vault backup: 2025-09-01 17:07:29
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@ -738,7 +738,7 @@ Figure 1: Blade aerodynamic axes coordinate system
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The user axes system is a custom coordinate system that can be defined by the user for outputting blade loads. It is defined in the Blades screen in the Blade Geometry tab. At the bottom of the screen it is possible to define the user defined axis directions for the z-axis and y-axis. The y-axis can follow either the untwisted root y-axis, principal elastic y-axis or the aerodynamic twist. The zaxis options and their implications are explained below.
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用户坐标系是一种自定义坐标系，可由用户定义以输出叶片载荷。它在“叶片几何”选项卡中的“叶片”屏幕中定义。在屏幕底部，可以定义用户自定义的 z 轴和 y 轴方向。y 轴可以跟随未扭转的根部 y 轴、主弹性 y 轴或气动扭角。z 轴选项及其含义如下所述。
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# User axes: Z-axis follows neutral axis or root z-axis #
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# User axes: Z-axis follows neutral axis or root z-axis
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The origin of the axes is specified as percentages of chord, parallel and perpendicular to the chord at each blade station as shown in Figure 1. The user can specify whether the z-axis is parallel to the root axis or the local neutral axis. Similarly, the user can independently specify whether the y-axis is aligned to the principal elastic axes orientation, the aerodynamic twist, or the root axis.
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坐标原点被指定为弦长的百分比，如图1所示，其方向与弦线平行和垂直于每个叶片站。用户可以指定 z 轴是否与根轴或局部中性轴平行。类似地，用户可以独立指定 y 轴是否与主弹性轴方向、气动扭角或根轴对齐。
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@ -502,10 +502,10 @@ Last updated 30-08-2024
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The selection and calculation of mode shape functions follows the idea that was originally suggested by (Craig, 2000) as a modification of the widely used Craig-Bampton method from (Craig, 1968). For both methods the stations are subdivided into **boundary stations** that may couple to other components and **interior stations** that do not couple. The boundary stations also represent the component nodes that may link to nodes of other components. In particular the station representing the proximal node is constrained completely in order to exclude rigid body displacement modes.
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With the applied method the modes are generally **selected as the union between attachment modes** that may couple to other components and **normal modes** that may be considered as internal vibration modes.
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模态振型函数的选择和计算遵循了 (Craig, 2000) 最初提出的思想，该思想是对 (Craig, 1968) 提出的广泛使用的 Craig-Bampton 方法的改进。对于这两种方法，测站被细分为可以与其他部件耦合的**边界测站**和不耦合的**内部测站**。边界测站也代表可以连接到其他部件节点的部件节点。特别地，代表近端节点的测站被完全约束，以排除刚体位移模态。
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模式形状函数的选择和计算遵循了(Craig, 2000)最初提出的思路，是对(Craig, 1968)广泛使用的 Craig-Bampton 方法的一种改进。对于这两种方法，站点被划分为可以与其他组件耦合的边界站点，以及不耦合的内部站点。边界站点也代表了可能链接到其他组件节点的组件节点。特别是，代表近端节点的站点被完全约束，以排除刚体位移模式。
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采用所应用的方法，模态通常被**选择为可以与其他部件耦合的连接模态和可以被视为内部振动模态的简正模态的并集**。
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采用该方法时，模式通常被选择为连接模式attachment modes（可能与其他组件耦合）与正常模式**normal modes**（可被视为内部振动模式）的并集。
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@ -6,7 +6,7 @@
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{"id":"82708a439812fdc7","type":"text","text":"# 10月已完成\n\n","x":-220,"y":134,"width":440,"height":560},
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{"id":"505acb3e6b119076","type":"text","text":"# 9月已完成\n","x":-700,"y":134,"width":440,"height":560},
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{"id":"30cb7486dc4e224c","type":"text","text":"# 11月已完成\n\n\n\n","x":260,"y":134,"width":440,"height":560},
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{"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\nP2 柔性部件 叶片、塔架变形算法 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\t\n- 梳理bladed动力学框架\n\t- 子结构文献阅读\n\t- 叶片模型建模 done\n- 共旋方法学习\n- DTU 变形量计算方法学习\n\n\nP1 线性化方法编写 搁置\n\nP1 湍流 气动 多体 控制联调\n\nP1 bladed对比--产出报告\n- 稳态变形量对比 -- steady power production loading、steady parked loading\n\n\nP2 如何优雅的存储、输出结果。\nP2 yaw 自由度再bug确认 已知原理了\n","x":-597,"y":-803,"width":453,"height":457},
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{"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\nP2 柔性部件 叶片、塔架变形算法 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\t\n- 梳理bladed动力学框架\n\t- 子结构文献阅读\n\t- 叶片模型建模 done\n- 共旋方法学习\n- DTU 变形量计算方法学习\n\n\nP1 线性化方法编写 搁置\nP1 气动、多体、控制、水动联调\nP1 湍流 气动 多体 控制联调\nP2 停机工况等调试\n\nP1 bladed对比--稳态，产出报告\n- 模态对比 两种描述方法不同，bladed方向更多，x y z deflection, x y z rotation，不好对比\n- 气动对比 aerodynamic info 轴向切向诱导因子，根部，尖部差距较大\n- 稳态变形量对比\n- 稳态变形量对比 -- steady power production loading、steady parked loading\n\n\nP2 如何优雅的存储、输出结果。\nP2 yaw 自由度再bug确认 已知原理了\n","x":-597,"y":-803,"width":453,"height":457},
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{"id":"86ab96a25a3bf82e","type":"text","text":" 湍流风+ 控制的联调，bladed也算一个算例\n- 加水动的联调\n- 8月份底完成这两个\n- 9月份完成停机等工况测试\n- 10月份明阳实际机型测试","x":580,"y":-803,"width":480,"height":220}
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],
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"edges":[]
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@ -214,8 +214,8 @@ $$
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F_{u,1}\!=\!\ddot{\beta}m u_{c g}-\dot{\beta}^{2}m\nu_{c g}+2\dot{\beta}m\dot{u}_{c g}+\left(T_{1}l_{c g}\sin(\overline{{{\theta}}}\,)\right)^{\prime}+\left(\nu^{\prime}\!\int_{s}^{R}T_{1}\mathrm{d}\rho\right)^{\prime}
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$$
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Where $u_{c g}=u+l_{p i}+l_{c g}\mathrm{cos}(\overline{{\theta}})-l_{c g}\theta\mathrm{sin}(\overline{{\theta}})$ and $\nu_{c g}=\nu+l_{c g}\mathrm{sin}(\overline{{\theta}})+l_{c g}\theta\mathrm{cos}(\overline{{\theta}})$ are the $x$ and $y$ coordinates of the center of gravity in the $(x,y,z)$ -frame, respectively, $\Gamma_{1}=2m\dot{\beta}\dot{\phi}((u+l_{p i})\mathrm{sin}(\beta)+\nu\mathrm{cos}(\beta)+l_{c g}\mathrm{sin}(\overline{{{\theta}}}+\beta))$ is the Coriolis force in the $z-$ -direction, associated with the angular velocity of the $(x,y,z)$ -frame about the $z$ -axis and about the $\hat{y}$ -axis. The first term in equation (13a) is the fictitious force\* in the $x$ -direction associated with the angular acceleration of the $(x,\,y,\,z)$ -frame about the $z-$ -axis. The second term is the fictitious centrifugal force associated with the angular velocity of the $(x,y,z)$ -frame about the $z$ -axis and the offset of $c g$ in the $x$ - direction. The third term is the Coriolis force associated with the angular velocity of the $(x,y,z)$ -frame about the $z$ -axis and the velocity of $c g$ in the $y$ -direction. The fourth term in equation (13a) is the spatial derivative of the moment caused by the offset of $c g$ and the Coriolis force $T_{1}$ . The last term is the bending moment caused by the Coriolis force $T_{1}$ on the remaining part of the blade, from this point to the tip. The influence from the rotor speed is described by
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其中 $u_{c g}=u+l_{p i}+l_{c g}\mathrm{cos}(\overline{{\theta}})-l_{c g}\theta\mathrm{sin}(\overline{{\theta}})$ 和 $\nu_{c g}=\nu+l_{c g}\mathrm{sin}(\overline{{\theta}})+l_{c g}\theta\mathrm{cos}(\overline{{\theta}})$ 分别是质心在 $(x,y,z)$ 坐标系中的 $x$ 和 $y$ 坐标，$\Gamma_{1}=2m\dot{\beta}\dot{\phi}((u+l_{p i})\mathrm{sin}(\beta)+\nu\mathrm{cos}(\beta)+l_{c g}\mathrm{sin}(\overline{{{\theta}}}+\beta))$ 是在 $z$ 方向上的科里奥利力，它与 $(x,y,z)$ 坐标系绕 $z$ 轴和绕 $\hat{y}$ 轴的角速度相关联。方程 (13a) 中的第一项是与 $(x,\,y,\,z)$ 坐标系绕 $z$ 轴的角加速度相关联的 $x$ 方向上的虚拟力*。第二项是与 $(x,y,z)$ 坐标系绕 $z$ 轴的角速度以及质心在 $x$ 方向上的偏移相关联的虚拟离心力。第三项是与 $(x,y,z)$ 坐标系绕 $z$ 轴的角速度以及质心在 $y$ 方向上的速度相关联的科里奥利力。方程 (13a) 中的第四项是由质心偏移和科里奥利力 $T_{1}$ 引起的力矩的空间导数。最后一项是由科里奥利力 $T_{1}$ 作用在叶片从该点到叶尖的剩余部分上所引起的弯矩。风轮转速的影响由下式描述：
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Where $u_{c g}=u+l_{p i}+l_{c g}\mathrm{cos}(\overline{{\theta}})-l_{c g}\theta\mathrm{sin}(\overline{{\theta}})$ and $\nu_{c g}=\nu+l_{c g}\mathrm{sin}(\overline{{\theta}})+l_{c g}\theta\mathrm{cos}(\overline{{\theta}})$ are the $x$ and $y$ coordinates of the center of gravity in the $(x,y,z)$ -frame, respectively, $T_{1}=2m\dot{\beta}\dot{\phi}((u+l_{p i})\mathrm{sin}(\beta)+\nu\mathrm{cos}(\beta)+l_{c g}\mathrm{sin}(\overline{{{\theta}}}+\beta))$ is the Coriolis force in the $z-$ -direction, associated with the angular velocity of the $(x,y,z)$ -frame about the $z$ -axis and about the $\hat{y}$ -axis. The first term in equation (13a) is the fictitious force\* in the $x$ -direction associated with the angular acceleration of the $(x,\,y,\,z)$ -frame about the $z-$ -axis. The second term is the fictitious centrifugal force associated with the angular velocity of the $(x,y,z)$ -frame about the $z$ -axis and the offset of $c g$ in the $x$ - direction. The third term is the Coriolis force associated with the angular velocity of the $(x,y,z)$ -frame about the $z$ -axis and the velocity of $c g$ in the $y$ -direction. The fourth term in equation (13a) is the spatial derivative of the moment caused by the offset of $c g$ and the Coriolis force $T_{1}$ . The last term is the bending moment caused by the Coriolis force $T_{1}$ on the remaining part of the blade, from this point to the tip. The influence from the rotor speed is described by
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其中 $u_{c g}=u+l_{p i}+l_{c g}\mathrm{cos}(\overline{{\theta}})-l_{c g}\theta\mathrm{sin}(\overline{{\theta}})$ 和 $\nu_{c g}=\nu+l_{c g}\mathrm{sin}(\overline{{\theta}})+l_{c g}\theta\mathrm{cos}(\overline{{\theta}})$ 分别是质心在 $(x,y,z)$ 坐标系中的 $x$ 和 $y$ 坐标，$T_{1}=2m\dot{\beta}\dot{\phi}((u+l_{p i})\mathrm{sin}(\beta)+\nu\mathrm{cos}(\beta)+l_{c g}\mathrm{sin}(\overline{{{\theta}}}+\beta))$ 是在 $z$ 方向上的科里奥利力，它与 $(x,y,z)$ 坐标系绕 $z$ 轴和绕 $\hat{y}$ 轴的角速度相关联。方程 (13a) 中的第一项是与 $(x,\,y,\,z)$ 坐标系绕 $z$ 轴的角加速度相关联的 $x$ 方向上的虚拟力。第二项是与 $(x,y,z)$ 坐标系绕 $z$ 轴的角速度以及质心在 $x$ 方向上的偏移相关联的虚拟离心力。第三项是与 $(x,y,z)$ 坐标系绕 $z$ 轴的角速度以及质心在 $y$ 方向上的速度相关联的科里奥利力。方程 (13a) 中的第四项是由质心偏移和科里奥利力 $T_{1}$ 引起的力矩的空间导数。最后一项是由科里奥利力 $T_{1}$ 作用在叶片从该点到叶尖的剩余部分上所引起的弯矩。风轮转速的影响由下式描述：
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$$
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@ -223,7 +223,7 @@ $$
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F_{u,2} &= -\dot{\phi}^{2}m\hat{u}_{cg}\cos(\beta) - \left[\dot{\phi}^{2}\left(m l_{cg}w_{0}\cos(\overline{\theta}) - \theta\sin(\overline{\theta})\right)\right]' \\
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&\quad - \left(l_{cg}T_{2}\right)' \cos(\overline{\theta}) \\
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&\quad - 2\dot{\phi}m l_{cg}\left(\dot{u}'\cos(\overline{\theta}) + \dot{\nu}'\sin(\overline{\theta})\right)\cos(\beta) \\
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&\quad - \left[\Big((u' + l_{pi}')\Big)_{s}^{R}\left(\dot{\phi}^{2}m w_{0} + T_{2}\right)\mathrm{d}\rho\right]' \\
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&\quad - \left[\Big(u' + l_{pi}'\Big)\int_{s}^{R}\left(\dot{\phi}^{2}m w_{0} + T_{2}\right)\mathrm{d}\rho\right]' \\
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F_{\nu,2} &= \dot{\phi}^{2}m\hat{u}_{cg}\sin(\beta) - \left[\dot{\phi}^{2}\left(m l_{cg}w_{0}\sin(\overline{\theta}) + \theta\cos(\overline{\theta})\right)\right]' \\
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&\quad - \left(l_{cg}T_{2}\right)' \sin(\overline{\theta}) \\
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@ -233,30 +233,31 @@ F_{\nu,2} &= \dot{\phi}^{2}m\hat{u}_{cg}\sin(\beta) - \left[\dot{\phi}^{2}\left(
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$$
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where $\hat{u}_{c g}=(u+l_{p i})\mathrm{cos}(\beta)-\nu\mathrm{sin}(\beta)+l_{c g}\mathrm{cos}(\overline{{{\theta}}}+\beta)-l_{c g}\theta\mathrm{sin}(\overline{{{\theta}}}+\beta)$ is the $\hat{x}$ coordinate of the center of gravity given in the $(\hat{x},\hat{y},\hat{z})$ -frame, $T_{2}=2m\dot{\phi}(\dot{u}\cos(\upbeta)-\dot{\nu}\sin(\beta))$ is the Coriolis force in the $z$ -direction associated with the rotation in the rotor plane and the velocity of $c g$ in the $\boldsymbol{\hat{x}}$ -direction The first term in equation (14a) is the fictitious centrifugal force associated with the rotation in the rotor plane and the offset of $c g$ in the $x_{\mathrm{{}}}$ -direction projected onto the $x_{\mathrm{{}}}$ -direction. The second and third terms in equation (14a) are the spatial derivative of the moment caused by the distance from $c g$ to $e a$ in the $x$ -direction and the fictitious centrifugal and the Coriolis force $T_{2}$ , respectively. The centrifugal force is associated with the rotation in the rotor plane and the offset of $c g$ from the center of rotation. The fourth term is the fictitious Coriolis force associated with the rotation of the blade in the rotor plane and the velocity of $c g$ in the $\hat{z}$ -direction The last term in equation (14a) is the bending moment from the fictitious centrifugal and the Coriolis force $T_{2}$ on the remaining part of the blade from this point to the tip. The influence from gravity is described by
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其中 $\hat{u}_{c g}=(u+l_{p i})\mathrm{cos}(\beta)-\nu\mathrm{sin}(\beta)+l_{c g}\mathrm{cos}(\overline{{{\theta}}}+\beta)-l_{c g}\theta\mathrm{sin}(\overline{{{\theta}}}+\beta)$ 是在 $(\hat{x},\hat{y},\hat{z})$ 坐标系中给出，重力中心 $\hat{x}$ 坐标，$T_{2}=2m\dot{\phi}(\dot{u}\cos(\upbeta)-\dot{\nu}\sin(\beta))$ 是与风轮平面内的旋转和 $c g$ 在 $\boldsymbol{\hat{x}}$ 方向上的速度相关的 $z$ 方向上的科里奥利力。方程 (14a) 中的第一项是与风轮平面内的旋转和 $c g$ 在 $x_{\mathrm{{}}}$ 方向上的偏移相关的虚构离心力，投影到 $x_{\mathrm{{}}}$ 方向上。方程 (14a) 中的第二项和第三项分别是由于 $c g$ 到 $e a$ 在 $x$ 方向上的距离引起的弯矩的空间导数，以及虚构的离心力和科里奥利力 $T_{2}$，分别。离心力与风轮平面内的旋转和 $c g$ 从转动中心的偏移相关联。第四项是与叶片在风轮平面内的旋转和 $c g$ 在 $\hat{z}$ 方向上的速度相关的虚构科里奥利力。方程 (14a) 中的最后一项是由于从该点到叶片末端的剩余部分上的虚构离心力和科里奥利力 $T_{2}$ 引起的弯矩。重力影响由描述。
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其中 $\hat{u}_{c g}=(u+l_{p i})\mathrm{cos}(\beta)-\nu\mathrm{sin}(\beta)+l_{c g}\mathrm{cos}(\overline{{{\theta}}}+\beta)-l_{c g}\theta\mathrm{sin}(\overline{{{\theta}}}+\beta)$ 是在 $(\hat{x},\hat{y},\hat{z})$ 坐标系中给出的质心的 $\hat{x}$ 坐标，$T_{2}=2m\dot{\phi}(\dot{u}\cos(\upbeta)-\dot{\nu}\sin(\beta))$ 是与风轮平面内的旋转以及质心在 ${\hat{x}}$ 方向的速度相关联的 $z$ 方向的科里奥利力。方程 (14a) 中的第一项是与风轮平面内的旋转以及质心在 $x_{\mathrm{{}}}$ 方向的偏移投影到 $x_{\mathrm{{}}}$ 方向相关联的虚拟离心力。方程 (14a) 中的第二项和第三项分别是质心到 $e a$ 在 $x$ 方向的距离引起的力矩的空间导数，以及虚拟离心力和科里奥利力 $T_{2}$。离心力与风轮平面内的旋转以及质心偏离旋转中心的偏移相关联。第四项是与叶片在风轮平面内的旋转以及质心在 $\hat{z}$ 方向的速度相关联的虚拟科里奥利力。方程 (14a) 中的最后一项是虚拟离心力和科里奥利力 $T_{2}$ 作用在叶片从该点到叶尖的剩余部分上的弯矩。重力影响由下式描述：
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$$
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\begin{array}{r l}&{F_{u,3}\!=\!m g\sin(\phi)\cos(\beta)\!+\!\left(\!\left(l_{c g}(u^{\prime}\!+\!l_{p i}^{\prime})\right)^{\prime}\cos(\overline{{\theta}})\cos(\beta)\!+\!\left(l_{c g}\nu^{\prime}\right)^{\prime}\sin(\overline{{\theta}})\cos(\beta)m g\sin(\phi)\!\right.}\\ &{\qquad\left.-\left(m l_{c g}\!\left(\cos(\overline{{\theta}})-\theta\sin(\overline{{\theta}})\right)\right)^{\prime}g\cos(\phi)\!+\!\left((u^{\prime}\!+\!l_{p i}^{\prime})\right)_{s}^{R}m g\cos(\phi)\mathrm{d}\rho\right)^{\prime}}\\ &{F_{u,3}\!=\!-\!m g\sin(\phi)\sin(\beta)\!+\!\left(\!\left(l_{c g}\left(u^{\prime}\!+\!l_{p i}^{\prime}\right)\right)^{\prime}\sin(\overline{{\theta}})\cos(\beta)\!-\!\left(l_{c g}\nu^{\prime}\right)^{\prime}\sin(\overline{{\theta}})\sin(\beta)\!\right)\!m g\sin(\phi)}\\ &{\qquad-\left(m l_{c g}\left(\sin(\overline{{\theta}})-\theta\cos(\overline{{\theta}})\right)\right)^{\prime}g\cos(\phi)\!+\!\left(\nu^{\prime}\!\int_{s}^{R}m g\cos(\phi)\mathrm{d}\rho\right)^{\prime}}\end{array}
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\begin{array}{r l}&{F_{u,3}\!=\!m g\sin(\phi)\cos(\beta)\!+\!\left(\!\left(l_{c g}(u^{\prime}\!+\!l_{p i}^{\prime})\right)^{\prime}\cos(\overline{{\theta}})\cos(\beta)\!+\!\left(l_{c g}\nu^{\prime}\right)^{\prime}\sin(\overline{{\theta}})\cos(\beta)m g\sin(\phi)\!\right.}\\ &{\qquad\left.-\left(m l_{c g}\!\left(\cos(\overline{{\theta}})-\theta\sin(\overline{{\theta}})\right)\right)^{\prime}g\cos(\phi)\!+\!\left((u^{\prime}\!+\!l_{p i}^{\prime})\right)\int_{s}^{R}m g\cos(\phi)\mathrm{d}\rho\right)^{\prime}}\\ &{F_{u,3}\!=\!-\!m g\sin(\phi)\sin(\beta)\!+\!\left(\!\left(l_{c g}\left(u^{\prime}\!+\!l_{p i}^{\prime}\right)\right)^{\prime}\sin(\overline{{\theta}})\cos(\beta)\!-\!\left(l_{c g}\nu^{\prime}\right)^{\prime}\sin(\overline{{\theta}})\sin(\beta)\!\right)\!m g\sin(\phi)}\\ &{\qquad-\left(m l_{c g}\left(\sin(\overline{{\theta}})-\theta\cos(\overline{{\theta}})\right)\right)^{\prime}g\cos(\phi)\!+\!\left(\nu^{\prime}\!\int_{s}^{R}m g\cos(\phi)\mathrm{d}\rho\right)^{\prime}}\end{array}
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$$
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where the first term in equation (15a) is the $x$ -component of the gravity force. The second term is the spatial derivative of the moment caused by the $\hat{x}$ -component of the gravity force and the offset of $c g$ in the $z$ -direction. The third term is the spatial derivative of the moment caused by the distance between $c g$ and $e a$ in the $x$ -direction and the $z$ -component of the gravity force. The last term in equation (15a) is the bending moment from the $z-$ -component of the gravity force on the remaining part of the blade, from this point to the tip. The restoring force caused by the bending stiffness of the blade is described by
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在方程 (15a) 中，第一项是重力在 $x$ 方向上的分量。第二项是由于重力在 $\hat{x}$ 方向上的分量以及 $z$ 方向上的 $c g$ 偏移量引起的弯矩的空间导数。第三项是由于 $c g$ 和 $e a$ 在 $x$ 方向上的距离以及重力在 $z$ 方向上的分量引起的弯矩的空间导数。方程 (15a) 中的最后一项是由于从该点到叶片末端，重力在 $z$ 方向上的分量作用在叶片剩余部分产生的弯矩。由叶片的弯曲刚度引起的回复力由以下方式描述：
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其中，方程(15a)中的第一项是重力在$x$方向的分量。第二项是由重力在$\hat{x}$方向的分量和质心($cg$)在$z$方向的偏移引起的力矩的空间导数。第三项是由质心($cg$)和$ea$在$x$方向的距离以及重力在$z$方向的分量引起的力矩的空间导数。方程(15a)中的最后一项是重力在$z$方向的分量作用在叶片剩余部分（从该点到叶尖）上的弯矩。由叶片的弯曲刚度引起的恢复力由下式描述：
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$$
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\begin{array}{r l}&{F_{u,4}=\big(E\big(I_{\xi}\cos^{2}\big(\tilde{\theta}\big)+I_{\eta}\sin^{2}\big(\tilde{\theta}\big)\big)u^{\prime\prime}\big)^{\prime\prime}+\big(E(I_{\xi}-I_{\eta})\cos\big(\tilde{\theta}\big)\sin\big(\tilde{\theta}\big)\nu^{\prime\prime}\big)^{\prime\prime}}\\ &{\qquad\qquad-\big(E(I_{\xi}-I_{\eta})\theta\big(u^{\prime\prime}\sin\big(2\tilde{\theta}\big)-\nu^{\prime\prime}\cos\big(2\tilde{\theta}\big)+I_{p i}^{\prime\prime}\sin\big(\tilde{\theta}\big)\cos\big(\tilde{\theta}\big)\big)\big)^{\prime\prime}}\\ &{F_{v,4}=\big(E\big(I_{\xi}\sin^{2}\big(\tilde{\theta}\big)+I_{\eta}\cos^{2}\big(\tilde{\theta}\big)\big)\nu^{\prime\prime}\big)^{\prime\prime}+\big(E(I_{\xi}-I_{\eta})\cos\big(\tilde{\theta}\big)\sin\big(\tilde{\theta}\big)u^{\prime\prime}\big)^{\prime\prime}}\\ &{\qquad+\left(E(I_{\xi}-I_{\eta})\theta\big(u^{\prime\prime}\cos\big(2\tilde{\theta}\big)+\nu^{\prime\prime}\sin\big(2\tilde{\theta}\big)\big)\right)^{\prime\prime}-\big(I_{p i}^{\prime\prime}\theta E(I_{\xi}\sin^{2}(\theta)+I_{\eta}\cos^{2}(\theta))\big)^{\prime\prime}}\end{array}
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\begin{array}{r l}&{F_{u,4}=\big(E\big(I_{\xi}\cos^{2}\big(\tilde{\theta}\big)+I_{\eta}\sin^{2}\big(\tilde{\theta}\big)\big)u^{\prime\prime}\big)^{\prime\prime}+\big(E(I_{\xi}-I_{\eta})\cos\big(\tilde{\theta}\big)\sin\big(\tilde{\theta}\big)\nu^{\prime\prime}\big)^{\prime\prime}}\\ &{\qquad\qquad-\big(E(I_{\xi}-I_{\eta})\theta\big(u^{\prime\prime}\sin\big(2\tilde{\theta}\big)-\nu^{\prime\prime}\cos\big(2\tilde{\theta}\big)+I_{p i}^{\prime\prime}\sin\big(\tilde{\theta}\big)\cos\big(\tilde{\theta}\big)\big)\big)^{\prime\prime}}\\ &{F_{v,4}=\big(E\big(I_{\xi}\sin^{2}\big(\tilde{\theta}\big)+I_{\eta}\cos^{2}\big(\tilde{\theta}\big)\big)\nu^{\prime\prime}\big)^{\prime\prime}+\big(E(I_{\xi}-I_{\eta})\cos\big(\tilde{\theta}\big)\sin\big(\tilde{\theta}\big)u^{\prime\prime}\big)^{\prime\prime}}\\ &{\qquad+\left(E(I_{\xi}-I_{\eta})\theta\big(u^{\prime\prime}\cos\big(2\tilde{\theta}\big)+\nu^{\prime\prime}\sin\big(2\tilde{\theta}\big)\big)\right)^{\prime\prime}-\big(l_{p i}^{\prime\prime}\theta E(I_{\xi}\sin^{2}(\theta)+I_{\eta}\cos^{2}(\theta))\big)^{\prime\prime}}\end{array}
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$$
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where the first term is the bending stiffness in the $x$ -direction, the second term is the coupling to the $\nu$ -direction, and the last term is the coupling to the twist. The principle moments of inertia are given by $I_{\xi}=\int\!\int_{A}\!\eta^{2}\mathrm{d}\eta\mathrm{d}\xi$ and $I_{\eta}=\int\int_{A}\!\xi^{2}\mathrm{d}\eta\mathrm{d}\xi.$ . The effect of an angular acceleration of the rotor is described by
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其中第一项为 $x$ 向弯曲刚度，第二项为与 $\nu$ 向的耦合，最后一项为与扭角的耦合。惯性矩由 $I_{\xi}=\int\int_{A}\eta^{2}\mathrm{d}\eta\mathrm{d}\xi$ 和 $I_{\eta}=\int\int_{A}\xi^{2}\mathrm{d}\eta\mathrm{d}\xi$ 给出。风轮的角加速度的影响由以下描述：
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||||
其中第一项是 $x$ 方向的弯曲刚度，第二项是与 $\nu$ 方向的耦合，最后一项是与扭转的耦合。主惯性矩由 $I_{\xi}=\int\!\int_{A}\!\eta^{2}\mathrm{d}\eta\mathrm{d}\xi$ 和 $I_{\eta}=\int\int_{A}\!\xi^{2}\mathrm{d}\eta\mathrm{d}\xi$ 给出。风轮角加速度的影响由
|
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|
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$$
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||||
F_{u,5}\!={m\ddot{\phi}w_{0}\cos(\beta)},\ \ \ F_{v,5}\!=\!-m{\ddot{\phi}w_{0}}\sin(\beta)
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$$
|
||||
|
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which is the fictitious angular acceleration of $c g$ associated with the angular acceleration of the $(x,y,z)$ -frame about the $Y.$ -axis. The right hand side of equations (12a) and (12b) describes the external forces, $f_{u}$ and $f_{\nu}$ are the forces in the $x\cdot$ - and $y$ -directions, respectively. The last term is the bending moment from the external force in the $z$ -direction on the remaining part of the blade, from this point to the tip.
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这与关于 $(x,y,z)$ -坐标系绕 $Y$-轴旋转产生的虚构角加速度 $c g$ 相关联。方程 (12a) 和 (12b) 的右侧描述了外部力，$f_{u}$ 和 $f_{\nu}$ 分别是 $x$ 和 $y$ 方向上的力。最后一个项是由于外部力在 $z$ 方向上作用于叶片剩余部分而产生的弯矩，从该点延伸至叶片末端。
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它是与 $(x,y,z)$ 坐标系绕 $Y.$ 轴的角加速度相关的 $cg$ 的虚假角加速度。方程 (12a) 和 (12b) 的右侧描述了外部力，$f_{u}$ 和 $f_{\nu}$ 分别是 $x\cdot$ 方向和 $y$ 方向的力。最后一项是 $z$ 方向的外部力作用在叶片剩余部分（从该点到叶尖）上的弯矩。
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|
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Blade Torsional Motion
|
||||
## Blade Torsional Motion
|
||||
|
||||
The equation of torsional motion is
|
||||
|
||||
@ -265,19 +266,20 @@ $$
|
||||
$$
|
||||
|
||||
where the rotor speed leads to the fictitious centrifugal forces:
|
||||
其中风轮转速导致虚构离心力：
|
||||
在风轮转速导致虚拟离心力的情况下：
|
||||
|
||||
$$
|
||||
F_{\theta,1}\!=\!m l_{c g}{\dot{\phi}}^{2}{\hat{u}}_{c g}\sin({\overline{{\theta}}}+\beta)+m l_{c g}w_{0}\phi^{2}\big(\nu^{\prime}\cos({\overline{{\theta}}})\!-\!(u^{\prime}\!+\!l_{p i}^{\prime})\sin({\overline{{\theta}}})\big)
|
||||
$$
|
||||
|
||||
where the first term is associated with the offset of $c g$ in the $\hat{x}$ -direction and the second is associated with the distance from the center of rotation to $c g$ . The influence from the pitch action is described by
|
||||
其中第一项与 $c g$ 在 $\hat{x}$ 方向上的偏移量相关联，第二项与旋转中心到 $c g$ 的距离相关联。俯仰作用的影响由以下描述：
|
||||
其中第一项与 $c g$ 在 $\hat{x}$ 方向上的偏移相关联，第二项与从旋转中心到 $c g$ 的距离相关联。变桨作用的影响由下式描述：
|
||||
|
||||
$$
|
||||
\begin{array}{l}{{F_{\theta,2}=(I_{c g}+m l_{c g}^{2})\ddot{\beta}-\ddot{\beta}m l_{c g}(u\cos(\overline{{{\theta}}})+\nu\sin(\overline{{{\theta}}}))+m l_{c g}\dot{\beta}^{2}\big((u+l_{p i})\sin(\overline{{{\theta}}})-\nu\cos(\overline{{{\theta}}})\big)}}\\ {{\mathrm{}}}\\ {{\mathrm{}\qquad+\,2m l_{c g}\dot{\beta}(\dot{u}\cos(\overline{{{\theta}}})+\dot{\nu}\sin(\overline{{{\theta}}}))}}\end{array}
|
||||
$$
|
||||
|
||||
where the first term is the fictitious angular acceleration associated with the angular acceleration of the $(x,y,$ , $z)$ -frame about the $z$ -axis. The second term is the fictitious centrifugal force associated with the rotation of the $(x,y,z)$ -frame about the $z-$ -axis. The last term is the fictitious Coriolis force associated with the rotation of the $(x,y,z)$ -frame about the $z$ -axis and the velocity of $c g$ in the chord direction. The acceleration of the rotor leads to the following term:
|
||||
其中第一项是与 $(x,y,z)$ -坐标系绕 $z$ 轴旋转相关的虚构角加速度；第二项是与 $(x,y,z)$ -坐标系绕 $z$ 轴旋转相关的虚构离心力；最后一项是与 $(x,y,z)$ -坐标系绕 $z$ 轴旋转以及 $c g$ 在弦向上的速度相关的虚构科里奥利力。风轮的加速度导致以下项：
|
||||
其中，第一项是与 $(x,y,z)$ 坐标系绕 $z$ 轴的角加速度相关联的虚角加速度。第二项是与 $(x,y,z)$ 坐标系绕 $z$ 轴旋转相关联的虚离心力。最后一项是与 $(x,y,z)$ 坐标系绕 $z$ 轴的旋转以及 $cg$ 在弦向的速度相关联的虚科里奥利力。风轮的加速度导致以下项：
|
||||
|
||||
$$
|
||||
F_{\theta,3}\,{=}\,{-}m\ddot{\phi}w_{0}l_{c g}\sin(\overline{{\theta}}+\beta)
|
||||
|
||||
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Reference in New Issue
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