vault backup: 2025-05-30 16:19:08

书籍/力学书籍/OpenFast/modeling of the uae wind turbine for refinement of fast_ad/auto/modeling of the uae wind turbine for refinement of fast_ad.md

@@ -1422,39 +1422,40 @@ $$
 $$  
 
 The previous five equations can be combined to give the following form of the angular velocity of the hub in the inertial reference frame:  
-
+前五个方程可以合并得到风轮在惯性参考系下的转速如下：
 $$
-^{E}\omega^{H}=\dot{\theta}_{s}{\pmb a}_{I}+\dot{\theta}_{7}{\pmb a}_{3}+\dot{q}_{6}{\pmb d}_{2}+\dot{q}_{5}{\pmb d}_{3}+\dot{q}_{4}{\pmb e}_{I}+\dot{q}_{3}{\pmb g}_{2}
+^{E}\omega^{H}=\dot{\theta}_{8}{\pmb a}_{1}+\dot{\theta}_{7}{\pmb a}_{3}+\dot{q}_{6}{\pmb d}_{2}+\dot{q}_{5}{\pmb d}_{3}+\dot{q}_{4}{\pmb e}_{1}+\dot{q}_{3}{\pmb g}_{2}
 $$  
 
-If the velocity of the axial deflection of the tower is assumed to be negligible, the velocity of the tower-top base plate (O) in the inertial reference frame, $\varepsilon_{\nu}o$ , is :  
+If the velocity of the axial deflection of the tower is assumed to be negligible, the velocity of the tower-top base plate (O) in the inertial reference frame, $^E{\nu}^O$ , is :  
-
+如果假设塔的轴向挠度速度可以忽略不计，则惯性参考系中塔顶底板（O）的速度，$^E{\nu}^O$ ，为：
 $$
-{\varepsilon}_{\pmb{\nu}}{o}=\dot{u}_{\gamma}{\pmb{a}}_{I}+\dot{u}_{\delta}{\pmb{a}}_{3}
+^E{\nu}^O=\dot{u}_{7}{\pmb{a}}_{1}+\dot{u}_{8}{\pmb{a}}_{3}
 $$  
 
-The velocity of any other point $\mathrm{T}$ on the flexible tower in the inertial frame, $\varepsilon_{\nu}^{\phantom{\mu}T},$ , is:  
+The velocity of any other point $\mathrm{T}$ on the flexible tower in the inertial frame, $^E{\nu}^T$ , is:  
-
+在惯性参考系中，柔塔上任意其他点 $\mathrm{T}$ 的速度，$^E{\nu}^T$ ，为：
 $$
-{{\bf\nabla}^{E}}{\bf\psi}^{T}=\bigl[\dot{q}_{7}\phi_{I T}\bigl(h\bigr)+\dot{q}_{9}\phi_{2T}\bigl(h\bigr)\bigr]{\bf\dot{q}}_{I}+\bigl[\dot{q}_{8}\phi_{I T}\bigl(h\bigr)+\dot{q}_{10}\phi_{2T}\bigl(h\bigr)\bigr]{\bf\dot{q}}_{3}
+^E{\nu}^T=\bigl[\dot{q}_{7}\phi_{I T}\bigl(h\bigr)+\dot{q}_{9}\phi_{2T}\bigl(h\bigr)\bigr]{\bf{{a}}}_{1}+\bigl[\dot{q}_{8}\phi_{I T}\bigl(h\bigr)+\dot{q}_{10}\phi_{2T}\bigl(h\bigr)\bigr]{\bf{a}}_{3}
 $$  
 
 where $h$ is the elevation of point $\mathrm{T}$ along the flexible part of the tower and ranges from zero to $H.$ Again $h$ equals zero at an elevation of $H_{S}$ relative to the Earth’s surface.  
+其中，$h$ 为塔身柔性部分上的点 $\mathrm{T}$ 的高度，范围从零到 $H$。 同样，$h$ 在相对于地球表面的高度 $H_{S}$ 时也等于零。
 
-The velocity of the nacelle center of mass (D) in the inertial reference frame, $\varepsilon_{\nu}^{\phantom{\mu}D}$ , is:  
+The velocity of the nacelle center of mass (D) in the inertial reference frame, $^E{\nu}^D$ , is:  
-
+风轮中心质量惯性参考系的速度，$^E{\nu}^D$ ，为：
 $$
-{}^{E}{\pmb{\nu}}^{D}{=}^{E}{\pmb{\nu}}^{o}{+}^{E}{\pmb{\omega}}^{N}\times{\pmb{r}}^{o D}
+{}^{E}{\pmb{\nu}}^{D}{=}^{E}{\pmb{\nu}}^{O}{+}^{E}{\pmb{\omega}}^{N}\times{\pmb{r}}^{O D}
 $$  
 
-where $\varepsilon_{\omega}^{\mathbf{\Gamma}}$ is the angular velocity of the nacelle in the inertial reference frame $\bigl(^{E}\omega^{N}={}^{E}\omega^{B}+$ $^B\omega^{N})$ .  Similarly, the velocity of the teeter pin (P) in the inertial reference frame, $\varepsilon_{\nu}^{\phantom{\mu}P}$ , is:  
+where $^{E}{\pmb{\omega}}^{N}$ is the angular velocity of the nacelle in the inertial reference frame $(^{E}{\pmb{\omega}}^{N}={}^{E}\omega^{B}+^B\omega^{N})$  .  Similarly, the velocity of the teeter pin (P) in the inertial reference frame, $^{E}{\pmb{\nu}}^{P}$ , is:  
-
+其中 $^{E}{\pmb{\omega}}^{N}$ 是在惯性参考系 $(^{E}{\pmb{\omega}}^{N}={}^{E}\omega^{B}+^B\omega^{N})$ 中塔架的角速度。 类似地，在惯性参考系中，铰链点 (P) 的速度 $^{E}{\pmb{\nu}}^{P}$ 为：
 $$
-{}^{E}{\pmb{\nu}}^{P}{=}^{E}{\pmb{\nu}}^{o}{+}^{E}{\pmb{\omega}}^{N}\times{\pmb{r}}^{o P}
+{}^{E}{\pmb{\nu}}^{P}{=}^{E}{\pmb{\nu}}^{O}{+}^{E}{\pmb{\omega}}^{N}\times{\pmb{r}}^{O P}
 $$  
 
-The velocities of the blade axes intersection point (Q) and the hub center of mass (C) in the inertial reference frame, $\varepsilon_{\pmb{\nu}^{Q}}$ and $E_{\nu}c$ respectively, are:  
+The velocities of the blade axes intersection point (Q) and the hub center of mass (C) in the inertial reference frame, $^{E}{\nu}^{Q}$ and $^{E}{\nu}^{C}$ respectively, are:  
-
+叶片轴线交点（Q）和风轮中心质量点（C）在惯性参考系中的速度，分别表示为 $^{E}{\nu}^{Q}$ 和 $^{E}{\nu}^{C}$，为：
 $$
 {}^{E}{\nu}^{Q}\!=\!{}^{E}{\nu}^{P}\!+\!{}^{E}{\omega}^{H}\times r^{P Q}
 $$  
@@ -1465,32 +1466,39 @@ $$
 {}^{E}{\pmb{\nu}}^{C}\,{=}^{E}{\pmb{\nu}}^{P}\,{+}^{E}{\pmb{\omega}}^{H}\times{\pmb{r}}^{P C}
 $$  
 
-Finally, the velocity of any point S on blade 1 in the inertial reference frame, $\varepsilon_{\nu}s$ , is:  
+Finally, the velocity of any point S on blade 1 in the inertial reference frame, $^{E}{\nu}^{S}$ , is:  
-
+最终，在惯性参考系中，叶片1上任意点S的速度，表示为 $^{E}{\nu}^{S}$ ，为：
 $$
-\scriptstyle{^{E}\nu^{s}=^{E}\nu^{^{Q}}+^{^{H}}\nu^{s}+^{E}\omega^{^{H}}\times r^{^{Q S}}}
+{^{E}\nu^{S}=^{E}\nu^{Q}+^H\nu^{S}+^{E}\omega^{H}\times r^{Q S}}
 $$  
 
-where $u_{\nu}s$ is the velocity of the point S on blade 1 relative to the rotating reference frame fixed in the hub (rotor) which is simply the time derivative of equation (3.29) performed while holding the $\ddot{\iota}$ s constant:  
+where $^H\nu^{S}$ is the velocity of the point S on blade 1 relative to the rotating reference frame fixed in the hub (rotor) which is simply the time derivative of equation (3.29) performed while holding the $i'$ s constant:  
-
+其中，$^H\nu^{S}$ 是风轮中心固定参考系中叶片 1 上点 S 的速度，它仅仅是方程 (3.29) 关于时间求导的结果，同时保持 $i'$ 不变：
 $$
-\mathbf{\Phi}^{H}\mathbf{\Phi}^{S}=\dot{u}(r,t)\mathbf{i}_{I}+\dot{\nu}(r,t)\mathbf{i}_{2}-\dot{w}(r,t)\mathbf{i}_{3}
+^H\nu^{S}=\dot{u}(r,t){i}_{1}+\dot{\nu}(r,t){i}_{2}-\dot{w}(r,t){i}_{3}
 $$  
 
 Many of the previously developed equations can be combined to expand the velocity of any point S on blade 1 in the inertial reference frame :  
+许多先前开发的方程可以组合起来，以扩展风轮叶片1上任意点S在惯性参考系中的速度：
 
 $$
-\begin{array}{c}{{{^E}_{\nu}s=\big(\dot{q}_{7}+\dot{q}_{9}\big)a_{I}+\big(\dot{q}_{\delta}+\dot{q}_{l\theta}\big)a_{3}+\big(\dot{\theta}_{\delta}a_{I}+\dot{\theta}_{7}a_{3}+\dot{q}_{6}d_{2}+\dot{q}_{5}d_{3}\big)\times r^{o p}+}}\\ {{{\big(\dot{\theta}_{\delta}a_{I}+\dot{\theta}_{7}a_{3}+\dot{q}_{6}d_{2}+\dot{q}_{5}d_{3}+\dot{q}_{4}d_{I}+\dot{q}_{3}g_{2}\big)\times r^{p Q}+}}}\\ {{{\big(\dot{\theta}_{s}a_{I}+\dot{\theta}_{7}a_{3}+\dot{q}_{6}d_{2}+\dot{q}_{5}d_{3}+\dot{q}_{4}d_{I}+\dot{q}_{3}g_{2}\big)\times r^{g s}+^{H}\!_{\nu}s}}}\end{array}
+\begin{array}{c}{{^{E}\nu^{S}=\big(\dot{q}_{7}+\dot{q}_{9}\big)a_{1}+\big(\dot{q}_{8}+\dot{q}_{10}\big)a_{3}+\big(\dot{\theta}_{8}a_{1}+\dot{\theta}_{7}a_{3}+\dot{q}_{6}d_{2}+\dot{q}_{5}d_{3}\big)\times r^{OP}+}}\\ {{{\big(\dot{\theta}_{8}a_{1}+\dot{\theta}_{7}a_{3}+\dot{q}_{6}d_{2}+\dot{q}_{5}d_{3}+\dot{q}_{4}d_{1}+\dot{q}_{3}g_{2}\big)\times r^{p Q}+}}}\\ {{{\big(\dot{\theta}_{8}a_{1}+\dot{\theta}_{7}a_{3}+\dot{q}_{6}d_{2}+\dot{q}_{5}d_{3}+\dot{q}_{4}d_{1}+\dot{q}_{3}g_{2}\big)\times r^{QS}+^{H}{\nu}^S}}}\end{array}
 $$  
 
 When expanded as in Eq. (3.92), all the velocities of the various points on the wind turbine system in the inertial reference frame can be expressed as:  
 
 $$
-\mathbf{\boldsymbol{\varepsilon}}_{\pmb{\nu}}^{E}\mathbf{\boldsymbol{\mathfrak{x}}}=\left(\sum_{r=l}^{l5}\mathbf{\boldsymbol{\varepsilon}}_{\mathbf{\boldsymbol{\nu}}_{r}^{X}}\boldsymbol{\dot{q}}_{r}\right)\!+\!\mathbf{\boldsymbol{\varepsilon}}_{\mathbf{\boldsymbol{\nu}}_{t}^{X}}
+^{E}\nu^{X}=\left(\sum_{r=1}^{15}{}^{E}{\mathbf{{\nu}}_{r}^{X}}{\dot{q}}_{r}\right)+{}^{E}{\mathbf{{\nu}}_{t}^{X}}
 $$  
 
 $$
-\begin{array}{l}{{{^E}_{\nu}{^s}=\stackrel{!}{(}\dot{q}_{7}\dot{+}\dot{q}_{9}\big)a_{I}+\stackrel{\cdot}{(}\dot{q}_{\delta}\dot{+}\dot{q}_{I0}\stackrel{\cdot}{)}\dot{\pmb{a}_{3}}+\stackrel{\cdot}{(}\dot{\theta}_{s}a_{I}+\dot{\theta}_{7}a_{s}+\dot{q}_{6}d_{2}+\dot{q}_{5}d_{3}\biggr)\times r^{o p}+}}\\ {{\ }}\\ {{\stackrel{\mathrm{(}\dot{\theta}_{s}a_{I}+\dot{\theta}_{7}a_{3}+\dot{q}_{6}d_{2}+\dot{q}_{5}d_{3}+\dot{q}_{4}d_{I}+\dot{q}_{3}g_{2}\biggr)\times r^{p Q}+}}\\ {{\ }}\\ {{\stackrel{\mathrm{(}\dot{\theta}_{s}a_{I}+\dot{\theta}_{7}a_{3}+\dot{q}_{6}d_{2}+\dot{q}_{5}d_{3}+\dot{q}_{4}d_{I}+\dot{q}_{3}g_{2}\biggr)\times r^{Q S}+{^H}_{\nu}{^s}+}}\\ {{\ }}\\ {{\stackrel{\mathrm{(}\dot{\theta}_{s}a_{I}+\dot{\theta}_{7}a_{3}+\dot{q}_{6}d_{2}+\dot{q}_{5}d_{3}+\dot{q}_{4}d_{I}+\dot{q}_{3}g_{2}\biggr)\times(r i_{3})}}\end{array}
+\begin{align*}
+{{}^E_{\nu}{^s} = \left(\dot{q}_{7} + \dot{q}_{9}\right) a_{I} + \left(\dot{q}_{\delta} + \dot{q}_{I0}\right) \dot{\pmb{a}}_{3} + \left(\dot{\theta}_{s} a_{I} + \dot{\theta}_{7} a_{s} + \dot{q}_{6} d_{2} + \dot{q}_{5} d_{3}\right) \times r^{op} \\
++ \left(\dot{\theta}_{s} a_{I} + \dot{\theta}_{7} a_{3} + \dot{q}_{6} d_{2} + \dot{q}_{5} d_{3} + \dot{q}_{4} d_{I} + \dot{q}_{3} g_{2}\right) \times r^{pQ} \\
++ \left(\dot{\theta}_{s} a_{I} + \dot{\theta}_{7} a_{3} + \dot{q}_{6} d_{2} + \dot{q}_{5} d_{3} + \dot{q}_{4} d_{I} + \dot{q}_{3} g_{2}\right) \times r^{QS} \\
++ {}^H_{\nu}{^s} \\
++ \left(\dot{\theta}_{s} a_{I} + \dot{\theta}_{7} a_{3} + \dot{q}_{6} d_{2} + \dot{q}_{5} d_{3} + \dot{q}_{4} d_{I} + \dot{q}_{3} g_{2}\right) \times (r i_{3})
+\end{align*}
 $$  
 
 where $^E{\nu_{r}^{X}}$ is the $r^{\mathrm{th}}$ partial velocity associated with point X, which can be a function of time and the generalized coordinates but not of their time derivatives, and $^E{\nu_{t}^{X}}$ is the sum of all the terms not of this form.  Similarly, the angular velocity of any reference frame $\mathrm{X}$ in the inertial reference frame, $^{E}\pmb{\omega}^{X},$ , can be expressed as:  

工作OKRs/25.2-5 OKR.canvas

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-		{"id":"2b068bfe5df15a72","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    （8.5/10）\n\n关键结果：对标Bladed模块完成  （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）","x":-96,"y":-307,"width":456,"height":347},
+		{"id":"2b068bfe5df15a72","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：对标Bladed模块完成  （9.5/10）\n\n关键结果：风机多体动力学文献调研情况完成 （5.5/10）","x":-96,"y":-307,"width":456,"height":347},
 		{"id":"01ee5c157d0deeae","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":-620,"y":80,"width":456,"height":347},
-		{"id":"cb9319d24c3e70e3","type":"text","text":"# 5月已完成\n\nP1 Steady Operational Loads求解器编写测试 \n- 变桨算法测试完成\n- 转速算法基本完成\n- 两个结合点测试 完成\n\nP1 Steady Parked Loads求解器编写及测试\n\nP1 simpack多体对CAE的需求梳理 分成塔架、叶片、传动链模型 完成\n\nP1 建立IEA 15yaml文件 完成\nP1 结果对比\n-  完成 bladed、fast模型建立，工况设置，对比","x":-240,"y":520,"width":440,"height":560},
+		{"id":"cb9319d24c3e70e3","type":"text","text":"# 5月已完成\n\nP1 Steady Operational Loads求解器编写测试 \n- 变桨算法测试完成\n- 转速算法基本完成\n- 两个结合点测试 完成\n\nP1 Steady Parked Loads求解器编写及测试\n\nP1 simpack多体对CAE的需求梳理 分成塔架、叶片、传动链模型 完成\n\nP1 建立IEA 15yaml文件 完成\nP1 结果对比\n-  完成 bladed、fast模型建立，工况设置，对比\n\nP1 集成yaml解析代码，测试功能是否正确 done","x":-240,"y":520,"width":440,"height":560},
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-		{"id":"58be7961ae7275a7","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- 浮动坐标系方法 如何用于梁模型 \n\t- Q 问孟航  不用浮动坐标系\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\n\nP1 结合yaml解析代码，联合气动更新对yaml文件的支持 \nP1 结果对比\n- Herowind 不带气动与fast3.5对比\n- Herowind 不带气动与fast4.0对比\n- Herowind 带气动与fast对比\n\nP1 如何优雅的存储、输出结果。\nP1 国产化适配交给甲子营，对接\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","x":-614,"y":-307,"width":450,"height":347}
+		{"id":"58be7961ae7275a7","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- 浮动坐标系方法 如何用于梁模型 \n\t- Q 问孟航  不用浮动坐标系\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\nP1 结果对比\n- Herowind 不带气动与fast3.5对比\n- Herowind 不带气动与fast4.0对比\n- Herowind 带气动与fast对比\n\nP1 如何优雅的存储、输出结果。\nP1 国产化适配交给甲子营，对接\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\nP1 模型线性化调研\n\n","x":-614,"y":-307,"width":450,"height":347}
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