journal/thrust shoulder and the bearing bush at the next moment, analyze the thermoelastic hydrodynamic lubrication characteristics of the composite bearing bush at the next moment, and then update its lubrication in real time Characteristic parameters;
  • W x , W y , and W z correspond to the axial, horizontal, and vertical loads respectively
  • P x , P y , and P z correspond to the axial, horizontal, and vertical bearing capacity
  • ⁇ corresponds to the journal inclination angle
  • a x , a y , a z correspond to axial, horizontal and vertical acceleration.
  • the present invention provides a method for calculating coupling lubrication and dynamic characteristic parameters of flanged bearings. Compared with the existing technology, it has the following beneficial effects:
  • Figure 1 is a flow chart of a method for calculating coupled lubrication and dynamic characteristic parameters of a flanged bearing provided by the present invention
  • Figure 2 is a calculation flow chart of the radial thrust thermoelastohydrodynamic coupling lubrication and dynamic model of the flange bearing provided by the present invention
  • Figure 3 is a flow chart of a specific calculation method for radial thrust thermoelastohydrodynamic coupling lubrication and dynamics of a flange bearing provided by the present invention.
  • the present invention discloses a method for calculating coupling lubrication and dynamic characteristic parameters of a flanged bearing, which includes the following steps:
  • the global parameters are input into the flange bearing radial thrust thermoelastohydrodynamic coupling lubrication module, and the oil film thickness of the radial bearing is calculated based on the input radial partial eccentricity and offset angle. ; Calculate the oil film thickness of the thrust part based on the initial assumed average oil film gap and thrust shoe inclination angle of the thrust part;
  • the boundary conditions include: the temperature of the oil inlet end of the radial part and the thrust part. is a given oil inlet temperature; the outside of the bearing bush is regarded as the convection heat exchange condition with the environment and the inside with the oil film; the heat at the oil outlet end of the radial part and the inner diameter area of the thrust part is calculated through the heat flow continuity condition.
  • super-relaxation iteration is used to increase the calculation speed until the temperature meets the convergence condition and is output.
  • the oil film bearing capacity is calculated integrally, and the micro-perturbation method is used to calculate the stiffness damping at the equilibrium position.
  • c is the radius gap
  • ⁇ represents the eccentricity
  • ⁇ represents the position angle of the bearing
  • ⁇ JE represents the elastic deformation of the radial part
  • ⁇ JT represents the thermal deformation of the radial part
  • the offset angle of the central section ⁇ j is the inclination angle of the journal in the main bearing shell
  • ⁇ r is the angle between the projection of the journal centerline and the eccentricity
  • ⁇ p is the circumferential inclination angle of a single tile
  • h p is the average oil film gap
  • r is the radial coordinate
  • ⁇ TE is the elastic deformation
  • ⁇ TT is the thermal deformation
  • ⁇ x , ⁇ y , ⁇ s , and ⁇ c are respectively the x-direction and y-direction pressure flow factors, shear flow factor and contact factor introduced when considering roughness, h J is the radial part of the oil film thickness, eta is Lubricating medium viscosity, p J is the oil film pressure distribution in the radial part, ⁇ is the relative rotation speed of the journal and the bearing bush, V is the axial speed of the journal, r is the inner diameter of the bearing, x is the x-direction position of the bearing, y is the y-direction position of the bearing , t is time.
  • ⁇ ⁇ and ⁇ r are respectively the circumferential and radial pressure flow factors introduced when considering roughness
  • r T represents the radial position of the thrust surface
  • h T is the oil film thickness of the thrust part
  • p T is the radial part
  • ⁇ is the circumferential position of the bearing, and the others are the same as the radial part.
  • T j,m is the oil film temperature at the interface between the radial part and the thrust part
  • j is the circumferential position
  • m corresponds to the axial position of the radial part and the radial position of the thrust part
  • U r The radial flow velocity of the oil film
  • v is the axial flow velocity of the oil film in the radial part
  • ⁇ z is the axial unit length of the radial part
  • ⁇ r is the radial unit length of the thrust part
  • the deformation matrix method to calculate thermal and elastic deformation is expressed as:
  • COL is the number of meshes in the circumferential direction
  • ROW is the number of meshes in the axial direction, corresponding to the number of radial meshes in the thrust part
  • Unit pressure is applied to the node ( ⁇ ′, z′) of the bearing inner hole surface, and the elastic deformation occurs at the node ( ⁇ , z); is the thermal deformation matrix, the thermal deformation produced at the ( ⁇ ,z) node due to unit temperature rise at the ( ⁇ ′,z′) node of the bearing material;
  • ⁇ is the circumferential unit length,
  • ⁇ z is the axial unit length, corresponding to the thrust part The radial element length;
  • the flow and pressure continuity conditions are:
  • P j,m is the oil film pressure at the interface between the radial part and the thrust part
  • j is the circumferential position
  • m corresponds to the axial position of the radial part and the radial position of the thrust part
  • h T is the Oil film thickness
  • h J is the oil film thickness of the radial part
  • ⁇ z is the axial unit length of the radial part
  • ⁇ r is the radial unit length of the thrust part.
  • the global parameters include: (1) Bearing parameters: bearing width, journal outer diameter (consistent with the corresponding shaft segment), radius clearance, initial eccentricity, initial offset angle, bearing roughness, bearing elastic modulus, Bearing Poisson's ratio, bearing thermal conductivity coefficient; (3) Other parameters: lubricating medium density, lubricating medium viscosity, oil inlet temperature, ambient temperature, rotation speed, load; (4) Calculation method parameters: number of bearing mesh divisions, bearing oil film Pressure convergence accuracy.
  • the perturbation Reynolds equation under the coupling effect is derived, the perturbation radial force and axial force are obtained by solving the calculation, and the stiffness damping of each part is calculated according to the coupling stiffness damping matrix.
  • the perturbation Reynolds equation method is established to solve the perturbation pressure under the stable condition, including the perturbation forces in the three directions of axial, horizontal and vertical directions.
  • the disturbance pressure is integrated to obtain the main stiffness damping and cross stiffness damping in each direction.
  • ⁇ J corresponds to the micro-perturbation term of the radial part
  • ⁇ T corresponds to the micro-perturbation term of the thrust part, when ⁇ is x, y, z, it corresponds to the horizontal, vertical and axial displacement perturbation terms, when ⁇ is corresponds to the horizontal, vertical and axial velocity disturbance terms;
  • the disturbance pressure is calculated through the above disturbance equation, the disturbance pressure is integrated to determine the coupling oil film stiffness and damping value of each part.
  • the specific expression is as follows:
  • K J and K T correspond to the radial and axial stiffness respectively
  • C J and C T correspond to the radial and axial damping respectively.
  • the three-dimensional motion equation is used to calculate the relative position of the crankshaft journal/thrust shoulder and the bearing bush at the next moment, analyze the thermoelastic hydrodynamic lubrication characteristics of the composite bearing bush at the next moment, and then update its lubrication characteristic parameters in real time;
  • W x , W y , and W z correspond to the axial, horizontal, and vertical loads respectively
  • P x , P y , and P z correspond to the axial, horizontal, and vertical bearing capacity
  • ⁇ corresponds to the journal inclination angle
  • a x , a y , a z correspond to axial, horizontal and vertical acceleration.
  • the global parameters are input into the radial thrust thermoelastohydrodynamic coupling lubrication module and calculated respectively according to the initial bearing position.
  • the energy equation of each part is used to solve the surface temperature of the flanged bearing pad.
  • the bearing pad surface temperatures of the separate radial and thrust parts are obtained.
  • the bearing pad surfaces of the radial part and the thrust part are corrected according to the thermal continuity condition.
  • Temperature the surface temperature of each part of the bearing bush taking into account the thermal coupling effect is obtained, that is, the temperature of the two parts is corrected through the heat flow continuity condition, and the surface temperature of each part of the bearing bush of the flanged bearing is further obtained taking the coupling effect into consideration;
  • the node thermal deformation is updated, and the oil film pressure of each part is updated through the flow continuity condition and pressure continuity condition.
  • the convergence condition is met, the output of each part of the flanged bearing considering the flow coupling effect at a given position is obtained.
  • Oil film pressure distribution that is, the bearing pad thermal deformation is updated according to the bearing pad surface temperature after considering the thermal flow coupling effect, and then the pressure distribution is corrected through the flow continuity condition to obtain the oil film pressure of each part considering the flow and pressure coupling effects;
  • the perturbation Reynolds equation method is further used to solve the perturbation pressure under the stable condition, and the stiffness damping is calculated integrally; that is, the perturbation Reynolds equation is used to solve the coupled axial perturbation
  • the disturbance pressure is integrated according to the stiffness damping definition formula, and the coupled stiffness damping of each part is calculated to characterize the stability of the flanged bearing.
  • the three-dimensional motion equation is used to calculate the relative position of the flanged bearing at the next moment.
  • the lubrication calculation domain at each moment is updated according to the displacement amount and then the calculation grid number is modified. Repeat the above calculate;

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Abstract

本发明公开了一种计算翻边轴承耦合润滑与动力学特性参数的方法，涉及柴油机仿真技术领域。本发明主要包含三个模块：翻边轴承径向止推热弹流耦合润滑模块，翻边轴承动力学特性参数计算模块和翻边轴承相对位置反馈模块。既考虑轴向一体运动对径向润滑轴向动压效应与止推润滑变间隙效应联动规律、径向一体运动对径向润滑变间隙效应与止推润滑变域效应联动规律；又考虑润滑油膜在翻边轴承公共边界上的流量、压力与热对流，最终形成翻边轴承径向与止推瞬态润滑耦合分析方法。在此基础上，进一步考虑耦合效应下的翻边轴承径向/轴向润滑油膜刚度、阻尼特性，实现对翻边轴承动力学与摩擦学的精确仿真，以解决翻边轴承润滑失效问题。

Description

一种计算翻边轴承耦合润滑与动力学特性参数的方法 技术领域
本发明涉及柴油机仿真技术领域，属于一种计算翻边轴承耦合润滑与动力学特性参数的方法。
背景技术
曲轴-轴承系统作为柴油机中的关键部分，其润滑性能会直接影响柴油机的可靠性和寿命。翻边轴承一般位于曲轴末端，是径向支撑曲轴并防止其轴向窜动的重要部件，极易出现油膜间隙很小的情况，润滑工况较为恶劣，经常伴随高温烧蚀现象，进而降低柴油机寿命。
目前国内针对翻边轴承的研究已有一定基础，但研究往往将翻边轴承简化为止推轴承，实际烧蚀的发生位置除了翻边轴瓦止推面外，还有径向部分靠近止推侧的瓦面，单独的径向或止推轴承简化分析无法解释这一现象。且随着曲轴的运行，轴承的动力学特性也会发生变化，进而影响翻边轴承的稳定性。
因此，提出一种计算翻边轴承耦合润滑与动力学特性参数的方法，建立一个综合考虑翻边轴承径向止推热弹流润滑与动力学特性的仿真模型，并建立翻边轴承径向止推部分的压力耦合与热耦合关系，从而更准确的阐释产生烧蚀的润滑机理，揭示瞬态过程中的翻边轴承润滑与动力学规律，为翻边轴承的烧蚀故障及失稳分析提供理论支撑，解决现有技术存在的困难，是本领域技术人员亟需解决的问题。
发明内容
有鉴于此，本发明提供了一种计算翻边轴承耦合润滑与动力学特性参数的方法，综合考虑翻边轴承径向止推热弹流润滑与动力学特性的仿真模型，并建立翻边轴承径向止推部分的压力耦合与热耦合关系，从而更准确的阐释产生烧蚀的润滑机理，揭示瞬态过程中的翻边轴承润滑与动力学规律，为翻边轴承的烧蚀故障及失稳分析提供理论支撑。
为了实现上述目的，本发明采用如下技术方案：
一种计算翻边轴承耦合润滑与动力学特性参数的方法，包括以下步骤：
S1、获取翻边轴承的结构参数和运行工况；
S2、设定时间t；
S3、利用翻边轴承径向止推热弹流耦合润滑模块，计算得到油膜承载力；
S4、完成S3后，利用翻边轴承动力学特性参数计算模块，计算刚度阻尼；
S5、完成S4后，利用翻边轴承相对位置反馈模块，判断是否完成内燃机计算周期，若是，则输出并保存翻边轴承工作特性参数结果；若否，则进行S6；
S6、根据对应时刻的载荷计算翻边轴承径向与轴向位移，更新止推部分计算域及网络，将各轴承下一时刻的相对位置作为翻边轴承径向止推热弹流耦合润滑模块及翻边轴承动力学特性参数计算模块的输入参数继续进行计算。
上述的方法，可选的，S3的具体内容为：根据输入的翻边轴承的结构参数和运行工况，计算径向部分和止推部分的油膜厚度；
在得到油膜厚度的基础上，引入考虑轴向速度的平均雷诺方程，求解平均雷诺方程，利用有限差分法，分别计算得到径向和止推部分的油膜压力分布，循环迭代直到满足压力收敛判断，压力边界采用雷诺边界条件；
利用有限差分法，分别求解径向部分和止推部分的三维能量方程、轴瓦的热传导方程，边界条件包括：径向部分与止推部分的进油端温度为给定进 油温度；轴瓦的外部均为与环境的对流换热条件；径向部分的出油端、止推部分的内径区域的热量通过热流量连续性条件计算；在每次循环迭代中更新，循环直至温度满足收敛条件；
利用变形矩阵法，根据计算出的油膜压力计算径向部分和止推部分各个节点的热变形，将热变形量代入油膜厚度，重复之前的油膜压力计算，直到热变形满足收敛；
在当前压力的基础上，利用弹性变形矩阵，计算径向部分和止推部分各个节点的弹性变形，代入油膜厚度方程中，重复之前的油膜压力计算，此时增加边界条件：径向部分靠近止推侧端面的压力与止推部分内径处油膜压力满足流量和压力连续性条件，循环计算直到弹性变形满足收敛，将油膜压力积分计算得到油膜承载力。
上述的方法，可选的，径向部分油膜厚度方程为：
其中，c为半径间隙，ε表示偏心率，θ表示轴承的位置角，δJE表示径向部分弹性变形量，δJT表示径向部分热变形量，中央截面偏位角，γj为轴颈在主轴瓦中的倾斜角；αr为轴颈中心线投影与偏心距之间的夹角；
止推部分油膜厚度方程为：
hT＝hp+r sin(θp)+δTE+δTT
式中，θp为单个瓦的周向倾角，hp为平均油膜间隙，r为径向坐标，δTE为弹性变形量，δTT为热变形量；
径向部分雷诺方程为：
其中，φx、φy、φs、φc分别为考虑粗糙度时，引入的x向、y向压力流量因子，剪切流量因子和接触因子，hJ为径向部分油膜厚度，η为润滑介质粘度，pJ为径向部分油膜压力分布，ω为轴颈与轴瓦相对转速，V为轴颈的轴向速度，r为轴承内径，x为轴承x向位置，y为轴承y向位置，t为时间。
止推部分雷诺方程为：
其中，φθ、φr分别为考虑粗糙度时，引入的周向、径向压力流量因子，rT表示止推面的径向位置，hT为止推部分油膜厚度，pT为径向部分油膜压力分布，θ为轴承周向位置，其他和径向部分一样。
上述的方法，可选的，热流量连续性条件为：


其中，Tj,m为径向部分与止推部分交接面的油膜温度，j为周向位置，m对应径向部分的轴向位置、止推部分的径向位置，Ur为止推部分的油膜径向流速，v为径向部分的油膜轴向流速，Δz为径向部分轴向单元长度，Δr为止推部分径向单元长度；
变形矩阵法计算热、弹性变形表示为：
其中，COL为周向的网格数，ROW为轴向的网格数，对应止推部分的径向网格数；为弹性变形矩阵，轴瓦内孔面(θ′,z′)节点作用单位压力，在 (θ,z)节点产生的弹性变形；为热变形矩阵，轴瓦材料(θ′,z′)节点作用单位温升，在(θ,z)节点产生的热变形；Δθ为周向单元长度，Δz为轴向单元长度对应止推部分的径向单元长度；
流量和压力连续性条件为：


其中，Pj,m为径向部分与止推部分交接面的油膜压力，j为周向位置，m对应径向部分的轴向位置、止推部分的径向位置，hT为止推部分的油膜厚度，hJ为径向部分的油膜厚度，Δz为径向部分轴向单元长度，Δr为止推部分径向单元长度。
上述的方法，可选的，S4中，计算得到油膜承载力后，推导耦合效应作用下的扰动雷诺方程，求解计算得到扰动径向力与轴向力，根据耦合刚度阻尼矩阵计算各部分的刚度阻尼。
上述的方法，可选的，计算耦合扰动力所用扰动雷诺方程为：

其中，ξJ对应径向部分的微扰动项，ξT对应止推部分的微扰动项，当ξ为x，y，z时对应表示水平、垂向以及轴向的位移扰动项，当ξ为时对应表示水平、垂向以及轴向的速度扰动项；
在通过上述扰动方程计算得到扰动压力后，对扰动压力进行积分，进而确定各部分的耦合油膜刚度和阻尼值，具体表达式如下：



其中，KJ，KT分别对应径向、轴向刚度，CJ，CT分别对应径向、轴向阻尼。
上述的方法，可选的，S6中，利用三维运动方程计算曲轴轴颈/止推肩与轴瓦下一时刻相对位置，分析下一时刻复合轴瓦热弹性流体动压润滑特性，进而实时更新其润滑特性参数；
求解径向与轴向位移，进而计算下一时刻径向与轴向位置的三维运动方程为：
其中，Wx，Wy，Wz分别对应轴向、水平、竖直向载荷，Px，Py，Pz对应轴向、水平、竖直向承载力，α对应轴颈倾斜角，ax，ay，az对应轴向、水平、竖直向加速度。
经由上述的技术方案可知，与现有技术相比，本发明公开提供了一种计算翻边轴承耦合润滑与动力学特性参数的方法，与现有技术相比，具有如下有益效果：
1、充分考虑了翻边轴瓦径向部分和止推部分的润滑耦合效应，将径向部分和止推部分的润滑状况结合在一起，压力与温度分布更符合实际情况。
2、考虑了轴向速度和止推部分的时变计算域，在径向止推一体运动下更能准确反映各时刻翻边轴承的状态，从而更准确模拟实际时变载荷下的翻边轴承的润滑性能。
3、考虑了翻边轴承耦合效应对动力学性能的影响，使刚度阻尼结果更符合实际运行情况，使翻边轴承稳定性分析更为准确。
附图说明
为了更清楚地说明本发明实施例或现有技术中的技术方案，下面将对实施例或现有技术描述中所需要使用的附图作简单地介绍，显而易见地，下面 描述中的附图仅仅是本发明的实施例，对于本领域普通技术人员来讲，在不付出创造性劳动的前提下，还可以根据提供的附图获得其他的附图。
图1为本发明提供的一种计算翻边轴承耦合润滑与动力学特性参数的方法流程图；
图2为本发明提供的翻边轴承径向止推热弹流耦合润滑与动力学模型的计算流程图；
图3为本发明提供的翻边轴承径向止推热弹流耦合润滑与动力学具体计算方法流程图。
具体实施方式
下面将结合本发明实施例中的附图，对本发明实施例中的技术方案进行清楚、完整地描述，显然，所描述的实施例仅仅是本发明一部分实施例，而不是全部的实施例。基于本发明中的实施例，本领域普通技术人员在没有做出创造性劳动前提下所获得的所有其他实施例，都属于本发明保护的范围。
在本申请中，术语“包括”、“包含”或者其任何其他变体意在涵盖非排他性的包含，从而使得包括一系列要素的过程、方法、物品或者设备不仅包括那些要素，而且还包括没有明确列出的其他要素，或者是还包括为这种过程、方法、物品或者设备所固有的要素。在没有更多限制的情况下，由语句“包括一个……”限定的要素，并不排除在包括所述要素的过程、方法、物品或者设备中还存在另外的相同要素。
参照图1所示，本发明公开了一种计算翻边轴承耦合润滑与动力学特性参数的方法，包括以下步骤：
S1、获取翻边轴承的结构参数和运行工况；
S2、设定时间t；
S3、利用翻边轴承径向止推热弹流耦合润滑模块，计算得到油膜承载力；
S4、完成S3后，利用翻边轴承动力学特性参数计算模块，计算刚度阻尼；
S5、完成S4后，利用翻边轴承相对位置反馈模块，判断是否完成内燃机计算周期，若是，则输出并保存翻边轴承工作特性参数结果；若否，则进行S6；
S6、根据对应时刻的载荷计算翻边轴承径向与轴向位移，更新止推部分计算域及网络，将各轴承下一时刻的相对位置作为翻边轴承径向止推热弹流耦合润滑模块及翻边轴承动力学特性参数计算模块的输入参数继续进行计算。
参见图2所示，进一步的，将全局参数输入到翻边轴承径向止推热弹流耦合润滑模块，根据输入的径向部分偏心率和偏位角大小，计算出径向轴承的油膜厚度；根据止推部分的初始假设平均油膜间隙和止推瓦倾角，计算出止推部分的油膜厚度；
基于油膜厚度，使用雷诺边界条件，采用有限差分法分别求解径向和止推部分雷诺方程，循环计算中采用超松弛迭代提高计算速度，直到油膜压力满足收敛条件输出；
然后求解各部分的温度场，利用有限差分法分别求解径向部分和止推部分油膜区域的三维能量方程、轴瓦区域的热传导方程，边界条件包括：径向部分与止推部分的进油端温度为给定进油温度；轴瓦的外部视为与环境、内部视为与油膜的对流换热条件；径向部分的出油端、止推部分的内径区域的热量通过热流量连续性条件计算。循环计算中采用超松弛迭代提高计算速度，直到温度满足收敛条件输出。
之后利用求得的温度场，通过变形矩阵法计算出各节点热变形量，代入油膜厚度方程中，重复上述压力与温度的计算，直到热变形量满足收敛条件；在当前温度的基础上进行弹性变形计算，基于目前的压力场，通过变形矩阵法计算出各节点弹性变形量，代入油膜厚度方程中，重复上述压力场的计算， 在压力场计算中增加边界条件：径向部分止推侧端面的油膜压力与止推部分内径处油膜压力满足流量和压力连续性条件，循环计算直到弹性变形量满足收敛条件，此时得到初始给定位置的翻遍轴承各部分的压力分布；
依据油膜压力分布，积分计算油膜承载力，利用微扰动法计算平衡位置的刚度阻尼。
进一步的，径向部分油膜厚度方程为：
其中，c为半径间隙，ε表示偏心率，θ表示轴承的位置角，δJE表示径向部分弹性变形量，δJT表示径向部分热变形量，中央截面偏位角，γj为轴颈在主轴瓦中的倾斜角；αr为轴颈中心线投影与偏心距之间的夹角；
止推部分油膜厚度方程为：
hT＝hp+r sin(θp)+δTE+δTT
式中，θp为单个瓦的周向倾角，hp为平均油膜间隙，r为径向坐标，δTE为弹性变形量，δTT为热变形量；
径向部分雷诺方程为：
其中，φx、φy、φs、φc分别为考虑粗糙度时，引入的x向、y向压力流量因子，剪切流量因子和接触因子，hJ为径向部分油膜厚度，η为润滑介质粘度，pJ为径向部分油膜压力分布，ω为轴颈与轴瓦相对转速，V为轴颈的轴向速度，r为轴承内径，x为轴承x向位置，y为轴承y向位置，t为时间。
止推部分雷诺方程为：
其中，φθ、φr分别为考虑粗糙度时，引入的周向、径向压力流量因子，rT表示止推面的径向位置，hT为止推部分油膜厚度，pT为径向部分油膜压力分布，θ为轴承周向位置，其他和径向部分一样。
进一步的，热流量连续性条件为：


其中，Tj,m为径向部分与止推部分交接面的油膜温度，j为周向位置，m对应径向部分的轴向位置、止推部分的径向位置，Ur为止推部分的油膜径向流速，v为径向部分的油膜轴向流速，Δz为径向部分轴向单元长度，Δr为止推部分径向单元长度；
变形矩阵法计算热、弹性变形表示为：
其中，COL为周向的网格数，ROW为轴向的网格数，对应止推部分的径向网格数；为弹性变形矩阵，轴瓦内孔面(θ′,z′)节点作用单位压力，在(θ,z)节点产生的弹性变形；为热变形矩阵，轴瓦材料(θ′,z′)节点作用单位温升，在(θ,z)节点产生的热变形；Δθ为周向单元长度，Δz为轴向单元长度，对应止推部分的径向单元长度；
流量和压力连续性条件为：


其中，Pj,m为径向部分与止推部分交接面的油膜压力，j为周向位置，m对应径向部分的轴向位置、止推部分的径向位置，hT为止推部分的油膜厚度，hJ为径向部分的油膜厚度，Δz为径向部分轴向单元长度，Δr为止推部分径向单元长度。
此外，全局参数其中包括：(1)轴承参数：轴承宽度，轴颈外径(与相对应轴段一致)，半径间隙，初始偏心率，初始偏位角，轴瓦粗糙度，轴瓦弹性模量，轴瓦泊松比，轴瓦热传导系数；(3)其他参数：润滑介质密度，润滑介质粘度，进油温度，环境温度，转速，载荷；(4)计算方法参数：轴承网格划分个数，轴承油膜压力收敛精度。
进一步的，S4中，计算得到油膜承载力后，推导耦合效应作用下的扰动雷诺方程，求解计算得到扰动径向力与轴向力，根据耦合刚度阻尼矩阵计算各部分的刚度阻尼。具体为，建立扰动雷诺方程法，求解得到该稳定情况下的扰动压力，包括轴向、水平和垂向三个方向的扰动力。对扰动压力进行积分，得到各向主刚度阻尼和交叉刚度阻尼。
进一步的，计算耦合扰动力所用扰动雷诺方程为：

其中，ξJ对应径向部分的微扰动项，ξT对应止推部分的微扰动项，当ξ为x，y，z时对应表示水平、垂向以及轴向的位移扰动项，当ξ为时对应表示水平、垂向以及轴向的速度扰动项；
在通过上述扰动方程计算得到扰动压力后，对扰动压力进行积分，进而确定各部分的耦合油膜刚度和阻尼值，具体表达式如下：



其中，KJ，KT分别对应径向、轴向刚度，CJ，CT分别对应径向、轴向阻尼。
进一步的，判断是否完成内燃机工作周期，若尚未计算完毕，根据对应时刻的载荷计算翻边轴承径向与轴向位移，更新计算域，其中止推部分和止推肩间润滑区域发生变化，需根据瞬态相对位移修改网格数与边界网格编号，进而修改计算域区间。当位移长度与单元网格数不能整除时，需要对更新后的计算域网格数向上取整，修改单元网格大小。将各轴承下一时刻的相对位置作为轴承润滑性能及动力学参数计算模块的输入参数继续进行计算；若已完成内燃机工作周期，则保存翻边轴承在周期内的工作特性结果。
进一步的，S6中，利用三维运动方程计算曲轴轴颈/止推肩与轴瓦下一时刻相对位置，分析下一时刻复合轴瓦热弹性流体动压润滑特性，进而实时更新其润滑特性参数；
在进行下一时刻润滑计算的过程中，对于径向部分，轴颈径向位置变化直接影响润滑偏心率，进而改变轴颈与径向部分间的几何间隙，影响油膜厚度；同时也会改变雷诺方程中的轴向速度。对于止推部分，轴向位置改变直接影响其与止推肩间的几何间隙，进而影响膜厚方程；同时止推部分和止推肩间润滑区域发生变化，需根据瞬态相对位移修改网格数与边界网格编号，进而修改计算域区间。当位移长度与单元网格数不能整除时，需要对更新后的计算域网格数向上取整，修改单元网格大小。
求解径向与轴向位移，进而计算下一时刻径向与轴向位置的三维运动方程为：
其中，Wx，Wy，Wz分别对应轴向、水平、竖直向载荷，Px，Py，Pz对应轴向、水平、竖直向承载力，α对应轴颈倾斜角，ax，ay，az对应轴向、水平、竖直向加速度。
更进一步的，径向止推热弹流耦合润滑模块以及翻边轴承耦合动力学计算模块中，将全局参数输入到所述径向止推热弹流耦合润滑模块中，根据初始轴承位置分别计算径向部分和止推部分初始位置的几何油膜厚度，之后分别利用对应的雷诺方程计算对应部分该位置下的油膜压力；
基于所得压力，利用各部分的能量方程求解翻边轴瓦表面温度，满足收敛后得到单独径向和单独止推部分的轴瓦表面温度，根据热连续性条件修正径向部分与止推部分的轴瓦表面温度，得到考虑热耦合效应的各部分轴瓦表面温度，即通过热流量连续性条件对两部分温度进行修正，进一步得到综合考虑耦合效应的翻边轴承各部分轴瓦表面温度；
基于稳定后的轴瓦表面温度，更新节点热变形，通过流量连续性条件和压力连续性条件更新各部分油膜压力，当满足收敛条件输出得到给定位置下考虑了流量耦合效应的翻边轴承各部分油膜压力分布；即根据考虑热流量耦合效应后的轴瓦表面温度更新轴瓦热变形，再通过流量连续性条件修正压力分布，得到考虑流量、压力耦合效应的各部分油膜压力；
根据各部分压力计算翻边轴承轴向与径向承载力，基于载荷修改轴承位置，重复上述操作，直至承载力满足载荷要求，得到该时刻下的轴承稳定润滑状态；
在得到综合考虑流量、热和压力耦合效应的油膜压力的基础上，进一步利用扰动雷诺方程法，求解得到该稳定情况下的扰动压力，积分计算刚度阻尼；即利用扰动雷诺方程求解耦合轴向扰动力和耦合径向扰动力，根据刚度阻尼定义式对扰动压力进行积分，计算各部分的耦合刚度阻尼，表征翻边轴承的稳定性。
在完成该时刻润滑及动力学特性计算的基础上，利用三维运动方程计算翻边轴承下一时刻的相对位置，同时根据位移量更新每个时刻的润滑计算域进而修改计算网格数，重复上述计算；
判断是否完成内燃机工作周期，若尚未计算完毕，将翻边轴承下一时刻的相对位置作为输入参数继续进行计算；若已经完成内燃机工作周期后，则输出并保存翻边轴承在所述周期内的工作特性结果。
本说明书中的各个实施例均采用递进的方式描述，各个实施例之间相同相似的部分互相参见即可，每个实施例重点说明的都是与其他实施例的不同之处。为了清楚地说明硬件和软件的可互换性，在上述说明中已经按照功能一般性地描述了各示例的组成及步骤。这些功能究竟以硬件还是软件方式来执行，取决于技术方案的特定应用和设计约束条件。专业技术人员可以对每个特定的应用来使用不同方法来实现所描述的功能，但是这种实现不应认为超出本发明的范围。
对所公开的实施例的上述说明，使本领域专业技术人员能够实现或使用本发明。对这些实施例的多种修改对本领域的专业技术人员来说将是显而易见的，本文中所定义的一般原理可以在不脱离本发明的精神或范围的情况下，在其它实施例中实现。因此，本发明将不会被限制于本文所示的这些实施例，而是要符合与本文所公开的原理和新颖特点相一致的最宽的范围。

Claims (7)

  1. 一种计算翻边轴承耦合润滑与动力学特性参数的方法，其特征在于，包括以下步骤：
    S1、获取翻边轴承的结构参数和运行工况；
    S2、设定时间t；
    S3、利用翻边轴承径向止推热弹流耦合润滑模块，计算得到油膜承载力；
    S4、完成S3后，利用翻边轴承动力学特性参数计算模块，计算刚度阻尼；
    S5、完成S4后，利用翻边轴承相对位置反馈模块，判断是否完成内燃机计算周期，若是，则输出并保存翻边轴承工作特性参数结果；若否，则进行S6；
    S6、根据对应时刻的载荷计算翻边轴承径向与轴向位移，更新止推部分计算域及网络，将各轴承下一时刻的相对位置作为翻边轴承径向止推热弹流耦合润滑模块及翻边轴承动力学特性参数计算模块的输入参数继续进行计算。
  2. 根据权利要求1所述的一种计算翻边轴承耦合润滑与动力学特性参数的方法，其特征在于，
    S3的具体内容为：根据输入的翻边轴承的结构参数和运行工况，计算径向部分和止推部分的油膜厚度；
    在得到油膜厚度的基础上，引入考虑轴向速度的平均雷诺方程，求解平均雷诺方程，利用有限差分法，分别计算得到径向和止推部分的油膜压力分布，循环迭代直到满足压力收敛判断，压力边界采用雷诺边界条件；
    利用有限差分法，分别求解径向部分和止推部分的三维能量方程、轴瓦的热传导方程，边界条件包括：径向部分与止推部分的进油端温度为给定进油温度；轴瓦的外部均为与环境的对流换热条件；径向部分的出油端、止推 部分的内径区域的热量通过热流量连续性条件计算；在每次循环迭代中更新，循环直至温度满足收敛条件；
    利用变形矩阵法，根据计算出的油膜压力计算径向部分和止推部分各个节点的热变形，将热变形量代入油膜厚度，重复之前的油膜压力计算，直到热变形满足收敛；
    在当前压力的基础上，利用弹性变形矩阵，计算径向部分和止推部分各个节点的弹性变形，代入油膜厚度方程中，重复之前的油膜压力计算，此时增加边界条件：径向部分靠近止推侧端面的压力与止推部分内径处油膜压力满足流量和压力连续性条件，循环计算直到弹性变形满足收敛，将油膜压力积分计算得到油膜承载力。
  3. 根据权利要求2所述的一种计算翻边轴承耦合润滑与动力学特性参数的方法，其特征在于，
    径向部分油膜厚度方程为：
    其中，c为半径间隙，ε表示偏心率，θ表示轴承的位置角，δJE表示径向部分弹性变形量，δJT表示径向部分热变形量，中央截面偏位角，γj为轴颈在主轴瓦中的倾斜角；αr为轴颈中心线投影与偏心距之间的夹角；
    止推部分油膜厚度方程为：
    hT＝hp+r sin(θp)+δTE+δTT
    式中，θp为单个瓦的周向倾角，hp为平均油膜间隙，r为径向坐标，δTE为弹性变形量，δTT为热变形量；
    径向部分雷诺方程为：
    其中，φx、φy、φs、φc分别为考虑粗糙度时，引入的x向、y向压力流量因子，剪切流量因子和接触因子，hJ为径向部分油膜厚度，η为润滑介质粘度，pJ为径向部分油膜压力分布，ω为轴颈与轴瓦相对转速，V为轴颈的轴向速度，r为轴承内径，x为轴承x向位置，y为轴承y向位置，t为时间；
    止推部分雷诺方程为：
    其中，φθ、φr分别为考虑粗糙度时，引入的周向、径向压力流量因子，rT表示止推面的径向位置，hT为止推部分油膜厚度，pT为径向部分油膜压力分布，θ为轴承周向位置，其他和径向部分一样。
  4. 根据权利要求2所述的一种计算翻边轴承耦合润滑与动力学特性参数的方法，其特征在于，
    热流量连续性条件为：


    其中，Tj,m为径向部分与止推部分交接面的油膜温度，j为周向位置，m对应径向部分的轴向位置、止推部分的径向位置，Ur为止推部分的油膜径向流速，v为径向部分的油膜轴向流速，Δz为径向部分轴向单元长度，Δr为止推部分径向单元长度；
    变形矩阵法计算热、弹性变形表示为：
    其中，COL为周向的网格数，ROW为轴向的网格数，对应止推部分的径向网格数；为弹性变形矩阵，轴瓦内孔面(θ′,z′)节点作用单位压力，在(θ,z)节点产生的弹性变形；为热变形矩阵，轴瓦材料(θ′,z′)节点作用单位温升，在(θ,z)节点产生的热变形；Δθ为周向单元长度，Δz为轴向单元长度，对应止推部分的径向单元长度；
    流量和压力连续性条件为：


    其中，Pj,m为径向部分与止推部分交接面的油膜压力，j为周向位置，m对应径向部分的轴向位置、止推部分的径向位置，hT为止推部分的油膜厚度，hJ为径向部分的油膜厚度，Δz为径向部分轴向单元长度，Δr为止推部分径向单元长度。
  5. 根据权利要求1所述的一种计算翻边轴承耦合润滑与动力学特性参数的方法，其特征在于，
    S4中，计算得到油膜承载力后，推导耦合效应作用下的扰动雷诺方程，求解计算得到扰动径向力与轴向力，根据耦合刚度阻尼矩阵计算各部分的刚度阻尼。
  6. 根据权利要求5所述的一种计算翻边轴承耦合润滑与动力学特性参数的方法，其特征在于，
    计算耦合扰动力所用扰动雷诺方程为：

    其中，ξJ对应径向部分的微扰动项，ξT对应止推部分的微扰动项，当ξ为x，y，z时对应表示水平、垂向以及轴向的位移扰动项，当ξ为时对应表示水平、垂向以及轴向的速度扰动项；
    在通过上述扰动方程计算得到扰动压力后，对扰动压力进行积分，进而确定各部分的耦合油膜刚度和阻尼值，具体表达式如下：



    其中，KJ，KT分别对应径向、轴向刚度，CJ，CT分别对应径向、轴向阻尼。
  7. 根据权利要求1所述的一种计算翻边轴承耦合润滑与动力学特性参数的方法，其特征在于，
    S6中，利用三维运动方程计算曲轴轴颈/止推肩与轴瓦下一时刻相对位置，分析下一时刻复合轴瓦热弹性流体动压润滑特性，进而实时更新其润滑特性参数；
    求解径向与轴向位移，进而计算下一时刻径向与轴向位置的三维运动方程为：
    其中，Wx，Wy，Wz分别对应轴向、水平、竖直向载荷，Px，Py，Pz对应轴向、水平、竖直向承载力，α对应轴颈倾斜角，ax，ay，az对应轴向、水平、竖直向加速度。
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