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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

@@ -1357,7 +1357,7 @@ Substituting Eq. (3.74) into Eq. (3.72) results in Eq. 3.75 for the potential en
 
 将公式 (3.74) 代入公式 (3.72) 得到公式 3.75，用于表示因风轮旋转而导致每个叶片的势能：
 $$
-\begin{array}{l}{{\displaystyle V_{R o t a t i o n}=\frac{I}{2}\varOmega^{2}\sum_{i=p}^{N+p-I}\sum_{j=p}^{N+p-I}\Biggl[M_{T i p}R\!\int_{\partial}^{R-R_{H}}\!\frac{d\varphi_{i}(r)}{d r}\frac{d\varphi_{j}(r)}{d r}d r\mathop{+}}}\\ {{\displaystyle\int_{0}^{R-R_{H}}\mu_{B}\bigl(r\bigr)\bigl(R_{H}+r\bigr)\biggl(\int_{0}^{r}\!\frac{d\varphi_{i}(r^{\prime})}{d r^{\prime}}\frac{d\varphi_{j}(r^{\prime})}{d r^{\prime}}d r^{\prime}\biggr)d r^{\prime}\Biggr]c_{i}(t)c_{j}(t)}}\end{array}
+\begin{array}{l}{{\displaystyle V_{R o t a t i o n}=\frac{1}{2}\varOmega^{2}\sum_{i=p}^{N+p-1}\sum_{j=p}^{N+p-1}\Biggl[M_{T i p}R\!\int_{\partial}^{R-R_{H}}\!\frac{d\varphi_{i}(r)}{d r}\frac{d\varphi_{j}(r)}{d r}d r\mathop{+}}}\\ {{\displaystyle\int_{0}^{R-R_{H}}\mu_{B}\bigl(r\bigr)\bigl(R_{H}+r\bigr)\biggl(\int_{0}^{r}\!\frac{d\varphi_{i}(r^{\prime})}{d r^{\prime}}\frac{d\varphi_{j}(r^{\prime})}{d r^{\prime}}d r^{\prime}\biggr)d r^{\prime}\Biggr]c_{i}(t)c_{j}(t)}}\end{array}
 $$  
 
 Consequently, the generalized stiffness of each blade is:  
@@ -1371,7 +1371,8 @@ where $E I_{B}(r)$ is the distributed stiffness of the beam (blades).
 After integrating by parts and simplifying, it can be shown that Eq. (3.76) is equivalent to16:  
 
 $$
-k_{i j}=\int_{o}^{R-R_{H}}E I_{B}(r)\frac{d^{2}\varphi_{i}(r)}{d r^{2}}\frac{d^{2}\varphi_{j}(r)}{d r^{2}}d r+}\\ {\varOmega^{2}\int_{o}^{R-R_{H}}\biggl[M_{T p}R+\int_{r}^{R-R_{H}}\mu_{B}(r^{\prime})(R_{H}+r^{\prime})d r^{\prime}\biggr]\frac{d\varphi_{i}(r)}{d r}\frac{d\varphi_{j}(r)}{d r}d r+\varOmega^{2}m_{i j}\,s i n(\theta)}
+k_{ij} = \int_{0}^{R-R_H} E I_B(r) \frac{d^2 \varphi_i(r)}{dr^2} \frac{d^2 \varphi_j(r)}{dr^2} \, dr + \\
+\Omega^2 \int_{0}^{R-R_H} \left[ M_{Tp} R + \int_{r}^{R-R_H} \mu_B(r') (R_H + r') \, dr' \right] \frac{d\varphi_i(r)}{dr} \frac{d\varphi_j(r)}{dr} \, dr + \Omega^2 m_{ij} \sin(\theta)
 $$  
 
 $$
@@ -1379,45 +1380,51 @@ $$
 $$  
 
 The distributed stiffness of the flexible part of each blade is generally greater edgewise than flapwise.  Otherwise there is essentially no difference in the computation of the generalized stiffness of the blades in the flapwise and edgewise directions, since centrifugal forces are assumed to be unaffected by blade deflection.  
+叶片柔性部分的分布式刚度通常在摆振方向上大于挥舞方向。 否则，在计算叶片（风轮叶片）的广义刚度时，挥舞方向和摆振方向没有本质区别，因为假设离心力不受叶片挠曲的影响。
 
 # 3.3 Kinematics  
 
 The geometry, coordinate systems, and DOFs of a two-bladed HAWT as modeled by FAST_AD and discussed in the previous two sections can be used to develop the kinematics expressions for the entire structure.  
 
-Applying the addition theorem for angular velocities17 yields the following form of the angular velocity of the hub in the inertial reference frame, $^E_{\omega^{H}}$ :  
+Applying the addition theorem for angular velocities17 yields the following form of the angular velocity of the hub in the inertial reference frame, ${}^E{\omega^{H}}$ :  
+FAST_AD 模拟并前两节讨论的两个叶片水平轴风力发电机组的几何形状、坐标系和自由度 (DOFs) 可用于推导整个结构的运动学表达式。
 
+应用角速度的叠加定理17，可得到风轮中心在惯性参考系中的角速度形式，即 ${}^E{\omega^{H}}$：
 $$
 {}^{E}{\pmb\omega}^{H}{=}^{E}{\pmb\omega}^{B}{+}^{B}{\pmb\omega}^{N}{+}^{N}{\pmb\omega}^{L}{+}^{L}{\pmb\omega}^{H}
 $$  
 
-where $\varepsilon_{\omega}^{\phantom{\omega}}$ is the angular velocity of the tower-top base plate in the inertial reference frame, $B_{\omega}^{\mathbf{\Gamma}}N$ is the angular velocity of the nacelle relative to the tower-top base plate, $^N\!_{\omega}\!^{L}$ is the angular velocity of the low-speed shaft relative to the nacelle, and $^{L}\omega^{H}$ is the angular velocity of the hub (rotor) relative to the low-speed shaft.  The angular velocity of the tower-top base plate in the inertial reference frame, $\varepsilon_{\omega}^{\phantom{}}\beta$ , is related to the deflection of the tower18:  
+where ${}^E{\omega^{H}}$ is the angular velocity of the tower-top base plate in the inertial reference frame, $^{B}{\pmb\omega}^{N}$ is the angular velocity of the nacelle relative to the tower-top base plate, $^N{\omega}^{L}$ is the angular velocity of the low-speed shaft relative to the nacelle, and $^{L}\omega^{H}$ is the angular velocity of the hub (rotor) relative to the low-speed shaft.  The angular velocity of the tower-top base plate in the inertial reference frame, $^E{\omega}^\beta$ , is related to the deflection of the tower18:  
+
+其中，$^E{\omega^{H}}$ 是惯性参考系下塔顶底板的角速度，$^B{\pmb\omega}^{N}$ 是相对于塔顶底板的舱体的角速度，$^N{\omega}^{L}$ 是相对于舱体的低速轴的角速度，$^{L}\omega^{H}$ 是相对于低速轴的风轮（转子）的角速度。塔顶底板在惯性参考系中的角速度，$^E{\omega}^\beta$ ，与塔的偏摆有关。
 
 $$
-^{E}{\pmb\omega}^{B}=\dot{\theta}_{s}{\pmb a}_{I}+\dot{\theta}_{\gamma}{\pmb a}_{3}
+^{E}{\pmb\omega}^{B}=\dot{\theta}_{8}{\pmb a}_{1}+\dot{\theta}_{7}{\pmb a}_{3}
 $$  
 
 The angular velocity of the nacelle relative to the tower-top base plate, $^B\omega_{\;\;}^{N}$ , has a component associated with the rate of yaw and the tilt rate:  
+风轮相对于塔顶底板的角速度，$^B\omega_{\;\;}^{N}$ ，包含与偏航速率和倾覆速率相关的分量：
 
 $$
-{\bf\nabla}^{B}{\pmb\omega}^{N}=\dot{q}_{\acute{\acute{\theta}}}{\pmb d}_{2}+\dot{q}_{\acute{s}}{\pmb d}_{3}
-$$  
+{}^{B}{\pmb\omega}^{N}=\dot{q}_{6}{\pmb d}_{2}+\dot{q}_{5}{\pmb d}_{3}
+$$
 
 The time derivative of the azimuth angle relates the angular velocity of the low-speed shaft to that of the nacelle:  
-
+偏航角的时间导数将低速轴的角速度与机舱的角速度联系起来：
 $$
-{}^{N}{\pmb\omega}^{L}=\dot{q}_{4}{\pmb e}_{I}
+{}^{N}{\pmb\omega}^{L}=\dot{q}_{4}{\pmb e}_{1}
 $$  
 
 Finally, the teeter rate relates the angular velocity of the hub (rotor) to that of the low-speed shaft:  
-
+最终，摆动速率将风轮的角速度与低速轴的角速度联系起来：
 $$
-{\mathbf{\nabla}^{L}}\omega^{H}=\dot{q}_{3}{\pmb{g}}_{2}
+{}^{L}\omega^{H}=\dot{q}_{3}{\pmb{g}}_{2}
 $$  
 
 The previous five equations can be combined to give the following form of the angular velocity of the hub in the inertial reference frame:  
 
 $$
-{{\^E}\omega}^{H}=\dot{\theta}_{s}{\pmb a}_{I}+\dot{\theta}_{7}{\pmb a}_{3}+\dot{q}_{6}{\pmb d}_{2}+\dot{q}_{5}{\pmb d}_{3}+\dot{q}_{4}{\pmb e}_{I}+\dot{q}_{3}{\pmb g}_{2}
+^{E}\omega^{H}=\dot{\theta}_{s}{\pmb a}_{I}+\dot{\theta}_{7}{\pmb a}_{3}+\dot{q}_{6}{\pmb d}_{2}+\dot{q}_{5}{\pmb d}_{3}+\dot{q}_{4}{\pmb e}_{I}+\dot{q}_{3}{\pmb g}_{2}
 $$  
 
 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 :  

学术讲座-交流-面试/2025.5.28 DNV年度用户会议.md

@@ -1,23 +1,23 @@
 ## bladed开发计划与进展
 
 
-###  turbine challenge
+###  turbine challenges
 
 - growth
-	- challege in structures aerodynamics stabilities
+	- challenge in structures aerodynamics stabilities
 - 固定式 - 行架式 - floating
 	- 计算数增加，时间增长、工况复杂
 - 浮式平台多种形式
 
 ### bladed4 
-100+ industral customers
+100+ industrial customers
 
 long flexible blades
 
 
 
 
-deep stall 
+### deep stall 
 
 叶片的高频振动，instability
 
@@ -34,30 +34,28 @@ BEM + no DS   BEM + BL model 都出现叶片抖动
 BEM + IAG model 不抖动，但是也出现停顿
 
 
-风场是否有负切变仿真能力
 
 
-
-bladed5
+### bladed5
 
 flexible turbine assembly tree
 superelement （）
 
-model imblence
+model imbalance
 - add 模块之间的offset
 
 
 better support of early blade design process
-independent meshes between aerodynamic and sur
+independent meshes between aerodynamic and structure
 
 基于api前处理和后处理
 
 
-bladed 5 new features
+### bladed 5 new features
 
-yaw bear model
+- yaw bear model
 
-add sensors to simulation
+- add sensors to simulation