A fast analysis method for dynamic characteristics of marine rotor-bearing system

Abstract

The present invention discloses a method for rapid analysis of dynamic characteristics of a marine rotor-bearing system, comprising the following steps: calculating the oil film force at different journal equilibrium positions according to bearing characteristics based on the Reynolds equation; calculating the bearing seat motion displacement under different hull motion forms; establishing a bearing-rotor dynamics model under basic motion, with the oil film force as an external force; and using a numerical iteration method to calculate the response of the bearing-rotor system. At each time step, the bearing oil film force is obtained by interpolation according to the journal equilibrium position; at the same time, the bearing seat displacement is changed at each time step. The present invention is suitable for calculating the dynamic response of the rotor system under the movement of the bearing base caused by the hull but not limited to the hull movement. The present invention can calculate the dynamic response of the rotor-bearing system under various hull motions, and the method can be generalized to calculate the dynamic response of the bearing-rotor under any basic motion. It has the advantages of wide application range and high calculation efficiency.

Description

Technical Field

[0001] The invention relates to a method for quickly analyzing dynamic characteristics of a marine rotor-bearing system, and in particular to a method for quickly analyzing dynamic characteristics of a marine rotor-bearing system that can consider different hull motions and has high calculation efficiency, and belongs to the field of rotor dynamics analysis. Background Art

[0002] With abundant marine resources and developed economies of coastal countries, the Maritime Silk Road is a link for economic and cultural exchanges among countries. The demand for energy, especially clean energy, along the islands and reefs is increasing. LNG (Liquefied Natural Gas) floating power generation ship is a comprehensive high-value-added ship. Compared with onshore power generation or shore power conversion, it has the advantages of low carbon and high efficiency, fast layout, small footprint, mobility, and low power generation cost, and has attracted much attention. With the continued demand for electricity in developing countries such as Southeast Asia, South Asia, the Caribbean and West Africa, and my country's in-depth development of island and reef resources in the South China Sea, LNG floating power generation ships will continue to receive attention. However, the dynamic characteristics analysis method of the large marine rotor system, which is the core component of the LNG floating power generation ship, is still lacking.

[0003] Zhang Lei from Xi'an Jiaotong University of Technology (Zhang Lei, Pei Shiyuan, Xu Hua. Research on the safety and stability of two types of ship rotor bearing systems under swaying conditions [J]. Science China: Technological Sciences, 2018, 48(4): 369-381.) used the rotor bearing system dynamics analysis software developed by the Institute of Lubrication Theory and Bearings of Xi'an Jiaotong University to analyze the dynamic characteristics of the rotor-bearing system supported by elliptical bearings and offset bearings under swaying conditions. However, the transient characteristics of the system were ignored during the analysis, and only the stability and safety of the system under different swaying angles were analyzed. Liu Shupeng from Harbin Institute of Technology (Liu Shupeng. Research on the dynamic characteristics of the rotor bearing system under the action of ship pitch and roll [D]; Harbin Institute of Technology, 2011.) constructed the Capone nonlinear oil film force model in his master's thesis to consider the nonlinear support force during ship motion. Only the dynamic characteristics of the ship rotor-sliding bearing system during ship roll and pitch motion were analyzed. This paper introduced the nonlinear oil film force into the rotor system model, which required the calculation of the oil film force at each load step, which was inefficient. Summary of the invention

[0004] The purpose of the invention is to solve the dilemma of dynamic analysis in the design of large-scale marine rotor systems.

[0005] In order to achieve the above object, the technical solution of the present invention is to provide a method for rapid analysis of dynamic characteristics of a marine rotor-bearing system, which is characterized by comprising the following steps:

[0006] Step 1: Calculate the oil film force at different journal equilibrium positions based on the Reynolds equation according to the bearing characteristics;

[0007] Step 2: Calculate the motion displacement of the rotor bearing base under different hull motion forms, where the hull motion forms include sway, heave, roll, pitch and bow. When the hull moves, the hull will drive the rotor base to move, thereby affecting the dynamic response of the rotor. The motion equation of the rotor bearing base under different hull motion forms is expressed as:

[0008] (1) Horizontal:

[0009] The displacement of the two bearings at the left and right ends of the rotor bearing base is consistent, then:

[0010] bear_y=A sway sin(2πf sway t)

[0011] Where, bear_y represents the displacement of the rotor bearing base in the Y-axis direction, A sway represents the amplitude of the hull's swaying motion, f sway Indicates the hull swaying motion frequency;

[0012] (2) Dangling

[0013] The displacement of the two bearings at the left and right ends of the rotor bearing base is consistent, then:

[0014] bear_z=A heave sin(2πf heave t)

[0015] Where, bear_z represents the displacement of the rotor bearing base in the Z-axis direction, A heave represents the amplitude of the hull heave motion, f heave Indicates the motion frequency of the hull heave;

[0016] (3) Roll

[0017] The displacement of the two bearings at the left and right ends of the rotor bearing base is consistent, then:

[0018]

[0019] Where α represents the angle between the plane formed by the rotor bearing center and the hull roll centerline and the vertical plane where the hull roll center is located, tanα = Y g / Z g , Y g It represents the horizontal distance between the rotor bearing center and the hull roll centerline, Z gIndicates the vertical distance between the rotor bearing center and the hull roll centerline; bear_y′ indicates the displacement of the rotor bearing base relative to the hull roll centerline coordinate in the Y-axis direction, bear_y′=-L roll sin(bear_θ x ), L roll Indicates the distance between the rotor bearing center and the hull roll centerline, bear_θ x Indicates the rolling angle of the bearing, bear_θ x =A roll sin(2πf roll t), A roll represents the amplitude of the ship's rolling motion, f roll Indicates the motion frequency of the ship's rolling motion; bear_z′=L roll cos(bear_θ x )-L roll ;

[0020] (4) Pitch

[0021] The positions of the two bearings at the left and right ends of the rotor bearing base are different, then:

[0022]

[0023] Where, bear_x represents the displacement of the rotor bearing base in the X-axis direction; tanα=(X g ±L shaft / 2) / Z g , X g Indicates the longitudinal distance between the rotor bearing center and the hull pitch centerline, L shaft Indicates the distance between two bearings; bear_x′=L pitch sin(bear_θ y ), L pitch Indicates the distance between the rotor bearing center and the hull pitch centerline, bear_θ y Indicates the bearing pitch angle, bear_θ y =A pitch sin(2πf pitch t), A pitch represents the motion amplitude of the hull pitching, f pitch Indicates the motion frequency of the hull pitching; bear_z′=L pitch cos(bear_θ y )-L pitch ;

[0024] (5) Bow swing

[0025] The positions of the two bearings at the left and right ends of the rotor bearing base are different, then:

[0026]

[0027] Where, bear_x represents the displacement of the rotor bearing base in the X-axis direction; tanα = Y g / (X g ±L shaft / 2); bear_x′=L yaw cos(bear_θ z )-L yaw , L yaw Indicates the distance between the rotor bearing center and the bow rolling centerline of the hull. bear_θ z Indicates the angle of the bearing pitch, bear_θ z =A yaw sin(2πf yaw t), A yaw represents the motion amplitude of the ship's bow roll, f yaw Indicates the motion frequency of the ship's bow roll; bear_y′=L yaw sin(bear_θ z );

[0028] Step 3, establish the bearing-rotor dynamics model under basic motion and take the oil film force as the external force;

[0029] Step 4, using a numerical iteration method to calculate the response of the bearing-rotor system, the numerical integration method uses but is not limited to the generalized-α integration method; at each time step, the corresponding bearing oil film force is obtained by interpolation according to the equilibrium position of the shaft neck, and at the same time, at each time step, the displacement of the rotor bearing base is changed based on the displacement of the rotor bearing base in the X-axis direction bear_x, the displacement in the Y-axis direction bear_y, and the displacement in the Z-axis direction bear_z calculated in step 2, so as to introduce the basic motion of the rotor bearing base in the process of solving the dynamic response of the bearing-rotor system, including the following steps:

[0030] At the initial time, i.e., t0=0, the initial displacement x0 and initial velocity of the rotor-bearing system are given. and initial acceleration ; Given the motion form of the rotor bearing base, the relative equilibrium position of the journal is obtained, and then the oil film force F of the bearing at this time is obtained oil; Assume that the time step of numerical integration is Δt, solve the dynamic equation to obtain the dynamic characteristics of the rotor-bearing system at the next moment t0+Δt; take the rotor state at t0+Δt as the reference, calculate the dynamics of the rotor at the next moment t0+Δt, and repeat the above steps to obtain the dynamic characteristics of the rotor bearing system under the motion of the hull, where:

[0031] The bearing-rotor system model is mainly modeled using the finite element method, including beam elements and concentrated mass elements. The overall dynamic equation of the system is expressed as:

[0032]

[0033] Where M is the mass matrix of the system; C and G are the damping matrix and gyro matrix of the rotor-bearing system respectively; K is the rotor stiffness; F oil is the bearing oil film force; F is the external load vector; is the acceleration at the current moment; is the speed at the current moment; x is the displacement vector of the rotor bearing base calculated in step 2, which is composed of bear_x, bear_y and bear_z.

[0034] Preferably, the step 1 comprises the following steps:

[0035] The unsteady Reynolds equation for a radial sliding bearing is expressed as:

[0036]

[0037] Where: r represents the journal radius; φ represents the angle between the journal equilibrium position and the Y axis; h represents the oil film thickness, h = C b +C p cosφ,C b and C p are the minimum clearance of the fixed bearing and the radial clearance of the bearing respectively; p represents the oil film pressure; μ represents the dynamic viscosity of the lubricating oil; ω represents the rotation frequency; V x and V y are the extrusion speeds of the journal center along the X-axis and Y-axis directions respectively;

[0038] The oil film of the sliding bearing is very thin, so at a certain speed, for a given journal equilibrium position (J x0 ,J y0 ), the pressure distribution of the oil film P is the journal equilibrium position (J x0 ,J y0 ) function, expressed as: P = P (J x0 ,J y0 )

[0039] The journal equilibrium position (J x0,J y0 ) when the oil film force (F x0 ,F y0 ), then:

[0040]

[0041] Wherein, θ represents the integral angle corresponding to the oil film distribution pressure, θ1 represents the starting angle of the bearing, θ2 represents the ending angle of the bearing, L represents the width of the bearing, and i represents the i-th bearing.

[0042] In this way, when the external environment such as temperature and pressure remains unchanged, for a specific speed, the oil film pressure of the bearing is only a nonlinear function of the journal position.

[0043] The present invention adopts the finite element method to construct a rotor-bearing system dynamics model, and can establish various complex forms of rotors; the corresponding relationship between the journal equilibrium position and the oil film supporting force is established in advance, and the oil film supporting force at this time can be directly obtained through the journal equilibrium position by interpolation; before analysis, the movement of the hull is converted into the movement of the bearing seat, and the movement displacement of the bearing seat is changed at each load step during the calculation process, and the relative equilibrium position of the journal is calculated at the same time to determine the bearing oil film supporting force.

[0044] Compared with the prior art, the beneficial effects of the present invention are: it can conveniently consider various hull motions, is applicable to various rotor forms, has a wide range of applications and high calculation efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 A flow chart of a method for rapid analysis of dynamic characteristics of a marine rotor-bearing system according to the present invention;

[0046] Figure 2 A schematic diagram of a rotor-bearing according to an embodiment of the present invention;

[0047] Figure 3 Supporting horizontal oil film forces at different equilibrium positions of an embodiment of the present invention;

[0048] Figure 4 Supporting vertical oil film forces at different equilibrium positions of an embodiment of the present invention;

[0049] Figure 5 This is a diagram of the axis trajectory of the journal under different rotation speeds according to an embodiment of the present invention. DETAILED DESCRIPTION

[0050] The present invention will be further described below in conjunction with specific embodiments. It should be understood that these embodiments are only used to illustrate the present invention and are not intended to limit the scope of the present invention. In addition, it should be understood that after reading the content taught by the present invention, those skilled in the art can make various changes or modifications to the present invention, and these equivalent forms fall within the scope limited by the appended claims of the application equally.

[0051] This embodiment discloses a method for rapid analysis of dynamic characteristics of a marine rotor-bearing system, comprising the following steps:

[0052] In the first step, the oil film force at different journal equilibrium positions is calculated based on the Reynolds equation according to the bearing characteristics;

[0053] The second step is to calculate the displacement of the bearing seat under different motion forms of the hull;

[0054] The third step is to establish the bearing-rotor dynamics model under the basic motion and take the oil film force as the external force;

[0055] The fourth step is to calculate the response of the bearing-rotor system using a numerical iteration method. The bearing oil film force is obtained by interpolation based on the equilibrium position of the journal at each time step; at the same time, the bearing seat displacement is changed at each time step.

[0056] In order to better understand the technical solution of the present invention, an example is provided below: The method of the present invention is used to analyze the dynamic characteristics of a rotor-bearing system of a floating ship under the swaying action of the hull. The rotor model is as follows: Figure 2 shown.

[0057] (1) For given bearing parameters, the bearing oil film force distribution at different journal equilibrium positions is calculated according to the Reynolds equation, as follows: Figure 3 and Figure 4 As shown. When calculating, the maximum possible range of movement of the journal is taken into account and divided according to the coordinates. In this example, the transverse coordinate of the journal is divided into (-1.5Cb, 0.02Cb, 1.5Cb), and the longitudinal coordinate is divided into (-1.2Cb, 0.02Cb, 1.0Cb), where Cb is the minimum bearing clearance. By establishing the relationship between the journal equilibrium position and the oil film support force, the oil film support force of the bearing at this time can be easily obtained directly according to the bearing equilibrium position, which greatly improves the calculation efficiency.

[0058] (2) The sway amplitude is 6m and the sway frequency is 0.1Hz. Under the sway of the ship, the two bearings move in the same trajectory, both moving along the y direction of the coordinate, and the law of their movement over time is:

[0059] bear_y=6sin(2π×0.1×t)

[0060] (3) According to the rotor structural characteristics, the finite element method is used to establish the rotor-bearing system model. The rotor is established using beam units, the rigid blades are established using a concentrated mass model, and the bearing oil film force is directly applied to the structural model. Finally, the rotor-bearing system dynamic equation is established.

[0061] (4) According to the dynamic equation, the generalized-α numerical integration method is used for calculation. At the initial moment, i.e., t0=0, it is assumed that the rotor and the bearing seat move together, i.e., the initial velocity and initial acceleration of the rotor are consistent with those of the bearing seat. That is:

[0062] Initial velocity: bear_v y =1.2πcos(2π×0.1×t)

[0063] Initial acceleration: bear_a y =-0.24π 2 sin(2π×0.1×t)

[0064] The initial displacement of the rotor, that is, the initial displacement of the journal is zero.

[0065] According to the correspondence between the journal equilibrium position and the bearing oil film force, the linear interpolation method can be conveniently used to obtain the bearing oil film force at this time according to the journal equilibrium position. Assuming the time step of numerical integration is Δt, the bearing oil film force and the rotor displacement, velocity, and acceleration are brought into the system dynamics equation, and the rotor dynamic characteristics at the next moment t0+Δt can be obtained by numerical integration. The rotor dynamic characteristics include the motion displacement of the new journal. Therefore, the rotor state at the moment t0+Δt can be used as a reference to calculate the dynamics of the rotor at the next moment t0+2Δt. By analogy, the dynamic characteristics of the rotor bearing system under the motion of the hull can be obtained. Under the action of the hull swaying, the journal axis trajectory diagram of the journal motion at different speeds is shown as follows Figure 5 shown.

Claims

1. A method for rapid analysis of dynamic characteristics of a marine rotor-bearing system, characterized in that: The following steps are involved: Step 1: Calculate the oil film force at different journal equilibrium positions based on the Reynolds equation according to the bearing characteristics; Step 2: Calculate the motion displacement of the rotor bearing base under different hull motion forms, where the hull motion forms include sway, heave, roll, pitch and bow pitch. The motion equation of the rotor bearing base under different hull motion forms is expressed as: (1) Horizontal: The displacement of the two bearings at the left and right ends of the rotor bearing base is consistent, then: bear_y=A sway sin(2πf sway t) Where, bear_y represents the displacement of the rotor bearing base in the Y-axis direction, A sway represents the amplitude of the hull's swaying motion, f sway Indicates the hull swaying motion frequency; (2) Dangling The displacement of the two bearings at the left and right ends of the rotor bearing base is consistent, then: bear_z=A heave sin(2πf heave t) Where, bear_z represents the displacement of the rotor bearing base in the Z-axis direction, A heave represents the amplitude of the hull heave motion, f heave Indicates the motion frequency of the hull heave; (3) Roll The displacement of the two bearings at the left and right ends of the rotor bearing base is consistent, then: Where α represents the angle between the plane formed by the rotor bearing center and the hull roll centerline and the vertical plane where the hull roll center is located, tanα = Y g / Z g , Y g It represents the horizontal distance between the rotor bearing center and the hull roll centerline, Z g Indicates the vertical distance between the rotor bearing center and the hull roll centerline; bear_y′ indicates the displacement of the rotor bearing base relative to the hull roll centerline coordinate in the Y-axis direction, bear_y′=-L roll sin(bear_θ x ), L roll Indicates the distance between the rotor bearing center and the hull roll centerline, bear_θ x Indicates the rolling angle of the bearing, bear_θ x =A roll sin(2πf roll t), A roll represents the amplitude of the ship's rolling motion, f roll Indicates the motion frequency of the ship's rolling motion; bear_z′=L roll cos(bear_θ x )-L roll ; (4) Pitch The positions of the two bearings at the left and right ends of the rotor bearing base are different, then: Where, bear_x represents the displacement of the rotor bearing base in the X-axis direction; tanα=(X g ±L shaft / 2) / Z g , X g Indicates the longitudinal distance between the rotor bearing center and the hull pitch centerline, L shaft Indicates the distance between two bearings; bear_x′=L pitch sin(bear_θ y ), L pitch Indicates the distance between the rotor bearing center and the hull pitch centerline, bear_θ y Indicates the bearing pitch angle, bear_θ y =A pitch sin(2πf pitch t), A pitch represents the motion amplitude of the hull pitching, f pitch Indicates the motion frequency of the hull pitching; bear_z′=L pitch cos(bear_θ y )-L pitch ; (5) Bow swing The positions of the two bearings at the left and right ends of the rotor bearing base are different, then: Where, bear_x represents the displacement of the rotor bearing base in the X-axis direction; tanα = Y g / (X g ±L shaft / 2); bear_x′=L yaw cos(bear_θ z )-L yaw , L yaw Indicates the distance between the rotor bearing center and the bow rolling centerline of the hull. bear_θ z Indicates the angle of the bearing pitch, bear_θ z =A yaw sin(2πf yaw t), A yaw represents the motion amplitude of the ship's bow roll, f yaw Indicates the motion frequency of the ship's bow roll; bear_y′=L yaw sin(bear_θ z ); Step 3, establish the bearing-rotor dynamics model under basic motion and take the oil film force as the external force; Step 4, using a numerical iteration method to calculate the response of the bearing-rotor system; at each time step, the corresponding bearing oil film force is obtained by interpolation according to the equilibrium position of the shaft journal, and at the same time, at each time step, the displacement of the rotor bearing base is changed based on the displacement of the rotor bearing base in the X-axis direction bear_x, the displacement in the Y-axis direction bear_y, and the displacement in the Z-axis direction bear_z calculated in step 2, so as to introduce the basic motion of the rotor bearing base in the process of solving the dynamic response of the bearing-rotor system, including the following steps: At the initial time, i.e., t0=0, the initial displacement x0 and initial velocity of the rotor-bearing system are given. and initial acceleration Knowing the motion form of the rotor bearing base, the relative equilibrium position of the journal is obtained, and then the oil film force F of the bearing at this time is obtained oil ; Assume that the time step of numerical integration is Δt, solve the dynamic equation to obtain the dynamic characteristics of the rotor-bearing system at the next moment t0+Δt; take the rotor state at t0+Δt as the reference, calculate the dynamics of the rotor at the next moment t0+Δt, and repeat the above steps to obtain the dynamic characteristics of the rotor bearing system under the motion of the hull, where: The overall dynamic equation of the system is expressed as: Where M is the mass matrix of the system; C and G are the damping matrix and gyro matrix of the rotor-bearing system respectively; K is the rotor stiffness; F oil is the bearing oil film force; F is the external load vector; is the acceleration at the current moment; is the speed at the current moment; x is the displacement vector of the rotor bearing base calculated in step 2, which is composed of bear_x, bear_y and bear_z.

2. A method for rapid analysis of dynamic characteristics of a marine rotor-bearing system according to claim 1, characterized in that: The step 1 comprises the following steps: The unsteady Reynolds equation for a radial sliding bearing is expressed as: Where: r represents the journal radius; φ represents the angle between the journal equilibrium position and the Y axis; h represents the oil film thickness, h = C b +C p cosφ,C b and C p are the minimum clearance of the fixed bearing and the radial clearance of the bearing respectively; p represents the oil film pressure; μ represents the dynamic viscosity of the lubricating oil; ω represents the rotation frequency; V x and V y are the extrusion speeds of the journal center along the X-axis and Y-axis directions respectively; At a certain speed, for a given journal equilibrium position (J x0 ,J y0 ), the pressure distribution of the oil film P is the journal equilibrium position (J x0 ,J y0 ) function, expressed as: P = P (J x0 ,J y0 ) The journal equilibrium position (J x0 ,J y0 ) when the oil film force (F x0 ,F y0 ), then: Wherein, θ represents the integral angle corresponding to the oil film distribution pressure, θ1 represents the starting angle of the bearing, θ2 represents the ending angle of the bearing, L represents the width of the bearing, and i represents the i-th bearing.

Images