WO2022267215A1 - 双馈风电机组传动系统扭振响应计算方法、装置及存储介质 - Google Patents

双馈风电机组传动系统扭振响应计算方法、装置及存储介质 Download PDF

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WO2022267215A1
WO2022267215A1 PCT/CN2021/114796 CN2021114796W WO2022267215A1 WO 2022267215 A1 WO2022267215 A1 WO 2022267215A1 CN 2021114796 W CN2021114796 W CN 2021114796W WO 2022267215 A1 WO2022267215 A1 WO 2022267215A1
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torsional vibration
wind turbine
planetary gear
fed wind
doubly
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PCT/CN2021/114796
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English (en)
French (fr)
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赵鹏程
任鑫
杨晓峰
王�华
王恩民
朱俊杰
杜静宇
万抒策
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中国华能集团清洁能源技术研究院有限公司
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Publication of WO2022267215A1 publication Critical patent/WO2022267215A1/zh

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    • 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

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  • the invention belongs to the technical field of torsional vibration of a wind power generating set, and in particular relates to a method, a device and a storage medium for calculating the torsional vibration response of a transmission system of a doubly-fed wind power generating set.
  • Carbon neutrality means that enterprises, groups or individuals calculate the total amount of greenhouse gas emissions directly or indirectly generated within a certain period of time, and offset their own carbon dioxide emissions through afforestation, energy conservation and emission reduction, etc., to achieve "zero carbon dioxide emissions" ".
  • carbon neutrality has been adopted by more and more large-scale events and conferences. Carbon neutrality can promote green life and production, and realize the green development of the whole society.
  • the power industry has the largest carbon emissions, accounting for 41%.
  • the future positioning of coal power should be that the total amount will be gradually reduced, and the function will be transformed into a regulating power source.
  • the most effective way for the power industry to gradually implement carbon neutrality is to make full use of wind energy, solar energy and water resources, which are abundant in nature, to increase the installed capacity of renewable clean energy power generation, so as to obtain additional benefits from carbon emission reduction.
  • the shafting models used in the torsional vibration analysis of doubly-fed wind turbines include three-mass and two-mass models.
  • the blade and the low-speed shaft are equivalent to a mass unit.
  • the gearbox has a certain rigidity and needs to be equivalent to a mass unit.
  • the high-speed shaft and the motor shaft are the third mass unit.
  • the object of the present invention is to provide a calculation method, device and storage medium for the torsional vibration response of the doubly-fed wind turbine transmission system, which improves the calculation accuracy and efficiency of the torsional vibration response, and provides Fatigue calculations provide the basis.
  • a method for calculating the torsional vibration response of a doubly-fed wind turbine transmission system comprising the following steps: S1: establishing a torsional vibration kinematics equation of the doubly-fed wind turbine planetary gear train;
  • S1 is specifically:
  • T in and T out are the input torque and output torque of the planetary gear train respectively; the meshing angle of the wheel;
  • r ps and r pp are the pitch circle radii of the sun gear and the planet gear respectively;
  • k rp and c rp are the mesh stiffness and mesh damping coefficient between the planetary gear and the ring gear, respectively;
  • the planetary gear In addition to rotating around its axis, the planetary gear also rotates around the center O of the planetary gear system with the planetary carrier.
  • the calculation formulas for the meshing force P sp and damping force D sp of the gear pair composed of the sun gear and the planetary gear are:
  • k sp and c sp are the mesh stiffness and mesh damping coefficients of the sun gear and planetary gear, respectively.
  • S2 is specifically:
  • the double-fed wind turbine is composed of two-stage planetary gear train and one-stage parallel gear pair.
  • the torsional vibration kinematics equation of the parallel gear pair is established, and the meshing effect of the parallel gear pair is equivalent to the meshing stiffness and damping;
  • F qg and D qg are the meshing force and damping force of the gear pair respectively, and the calculation formula is:
  • S3 is specifically:
  • ⁇ T Lt is the external load moment acting on the shaft end (k-1);
  • the state vector of the transfer process is composed of torque and torsion angle, and substituted into the Newmark- ⁇ formula, then the transfer form of the state vector on the right and left sides of the shaft segment (k-1) is:
  • the torsional vibration transfer equation from the right side of the shaft section (k-1) to the left side of the shaft section k is:
  • S4 is specifically:
  • the output state vector on the left side of the rear axle section of the planetary gear system can be calculated:
  • S5 is specifically:
  • the invention discloses a computer device, including a memory, a processor, and a computer program stored in the memory and operable on the processor.
  • the processor executes the computer program, the above-mentioned method for calculating the torsional vibration response of the doubly-fed wind turbine drive system is realized. A step of.
  • the invention discloses a computer-readable storage medium.
  • the computer-readable storage medium stores a computer program.
  • the steps of the method for calculating the torsional vibration response of the doubly-fed wind turbine transmission system are realized.
  • the present invention has the following beneficial technical effects:
  • the method for calculating the torsional vibration response of the doubly-fed wind turbine transmission system disclosed by the present invention establishes a multi-stage lumped mass model of the shaft system-planetary gear-parallel gear pair, which focuses on the consideration of the torsional moment and torsional strain of the planetary gear system and the parallel gear pair Transfer relationship, further use the method of combining the transfer matrix and Newmark- ⁇ to obtain the transfer matrix of the entire system, and calculate the response when the torsional vibration fault occurs.
  • the adoption of the present invention The calculation results of the method are more accurate, and can more truly reflect the coupling oscillation characteristics between the machine and the network, and at the same time obtain the torsional vibration response at the details of the system.
  • the existing method usually adopts the finite element method for fine calculation, but the calculation process is complicated and the calculation efficiency is low.
  • the method of the present invention can greatly improve the calculation efficiency under the premise of ensuring the calculation accuracy.
  • it is beneficial to further analyze the mechanism of the torsional vibration failure of the fan, find out the cause of the failure, thereby effectively deal with the source of the failure or take effective suppression measures to prevent serious damage to the shaft system and ensure the safe operation of the unit.
  • Figure 1 is the torsional vibration model of the planetary gear train of the doubly-fed wind turbine
  • Fig. 2 is the torsional vibration model of the parallel gear pair of double-fed wind turbine
  • Fig. 3 is a multi-segment lumped mass model of the shafting of the doubly-fed wind turbine
  • Figure 4 is the torsional vibration model of the doubly-fed wind turbine planetary gear-shafting connection
  • Fig. 5 is the torsional vibration model of parallel gear-shafting connection of doubly-fed wind turbine
  • Fig. 6 is a torsional vibration response model diagram at the dangerous section of the transmission system in the embodiment.
  • the calculation method for the torsional vibration response of the doubly-fed wind turbine transmission system includes the following steps:
  • Step 1 As shown in Figure 1, in the 2K-H planetary gear dynamics model, when there are N planetary gears, the system contains N+2 degrees of freedom in total.
  • T in and T out are the input torque and output torque of the planetary gear train respectively; the meshing angle of the wheel;
  • r ps and r pp are the pitch circle radii of the sun gear and the planet gear respectively;
  • k rp and c rp are the mesh stiffness and mesh damping coefficient between the planetary gear and the ring gear, respectively;
  • the planetary gear In addition to rotating around its axis, the planetary gear also rotates around the center O of the planetary gear system with the planetary carrier.
  • the calculation formulas for the meshing force P sp and damping force D sp of the gear pair composed of the sun gear and the planetary gear are:
  • k sp and c sp are the mesh stiffness and mesh damping coefficients of the sun gear and planetary gear, respectively.
  • Step 2 Doubly-fed wind turbines are generally composed of two-stage planetary gear trains and one-stage parallel gear pairs.
  • the torsional vibration model of the gears is established.
  • the meshing effect of the parallel gear pairs is equivalent to the meshing stiffness and damping.
  • the gear dynamics model is as follows: Shown in accompanying drawing 2.
  • F qg and D qg are the meshing force and damping force of the gear pair respectively, and the calculation formula is:
  • Step 3 To solve the nonlinear problem of the system, the time domain stepwise integration method is often used.
  • the present invention selects Newmark- ⁇ stepwise integral method for use, and Newmark- ⁇ formula is:
  • ⁇ and ⁇ are the parameters of Newmark- ⁇ , where ⁇ provides the weight of the contribution of the initial and final acceleration to the displacement change within the corresponding time step, and similarly ⁇ is the initial and final acceleration within the time step, which is controlled by The amount of artificial damping resulting from the step-by-step method.
  • ⁇ T Lt is the external load moment acting on the shaft end (k-1);
  • the state vector of the transfer process is composed of torque and torsion angle, and substituted into the Newmark- ⁇ formula, then the transfer form of the state vector on the right and left sides of the shaft segment (k-1) is:
  • the torsional vibration transfer equation from the right side of the shaft section (k-1) to the left side of the shaft section k is:
  • Step 4 As shown in Figure 4, it is the torsional vibration model of the double-fed wind turbine planetary gear-shafting connection.
  • the formula in step 1 is changed to an incremental form, and the planetary
  • the ⁇ Tin and ⁇ c of the wheel input are known quantities, and the expressions of the output state quantities ⁇ Tout and ⁇ s are obtained from the formula in step 1 and written in matrix form as:
  • the output state vector on the left side of the rear axle section of the planetary gear system can be calculated:
  • Step 5 As shown in Figure 5, the torsional vibration model of the double-fed wind turbine parallel gear-shaft connection is obtained. For the parallel gear pair, the transfer relationship of the torsional vibration response state vector between its output and input is obtained:
  • Table 1 is the mechanical parameters of the first-stage planetary gear, the second-stage planetary gear and the parallel gear pair respectively:
  • the present invention also provides a computer device, including a memory, a processor, and a computer program stored in the memory and operable on the processor.
  • a computer program stored in the memory and operable on the processor.
  • the method for calculating the torsional vibration response of the doubly-fed wind turbine transmission system of the present invention can be in the form of a complete hardware embodiment, a complete software embodiment or a combination of software and hardware.
  • the present invention may take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) having computer-usable program code embodied therein. If the method for calculating the torsional vibration response of the doubly-fed wind turbine transmission system of the present invention is realized in the form of a software function unit and sold or used as an independent product, it can be stored in a computer-readable storage medium.
  • a computer-readable storage medium is also provided.
  • the present invention implements all or part of the processes in the methods of the above-mentioned embodiments, and can also be completed by instructing related hardware through computer programs.
  • the computer program can be stored in the computer-readable storage medium, and when the computer program is executed by the processor, the steps of the above-mentioned various method embodiments can be realized.
  • the computer program includes computer program code, and the computer program code may be in the form of source code, object code, executable file or some intermediate form.
  • Computer-readable storage media includes both volatile and non-permanent, removable and non-removable media by any method or technology for storage of information.
  • Computer-readable Information may be computer readable instructions, data structures, modules of a program, or other data. It should be noted that the content contained in the computer-readable medium may be appropriately increased or decreased according to the requirements of legislation and patent practice in the jurisdiction. For example, in some jurisdictions, computer-readable media Excludes electrical carrier signals and telecommunication signals.
  • the computer storage medium may be any available medium or data storage device that can be accessed by a computer, including but not limited to magnetic storage (such as floppy disk, hard disk, magnetic tape, magneto-optical disk (MO), etc.), optical storage (such as CD, DVD, BD, HVD, etc.), and semiconductor memory (such as ROM, EPROM, EEPROM, non-volatile memory (NANDFLASH), solid-state disk (SSD)), etc.
  • magnetic storage such as floppy disk, hard disk, magnetic tape, magneto-optical disk (MO), etc.
  • optical storage such as CD, DVD, BD, HVD, etc.
  • semiconductor memory such as ROM, EPROM, EEPROM, non-volatile memory (NANDFLASH), solid-state disk (SSD)
  • a computer device comprising a memory, a processor, and a computer program stored in the memory and operable on the processor, the processor implements the computer program when executing the computer program. Steps of calculation method for torsional vibration response of doubly-fed wind turbine transmission system.
  • the processor may be a central processing unit (Central Processing Unit, CPU), or other general-purpose processors, digital signal processors (Digital Signal Processor, DSP), application specific integrated circuits (Application Specific Integrated Circuit, ASIC), off-the-shelf programmable gate arrays (Field-Programmable Gate Array, FPGA) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc.
  • CPU Central Processing Unit
  • DSP Digital Signal Processor
  • ASIC Application Specific Integrated Circuit
  • FPGA Field-Programmable Gate Array

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  • General Engineering & Computer Science (AREA)
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Abstract

本发明公开了一种双馈风电机组传动系统扭振响应计算方法、装置及存储介质，属于风力发电机组扭振技术领域。通过对轴系扭转振响应进行分析，为轴系扭转振动疲劳损伤的评估提供准备。基于转轴、行星齿轮系统和平行齿轮副的扭转振动模型和运动微分方程，建立传动系统的集中质量模型，引入Newmark-β表达式，推导风机传动系统各质量单元间状态量的传递关系，最后采用传递矩阵计算传动系统集中质量模型中各个质量块的扭振响应。相较于简单集中质量模型，能真实反映机网之间的耦合振荡特性，同时获得轴系细节处的扭振响应，同时相比于有限元法，大大提高了计算效率。

Description

双馈风电机组传动系统扭振响应计算方法、装置及存储介质 技术领域
本发明属于风力发电机组扭振技术领域，具体涉及一种双馈风电机组传动系统扭振响应计算方法、装置及存储介质。
背景技术
碳中和是指企业、团体或个人测算在一定时间内直接或间接产生的温室气体排放总量，通过植树造林、节能减排等形式，以抵消自身产生的二氧化碳排放量，实现二氧化碳“零排放”。碳中和作为一种新型环保形式，目前已经被越来越多的大型活动和会议采用。碳中和能够推动绿色的生活、生产，实现全社会绿色发展，分行业来看，电力行业碳排放量最多，占比达41％。在碳中和目标下，煤电未来的定位应该是，总量逐步减少，功能向调节性电源转变。让电力行业逐步实行碳中和最有效的方式就是充分利用自然界储备丰富的风能、太阳能和水资源等，提升可再生清洁能源发电装机容量，从而获得碳减排的额外收益。
随着风电上网比例不断提高，风电机组对电力系统稳定性的影响也随之增加，其中风电机组扭振是电力系统稳定性与风机传动系统相互影响的典型故障。
目前，用于双馈风电机组扭振分析中的轴系模型包括三质量块和两质量块模型。三质量块模型将叶片及低速轴等效为1个质量块单元，齿轮箱具有一定刚性，需要等效为1个质量块单元，高速轴及电机轴为第3个质量单元。也有文献指出，由于叶片转动惯量较大，应将其单独等效为1个集中质量单元，将低速轴等效为1个质量块单元，高速轴和发电机转子等效为第3个质量块单元，而将齿轮箱的转动惯量根据2个啮合齿轮转速分摊到低速轴和高速轴。这些简单集中质量模型无法反映机网之间耦合振荡特性，并且在进行轴系扭振响应计算时无法获取轴系细节处的响应特性。当采用有限元法计算轴系细节扭振响应时计算量大，仿真计算时间长。
发明内容
为了解决上述现有技术中存在的缺陷，本发明的目的在于提供一种双馈风电机组传动系统扭振响应计算方法、装置及存储介质，提高了扭转振动响应计算精度和计算效率，为扭振疲劳计算提供了基础。
本发明是通过以下技术方案来实现：
一种双馈风电机组传动系统扭振响应计算方法，包括以下步骤：S1：建立双馈风电机组行星齿轮系的扭转振动运动学方程；
S2：建立双馈风电机组平行齿轮副的扭转振动运动学方程；
S3：建立双馈风电机组轴系的多段集中质量模型和轴系扭转振动传递矩阵方程，求解轴系输出和输入状态向量的关系表达式；
S4：求解行星齿轮系后连接轴系与行星齿轮系前一段轴系的状态向量关系表达式；
S5：求解平行齿轮副后连接轴系与平行齿轮副前一段轴系的状态向量关系表达式；
S6：建立行星齿轮系-平行齿轮副-轴系的整体传递矩阵，并计算在给定故障输入下，双馈风电机组传动系统的扭振响应。
优选地，S1具体为：
在2K-H型行星轮动力学模型中，当含有N个行星轮时，系统共包含N+2个自由度；
由行星轮传动特性，得到其扭转振动运动学方程：
Figure PCTCN2021114796-appb-000001
其中，T in和T out分别是行星齿轮系的输入力矩和输出力矩；θ i(i＝c,p,s)分别是行星架、行星轮和太阳轮的扭角；T是行星轮和太阳轮的啮合角；
r c是行星架的等效半径，计算公式为：
r c＝r ps+r pp；
r ps、r pp分别是太阳轮和行星轮的节圆半径；
齿圈和行星轮组成的齿轮副啮合力P rp和阻尼力D rp计算公式分别为：
P rp＝k rp(r pθ p-r ccosTθ c)；
Figure PCTCN2021114796-appb-000002
其中k rp和c rp分别是行星轮和内齿圈之间的啮合刚度和啮合阻尼系数；
行星轮除了围绕其所在轴转动外，还随行星架围绕行星轮系统中心O做旋转运动，太阳轮和行星轮组成的齿轮副啮合力P sp和阻尼力D sp计算公式分别为：
P sp＝k sp(r pθ p+r ccosTθ c-r sθ s)；
Figure PCTCN2021114796-appb-000003
其中k sp和c sp分别是太阳轮和行星轮的啮合刚度和啮合阻尼系数。
进一步优选地，S2具体为：
双馈风电机组由两级行星轮系和一级平行齿轮副组成，建立平行齿轮副的扭转振动运动学方程，其中平行齿轮副的啮合作用以啮合刚度和阻尼等效；
建立平行齿轮副的扭转振动运动学方程：
Figure PCTCN2021114796-appb-000004
式中，F qg和D qg分别为齿轮副的啮合力和阻尼力，计算公式为：
Figure PCTCN2021114796-appb-000005
其中，r i(i＝q,g)分别是主动轮和被动轮的基圆半径；k m是齿轮副的啮合综合刚度；c m是齿轮副的啮合阻尼；T′ in和T′ out分别是齿轮副的输入和输出扭矩。
进一步优选地，S3具体为：
建立双馈风电机组轴系的多段集中质量模型，质量块之间的连接等效为弹簧-阻尼单元；
轴系扭转振动的动力学模型时间增量形式为：
Figure PCTCN2021114796-appb-000006
其中，ΔT Lt是作用在轴端(k-1)上的外载荷力矩；
以力矩和扭角组成传递过程的状态向量，并代入Newmark-β公式，则轴段(k-1)右侧与左侧的状态向量传递形式为：
Figure PCTCN2021114796-appb-000007
其中，
Figure PCTCN2021114796-appb-000008
轴段(k-1)右侧到轴段k左侧的扭转振动传递方程为：
Figure PCTCN2021114796-appb-000009
Figure PCTCN2021114796-appb-000010
代入Newmark-β公式并整理为传递矩阵形式：
Figure PCTCN2021114796-appb-000011
其中，
Figure PCTCN2021114796-appb-000012
Figure PCTCN2021114796-appb-000013
进一步优选地，S4具体为：
将双馈风电机组行星齿轮系的扭转振动运动学方程改写为增量形式，并以行星轮输入的ΔTin和Δθc为已知量，得到输出状态量ΔTout和Δθs的表达式并写成矩阵形式为并以行星轮输入的ΔT in和Δθ c为已知量，得到输出状态量ΔT out和Δθ s的表达式并写成矩阵形式为：
Figure PCTCN2021114796-appb-000014
Figure PCTCN2021114796-appb-000015
Figure PCTCN2021114796-appb-000016
Figure PCTCN2021114796-appb-000017
Figure PCTCN2021114796-appb-000018
Figure PCTCN2021114796-appb-000019
Figure PCTCN2021114796-appb-000020
Figure PCTCN2021114796-appb-000021
Figure PCTCN2021114796-appb-000022
Figure PCTCN2021114796-appb-000023
可计算得到行星轮系统后轴段左侧输出状态向量：
Figure PCTCN2021114796-appb-000024
进一步优选地，S5具体为：
对于平行齿轮副，得到其输出和输入之间的扭振响应状态向量的传递关系：
Figure PCTCN2021114796-appb-000025
Figure PCTCN2021114796-appb-000026
Figure PCTCN2021114796-appb-000027
Figure PCTCN2021114796-appb-000028
Figure PCTCN2021114796-appb-000029
Figure PCTCN2021114796-appb-000030
Figure PCTCN2021114796-appb-000031
本发明公开了一种计算机设备，包括存储器、处理器以及存储在存储器中并可在处理器上运行的计算机程序，处理器执行计算机程序时实现上述的双馈风电机组传动系统扭振响应计算方法的步骤。
本发明公开了一种计算机可读存储介质，计算机可读存储介质存储有计算机程序，计算机程序被处理器执行时实现上述的双馈风电机组传动系统扭振响应计算方法的步骤。
与现有技术相比，本发明具有以下有益的技术效果：
本发明公开的双馈风电机组传动系统扭振响应计算方法，建立的轴系-行星轮-平行齿轮副的多段集中质量模型，重点考虑了行星齿轮系统和平行齿轮副的扭转力矩和扭转应变的传递关系，进一步利用传递矩阵与Newmark-β相结合的方法，得到了整个系统的传递矩阵，计算出发生扭振故障时的响应，相较于目前普遍采用的简单集中质量模型，采用本发明的方法计算结果更加准确，也更能真实反映机网之间的耦合振荡特性，同时获得系统细节处的扭振响应。目前现有的方法进行精细计算常采用有限元法，但计算过程复杂，计算效率低，采用本发明的方法可以在保证计算精度的前提下大大提高了计算效率。通过本发明的计算，有利于进一步分析出风机扭振故障发生的机理，找到故障发生的原因，从而有效处理故障源或采取有效的抑制措施，防止对轴系造成严重损失，保障机组安全运行。
附图说明
图1为双馈风力发电机组行星齿轮系的扭转振动模型；
图2为双馈风力发电机组平行齿轮副的扭转振动模型；
图3为双馈风力发电机组轴系的多段集中质量模型；
图4为双馈风力发电机组行星齿轮-轴系连接扭转振动模型；
图5为双馈风力发电机组平行齿轮-轴系连接扭转振动模型；
图6为实施例中传动系统危险截面处的扭振响应模型图。
具体实施方式
下面以附图和具体实施例对本发明做进一步的详细说明，所述是对本发明的解释而不是限定。
双馈风电机组传动系统扭振响应计算方法，包括以下步骤：
步骤1：如图1，在2K-H型行星轮动力学模型中，当含有N个行星轮时，系统共包含N+2个自由度。
由行星轮传动特性，得到其扭转运动微分方程：
Figure PCTCN2021114796-appb-000032
其中，T in和T out分别是行星齿轮系的输入力矩和输出力矩；θ i(i＝c,p,s)分别是行星架、行星轮和太阳轮的扭角；T是行星轮和太阳轮的啮合角；
r c是行星架的等效半径，计算公式为：
r c＝r ps+r pp；
r ps、r pp分别是太阳轮和行星轮的节圆半径；
齿圈和行星轮组成的齿轮副啮合力P rp和阻尼力D rp计算公式分别为：
P rp＝k rp(r pθ p-r ccosTθ c)；
Figure PCTCN2021114796-appb-000033
其中k rp和c rp分别是行星轮和内齿圈之间的啮合刚度和啮合阻尼系数；
行星轮除了围绕其所在轴转动外，还随行星架围绕行星轮系统中心O做旋转运动，太阳轮和行星轮组成的齿轮副啮合力P sp和阻尼力D sp计算公式分别为：
P sp＝k sp(r pθ p+r ccosTθ c-r sθ s)；
Figure PCTCN2021114796-appb-000034
其中k sp和c sp分别是太阳轮和行星轮的啮合刚度和啮合阻尼系数。
步骤2：双馈风电机组一般是由两级行星轮系和一级平行齿轮副组成，建立齿轮的扭转振动模型，其中平行齿轮副的啮合作用以啮合刚度和阻尼等效，齿轮动力学模型如附图2所示。
建立平行齿轮的扭转振动动力学方程：
Figure PCTCN2021114796-appb-000035
式中，F qg和D qg分别为齿轮副的啮合力和阻尼力，计算公式为：
Figure PCTCN2021114796-appb-000036
其中，r i(i＝q,g)分别是主动轮和被动轮的基圆半径；k m是齿轮副的啮合综合刚度；c m是齿轮副的啮合阻尼；T′ in和T′ out分别是齿轮副的输入和输出扭矩。
步骤3：解决系统的非线性问题，常使用时域逐步积分法。本发明选用Newmark-β逐步积分法，Newmark-β公式为：
Figure PCTCN2021114796-appb-000037
其中β和γ是Newmark-β的参数，其中β提供在相应的时间步长内的初始和最终加速度对位移变化贡献的权重，同理γ是时间步长内初始和最终加速度，它控制了由逐步法导致的人工阻尼量。
将Newmark-β公式并整理为增量形式：
Figure PCTCN2021114796-appb-000038
如图3，建立双馈风电机组轴系的多段集中质量模型，质量块之间的连接等效为弹簧-阻尼单元。
轴系扭转振动的动力学模型时间增量形式为：
Figure PCTCN2021114796-appb-000039
其中，ΔT Lt是作用在轴端(k-1)上的外载荷力矩；
以力矩和扭角组成传递过程的状态向量，并代入Newmark-β公式，则轴段(k-1)右侧与左侧的状态向量传递形式为：
Figure PCTCN2021114796-appb-000040
其中，
Figure PCTCN2021114796-appb-000041
轴段(k-1)右侧到轴段k左侧的扭转振动传递方程为：
Figure PCTCN2021114796-appb-000042
Figure PCTCN2021114796-appb-000043
代入Newmark-β公式并整理为传递矩阵形式：
Figure PCTCN2021114796-appb-000044
其中，
Figure PCTCN2021114796-appb-000045
Figure PCTCN2021114796-appb-000046
步骤4：如图4，为双馈风力发电机组行星齿轮-轴系连接扭转振动模型，为推导系统传递矩阵，在发生扭振故障时，将步骤1中公式改为增量形式，并以行星轮输入的ΔTin和Δθc为已知量，步骤1中公式得到输出状态量ΔTout和Δθs的表达式并写成矩阵形式为：
Figure PCTCN2021114796-appb-000047
Figure PCTCN2021114796-appb-000048
Figure PCTCN2021114796-appb-000049
Figure PCTCN2021114796-appb-000050
Figure PCTCN2021114796-appb-000051
Figure PCTCN2021114796-appb-000052
Figure PCTCN2021114796-appb-000053
Figure PCTCN2021114796-appb-000054
Figure PCTCN2021114796-appb-000055
Figure PCTCN2021114796-appb-000056
可计算得到行星轮系统后轴段左侧输出状态向量：
Figure PCTCN2021114796-appb-000057
步骤5：如图5，为双馈风力发电机组平行齿轮-轴系连接扭转振动模型，对于平行齿轮副，得到其输出和输入之间的扭振响应状态向量的传递关系：
Figure PCTCN2021114796-appb-000058
Figure PCTCN2021114796-appb-000059
Figure PCTCN2021114796-appb-000060
Figure PCTCN2021114796-appb-000061
Figure PCTCN2021114796-appb-000062
Figure PCTCN2021114796-appb-000063
Figure PCTCN2021114796-appb-000064
由此可建立轴系＝行星轮-平行齿轮副的传递矩阵。
以某1.5MW双馈风力发电机组为例，表1、表2和表3分别是第一级行星轮、第二级行星轮和平行齿轮副的机械参数：
表1低速级齿轮箱参数
Figure PCTCN2021114796-appb-000065
表2中间级齿轮箱参数
Figure PCTCN2021114796-appb-000066
表3高速级齿轮箱参数
Figure PCTCN2021114796-appb-000067
采用上述方法，以发生两相短路激发的扭振为例，最终可计算出传动系统危险截面处的转速差响应波形图，结果如图6所示。
本发明还提供一种计算机设备，包括存储器、处理器以及存储在所述存储器中并可在所述处理器上运行的计算机程序，所述处理器执行所述计算机程序时实现本发明所述双馈风电机组传动系统扭振响应计算方法的步骤。
本发明双馈风电机组传动系统扭振响应计算方法可采用完全硬件实施例、完全软件实施例或结合软件和硬件方面的实施例的形式。而且，本发明可采用在一个或多个其中包含有计算机可用程序代码的计算机可用存储介质(包括但不限于磁盘存储器、CD-ROM、光学存储器等)上实施的计算机程序产品的形式。本发明双馈风电机组传动系统扭振响应计算方法如果以软件功能单元的形式实现并作为独立的产品销售或使用时，可以存储在一个计算机可读取存储介质中。
基于这样的理解，在示例性实施例中，还提供了一种计算机可读存储介质，本发明实现上述实施例方法中的全部或部分流程，也可以通过计算机程序来指令相关的硬件来完成，所述的计算机程序可存储于该计算机可读存储介质中，该计算机程序在被处理器执行时，可实现上述各个方法实施例的步骤。其中，所述计算机程序包括计算机程序代码，所述计算机程序代码可以为源代码形式、对象代码形式、可执行文件或某些中间形式等。计算机可读存储介质包括永久性和非永久性、可移动和非可移动媒体可以由任何方法或技术来实现信息存储。信息可以是计算机可读指令、数据结构、程序的模块或其他数据。需要说明的是，所述计算机可读介质包含的内容可以根据司法管辖区内立法和专利实践的要求进行适当的增减，例如在某些司法管辖区，根据立法和专利实践，计算机可读介质不包括电载波信号和电信信号。其中，所述计算机存储介质可以是计算机能够存取的任何可用介质或数据存储设备，包括但不限于磁性存储器(例如软盘、硬盘、磁带、磁光盘(MO)等)、光学存储器(例如CD、DVD、BD、HVD等)、以及半导体存储器(例如ROM、EPROM、EEPROM、非易失性存储器(NANDFLASH)、固态硬盘(SSD))等。
在示例性实施例中，还提供计算机设备，包括存储器、处理器以及存储在所述存储器中并可在所述处理器上运行的计算机程序，所述处理器执行所述计算机程序时实现所述双馈风电机组传动系统扭振响应计算方法的步骤。处理器可能是中央处理单元(CentralProcessingUnit，CPU)，还可以是其他通用处理器、数字信号处理器(DigitalSignalProcessor、DSP)、专用集成电路(ApplicationSpecificIntegratedCircuit，ASIC)、现成可编程门阵列(Field-ProgrammableGateArray，FPGA)或者其他可编程逻辑器件、分立门或者晶体管逻辑器件、分立硬件组件等。
需要说明的是，以上所述仅为本发明实施方式的一部分，根据本发明所描述的系统所做的等效变化，均包括在本发明的保护范围内。本发明所属技术领域的技术人员可以对所描述的具体实例做类似的方式替代，只要不偏离本发明的结构或者超越本权利要求书所定义的范围，均属于本发明的保护范围。

Claims (8)

  1. 一种双馈风电机组传动系统扭振响应计算方法，其特征在于，包括：
    S1：建立双馈风电机组行星齿轮系的扭转振动运动学方程；
    S2：建立双馈风电机组平行齿轮副的扭转振动运动学方程；
    S3：建立双馈风电机组轴系的多段集中质量模型和轴系扭转振动传递矩阵方程，求解轴系输出和输入状态向量的关系表达式；
    S4：求解行星齿轮系后连接轴系与行星齿轮系前一段轴系的状态向量关系表达式；
    S5：求解平行齿轮副后连接轴系与平行齿轮副前一段轴系的状态向量关系表达式；
    S6：建立行星齿轮系-平行齿轮副-轴系的整体传递矩阵，并计算在给定故障输入下，双馈风电机组传动系统的扭振响应。
  2. 如权利要求1所述的双馈风电机组传动系统扭振响应计算方法，其特征在于，S1具体为：
    在2K-H型行星轮动力学模型中，当含有N个行星轮时，系统共包含N+2个自由度；
    由行星轮传动特性，得到其扭转振动运动学方程：
    Figure PCTCN2021114796-appb-100001
    其中，T in和T out分别是行星齿轮系的输入力矩和输出力矩；θ i(i＝c,p,s)分别是行星架、行星轮和太阳轮的扭角；T是行星轮和太阳轮的啮合角；
    r c是行星架的等效半径，计算公式为：
    r c＝r ps+r pp；
    r ps、r pp分别是太阳轮和行星轮的节圆半径；
    齿圈和行星轮组成的齿轮副啮合力P rp和阻尼力D rp计算公式分别为：
    P rp＝k rp(r pθ p-r ccosTθ c)；
    Figure PCTCN2021114796-appb-100002
    其中k rp和c rp分别是行星轮和内齿圈之间的啮合刚度和啮合阻尼系数；
    行星轮除了围绕其所在轴转动外，还随行星架围绕行星轮系统中心O做旋转运动，太阳轮和行星轮组成的齿轮副啮合力P sp和阻尼力D sp计算公式分别为：
    P sp＝k sp(r pθ p+r ccosTθ c-r sθ s)；
    Figure PCTCN2021114796-appb-100003
    其中k sp和c sp分别是太阳轮和行星轮的啮合刚度和啮合阻尼系数。
  3. 如权利要求2所述的双馈风电机组传动系统扭振响应计算方法，其特征在于，S2具体为：
    双馈风电机组由两级行星轮系和一级平行齿轮副组成，建立平行齿轮副的扭转振动运动学方程，其中平行齿轮副的啮合作用以啮合刚度和阻尼等效；
    建立平行齿轮副的扭转振动运动学方程：
    Figure PCTCN2021114796-appb-100004
    式中，F qg和D qg分别为齿轮副的啮合力和阻尼力，计算公式为：
    Figure PCTCN2021114796-appb-100005
    其中，r i(i＝q,g)分别是主动轮和被动轮的基圆半径；k m是齿轮副的啮合综合刚度；c m是齿轮副的啮合阻尼；T' in和T' out分别是齿轮副的输入和输出扭矩。
  4. 如权利要求3所述的双馈风电机组传动系统扭振响应计算方法，其特征在于，S3具体为：
    建立双馈风电机组轴系的多段集中质量模型，质量块之间的连接等效为弹簧-阻尼单元；
    轴系扭转振动的动力学模型时间增量形式为：
    Figure PCTCN2021114796-appb-100006
    其中，ΔT Lt是作用在轴端(k-1)上的外载荷力矩；
    以力矩和扭角组成传递过程的状态向量，并代入Newmark-β公式，则轴段(k-1)右侧与左侧的状态向量传递形式为：
    Figure PCTCN2021114796-appb-100007
    其中，
    Figure PCTCN2021114796-appb-100008
    轴段(k-1)右侧到轴段k左侧的扭转振动传递方程为：
    Figure PCTCN2021114796-appb-100009
    Figure PCTCN2021114796-appb-100010
    代入Newmark-β公式并整理为传递矩阵形式：
    Figure PCTCN2021114796-appb-100011
    其中，
    Figure PCTCN2021114796-appb-100012
    Figure PCTCN2021114796-appb-100013
  5. 如权利要求4所述的双馈风电机组传动系统扭振响应计算方法，其特征在于，S4具体为：
    将双馈风电机组行星齿轮系的扭转振动运动学方程改写为增量形式，并以行星轮输入的ΔT in和Δθ c为已知量，得到输出状态量ΔT out和Δθ s的表达式并写成矩阵形式为：
    Figure PCTCN2021114796-appb-100014
    Figure PCTCN2021114796-appb-100015
    Figure PCTCN2021114796-appb-100016
    Figure PCTCN2021114796-appb-100017
    Figure PCTCN2021114796-appb-100018
    Figure PCTCN2021114796-appb-100019
    Figure PCTCN2021114796-appb-100020
    Figure PCTCN2021114796-appb-100021
    Figure PCTCN2021114796-appb-100022
    Figure PCTCN2021114796-appb-100023
    可计算得到行星轮系统后轴段左侧输出状态向量：
    Figure PCTCN2021114796-appb-100024
  6. 如权利要求5所述的双馈风电机组传动系统扭振响应计算方法，其特征在于，S5具体为：
    对于平行齿轮副，得到其输出和输入之间的扭振响应状态向量的传递关系：
    Figure PCTCN2021114796-appb-100025
    Figure PCTCN2021114796-appb-100026
    Figure PCTCN2021114796-appb-100027
    Figure PCTCN2021114796-appb-100028
    Figure PCTCN2021114796-appb-100029
    Figure PCTCN2021114796-appb-100030
    Figure PCTCN2021114796-appb-100031
  7. 一种计算机设备，其特征在于，包括存储器、处理器以及存储在所述存储器中并可在所述处理器上运行的计算机程序，所述处理器执行所述计算机程序时实现如权利要求1至6任一项所述的双馈风电机组传动系统扭振响应计算方法的步骤。
  8. 一种计算机可读存储介质，所述计算机可读存储介质存储有计算机程序，其特征在于，所述计算机程序被处理器执行时实现如权利要求1至6任一项所述的双馈风电机组传动系统扭振响应计算方法的步骤。
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CN116988935A (zh) * 2023-09-26 2023-11-03 哈尔滨理工大学 一种双馈感应风力发电机扭振抑制系统及方法
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