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.obsidian/plugins/copilot/data.json
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.obsidian/plugins/copilot/data.json
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@ -266,7 +266,7 @@
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},
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{
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"name": "Translate to Chinese",
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"prompt": "<instruction>Translate the text below into Chinese:\n 1. Preserve the meaning and tone\n 2. Maintain appropriate cultural context\n 3. Keep formatting and structure\n 4. Blade翻译为叶片，flapwise翻译为挥舞，edgewise翻译为摆振，pitch angle翻译成变桨角度，twist angle翻译为扭角，rotor翻译为风轮，span翻译为展向，deflection翻译为变形，normal mode翻译为简正模式，jacket 翻译为导管架，superelement翻译为超单元\n Return only the translated text.</instruction>\n\n<text>{copilot-selection}</text>",
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"prompt": "<instruction>Translate the text below into Chinese:\n 1. Preserve the meaning and tone\n 2. Maintain appropriate cultural context\n 3. Keep formatting and structure\n 4. Blade翻译为叶片，flapwise翻译为挥舞，edgewise翻译为摆振，pitch angle翻译成变桨角度，twist angle翻译为扭角，rotor翻译为风轮，span翻译为展向，deflection翻译为变形，mode翻译为模态，normal mode翻译为简正模态，jacket 翻译为导管架，superelement翻译为超单元\n Return only the translated text.</instruction>\n\n<text>{copilot-selection}</text>",
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"showInContextMenu": true,
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"modelKey": "gemma3:12b|ollama"
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},
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@ -1,6 +1,7 @@
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# Linear Analysis Background
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The linear analysis calculations reduce the Bladed aeroelastic model to a linear system at each operating point requested by the user. The linear system of equations in state-space form is represented by
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线性分析计算将Bladed气弹模型简化为用户请求的**每个工作点处的线性系统**。**以状态空间形式表示的线性方程组为**：
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$$
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\begin{array}{r}{\underline{{\dot{\mathbf{x}}}}=\mathbf{A}\underline{{\mathbf{x}}}+\mathbf{B}\underline{{\mathbf{u}}}}\\ {\underline{{\mathbf{y}}}=\mathbf{C}\underline{{\mathbf{x}}}+\mathbf{D}\underline{{\mathbf{u}}}}\end{array}
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@ -12,9 +13,9 @@ $$
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\underline{{\mathbf{x}}}=\mathbf{x}-\mathbf{x_{0}},\quad\underline{{\mathbf{y}}}=\mathbf{y}-\mathbf{y_{0}},\quad\mathrm{~and~}\quad\underline{{\mathbf{u}}}=\mathbf{u}-\mathbf{u_{0}}
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$$
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where x is a vector of states representing the system, u is the vector of system inputs and $\mathbf{y}$ is the vector of system outputs. The normalised vectors x,y and u are representing the deviation from equilibrium.
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where $\mathbf{x}$ is a vector of states representing the system, $\mathbf{u}$ is the vector of system inputs and $\mathbf{y}$ is the vector of system outputs. The normalised vectors $\underline{{\mathbf{x}}}、\underline{{\mathbf{y}}}$ and $\underline{{\mathbf{u}}}$ are representing the deviation from equilibrium.
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The matrices A, B, C and D represent the linearised relationship between these vectors. This represents a simplification of the full Bladed model which uses a fully non-linear set of equations to calculate the state derivatives and outputs
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The matrices $\mathbf{A}$, $\mathbf{B}$, $\mathbf{C}$ and $\mathbf{D}$ represent the linearised relationship between these vectors. This represents a simplification of the full Bladed model which uses a fully non-linear set of equations to calculate the state derivatives and outputs
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$$
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\begin{array}{r}{\dot{\mathbf{x}}=f(t,\mathbf{x},\mathbf{u})}\\ {\mathbf{y}=h(t,\mathbf{x},\mathbf{u}).}\end{array}
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@ -24,6 +25,19 @@ It is important to note that in order to enable proper linearised wind turbine d
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· Azimuthal dependency shall be removed which includes wind shear, yaw, rotor imbalance, etc.
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· Physical effects that cannot be linearised shall be removed, for instance wind turbulence, stickslip, etc.
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其中 $\mathbf{x}$ 是状态向量，代表系统状态；$\mathbf{u}$ 是系统输入向量；$\mathbf{y}$ 是系统输出向量。归一化向量 $\underline{{\mathbf{x}}}、\underline{{\mathbf{y}}}$ 和 $\underline{{\mathbf{u}}}$ 代表偏离平衡态的量。
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矩阵 $\mathbf{A}$、$\mathbf{B}$、$\mathbf{C}$ 和 $\mathbf{D}$ 代表这些向量之间的线性化关系。这代表对完整叶片（Blade）模型的一个简化，该模型使用一组完全非线性方程来计算状态导数和输出。
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$$
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\begin{array}{r}{\dot{\mathbf{x}}=f(t,\mathbf{x},\mathbf{u})}\\ {\mathbf{y}=h(t,\mathbf{x},\mathbf{u}).}\end{array}
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$$
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需要注意的是，为了能够建立适当的线性化风轮动力学系统，需要考虑以下模型准备原则：
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· 需移除方位角依赖性，包括风切变、偏航、风轮不平衡等。
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· 需移除无法线性化的物理效应，例如风湍流、黏滞滑动等。
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In Bladed, the states fall into two main categories:
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@ -39,22 +53,49 @@ For each input or state, Bladed then makes a series of perturbations of increasi
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The elements of the matrices A, B, C and D can then be derived by performing a linear regression of the state derivative against the input or state value at all its perturbed values and its equilibrium value. The gradient of the linear regression gives the value of the element. If the correlation coefficient is less than the minimum correlation coefficient , then the relationship is considered void, and a zero value is given to the element.
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在Bladed中，状态可分为两大类：
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1. 弹性动力学 (Elastodynamic)：这些状态代表系统的结构模态。**弹性动力学模态由二阶运动方程控制**。因此，为了在状态空间形式中表示，每个模态由两个状态表示——位移和速度。这还包括主要的风轮刚体自由度。
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2. 气动学 (Aerodynamic)：这些主要用于模拟动态失速和动态尾流。**这些状态通常是一阶的**，因为它们与时滞有关。
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在版本4.7及更早版本中，气动学状态不包含在模型线性化中。在版本4.8及更高版本的气动学公式中，用户可以选择是否包含气动学状态。
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为了进行线性分析，Bladed依次取每个工作点，并找到涡轮机的稳态条件（如同时域运行中的初始条件）。这意味着风轮没有加速，模态变形使得弹性载荷平衡外部载荷。这定义了$\mathbf{x_{0}},\,\mathbf{y_{0}}$和$\mathbf{u_{0}}$的值，即所有扰动围绕的主要平衡点。
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对于每个输入或状态，Bladed然后在平衡点两侧进行一系列幅度逐渐增加的扰动。人为地增加或减少状态或输入的数值，用这些修改后的数值求解系统，并记录状态导数和输出。扰动的数量和最大扰动幅度可以由用户定义。
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然后，可以通过对状态导数与所有扰动值及其平衡值之间的关系进行线性回归，来推导矩阵A、B、C和D的元素。线性回归的梯度给出元素的值。如果相关系数小于最小相关系数，则认为该关系无效，并给该元素赋予零值。
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Figure 1: Example linear regression calculating element ${\bf A}_{7,4}$ with a value of -1.315, with a correlation coefficient of 0.9982. The equilibrium point is shown in green
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图 1：示例线性回归计算单元 ${\bf A}_{7,4}$，其值为 -1.315，相关系数为 0.9982。平衡点以绿色显示。
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Last updated 30-08-2024
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# Multi-blade Coordinate Transformation
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For linearisation calculations or Campbell diagrams it is recommended to select the multi-blade coordinate transformation, which generates coupled modes referring to the non-rotating coordinate system including the backward and forward whirling modes of the rotor. This is based on theory developed in (Bir, 2008) and (Hansen, 2003). The linearised model is significantly azimuth-dependent, but when transformed to non-rotating coordinates the resulting model of the structural dynamics should be only weakly azimuth-dependent. However, for 2-bladed turbines there is still a strong azimuth dependency.
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为了线性化计算或坎贝尔图的绘制，建议选择多叶片坐标变换，该变换会生成与非旋转坐标系耦合的模态，包括风轮的后向和前向挥舞模态。这基于 (Bir, 2008) 和 (Hansen, 2003) 中提出的理论。线性化后的模型对方位角高度依赖，但当变换到非旋转坐标系后，结构动力学模型应仅表现出微弱的方位角依赖性。然而，对于2叶片风轮，仍然存在较强的方位角依赖性。
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# Single mode transformation
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## Single mode transformation
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The transformation matrix of displacements of a 3-blade system with azimuths $\psi_{1}$ to $\psi_{3}$ from nonrotating to rotating coordinates is given by
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一个三叶片系统，其方位角为 $\psi_{1}$ 到 $\psi_{3}$，从非旋转坐标系到旋转坐标系的位移变换矩阵如下：
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$$
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\begin{array}{r}{\left[\!\!\begin{array}{l}{q_{1}}\\ {q_{2}}\\ {q_{3}}\end{array}\!\!\right]=\tilde{\mathbf{t}}_{N R\rightarrow R}\left[\!\!\begin{array}{l}{q_{0}}\\ {q_{c}}\\ {q_{s}}\end{array}\!\!\right],}\end{array}
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\begin{align}
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\begin{bmatrix}
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q_{1} \\
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q_{2} \\
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q_{3} \\
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\end{bmatrix} &= \widetilde{{t}}_{NR \rightarrow R}
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\begin{bmatrix}
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q_{0} \\
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q_{c} \\
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q_{s} \\
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\end{bmatrix},
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\end{align}
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$$
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with
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@ -64,58 +105,88 @@ $$
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$$
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Multi-blade coordinate transformations are often quoted in the above form, but the primary aim is to go the other way and transform from rotating to non-rotating coordinates. The transformation matrix of displacements of a 3-blade system from rotating to non-rotating coordinates is the inverse of the above matrix given by
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多叶片坐标变换通常以上述形式引用，但主要目的是反向变换，从旋转坐标系变换到非旋转坐标系。一个3叶片系统的位移从旋转坐标系变换到非旋转坐标系的变换矩阵，是上述矩阵的逆矩阵，由以下给出：
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$$
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\mathbf{t}_{R\rightarrow N R}=\frac{1}{3}\left[2\cos\psi_{1}\quad2\cos\psi_{2}\quad2\cos\psi_{3}\right].
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\begin{align}
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{t}_{R \rightarrow NR} = \frac{1}{3}\begin{bmatrix}
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1 & 1 & 1 \\
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2\cos\psi_{1} & 2\cos\psi_{2} & 2\cos\psi_{3} \\
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2\sin\psi_{1} & 2\sin\psi_{2} & 2\sin\psi_{3} \\
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\end{bmatrix}.
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\end{align}
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$$
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Note, that the inverse relation does not hold for the derivatives of this matrix.
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The general transformation matrix for a turbine with an arbitrary number of blades $(n)$
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注意，此矩阵的导数不满足逆关系。
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对于具有任意数量叶片 $(n)$ 的风轮的通用变换矩阵
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$$
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\mathbf{t}_{R\rightarrow N R}=\frac{1}{n}\left[\begin{array}{c c c c c}{1}&{1}&{1}&{\cdots}&{1}\\ {2\cos\psi_{1}}&{2\cos\psi_{2}}&{2\cos\psi_{3}}&{\cdots}&{2\cos\psi_{n}}\\ {2\sin\psi_{1}}&{2\sin\psi_{2}}&{2\sin\psi_{3}}&{\cdots}&{2\sin\psi_{n}}\\ {2\cos j\psi_{1}}&{2\cos j\psi_{2}}&{2\cos j\psi_{3}}&{\cdots}&{2\cos j\psi_{n}}\\ {2\sin j\psi_{1}}&{2\sin j\psi_{2}}&{2\sin j\psi_{3}}&{\cdots}&{2\sin j\psi_{n}}\\ {\vdots}&{\vdots}&{\vdots}&{\ddots}&{\vdots}\\ {1}&{-1}&{1}&{\cdots}&{(-1)^{n}}\end{array}\right],
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$$
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where the last row is the transformation to the differential mode and exists only if there is an even number of blades. For odd bladed turbines, the last row will be a sine cyclic row. The counter $j$
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goes from 1 to $(n-1)/2$ $^n$ is odd, and from 2 to $(n-2)/2$ ü $^{n}$ is even.
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where the last row is the transformation to the differential mode and exists only if there is an even number of blades. For odd bladed turbines, the last row will be a sine cyclic row. The counter $j$ goes from 1 to $(n-1)/2$ if $n$ is odd, and from 2 to $(n-2)/2$ if ${n}$ is even.
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Dropping the matrix representation the non-rotating coordinates can be calculated as
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其中最后一行是变换到微分模态，且仅在叶片数量为偶数时存在。对于叶片数量为奇数的风轮，最后一行将是一个正弦循环行。计数器 $j$ 从 1 到 $(n-1)/2$ (当 $n$ 为奇数时)，从 2 到 $(n-2)/2$ (当 ${n}$ 为偶数时)。
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省略矩阵表示，非旋转坐标可以计算如下：
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$$
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\begin{array}{l}{\displaystyle q_{0}=\frac{1}{n}\sum_{i=1}^{n}q_{i}}\\ {\displaystyle q_{c j}=\frac{2}{n}\sum_{i=1}^{n}q_{i}\cos{\left(j\psi_{i}\right)}}\\ {\displaystyle q_{s j}=\frac{2}{n}\sum_{i=1}^{n}q_{i}\sin{\left(j\psi_{i}\right)}}\\ {\displaystyle q_{d}=\frac{1}{n}\sum_{i=1}^{n}q_{i}(-1)^{n}}\end{array}
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$$
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Returning to the specific case of 3-bladed turbines as an example, the derivative transformation matrices are now calculated. Each azimuth angle $\psi_{i}$ can be expressed in terms of the (assumed constant) rotorspeed $\Omega$ and initial azimuth angle $\Psi_{i}$ as linear relationship
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Returning to the specific case of 3-bladed turbines as an example, the derivative transformation matrices are now calculated. Each azimuth angle $\psi_{i}$ can be expressed in terms of the (assumed constant) rotor speed $\Omega$ and initial azimuth angle $\Psi_{i}$ as linear relationship
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以三叶风轮为例，现在计算导数变换矩阵。每个方位角 $\psi_{i}$ 可以表示为（假设恒定的）风轮转速 $\Omega$ 和初始方位角 $\Psi_{i}$ 的线性关系。
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$$
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\psi_{i}=\Omega t+\Psi_{i}.
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$$
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Taking the time-derivatives of the transformation matrix gives
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对变换矩阵求时间导数，得到：
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$$
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\dot{\bf t}_{R\rightarrow N R}=\frac{\Omega}{3}\left[\!\!\!\begin{array}{c c c}{{0}}&{{0}}&{{0}}\\ {{-2\sin\psi_{1}}}&{{-2\sin\psi_{2}}}&{{-2\sin\psi_{3}}}\\ {{2\cos\psi_{1}}}&{{2\cos\psi_{2}}}&{{2\cos\psi_{3}}}\end{array}\!\!\right]
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\begin{align*}
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\dot{{t}}_{R \rightarrow NR} =
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\frac{\Omega}{3}
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\begin{bmatrix}
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0 & 0 & 0 \\
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- 2\sin\psi_{1} & - 2\sin\psi_{2} & - 2\sin\psi_{3} \\
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2\cos\psi_{1} & 2\cos\psi_{2} & 2\cos\psi_{3} \\
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\end{bmatrix}
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\end{align*}
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$$
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and
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$$
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\ddot{\bf t}_{R\rightarrow N R}=-\frac{\Omega^{2}}{3}\left[\!\!\!\begin{array}{c c c}{{0}}&{{0}}&{{0}}\\ {{2\cos\psi_{1}}}&{{2\cos\psi_{2}}}&{{2\cos\psi_{3}}}\\ {{2\sin\psi_{1}}}&{{2\sin\psi_{2}}}&{{2\sin\psi_{3}}}\end{array}\!\!\right]
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\begin{align*}
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\ddot{{t}}_{R \rightarrow NR} =
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- \frac{\Omega^{2}}{3}
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\begin{bmatrix}
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0 & 0 & 0 \\
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2\cos\psi_{1} & 2\cos\psi_{2} & 2\cos\psi_{3} \\
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2\sin\psi_{1} & 2\sin\psi_{2} & 2\sin\psi_{3} \\
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\end{bmatrix}
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\end{align*}
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$$
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for the first and second derivatives, respectively.
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# System transformation matrix
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## System transformation matrix
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A transformation matrix for the whole state list, including both displacement and velocity states, is required. For the displacement states we have already established in Equation (1) that
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需要一个包含位移和速度状态的整个状态列表的变换矩阵。正如我们在公式(1)中已经确立的，对于位移状态，
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$$
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{\bf q}_{N R}={\bf t}_{R\rightarrow N R}{\bf q}_{R}
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$$
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holds. Taking the time-derivative of Equation (1) gives
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holds. Taking the time-derivative of Equation (1) gives 对公式(1)求时间导数，得到：
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$$
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\dot{\bf q}_{N R}={\bf t}_{R\rightarrow N R}\dot{\bf q}_{R}+\dot{\bf t}_{R\rightarrow N R}{\bf q}_{R}
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@ -123,35 +194,84 @@ $$
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for the velocity states.
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Combining qvR and qnR to a vector of all states (both displacements and velocities) allows us to define a common transformation matrix $\mathbf{T}$ that is of the same dimensions as A. We define
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Combining ${\bf q}_{N R}$ and $\dot{\bf q}_{N R}$ to a vector of all states (both displacements and velocities) allows us to define a common transformation matrix $\mathbf{T}$ that is of the same dimensions as $A$. We define
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将 ${\bf q}_{N R}$ 和 $\dot{\bf q}_{N R}$ 组合成一个包含所有状态（位移和速度）的向量，允许我们定义一个与 $A$ 具有相同维度的公共变换矩阵 $\mathbf{T}$。 我们定义
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$$
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\mathbf{T}:=\left[\begin{array}{c c}{\mathbf{\{t}}_{R\rightarrow N R}}&{0}\\ {\vdots}&{\mathbf{t}_{R\rightarrow N R}}\end{array}\right]
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\begin{align}
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{T} &:= \begin{bmatrix}
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{t}_{R \rightarrow NR} & 0 \\
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\dot{{t}}_{R \rightarrow NR} & {t}_{R \rightarrow NR} \\
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\end{bmatrix}
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\end{align}
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$$
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allowing us to express the combined vector as
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$$
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\begin{array}{r}{\left[\mathbf{q}_{N R}\right]=\left[\mathbf{\dot{t}}_{R\rightarrow N R}\mathbf{\Phi}\;\;\;\;\;\;\;0\mathbf{\Phi}\right]\left[\mathbf{q}_{R}\right].}\end{array}
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\begin{align}
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\begin{bmatrix}
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q_{NR} \\
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\dot{q}_{NR}
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\end{bmatrix}
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&=
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\begin{bmatrix}
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t_{R \rightarrow NR} & 0 \\
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\dot{t}_{R \rightarrow NR} & t_{R \rightarrow NR}
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\end{bmatrix}
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\begin{bmatrix}
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q_{R} \\
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\dot{q}_{R}
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\end{bmatrix}.
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\end{align}
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$$
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Note that in general the displacement and velocity states are not ordered in this way and a permutation of the system transformation matrix $\mathbf{T}$ will occur. The system transformation matrix is not singular and the inverse can be calculated.
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The derivative of the system transformation matrix is trivially inferred as
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需要注意的是，一般来说，位移和速度状态并非以这种方式排列，系统变换矩阵 $\mathbf{T}$ 会发生置换。系统变换矩阵非奇异，可以计算其逆矩阵。
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系统变换矩阵的导数可以很容易地推导出来。
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$$
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\dot{\mathbf{T}}=\left[\!\!\begin{array}{c c}{\dot{\mathbf{t}}_{R\rightarrow N R}}&{0}\\ {\ddot{\mathbf{t}}_{R\rightarrow N R}}&{\dot{\mathbf{t}}_{R\rightarrow N R}}\end{array}\!\!\right].
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\begin{align}
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\dot{{T}}=
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\begin{bmatrix}
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\dot{{t}}_{R \rightarrow NR} & 0 \\
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\ddot{{t}}_{R \rightarrow NR} & \dot{{t}}_{R \rightarrow NR} \\
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\end{bmatrix}.
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\end{align}
|
||||
$$
|
||||
|
||||
# Transforming the A,B,C,D matrices
|
||||
## Transforming the A,B,C,D matrices
|
||||
|
||||
We consider the linear model equations in the rotating frame of reference and define
|
||||
|
||||
我们考虑在旋转参考系中的线性模型方程，并定义：
|
||||
$$
|
||||
\mathbf{x}_{R}:=\left[\mathbf{q}_{R}\right]
|
||||
\begin{align}
|
||||
|
||||
{x}_{R} := \begin{bmatrix}
|
||||
|
||||
{q}_{R} \\ \dot{{q}}_{R}
|
||||
|
||||
\end{bmatrix}
|
||||
|
||||
\end{align}
|
||||
$$
|
||||
|
||||
to express the principal system as
|
||||
to express the principal system as 为了表达主要系统为
|
||||
|
||||
$$
|
||||
\begin{array}{r}{\dot{\mathbf{x}}_{R}=\mathbf{A}_{R}\mathbf{x}_{R}+\mathbf{B}_{R}\mathbf{u}}\\ {\mathbf{y}=\mathbf{C}_{R}\mathbf{x}_{R}+\mathbf{D}_{R}\mathbf{u}}\end{array}
|
||||
@ -160,7 +280,9 @@ $$
|
||||
with respect to rotating blade coordinates.
|
||||
|
||||
The transformation of the state vector from rotating to non-rotating coordinates is given as
|
||||
相对于旋转叶片坐标系。
|
||||
|
||||
状态向量从旋转坐标系变换到非旋转坐标系的表达式如下：
|
||||
$$
|
||||
\mathbf{x}_{N R}=\mathbf{T}\mathbf{x}_{R}
|
||||
$$
|
||||
@ -188,7 +310,7 @@ from there.
|
||||
Similar transformation in Equation (16) gives
|
||||
|
||||
$$
|
||||
\begin{array}{r}{\mathbf{y}=\mathbf{C}_{R}\mathbf{x}_{R}+\mathbf{D}_{R}\mathbf{u}}\\ {=\mathbf{C}_{R}\mathbf{T}^{-1}\mathbf{x}_{N R}+\mathbf{D}_{R}\mathbf{u}}\end{array}
|
||||
\begin{array}{r}{\mathbf{y}=\mathbf{C}_{R}\mathbf{x}_{R}+\mathbf{D}_{R}\mathbf{u}}\\ \\{=\mathbf{C}_{R}\mathbf{T}^{-1}\mathbf{x}_{N R}+\mathbf{D}_{R}\mathbf{u}}\end{array}
|
||||
$$
|
||||
|
||||
for the output y of the linear system. We now define
|
||||
@ -200,15 +322,23 @@ $$
|
||||
for the matrices concerned with the output of the linear model. This completes the derivation of a linear model with respect to a non-rotating frame
|
||||
|
||||
Rotational transformations are exclusively applied to states, which represent the degress of freedom in a mathematical model defined for all blades. These states include blade mode states as well as dynamic stall states, whereas any other individual-blade states such as pitch positions, rates, actuator internal states etc. are not transformed. The matrix T just has unit diagonal elements for rows and columns corresponding to the states and state derivatives which are not transformed. For other rows and columns, the elements of T represent the basic transformation defined above for each group of modes. Note that the elements connecting states and state derivatives also need to be defined by differentiating the equations of the basic transformation, bearing in mind that the derivative of the azimuth angle is equal to the rotor speed (which is assumed constant for this purpose). Model inputs and outputs are not transformed.
|
||||
对于与线性模型输出相关的矩阵，本部分内容完成了对非旋转参考系下的线性模型推导。
|
||||
|
||||
旋转变换仅应用于状态，这些状态代表了定义在所有叶片上的数学模型中的自由度。这些状态包括叶片模态和动态失速状态，而其他任何单个叶片状态，例如桨距角位置、速率、执行器内部状态等，均不进行变换。矩阵 T 在未进行变换的状态和状态导数对应的行和列上具有单位对角线元素。对于其他行和列，T 的元素代表上述为每组模态定义的基变换。需要注意的是，连接状态和状态导数的元素也需要通过对基变换方程进行微分来定义，同时考虑到方位角的变化率等于风轮转速（出于本目的，假设其为常数）。模型输入和输出不进行变换。
|
||||
|
||||
|
||||
Last updated 26-11-2024
|
||||
|
||||
# Calculating Coupled Modes
|
||||
# Coupled Modes
|
||||
## Calculating Coupled Modes
|
||||
|
||||
The Campbell diagram and blade stability analyses are analyses of the matrix A at each specified operating point. Each coupled mode corresponds to an eigenvalue and its eigenvector. Given a (complex) eigenvalue, $\lambda,$ of A, Bladed reports the undamped frequency $\displaystyle(\omega_{n}),$ damped frequency ( $\omega_{d}$ ) and damping ratio $(\zeta)$ according to Figure 1.
|
||||
The Campbell diagram and blade stability analyses are analyses of **the matrix A** at each specified operating point. Each coupled mode corresponds to an eigenvalue and its eigenvector. Given a (complex) eigenvalue, $\lambda,$ of A, Bladed reports the undamped frequency $\displaystyle(\omega_{n}),$ damped frequency ( $\omega_{d}$ ) and damping ratio $(\zeta)$ according to Figure 1.
|
||||
|
||||
坎贝尔图和叶片稳定性分析是对在每个指定工作点处的**矩阵 A** 的分析。**每个耦合模态对应一个特征值及其特征向量**。**给定矩阵 A 的一个（复数）特征值 λ**，Bladed 会根据图 1 报告无阻尼频率undamped frequency (ωn)、阻尼频率damped frequency (ωd) 和阻尼比 (ζ)。
|
||||
|
||||
|
||||
Figure 1: Argand Diagram
|
||||
Figure 1: Argand Diagram阿根图
|
||||
|
||||
|
||||
The uncoupled mode contributions to each coupled mode are determined by its eigenvector. If the coupled mode has contributions from second-order states (structural states), which are represented by two states in the state vector, then the displacement state is used to determine the contribution.
|
||||
|
||||
@ -216,28 +346,40 @@ In their raw form, these eigenvector contributions represent the relative displa
|
||||
|
||||
The phase of each contribution, $\phi_{i\,,}$ is determined by the argument of the corresponding complex eigenvector element, $v_{i},$ i.e.
|
||||
|
||||
每个耦合模态的未耦合模态贡献由其本征向量决定。如果耦合模态具有二阶状态（结构状态）的贡献，这些状态由状态向量中的两个状态表示，则使用位移状态来确定贡献。
|
||||
|
||||
以原始形式，这些本征向量贡献代表每个模态的相对位移，可用于构建耦合模态形状。然而，在坎贝尔图中，这些贡献已被归一化。这是通过修改本征向量矩阵来实现的，使得每一行和每一列都具有单位和。这会增加具有高质量和刚度的模态的百分比贡献，这些模态在位移中贡献很小，但在能量方面贡献很大。
|
||||
|
||||
每个贡献的相位，$\phi_{i\,,}$ 由相应复本征向量元素的参数决定，即 $v_{i},$ 即。
|
||||
$$
|
||||
\phi_{i}=\arctan\left(\frac{\operatorname{Im}\left(v_{i}\right)}{\operatorname{Re}\left(v_{i}\right)}\right).
|
||||
$$
|
||||
|
||||
Last updated 26-11-2024
|
||||
|
||||
# Naming Coupled Modes
|
||||
## Naming Coupled Modes
|
||||
|
||||
In cases where coupled modes are computed such as in the Campbell diagram analysis the following sections gives details on the naming. A focus is placed on the behaviour when the multiblade coordinate transform is used.
|
||||
在计算耦合模态，例如在坎贝尔图分析中，以下章节将详细介绍命名规范。重点关注多叶片坐标变换使用时的行为。
|
||||
|
||||
# Support structure modes
|
||||
### Support structure modes
|
||||
|
||||
For support structure modes, the coupled mode is named after the whole-tower mode that gives the highest contribution. Whole-tower modes are uniquely calculated for the linearisation calculations through a subsequent eigen analysis with fixed-free boundary conditions. This analysis considers the effect of the RNA and any other masses at distal nodes. In case multiple coupled support structure modes share the same whole-tower mode as its prime contributor, then the coupled mode name is made unique by appending letters A,B,C, and so on.
|
||||
对于支撑结构模态，耦合模态以对贡献最大的整个塔架模态命名。整个塔架模态通过后续带有固定-自由边界条件的特征分析来计算，用于线性化计算。该分析考虑了RNA（叶片）以及位于远端节点上的其他质量的影响。如果多个耦合支撑结构模态共享相同的整塔模态作为其主要贡献者，则通过附加字母A、B、C等来使耦合模态名称唯一化。
|
||||
|
||||
# Rotor modes rotating frame
|
||||
### Rotor modes rotating frame
|
||||
|
||||
If no MBC transformation is used for the rotor modes, then the following logic applies to naming the coupled rotor modes:
|
||||
If no MBC(Multi-blade Coordinate) transformation is used for the rotor modes, then the following logic applies to naming the coupled rotor modes:
|
||||
|
||||
· If a single blade mode gives $>\!75\%$ contribution to the coupled rotor mode, then the coupled rotor mode is named after that blade mode. In other words, the mode is called "Blade" instead of "Rotor" mode.
|
||||
· Else, the rotor mode is named after its prime contributor and made unique by appending letters $\mathsf{A},\mathsf{B},\mathsf{C},$ etc. in case multiple coupled rotor modes share the same uncoupled blade mode as prime contributor
|
||||
|
||||
# Rotor modes non-rotating frame
|
||||
如果未使用多叶片坐标变换(MBC)来描述风轮模态，则以下逻辑适用于命名耦合风轮模态：
|
||||
|
||||
· 如果单个叶片模态贡献超过75%，则将耦合风轮模态命名为该叶片模态。换句话说，该模态被称为“叶片”模态，而不是“风轮”模态。
|
||||
· 否则，耦合风轮模态以其主要贡献者命名，并通过附加字母A、B、C等来使其独一无二，以防多个耦合风轮模态共享相同的未耦合叶片模态作为主要贡献者。
|
||||
|
||||
### Rotor modes non-rotating frame
|
||||
|
||||
If an MBC transform is applied then the individual blade modes are transformed to a set of rotor modes. For a three bladed rotor there typically is a collective, cosine-cyclic and sine-cyclic rotor mode. The 1st flapwise modes of all blades will be renamed to rotor 1st flapwise collective, rotor 1st flapwise sine-cyclic and rotor 1st flapwise cosine cyclic. In case the number of blades is even there will be a differential mode as well.
|
||||
|
||||
@ -245,18 +387,29 @@ After the transformation and renaming of the individual blade modes the coupled
|
||||
|
||||
Coupled mode name 1st uncoupled mode 2nd uncoupled mode Phase angle $(\phi_{2}-\phi_{1})$
|
||||
|
||||
如果应用了 MBC 变换，则各个叶片模态将被转换成一组风轮模态。对于三叶风轮，通常存在集变模态collective、余弦循环模态cosine-cyclic和正弦循环sine-cyclic模态。所有叶片的 1 阶挥舞模态将被重命名为风轮 1 阶挥舞集变模态、风轮 1 阶挥舞正弦循环模态和风轮 1 阶挥舞余弦循环模态。如果叶片数量为偶数，则还会存在摆振模态。
|
||||
|
||||
<html><body><table><tr><td>Forward whirl</td><td>Sine cyclic</td><td>Cosine cyclic</td><td>> 0.0</td></tr><tr><td></td><td>Cosine cyclic</td><td>Sine cyclic</td><td><0.0</td></tr><tr><td>Backward whirl</td><td>Sine cyclic</td><td>Cosine cyclic</td><td>< 0.0</td></tr><tr><td></td><td>Cosine cyclic</td><td>Sine cyclic</td><td>> 0.0</td></tr></table></body></html>
|
||||
在转换和重命名各个叶片模态之后，命名耦合风轮模态。旋转模态的识别遵循下表中的逻辑。
|
||||
|
||||
| Coupled mode name | 1st uncoupled mode | 2nd uncoupled mode | Phase angle ($\phi_{2}-\phi_{1})$) |
|
||||
| ----------------- | ------------------ | ------------------ | ---------------------------------- |
|
||||
| Forward whirl | Sine cyclic | Cosine cyclic | > 0.0 |
|
||||
| | Cosine cyclic | Sine cyclic | < 0.0 |
|
||||
| Backward whirl | Sine cyclic | Cosine cyclic | < 0.0 |
|
||||
| | Cosine cyclic | Sine cyclic | > 0.0 |
|
||||
|
||||
If a coupled mode does not meet the criteria of the whirling modes, then the mode is named after its prime contributor. This is analogous with the naming logic of rotor modes in the rotating frame and support structure modes
|
||||
如果一个耦合模态不符合颤动模态的标准，则该模态会被命名为其主要贡献者的名称。这与风轮在旋转参考系中的模态以及支撑结构模态的命名逻辑类似。
|
||||
|
||||
Last updated 04-12-2024
|
||||
|
||||
# Joining Coupled Modes across Operating Points
|
||||
# Joining Coupled Modes across Operating Points 连接不同工况下的耦合模态
|
||||
|
||||
The Campbell diagram displays the frequencies of different coupled displacement modes with respect to the rotor speed together with the most important excitation frequencies given in terms of multiples of the rotor frequency (P). In addition to the frequencies of the coupled modes, the Campbell diagram displays the corresponding damping ratios, which include the effect of structural damping as well as aerodynamic damping. Both characteristics are calculated as described in the article Calculating Coupled Modes and are useful for identifying the critical Operating points that need further analysis.
|
||||
|
||||
# The Joining Process
|
||||
**坎贝尔图显示了不同耦合位移模态相对于风轮转速的频率**，以及以风轮频率（P）的倍数给出的最重要激励频率。 除了耦合模态的频率，坎贝尔图还显示了相应的阻尼比，其中包括结构阻尼和气动阻尼的影响。 这两个特征的计算方法如文章“Calculating Coupled Modes”中所述，可用于识别需要进一步分析的关键运行点。
|
||||
|
||||
## The Joining Process连接过程
|
||||
|
||||
Given a set of coupled modes at each operating point, a fundamental step in creating the resulting Campbell diagram is to identify similar modes at adjacent operating points, which allows for joining similar modes across the operating points with line segments, giving the user the impression of continuous change in frequency against rotor speed (or wind speed). This joining process is generally challenging because the coupled modes evolve and change in their contributions between the operating points.
|
||||
|
||||
@ -264,11 +417,18 @@ Similar coupled modes at two adjacent operating points are identified by compari
|
||||
|
||||
To ensure that the coupled mode series in the resulting Campbell diagram primarily involves structural dynamics, an initial calculation of coupled modes with only structural states is performed at the first operating point. These structure-only modes are then joined with the coupled modes at the first operating point as described above, which effectively excludes coupled modes that mainly have contributions from aerodynamic states.
|
||||
|
||||
给定一组在每个工作点耦合的模态，**创建最终的坎贝尔图的关键步骤是识别相邻工作点中相似的模态**，**这使得能够用线段连接这些相似的模态**，**从而给用户留下频率随风轮转速（或风速）连续变化的印象**。这种连接过程通常具有挑战性，**因为耦合模态在工作点之间会演变和改变其贡献**。
|
||||
|
||||
**通过比较在扩展模态保证准则（MACX）（Vacher, Jacquier, 和 Buchales, 2010）下的复特征向量和频率，并采用频率加权，可以识别出两个相邻工作点中的相似耦合模态**。更具体地说，会为两个工作点中所有耦合模态组合计算频率加权 MACX 数值，形成一个评分矩阵，然后使用该矩阵通过 GaleShapley 算法（Gale & Shapley, 1962）连接这些模态。所有工作点中一系列相似的模态构成一个耦合模态序列，它代表了最终坎贝尔图中的一条线。
|
||||
|
||||
为了确保最终坎贝尔图中的耦合模态序列主要涉及结构动力学，在第一个工作点执行一次仅包含结构状态的耦合模态计算。然后，将这些仅结构模态与如上所述的第一个工作点的耦合模态连接起来，这有效地排除了主要来自气动状态贡献的耦合模态。
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
Figure 1: Illustration of the joining process showing how the coupled modes are connected at the operating points. Dots represent coupled modes. Coloured lines represent coupled mode series.
|
||||
Figure 1: Illustration of the joining process showing how the coupled modes are connected at the operating points. Dots represent coupled modes. Coloured lines represent coupled mode series. 图 1：连接过程示意图，展示了耦合模态在工作点处的连接方式。点代表耦合模态。彩色线条代表耦合模态级数。
|
||||
|
||||
The resulting joining process is then:
|
||||
|
||||
@ -276,7 +436,13 @@ The resulting joining process is then:
|
||||
2. Join the structure-only modes with the coupled modes at the first operating point. It is noted that the number of coupled modes is generally larger than the number of mode series, which means that not all coupled modes are included in a mode series.
|
||||
3. Join the coupled modes that were included in a mode series at the current point (first operating point) with the coupled modes at the next point (second operating point). Repeat until the last operating point is reached.
|
||||
|
||||
# Naming and Exclusion of Coupled Mode Series
|
||||
接下来的连接过程如下：
|
||||
|
||||
4. 计算在第一个工作点的一组仅结构模态。这些模态也将构成模态序列的基础，代表最终的坎贝尔图中的线。
|
||||
5. 将仅结构模态与在第一个工作点的耦合模态连接起来。需要注意的是，耦合模态的数量通常大于模态序列的数量，这意味着并非所有耦合模态都包含在模态序列中。
|
||||
6. 将在当前点（第一个工作点）包含在模态序列中的耦合模态与下一个点（第二个工作点）的耦合模态连接起来。重复此过程直至到达最后一个工作点。
|
||||
|
||||
### Naming and Exclusion of Coupled Mode Series
|
||||
|
||||
A coupled mode series is named according to the contributions of the structure-only coupled modes at the first operating point only (more details on coupled mode naming can be found here). The contributions and therefore the shape of a coupled mode can change significantly between the range of operating points, and therefore the characteristic of a mode cannot be determined from the name alone.
|
||||
|
||||
@ -284,25 +450,41 @@ A coupled mode series, which includes coupled modes with real eigenvalues (and t
|
||||
|
||||
A coupled mode series is also excluded if the coupled mode frequencies at all operating points exceed a user-defined maximum value.
|
||||
|
||||
一种耦合模态级数，仅根据第一个工作点处的结构-模态耦合贡献来命名（关于耦合模态命名的更多细节请参见此处）。耦合模态的贡献，因此其形状，在工作点范围的不同情况下可能会发生显著变化，因此仅凭名称无法确定模态的特性。
|
||||
|
||||
一种耦合模态级数，其中包含所有工作点处具有**实特征值**（因此没有振荡行为）的耦合模态，将被排除在最终的坎贝尔图之外。这是因为此类模态无法引起共振行为，**而坎贝尔图的主要目的是检测共振行为。**
|
||||
|
||||
如果所有工作点处的耦合模态频率超过用户定义的上限值，则该耦合模态级数也会被排除。
|
||||
|
||||
Last updated 26-11-2024
|
||||
|
||||
# Align Wind Field with Hub Axis
|
||||
|
||||
Figure 1 illustrates that azimuthal dependency is still invoked in certain cases even though the considerations given in the linear analysis background are followed. This occurs when a tilt angle is considered in the calculations and when the tower flexibility is strongly affecting the rotor orientation. Figure 1 (left) provides an ilustration of the azimuthally independent system, indicating that the solution will be the same regardless of the azimuth angle of the rotor. However, when the tilt angle is considered, Figure 1 (middle), the loads perceived by the upper side of the rotor and the lower side of the rotor vary. This creates an imbalance of the loads similar as adding "a virtual wind shear" on the rotor plane. The situation is worse when the flexibility of the tower affects the rotor orientation strongly as illustrated in Figure 1 (right). Here, one can see that the hub orientation might be tilted even greater which creates a stronger loads imbalance across the rotor.
|
||||
|
||||
图1所示，即使遵循线性分析背景中的考虑因素，在某些情况下仍然需要调用方位角依赖性。当计算中考虑倾角，且塔架柔度强烈影响风轮姿态时，这种情况会发生。图1（左）提供了一个方位角独立的系统示意图，表明无论风轮的方位角角度如何，解都是相同的。然而，当考虑倾角时，如图1（中间）所示，风轮上部和下部受到的载荷会发生变化。这会产生类似于在风轮平面上添加“虚拟风切变”的载荷不平衡。当塔架柔度强烈影响风轮姿态时，情况会更加糟糕，如图1（右）所示。在这里，可以看到轮毂姿态可能会倾斜得更大，从而在风轮上产生更强的载荷不平衡。
|
||||
|
||||
|
||||
|
||||
|
||||
Figure 1: llustration of the hub axis orientation relative to the incoming wind direction in the linearisation calculation. Left: rigid wind turbine without tilt angle, middle: rigid wind turbine with tilt angle being considered, right: flexible turbine with tilt angle being considered.
|
||||
图1：线性化计算中，风轮轴向相对于迎风方向的示意图。左：无倾角刚性风轮，中：考虑倾角的刚性风轮，右：考虑倾角的柔性风轮。
|
||||
|
||||
|
||||
To avoid the imbalance of the loads due to the tilted hub orientation, Bladed introduces a correction to align the wind field according to the tilted hub axis orientation. The mechanism is clearly illustrated in Figure 2. It can be observed that when the wind field is aligned with the tilted hub axis, the loads experienced by the rotor will be independent of the azimuth angle. This effectively removes the azimuthal dependency of the system due to tilted hub axis orientation. This correction may also be applied for floating wind turbines as illustrated in Figure 3.
|
||||
|
||||
为了避免倾斜轴向导致的载荷不平衡，Bladed 引入了一种校正措施，以使风场与倾斜轴向对齐。该机制在图2中清晰地说明。可以观察到，当风场与倾斜轴向对齐时，风轮受到的载荷将与偏航角无关。这有效地消除了由于倾斜轴向引起的系统偏航角依赖性。 这种校正也可以应用于浮式风力发电机，如图3所示。
|
||||
|
||||
|
||||
Figure 2: Aligning wind field to the tilted hub axis orientation for an onshore wind turbine or a bottom-fixed offshore wind turbine. Left: Azimuthally dependent system, right: azimuthally independent system.
|
||||
图2：针对陆上风力发电机或固定基础海上风力发电机，将风场对准倾斜的轴向。左：方位角相关的系统，右：方位角无关的系统。
|
||||
|
||||
|
||||
Figure 3: Aligning wind field to the tilted hub axis orientation for a floating wind turbine. Left: Azimuthally dependent system, right: azimuthally independent system.
|
||||
图3：针对浮动式风力发电机，将风场对准倾斜的轴向。左：方位角相关的系统，右：方位角无关的系统。
|
||||
|
||||
The hub axis is determined during the initial conditions routine, where the rotor is not accelerating and the modal deflections are such that the elastic loads balance the external loading. Within the initial conditions routine, iterations are performed and the wind field is adjusted accordingly for every iteration to be parallel to the tilted hub axis. After the the conditions are found, the wind field orientation is fixed to the last found tilted angle in the initial conditions routine. Then, the system is perturbed using the fixed wind field orientation for calculating any of the linearisation type calculations available in Bladed. This process is done for every operating point simulated.
|
||||
|
||||
初始条件程序中确定风轮中心轴，此时风轮未加速，模态变形使得弹性载荷与外部载荷平衡。在初始条件程序中，进行迭代计算，并在每次迭代中调整风场，使其与倾斜的风轮中心轴平行。一旦找到合适的条件，风场方向就被固定在初始条件程序中最后确定的倾斜角度。随后，系统使用固定的风场方向进行扰动，用于计算Bladed中可用的任何线性化类型计算。此过程针对每个模拟的工作点进行。
|
||||
|
||||
Last updated 30-08-2024
|
||||
@ -1455,9 +1455,9 @@ differences in foundation stiffness. Consequently, the stiffness of the foundati
|
||||
|
||||
The FE model displacements are found by solving: $\mathbf{f}=\mathbf{K}\mathbf{x},$ to find x for the support structure, where
|
||||
|
||||
f is the vector of applied loads $=$ (externalloads $^+$ inertial loads) on each node of the support structure,
|
||||
K is the FE stiffness matrix for the support structure. This is constant.
|
||||
x is the vector of support structure nodal displacements
|
||||
$f$ is the vector of applied loads $=$ (externalloads $^+$ inertial loads) on each node of the support structure,
|
||||
$K$ is the FE stiffness matrix for the support structure. This is constant.
|
||||
$x$ is the vector of support structure nodal displacements
|
||||
|
||||
The vector of FE displacements, x, can then be used as lookup in the non-linear p-y curve.
|
||||
|
||||
@ -1465,21 +1465,45 @@ Unfortunately, f is not known at the start of each time step, as it includes the
|
||||
|
||||
An algorithm schematic is presented in Figure 2 which shows the calculation carried out in Bladed when using the dynamic non-linear foundation load feature. The number of each step maps directly to the numbers in the flow diagrams depicted in Figure 2. Note that steps 1-4 are described in calculation procedure.
|
||||
|
||||
对于非线性地基 p-y 曲线，支撑结构模态变形通常不够精确，无法用于在 p-y 曲线中查找地基载荷。这是因为 p-y 曲线的非线性特性意味着，微小的位移差异可能导致地基刚度的巨大变化。因此，如果使用模态位移来查找地基载荷，则地基的刚度和反作用力可能无法准确预测。因此，最好直接使用有限元 (FE) 模型位移，因为它们能更准确地确定用于 p-y 曲线查找的地基变形。
|
||||
|
||||
FE 模型位移是通过求解：$\mathbf{f}=\mathbf{K}\mathbf{x},$ 来找到支撑结构的 x，其中
|
||||
|
||||
$f$ 是施加载荷矢量 = (外加载荷 + 惯性载荷) 在支撑结构的每个节点上，
|
||||
$K$ 是支撑结构的 FE 刚度矩阵。此值是恒定的。
|
||||
$x$ 是支撑结构节点位移矢量
|
||||
|
||||
然后，可以将 FE 位移矢量 x 用于非线性 p-y 曲线的查找。
|
||||
|
||||
不幸的是，在每个时间步的开始时，f 是未知的，因为它包括惯性力的影响，而惯性力取决于系统加速度。因此，在每个时间步的开始时，x 也是未知的，因此 Bladed 必须使用前一个时间步的 x 来计算地基施加载荷。
|
||||
|
||||
图 2 提供了算法示意图，显示了在 Bladed 使用动态非线性地基载荷功能时执行的计算。每个步骤的编号直接对应于图 2 中流程图中的编号。请注意，步骤 1-4 描述了计算程序。
|
||||
|
||||
|
||||
5. The modal accelerations are used to calculate the acceleration of each node, and therefore the inertial loading at each node can be calculated.
|
||||
|
||||
6. The equation $\mathbf{f}=\mathbf{K}\mathbf{x}$ is solved. The applied loads include contributions from inertia and external loading. $\mathbf{\deltaK}$ is the support structure stiffness matrix. The FE deflections x are found.
|
||||
6. The equation $\mathbf{f}=\mathbf{K}\mathbf{x}$ is solved. The applied loads include contributions from inertia and external loading. $\mathbf{K}$ is the support structure stiffness matrix. The FE deflections x are found.
|
||||
|
||||
7. The FE deflections x are used to lookup the foundation forces in the p-y curves.
|
||||
|
||||
8. On the following time step, the foundation applied loads are used when evaluating the structural dynamics in step 3.
|
||||
|
||||
9. 模态的加速度用于计算每个节点的加速度，因此可以计算出每个节点上的惯性载荷。
|
||||
|
||||
10. 求解方程 $\mathbf{f}=\mathbf{K}\mathbf{x}$。 所施加的载荷包括惯性和外部载荷的贡献。 $\mathbf{K}$ 是支撑结构刚度矩阵。 得到有限元挠度 $x$。
|
||||
|
||||
11. 有限元挠度 $x$ 用于在 p-y 曲线中查找地基反力。
|
||||
|
||||
12. 在下一个时间步内，地基施加的载荷用于在第 3 步中评估结构动力学。
|
||||
|
||||
|
||||
|
||||
Figure 2: Schematic of calculation procedure of structural dynamics in time domain simulations, including dynamic non-linear p-y curve forces (shown with blue arrows)
|
||||
|
||||
Last updated 30-08-2024
|
||||
|
||||
# Modelling Moorings for Floating Turbines Catenary mooring model: Auto-population
|
||||
# Modelling Moorings for Floating Turbines
|
||||
## Catenary mooring model: Auto-population悬索系泊模型：自动填充
|
||||
|
||||
This section describes the theory behind the auto-population functionality for the "Manually defined" sub-type of catenary moorings.
|
||||
|
||||
@ -1490,6 +1514,15 @@ The classical catenary equations required to describe the statics of a single mo
|
||||
Consider a cable which is partially suspended and partially lying on the seabed as sketched in Figure 1. The cable might be slack to reduce anchor loads and an initial pretension might be induced through use of winches, to pull on the cables to give a desired cable configuration. In such arrangements, the principal loads in the line are the self weight $(w)$ , and the analysis can be based on the equations for elastic catenary lines.
|
||||
|
||||
Referring to Figure 1, the base catenary equations for a mooring line can be defined for an element in the mooring line $(d s)$
|
||||
本节描述了针对“手动定义”子类型缆系浮吊系泊线的自填充功能背后的理论。
|
||||
|
||||
在Bladed中，伞形缆系浮吊系泊线由非线性施加载荷表示，这些施加载荷是从组合刚度、阻尼和惯性矩阵计算得出的。对于单节缆系浮吊系泊线，刚度矩阵可以根据本节所述的一组线属性进行自填充。
|
||||
|
||||
描述单节缆系浮吊系泊线静力学的经典伞形缆系浮吊系泊线方程在许多参考文献中都有给出，例如（Faltinsen, 1990）。在本节中，仅提及简要概述。
|
||||
|
||||
考虑如图1所示，部分悬挂和部分位于海床上的缆绳。为了减轻锚定载荷，缆绳可能处于松弛状态，并且可以通过使用绞盘施加初始预张力，以拉动缆绳以获得所需的缆绳配置。在这种布置中，缆绳中的主要载荷是自重 $(w)$，分析可以基于弹性伞形缆系浮吊系泊线方程进行。
|
||||
|
||||
如图1所示，可以为伞形缆系浮吊系泊线中的一个元素 $(d s)$ 定义基本的伞形缆系浮吊系泊线方程。
|
||||
|
||||
$$
|
||||
\begin{array}{l}{\displaystyle{d T-\rho g A d z=\left[w\sin\varphi-F_{h_{t}}\left(1+\frac{T}{A E}\right)\right]d s}}\\ {\displaystyle{\qquad}}\\ {\displaystyle{T d\varphi-\rho g A z d\varphi=\left[w\cos\varphi+F_{h_{n}}\left(1+\frac{T}{A E}\right)\right]d s}}\end{array}
|
||||
@ -1507,12 +1540,26 @@ We further use
|
||||
|
||||
$A$ as the line sectional area, $\boldsymbol{E}$ as the elastic stiffness (Young modulus) $T$ as the tension in the line element
|
||||
|
||||
Explicit solutions of the above equations are only found for simple cases, and some simplified solutions are given in the literature. An example of such solutions is obtained for an inelastic cable, assumed to be homogeneous with constant weight $(w)$ (per unit length), and with large associated stiffness $\boldsymbol{E}$ (so the elasticity in the line is neglected). The hydrodynamic mean loads are also assumed to be zero ( $\'{}F_{h_{t}}=F_{h_{n}}=0\'{}$ ). The derivation of such equations can be found in [Faltinsen, 1990].
|
||||
Explicit solutions of the above equations are only found for simple cases, and some simplified solutions are given in the literature. An example of such solutions is obtained for an inelastic cable, assumed to be homogeneous with constant weight $(w)$ (per unit length), and with large associated stiffness $\boldsymbol{E}$ (so the elasticity in the line is neglected). The hydrodynamic mean loads are also assumed to be zero ( ${}F_{h_{t}}=F_{h_{n}}=0{}$ ). The derivation of such equations can be found in [Faltinsen, 1990].
|
||||
其中我们假设：
|
||||
|
||||
· 水平的海床，以及包含系泊线的简化的几何描述，全部位于同一平面 $(x_{1},x_{3})$ 内；
|
||||
· 忽略线段的弯曲刚度，这对于具有大曲率半径的链条和缆绳来说是一个很好的近似；
|
||||
· 我们用 $F_{h_{n}}$ 和 $F_{h_{t}}$ 分别表示作用于线段单元的法向和切向平均流体力；
|
||||
· 以及线段在水中的单位长度重量，用 $_w$ 表示。
|
||||
|
||||
此外，我们还使用：
|
||||
|
||||
$A$ 表示线段的横截面积，$\boldsymbol{E}$ 表示弹性刚度（杨氏模量），$T$ 表示线段单元的张力。
|
||||
|
||||
上述方程的显式解仅适用于简单情况，一些简化的解见文献。例如，对于一个假设为均匀且具有恒定重量 $(w)$（单位长度）且具有大相关刚度 $\boldsymbol{E}$（因此忽略线段的弹性）的非弹性缆绳，可以得到一种解。流体平均载荷也被假设为零 ( ${}F_{h_{t}}=F_{h_{n}}=0{}$ )。此类方程的推导见 [Faltinsen, 1990]。
|
||||
|
||||
|
||||
|
||||
Figure 1: Schematic drawing of a common arrangement of a mooring line that is lying on the seabed (Faltinsen, 1990).
|
||||
|
||||
For the special case of an inelastic and homogeneous mooring line, composed with only one segment, and for which the mean hydrodynamic loads are zero, the classic inelastic catenary equations are given by:
|
||||
对于一种特殊情况，即由单一节段组成的不弹性且均匀的系泊缆绳，且平均水动力载荷为零时，经典的非弹性悬链线方程如下：
|
||||
|
||||
$$
|
||||
\begin{array}{l}{\displaystyle s=\frac{T_{x}}{w}\sinh\left(\frac{w}{T_{x}}x\right)}\\ {\displaystyle\,z=\frac{T_{x}}{w}\left[\cosh\left(\frac{w}{T_{x}}x\right)-1\right]}\\ {\displaystyle T_{z}=w s}\\ {\displaystyle T=\sqrt{T_{x}^{2}+T_{z}^{2}}}\end{array}
|
||||
@ -1520,10 +1567,11 @@ $$
|
||||
|
||||
where
|
||||
|
||||
$_x$ and $_z$ are the coordinates of the mooring line,
|
||||
$x$ and $z$ are the coordinates of the mooring line,
|
||||
$\pmb{s}$ is the length of the mooring line from the origin to a certain point $\left({{\bf{x}},}{\bf{Z}}\right)$ in the line, $\boldsymbol{w}$ is the weight (force) per unit length of the mooring line,
|
||||
$T_{x}$ is the horizontal tension in the mooring line (constant),
|
||||
$T_{z}$ is the vertical tension in the mooring line at a certain point $(x,z)$ in the line, $_T$ is the resultant tension of the mooring line at a point $(x,z)$ in the line.
|
||||
$T_{z}$ is the vertical tension in the mooring line at a certain point $(x,z)$ in the line,
|
||||
$T$ is the resultant tension of the mooring line at a point $(x,z)$ in the line.
|
||||
|
||||
Note that these equations (3, 4, 5, 6) are defined in a plane $(x,z)$ and are associated with a coordinate system with the origin located at the point of contact between the mooring line and the sea floor. The $_x$ axis should point towards the attachment point, and the $_z$ axis towards the water free surface, see Figure 2.
|
||||
|
||||
@ -1590,7 +1638,7 @@ $$
|
||||
T=\sqrt{T_{x}^{2}+T_{z}^{2}}.
|
||||
$$
|
||||
|
||||
# Dynamic mooring model
|
||||
## Dynamic mooring model
|
||||
|
||||
The dynamic mooring model, unlike other models, represents a mooring line in an explicit and fully-coupled manner. Normally the multibody dynamics (MB) model includes just the turbine, with moorings treated as just one of many load sources treated separately from the model. Such sources only interact with the MB model by means of applied loads at nodes. In the case of dynamic moorings, the MB model is extended to include the mooring lines themselves. Hydrostatic and hydrodynamic loads are calculated and applied to mooring elements (segments) in the same way as for support structure elements. Hydrodynamic loads are based on Morison's equation, which is appropriate for the slender elements involved. The Morison drag term can be applied axially as well as perpendicular to the segment, with separate drag coefficient values defined for each of the two cases. In the MB tree structure, the proximal ends of the mooring lines are attached to the fairleads and the distal ends terminate at the anchors, so in MB terms they are not connected to anything.
|
||||
|
||||
|
||||
@ -1,11 +1,11 @@
|
||||
{
|
||||
"nodes":[
|
||||
{"id":"8359617e1edc48ba","type":"text","text":"状态指标：\n推进OKR的时候也要关注这些事情，它们是完成OKR的保障。\n\n\n效率状态 green","x":-76,"y":-306,"width":456,"height":347},
|
||||
{"id":"a4eaccbbfadaaf17","type":"text","text":"# 目标：多体动力学模块完善\n### 每周盘点一下它们\n\n\n关键结果：建模原理、建模方法掌握 （9/10）\n\n关键结果：风机多体动力学文献调研情况完成 （5.5/10）\n关键结果：风机模型线性化原理、方法掌握 （5/10）","x":-76,"y":-693,"width":456,"height":347},
|
||||
{"id":"a4eaccbbfadaaf17","type":"text","text":"# 目标：多体动力学模块完善\n### 每周盘点一下它们\n\n\n关键结果：建模原理、建模方法掌握 （9/10）\n\n关键结果：风机多体动力学文献调研情况完成 （5.5/10）\n关键结果：风机模型线性化原理、方法掌握 （5.5/10）","x":-76,"y":-693,"width":456,"height":347},
|
||||
{"id":"d2c5e076ba6cf7d7","type":"text","text":"# 推进计划\n未来四周计划推进的重要事情\n\n文献调研启动\n\n建模重新推导\n\n\n","x":-600,"y":-306,"width":456,"height":347},
|
||||
{"id":"82708a439812fdc7","type":"text","text":"# 7月已完成\n\n","x":-220,"y":134,"width":440,"height":560},
|
||||
{"id":"505acb3e6b119076","type":"text","text":"# 6月已完成\n\n\nP1 结果对比\n- Herowind 带3.5气动与fast3.5对比 相同\n- Herowind 带4.0气动与fast4.0对比 相同\n- Herowind 带hrl气动与fast对比 需气动支持15MW\n\nP1 Bladed交流问题汇总","x":-700,"y":134,"width":440,"height":560},
|
||||
{"id":"c18d25521d773705","type":"text","text":"# 计划\n这周要做的3~5件重要的事情，这些事情能有效推进实现OKR。\n\nP1 必须做。P2 应该做\n\n\nP1 柔性部件 叶片、塔架主动力惯性力算法 主线\n- 变形体动力学 简略看看ing\n- 柔性梁弯曲变形振动学习，主线 \n\t- 广义质量 刚度矩阵及含义\n- 如何静力学求解\n\t- 基于本构方程 读孟的论文\n\t- normal mode shape 能否使用？\n\nP1 模型线性化原理\nP1 结果对比\n- Bladed与FAST之间的对比 去掉角度 不能直接比较\n- 坐标系转换\n\nP2 如何优雅的存储、输出结果。\nP1 推进气动、控制、多体、水动 耦合计算\nP2 yaw 自由度再bug确认 已知原理了\n\n \n","x":-594,"y":-693,"width":450,"height":347},
|
||||
{"id":"c18d25521d773705","type":"text","text":"# 计划\n这周要做的3~5件重要的事情，这些事情能有效推进实现OKR。\n\nP1 必须做。P2 应该做\n\n\nP1 柔性部件 叶片、塔架主动力惯性力算法 主线\n- 变形体动力学 简略看看ing\n- 柔性梁弯曲变形振动学习，主线 \n\t- 广义质量 刚度矩阵及含义\n- 如何静力学求解\n\t- 基于本构方程 读孟的论文\n\t- normal mode shape 能否使用？\n\t- F = kx 外载与弹性势能相等\n\nP1 模型线性化原理 \n- Bladed 线性化理论手册已读\n- 梳理Bladed线性化方法框架\n-\nP1 结果对比\n- Bladed与FAST之间的对比 去掉角度 不能直接比较\n- 坐标系转换\n\nP2 如何优雅的存储、输出结果。\nP1 推进气动、控制、多体、水动 耦合计算\nP2 yaw 自由度再bug确认 已知原理了\n","x":-594,"y":-693,"width":450,"height":347},
|
||||
{"id":"30cb7486dc4e224c","type":"text","text":"# 8月已完成\n\n","x":260,"y":134,"width":440,"height":560}
|
||||
],
|
||||
"edges":[]
|
||||
|
||||
Binary file not shown.
BIN
工作总结/周报/周报81-郭翼泽.docx
Normal file
BIN
工作总结/周报/周报81-郭翼泽.docx
Normal file
Binary file not shown.
@ -1,10 +1,10 @@
|
||||
{
|
||||
"nodes":[
|
||||
{"id":"04da78b746646560","type":"text","text":"状态指标：\n推进OKR的时候也要关注这些事情，它们是完成OKR的保障。\n\n\n","x":34,"y":-186,"width":456,"height":347},
|
||||
{"id":"5aac58c184e57887","type":"text","text":"# 计划\n这周要做的3~5件重要的事情，这些事情能有效推进实现OKR。\n\nP1 必须做。P2 应该做\n\n\nP1 海龟系统测试\n- 代理测试，yiy.one.config会变\n\n\nP1 公众号开发路线探索\n\n\n","x":-490,"y":-573,"width":450,"height":347},
|
||||
{"id":"85cce24e1132f21f","type":"text","text":"# 目标：海龟 短剧 AI项目推进\n### 每周盘点一下它们\n\n\n关键结果：海龟系统现在版本测试，网页版本 （5/10）\n\n关键结果：公众号系统实现（5/10）\n\n关键结果：文献调研智能体搭建 （5/10）","x":34,"y":-573,"width":456,"height":347},
|
||||
{"id":"5aac58c184e57887","type":"text","text":"# 计划\n这周要做的3~5件重要的事情，这些事情能有效推进实现OKR。\n\nP1 必须做。P2 应该做\n\n\nP1 海龟系统测试\n- yiy.one.config会变 检测是否变化，重新修改以及重新加载\n- soket5 代理如何异步中使用\n\n\nP1 公众号开发路线探索\n\n\n","x":-490,"y":-573,"width":450,"height":347},
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{"id":"85cce24e1132f21f","type":"text","text":"# 目标：海龟 短剧 AI项目推进\n### 每周盘点一下它们\n\n\n关键结果：海龟系统现在版本测试 （9/10）\n\n关键结果：公众号系统实现（5/10）\n\n关键结果：文献调研智能体搭建 （5/10）","x":34,"y":-573,"width":456,"height":347},
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{"id":"52c483d4870680c3","type":"text","text":"# 推进计划\nRag系统、agent系统调研\n新闻 公众号\n小说推广系统 可能容易实现一些\n","x":-490,"y":-186,"width":456,"height":347},
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{"id":"0b25ceb1c28f6da1","type":"text","text":"# 五月已完成\n\n短剧自动化系统维护\nP1 剧功能完善 完成\nP1 海龟方法回顾与代码编写 \n- 邮件交互方法 完成\n","x":-210,"y":234,"width":440,"height":340}
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{"id":"0b25ceb1c28f6da1","type":"text","text":"# 六月已完成\n\nP1 海龟系统测试\n- 代理测试，5分钟间隔，全天监控成功1次\n- 代理池增加，但是没用\n","x":-482,"y":240,"width":440,"height":340}
|
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],
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"edges":[]
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}
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