From 21edf9c30f0ace115ff2da96e961a30902e44394 Mon Sep 17 00:00:00 2001 From: yz Date: Tue, 15 Apr 2025 08:46:02 +0800 Subject: [PATCH] 11 --- .../FASTKinematics/auto/FASTKinematics.md | 4 +- .../auto/Kane-Dynamics-Theory-Applications.md | 35 +- ...NAMICS OF MULTIBODY SYSTEMS(SECOND EDITION) (刘延柱 戈新生 潘振宽) (Z-Library).md | 4 +- .../WindTurbine_Kane推导_rigid.ipynb | 263 +++++++- 多体+耦合求解器/sympy_test.ipynb | 16 + .../资料收集/FAST 中耦合叶片模态.md | 1 + 多体+耦合求解器/风机模型.excalidraw.md | 559 ++++++++---------- 工作OKRs/25.2-5 OKR.canvas | 4 +- 工作总结/周报/~$71-郭翼泽.docx | Bin 0 -> 162 bytes 工作总结/周报/周报71-郭翼泽.docx | Bin 20367 -> 20304 bytes 工作总结/周报/周报72-郭翼泽.docx | Bin 0 -> 20329 bytes 生活OKRs/25.2-5 OKR.canvas | 5 +- 补课/多体动力学/框架.canvas | 10 +- 13 files changed, 533 insertions(+), 368 deletions(-) create mode 100644 多体+耦合求解器/sympy_test.ipynb create mode 100644 多体+耦合求解器/资料收集/FAST 中耦合叶片模态.md create mode 100644 工作总结/周报/~$71-郭翼泽.docx create mode 100644 工作总结/周报/周报72-郭翼泽.docx diff --git a/力学书籍/OpenFast/FASTKinematics/auto/FASTKinematics.md b/力学书籍/OpenFast/FASTKinematics/auto/FASTKinematics.md index 52e2327..9a5385a 100644 --- a/力学书籍/OpenFast/FASTKinematics/auto/FASTKinematics.md +++ b/力学书籍/OpenFast/FASTKinematics/auto/FASTKinematics.md @@ -177,7 +177,7 @@ The equations for $^E_{\nu_{r}^{S2}}\left(r\right)$ and $^E_{\nu_{t}^{S2}}\left( Angular Accelerations: -Recall that: $^{E}\pmb{\alpha}^{N_{i}}\left(\ddot{q},\dot{q},q,t\right)\!=\!\left(\sum_{r=l}^{22}^{E}\pmb{\omega}_{r}^{N_{i}}\left(q,t\right)\ddot{q}_{r}\right)\!+\!\left[\sum_{r=l}^{22}\frac{d}{d t}\!\left(^{E}\pmb{\omega}_{r}^{N_{i}}\left(q,t\right)\right)\!\dot{q}_{r}\right]\!+\!\frac{d}{d t}\!\left(^{E}\pmb{\omega}_{t}^{N_{i}}\left(q,t\right)\right)\!\left(^{E}\pmb{\omega}_{p}^{N_{i}}\left(q,t\right)\right),$ for each rigid body $N_{i}$ in the system. Note that the $\frac{d}{d t}\Big(^{E}\omega_{r}^{N_{i}}\Big)$ terms are all vector functions of $\left({\dot{q}},q,t\right)$ and that all of the $\frac{d}{d t}\Big(^{E}\omega_{t}^{N_{i}}\Big)$ terms are zero as will be shown. +Recall that: $^{E}\pmb{\alpha}^{N_{i}}\left(\ddot{q},\dot{q},q,t\right)\!=\!\left(\sum_{r=l}^{22}^{E}\pmb{\omega}_{r}^{N_{i}}\left(q,t\right)\ddot{q}_{r}\right)\!+\!\left[\sum_{r=l}^{22}\frac{d}{d t}\!\left(^{E}\pmb{\omega}_{r}^{N_{i}}\left(q,t\right)\right)\!\dot{q}_{r}\right]\!+\!\frac{d}{d t}\!\left(^{E}\pmb{\omega}_{t}^{N_{i}}\left(q,t\right)\right)\!\left(^{E}\pmb{\omega}_{p}^{N_{i}}\left(q,t\right)\right)$ for each rigid body $N_{i}$ in the system. Note that the $\frac{d}{d t}\Big(^{E}\omega_{r}^{N_{i}}\Big)$ terms are all vector functions of $\left({\dot{q}},q,t\right)$ and that all of the $\frac{d}{d t}\Big(^{E}\omega_{t}^{N_{i}}\Big)$ terms are zero as will be shown. $$ \begin{array}{l}{\displaystyle\frac{d}{d t}\Big(\sp\varepsilon\omega_{r}^{X}\Big)=O}\\ {\displaystyle\frac{d}{d t}\Big(\sp\varepsilon\omega_{{r}}^{X}\Big)=O}\end{array} @@ -200,7 +200,7 @@ The equations for ${\frac{d}{d t}}\Big[^{\,E}\pmb{\omega}_{r}^{{\scriptscriptsty Linear Accelerations: -Recall that: $\varepsilon_{\mathbf{}}\boldsymbol{\alpha}^{X_{i}}\left(\ddot{q},\dot{q},q,t\right)\!=\!\!\left(\sum_{r=l}^{22}\varepsilon_{\nu_{r}^{X_{i}}}\left(q,t\right)\ddot{q}_{r}\right)\!+\!\!\left[\sum_{r=l}^{22}\!\frac{d}{d t}\!\left({^{\varepsilon}\nu_{r}^{X_{i}}}\left(q,t\right)\right)\!\dot{q}_{r}\right]\!+\!\frac{d}{d t}\!\left({^{\varepsilon}\nu_{{^I}}^{X_{i}}}\left(q,t\right)\right)\!\left({^{\varepsilon}\nu_{{^I}}^{X_{i}}}\left(q,t\right)\right)\!+\!\frac{d}{d t}\!\left({^{\varepsilon}\nu_{{^I}}^{X_{i}}}\left(q,t\right)\right)\!+\!{^{\varepsilon}\nu_{{^I}}^{X_{i}}}\left(q,t\right),$ for each point $X_{i}$ in the system. Note that the ${\frac{d}{d t}}{\Big(}^{E}\nu_{r}^{X_{i}}{\Big)}$ terms are all vector functions of $\left({\dot{q}},q,t\right)$ and that all of the ${\frac{d}{d t}}{\Big(}^{E}\nu_{t}^{X_{i}}{\Big)}$ terms are zero as will be shown. +Recall that: ${}^E{\alpha}^{X_{i}}\left(\ddot{q},\dot{q},q,t\right)\!=\!\!\left(\sum_{r=1}^{22}{}^E{V_{r}^{X_{i}}}\left(q,t\right)\ddot{q}_{r}\right)\!+\!\!\left[\sum_{r=1}^{22}\!\frac{d}{d t}\!\left({}^E{V_{r}^{X_{i}}}\left(q,t\right)\right)\!\dot{q}_{r}\right]\!+\!\frac{d}{d t}\!\left({}^EV_{r}^{X_{i}}\left(q,t\right)\right)$ for each point $X_{i}$ in the system. Note that the ${\frac{d}{d t}}{\Big(}^{E}\nu_{r}^{X_{i}}{\Big)}$ terms are all vector functions of $\left({\dot{q}},q,t\right)$ and that all of the ${\frac{d}{d t}}{\Big(}^{E}\nu_{t}^{X_{i}}{\Big)}$ terms are zero as will be shown. $$ \begin{array}{l}{\displaystyle\frac{d}{d t}\Big(\sp\varepsilon\pmb{\nu}_{r}^{z}\Big)=O}\\ {\displaystyle\frac{d}{d t}\Big(\sp\varepsilon\pmb{\nu}_{{\pmb\nu}}^{z}\Big)=O}\end{array} diff --git a/力学书籍/力学/Kane-Dynamics-Theory-Applications/auto/Kane-Dynamics-Theory-Applications.md b/力学书籍/力学/Kane-Dynamics-Theory-Applications/auto/Kane-Dynamics-Theory-Applications.md index 7a74bb9..ae8c24e 100644 --- a/力学书籍/力学/Kane-Dynamics-Theory-Applications/auto/Kane-Dynamics-Theory-Applications.md +++ b/力学书籍/力学/Kane-Dynamics-Theory-Applications/auto/Kane-Dynamics-Theory-Applications.md @@ -1088,35 +1088,38 @@ $$ # 2.5 ANGULAR ACCELERATION -The angular acceleration Aa of a rigid body B in a reference frame A is defined as the first time-derivative in A of the angular velocity of B in A (see Sec. 2.1): +The angular acceleration ${}^{A}{\alpha}^{B}$ of a rigid body B in a reference frame A is defined as the first time-derivative in A of the angular velocity of B in A (see Sec. 2.1): +刚体的角加速度 ${}^{A}{\alpha}^{B}$ 在参考系 A 中定义为 A 中对 B 在 A 中的角速度的一阶时间导数（见第 2.1 节）： + $$ -A_{\mathfrak{A}}{}^{B}\triangleq\frac{{}^{A}d^{A}\mathfrak{A}^{B}}{d t} +{}^{A}{\alpha}^{B}\triangleq\frac{{}^{A}d^{A}\omega^{B}}{d t} $$ -Since the first time-derivatives of $\mathbf{\mathit{A}}_{\mathbf{\Theta}\mathbf{\tilde{0}}}\mathbf{\mathit{B}}$ in $\pmb{A}$ andin $B$ are equal toeach other, as becomes evident when one replaces v in Eq. (2.3.1) with 4o", Eq. (1) implies that +Since the first time-derivatives of ${}^{A}\omega^{B}$ in $\pmb{A}$ and in $B$ are equal to each other, as becomes evident when one replaces v in Eq. (2.3.1) with 4o", Eq. (1) implies that +由于 ${}^{A}\omega^{B}$ 在 $A$ 和 $B$ 处的首次时间导数彼此相等，正如在方程 (2.3.1) 中将 v 替换为 4o" 时显而易见，则方程 (1) 意味着 +$$ +{}^{A}{\alpha}^{B}\triangleq\frac{{}^{B}d^{A}\omega^{B}}{d t} +$$ + +which furnishes a convenient way to find ${}^{A}{\alpha}^{B}$ when ${}^{A}\omega^{B}$ has been expressed in terms of components parallel to unit vectors fixed in $\boldsymbol{B}$ +这为寻找${}^{A}{\alpha}^{B}$提供了一种便捷的方法，当 ${}^{A}\omega^{B}$ 已经用平行于固定在 $\boldsymbol{B}$ 中的单位向量的组件表示时。 + +If $A_{1},...,A_{n}$ are $n$ auxiliary reference frames, ${}^{A}{\alpha}^{B}$ is not, in general, equal to the sum ${}^{A}{\alpha}^{A_{i}} + {}^{A_{1}}{\alpha}^{A_{2}} + ... +{}^{A_{n}}{\alpha}^{B}$ . Thus, Eq. (2.4.1) does not, in general, have an angular acceleration counterpart. + +The angular velocity of $\boldsymbol{B}$ in $A$ can always be expressed as ${}^{A}\mathbf{\omega}^{B}=\omega\mathbf{k}_{\omega}$ , where $\mathbf{k}_{\omega}$ is a unit vector parallel to ${}^{A}\mathbf{\omega}^{B}$ ; similarly ${}^{A}{\alpha}^{B}$ can always be expressed as ${}^{A}{\alpha}^{B}=\alpha\mathbf{k}_{\alpha}$ , where $\mathbf{k}_{\alpha}$ is a unit vector parallel to ${}^{A}{\alpha}^{B}$ In general, $\mathbf{k}_{\omega}$ differs from $\mathbf{k}_{\alpha}$ ， and $\alpha\neq d\omega/d t$ . But when $\boldsymbol{B}$ has a simple angular velocity in $A$ (see Sec. 2.2), and ${}^{A}\mathbf{\omega}^{B}$ is expressed as in Eq. (2.2.1), then $$ -A_{\mathfrak{A}}B=\frac{B_{d}A_{\mathfrak{A}}^{B}}{d t} +{}^{A}{\alpha}^{B}=\alpha\mathbf{k} $$ -which furnishes a convenient way to find AaB when Ao3 has been expressed in terms of components parallel to unit vectors fixed in $\boldsymbol{B}$ - -If $A_{1},...,A_{n}$ are $n$ auxiliary reference frames, $A_{\alpha}B$ is not, in general, equal to the sum $\mathbf{\dot{\alpha}}^{A}\mathbf{\alpha}^{A_{1}}+\mathbf{\alpha}^{A_{1}}\mathbf{\alpha}^{A_{2}}+\mathbf{\beta}^{\dots}+\mathbf{\alpha}^{A_{n}}\mathbf{\alpha}^{B}$ . Thus, Eq. (2.4.1) does not, in general, have an angular acceleration counterpart. - -The angular velocity of $\boldsymbol{B}$ in $A$ can always be expressed as ${}^{A}\mathbf{\omega}\mathbf{\omega}^{B}=\omega\mathbf{k}_{\omega}$ , where $\mathbf{k}_{\omega}$ is a unit vector parallel to $\mathbf{\mathit{A}_{G D}}\mathbf{\mathit{B}}$ ; similarly $A_{\widetilde{\mathbf{z}}}B$ can always be expressed as $^{A}\pmb{\alpha}^{B}=\alpha\mathbf{k}_{\alpha}$ , where $\mathbf{k}_{\alpha}$ is a unit vector parall to $A_{\pmb{\alpha}}B$ In general, $\mathbf{k}_{\omega}$ differs from $\mathbf{k}_{\alpha}$ ， and $\alpha\neq d\omega/d t$ . But when $\boldsymbol{B}$ has a simple angular velocity in $A$ (see Sec. 2.2), and $\mathbf{\Pi}^{A}\mathbf{\Pi}_{\mathbf{G}\mathbf{\tilde{D}}}\mathbf{\scriptscriptstyle{B}}$ is expressed as in Eq. (2.2.1), then - -$$ -A_{\alpha}B_{\mathrm{\Phi}}={\mathfrak{X}}\mathbf{k} -$$ - -where $\pmb{\alpha}_{\ast}$ called a scalar angular acceleration, is given by +where $\alpha$ called a scalar angular acceleration, is given by $$ \alpha={\frac{d\omega}{d t}} $$ -Example Referring to the example in Sec. 2.4 and to Fig. 2.4.1, one can find an expression for the angular acceleration of the cone $\pmb{B}$ inreferenceframe $\pmb{A}$ asfollows: +Example Referring to the example in Sec. 2.4 and to Fig. 2.4.1, one can find an expression for the angular acceleration of the cone $\pmb{B}$ in reference frame $\pmb{A}$ as follows: $$ {\begin{array}{r l}&{{\mathbf{\nabla}}_{a{\pmb{\alpha}}^{B}}={\cfrac{a_{d}}{d t}}({\dot{q}}_{1}{\mathbf{k}}_{2}+{\dot{q}}_{2}{\mathbf{k}}_{7}+{\dot{q}}_{3}{\mathbf{k}}_{3})}\\ &{\qquad={\ddot{q}}_{1}{\mathbf{k}}_{2}+{\dot{q}}_{1}{\cfrac{a_{d}{\mathbf{k}}_{2}}{d t}}+{\ddot{q}}_{2}{\mathbf{k}}_{7}+{\dot{q}}_{2}{\cfrac{a_{d}{\mathbf{k}}_{7}}{d t}}+{\ddot{q}}_{3}{\mathbf{k}}_{3}+{\dot{q}}_{3}{\cfrac{a_{d}{\mathbf{k}}_{3}}{d t}}}\end{array}}\,,{\mathbf{\dot{\xi}}}_{{\begin{array}{r}{{\dot{\mathbf{\xi}}}_{{\mathrm{~f~i~s~}}^{A}}\end{array}}}}\,,{\mathbf{\dot{\xi}}}_{{\begin{array}{r}{{\dot{\mathbf{\xi}}}_{{\mathrm{~f~i~s~}}^{A}}\end{array}}}}\,, diff --git a/力学书籍/力学/多体系统动力学（第2版）＝DYNAMICS OF MULTIBODY SYSTEMS(SECOND EDITION) (刘延柱 戈新生 潘振宽) (Z-Library)/auto/多体系统动力学（第2版）＝DYNAMICS OF MULTIBODY SYSTEMS(SECOND EDITION) (刘延柱 戈新生 潘振宽) (Z-Library).md b/力学书籍/力学/多体系统动力学（第2版）＝DYNAMICS OF MULTIBODY SYSTEMS(SECOND EDITION) (刘延柱 戈新生 潘振宽) (Z-Library)/auto/多体系统动力学（第2版）＝DYNAMICS OF MULTIBODY SYSTEMS(SECOND EDITION) (刘延柱 戈新生 潘振宽) (Z-Library).md index 794e7f5..3c3ebce 100644 --- a/力学书籍/力学/多体系统动力学（第2版）＝DYNAMICS OF MULTIBODY SYSTEMS(SECOND EDITION) (刘延柱 戈新生 潘振宽) (Z-Library)/auto/多体系统动力学（第2版）＝DYNAMICS OF MULTIBODY SYSTEMS(SECOND EDITION) (刘延柱 戈新生 潘振宽) (Z-Library).md +++ b/力学书籍/力学/多体系统动力学（第2版）＝DYNAMICS OF MULTIBODY SYSTEMS(SECOND EDITION) (刘延柱 戈新生 潘振宽) (Z-Library)/auto/多体系统动力学（第2版）＝DYNAMICS OF MULTIBODY SYSTEMS(SECOND EDITION) (刘延柱 戈新生 潘振宽) (Z-Library).md @@ -6554,7 +6554,7 @@ $$ F^{\,^{*\,(r)}}\;=\;F^{\,^{*}}\,\cdot\,\pmb{v}_{\!_{0}}^{(\,r\,)}\;+\;M^{\,^{*}}\,\cdot\,\pmb{\omega}^{(\,r\,)} $$ -其中， $\pmb{v}_{0}^{(r)}$ 及 $\pmb{\omega}^{(r)}$ 为刚体上任意选定的参考点 $o$ 的第 $r$ 偏速度及刚体的第 $r$ 偏角速度，F和M为刚体上作用的外力主动力主矢及对O点的主矩，F\*及M\*为刚体的惯性力主矢及对 $o$ 点的主矩。设 $\pmb{\rho}_{\nu}$ 为刚体中任意点 $P_{\nu}$ 相对 $o$ 点的矢径，$\boldsymbol{P}_{\nu}$ 处作用的主动力和惯性力以小写的 $\boldsymbol{f}_{\nu}\,,\boldsymbol{f}_{\nu}^{*}$ 表示，则有 +其中， $\pmb{v}_{0}^{(r)}$ 及 $\pmb{\omega}^{(r)}$ 为刚体上任意选定的参考点 $o$ 的第 $r$ 偏速度及刚体的第 $r$ 偏角速度，$F$和$M$为刚体上作用的外力主动力主矢及对O点的主矩，$F^*$及$M^*$为刚体的惯性力主矢及对 $o$ 点的主矩。设 $\pmb{\rho}_{\nu}$ 为刚体中任意点 $P_{\nu}$ 相对 $o$ 点的矢径，$\boldsymbol{P}_{\nu}$ 处作用的主动力和惯性力以小写的 $\boldsymbol{f}_{\nu}\,,\boldsymbol{f}_{\nu}^{*}$ 表示，则有 $$ \begin{array}{r c l}{{\pmb F}\ =}&{{\displaystyle\sum_{\nu}{\pmb f}_{\nu}\,,}}&{{\pmb M}\ =\ \sum_{\nu}{\pmb\rho}_{\nu}\ \times{\pmb f}_{\nu}}\\ {{\pmb F}^{\star}\ =}&{{\displaystyle\sum_{\nu}{\pmb f}_{\nu}^{\star}\ =-\ \sum_{\nu}{\pmb m}_{\nu}\,\ddot{\pmb r}_{\nu}}}&{{=-\ \dot{\pmb p}\,.}}\end{array} @@ -6746,7 +6746,7 @@ $$ (6.3.18) -可见，对于完整系统，凯恩方法中的广义主动力 ${\boldsymbol{F}}^{(r)}$ 等同于拉格朗日方程中的广义力 $Q_{r}$ D +可见，对于完整系统，凯恩方法中的广义主动力 ${\boldsymbol{F}}^{(r)}$ 等同于拉格朗日方程中的广义力 $Q_{r}$ 。 例6.2设例6.1所讨论系统中刚体上作用的主动力主矢及对 $o$ 点的主矩为 $F$ 及 $M$ ,其作用线均在运动平面内，弹簧变形前的长度为 $l$ ，刚度为 $K$ ，刚体 $B$ 的质量及相对 $\boldsymbol{e}_{3}$ 的惯量矩为 $m$ 及 $J$ ，质点 $P$ 的质量为 $m_{p}$ 。试用凯恩方法导出此系统的动力学方程。 diff --git a/多体+耦合求解器/WindTurbine_Kane推导_rigid.ipynb b/多体+耦合求解器/WindTurbine_Kane推导_rigid.ipynb index 8407987..6f0d61a 100644 --- a/多体+耦合求解器/WindTurbine_Kane推导_rigid.ipynb +++ b/多体+耦合求解器/WindTurbine_Kane推导_rigid.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "code", - "execution_count": 120, + "execution_count": 72, "metadata": {}, "outputs": [], "source": [ @@ -13,7 +13,7 @@ }, { "cell_type": "code", - "execution_count": 121, + "execution_count": 73, "metadata": {}, "outputs": [], "source": [ @@ -33,7 +33,7 @@ }, { "cell_type": "code", - "execution_count": 122, + "execution_count": 74, "metadata": {}, "outputs": [], "source": [ @@ -61,7 +61,7 @@ }, { "cell_type": "code", - "execution_count": 123, + "execution_count": 75, "metadata": {}, "outputs": [ { @@ -73,7 +73,7 @@ "0" ] }, - "execution_count": 123, + "execution_count": 75, "metadata": {}, "output_type": "execute_result" } @@ -92,7 +92,7 @@ }, { "cell_type": "code", - "execution_count": 124, + "execution_count": 76, "metadata": {}, "outputs": [ { @@ -104,7 +104,7 @@ "cos(q_yaw) a_x + -sin(q_yaw) a_z" ] }, - "execution_count": 124, + "execution_count": 76, "metadata": {}, "output_type": "execute_result" } @@ -129,7 +129,7 @@ }, { "cell_type": "code", - "execution_count": 125, + "execution_count": 77, "metadata": {}, "outputs": [ { @@ -143,7 +143,7 @@ "↪ _overhang⋅sin(q_yaw)⋅cos(θₜᵢₗₜ) a_z" ] }, - "execution_count": 125, + "execution_count": 77, "metadata": {}, "output_type": "execute_result" } @@ -159,7 +159,7 @@ }, { "cell_type": "code", - "execution_count": 126, + "execution_count": 78, "metadata": {}, "outputs": [], "source": [ @@ -182,7 +182,7 @@ }, { "cell_type": "code", - "execution_count": 127, + "execution_count": 79, "metadata": {}, "outputs": [ { @@ -196,7 +196,7 @@ "↪ w⋅cos(θₜᵢₗₜ) c_z, u_yaw a_y, u_yaw a_y, (u_drtr + u_geaz) c_x + u_yaw a_y)" ] }, - "execution_count": 127, + "execution_count": 79, "metadata": {}, "output_type": "execute_result" } @@ -217,7 +217,7 @@ }, { "cell_type": "code", - "execution_count": 128, + "execution_count": 80, "metadata": {}, "outputs": [ { @@ -242,7 +242,7 @@ "↪ _yaw⋅cos(θₜᵢₗₜ) c_z + u_ẏaw a_y⎠" ] }, - "execution_count": 128, + "execution_count": 80, "metadata": {}, "output_type": "execute_result" } @@ -260,7 +260,7 @@ }, { "cell_type": "code", - "execution_count": 129, + "execution_count": 81, "metadata": {}, "outputs": [ { @@ -272,7 +272,7 @@ "(d_y, 0, 0)" ] }, - "execution_count": 129, + "execution_count": 81, "metadata": {}, "output_type": "execute_result" } @@ -287,7 +287,7 @@ }, { "cell_type": "code", - "execution_count": 130, + "execution_count": 82, "metadata": {}, "outputs": [ { @@ -299,7 +299,7 @@ "((u_drtr + u_geaz) c_x + u_yaw a_y, sin(θₜᵢₗₜ) c_x + cos(θₜᵢₗₜ) c_y, c_x, c_x)" ] }, - "execution_count": 130, + "execution_count": 82, "metadata": {}, "output_type": "execute_result" } @@ -314,7 +314,7 @@ }, { "cell_type": "code", - "execution_count": 131, + "execution_count": 83, "metadata": {}, "outputs": [ { @@ -326,22 +326,22 @@ "(Nx d_x + Ny d_y + Nz d_z, Nz d_x + -Nx d_z, Nz d_x + -Nx d_z, 0, 0)" ] }, - "execution_count": 131, + "execution_count": 83, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# U点\n", - "v_U_1 = U.vel(A).diff(u_yaw, A).express(D)\n", - "v_U_2 = U.vel(A).diff(u_drtr, A).express(D)\n", - "v_U_3 = U.vel(A).diff(u_geaz, A).express(D)\n", + "v_U_1 = U.vel(A).diff(u_yaw, A)\n", + "v_U_2 = U.vel(A).diff(u_drtr, A)\n", + "v_U_3 = U.vel(A).diff(u_geaz, A)\n", "U.pos_from(O).express(D), w_D_1.cross(U.pos_from(O).express(D)), v_U_1, v_U_2, v_U_3" ] }, { "cell_type": "code", - "execution_count": 132, + "execution_count": 84, "metadata": {}, "outputs": [ { @@ -353,7 +353,7 @@ "(Iₓ d_x + I_y d_y + I_z d_z, I_z d_x + -Iₓ d_z, I_z d_x + -Iₓ d_z, 0, 0)" ] }, - "execution_count": 132, + "execution_count": 84, "metadata": {}, "output_type": "execute_result" } @@ -368,32 +368,231 @@ }, { "cell_type": "code", - "execution_count": 133, + "execution_count": 85, "metadata": {}, "outputs": [ { "data": { "text/latex": [ - "$\\displaystyle \\left( L_{overhang} \\cos{\\left(\\theta_{tilt} \\right)}\\mathbf{\\hat{d}_x} + (L_{overhang} \\sin{\\left(\\theta_{tilt} \\right)} + L_{t2s})\\mathbf{\\hat{d}_y}, \\ - L_{overhang} \\cos{\\left(\\theta_{tilt} \\right)}\\mathbf{\\hat{d}_z}, \\ - L_{overhang} \\cos{\\left(\\theta_{tilt} \\right)}\\mathbf{\\hat{d}_z}, \\ 0, \\ 0\\right)$" + "$\\displaystyle \\left( L_{overhang} \\cos{\\left(\\theta_{tilt} \\right)}\\mathbf{\\hat{d}_x} + (L_{overhang} \\sin{\\left(\\theta_{tilt} \\right)} + L_{t2s})\\mathbf{\\hat{d}_y}, \\ - L_{overhang} \\cos{\\left(\\theta_{tilt} \\right)}\\mathbf{\\hat{d}_z}, \\ - L_{overhang} \\cos{\\left(\\theta_{tilt} \\right)}\\mathbf{\\hat{c}_z}, \\ 0, \\ 0\\right)$" ], "text/plain": [ "(L_overhang⋅cos(θₜᵢₗₜ) d_x + (L_overhang⋅sin(θₜᵢₗₜ) + Lₜ₂ₛ) d_y, -L_overhang⋅c ↪\n", "\n", - "↪ os(θₜᵢₗₜ) d_z, -L_overhang⋅cos(θₜᵢₗₜ) d_z, 0, 0)" + "↪ os(θₜᵢₗₜ) d_z, -L_overhang⋅cos(θₜᵢₗₜ) c_z, 0, 0)" ] }, - "execution_count": 133, + "execution_count": 85, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# P点\n", - "v_P_1 = P.vel(A).diff(u_yaw, A).express(D)\n", - "v_P_2 = P.vel(A).diff(u_drtr, A).express(D)\n", - "v_P_3 = P.vel(A).diff(u_geaz, A).express(D)\n", + "v_P_1 = P.vel(A).diff(u_yaw, A)\n", + "v_P_2 = P.vel(A).diff(u_drtr, A)\n", + "v_P_3 = P.vel(A).diff(u_geaz, A)\n", "P.pos_from(O).express(D), w_D_1.cross(P.pos_from(O).express(D)), v_P_1, v_P_2, v_P_3" ] + }, + { + "cell_type": "code", + "execution_count": 86, + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle \\left[\\begin{matrix}L_{overhang} g m_{hub} \\cos{\\left(\\theta_{tilt} \\right)} \\cos{\\left(q_{drtr} + q_{geaz} \\right)} + Nx g m_{nac}\\\\0\\\\0\\end{matrix}\\right]$" + ], + "text/plain": [ + "⎡L_overhang⋅g⋅m_hub⋅cos(θₜᵢₗₜ)⋅cos(q_drtr + q_geaz) + Nx⋅g⋅m_nac⎤\n", + "⎢ ⎥\n", + "⎢ 0 ⎥\n", + "⎢ ⎥\n", + "⎣ 0 ⎦" + ] + }, + "execution_count": 86, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# 主动力\n", + "# yaw\n", + "F_yaw = sm.Function('q_yaw, u_yaw')\n", + "# 考虑 机舱重力，轮毂重力\n", + "m_nac, g, m_hub = sm.symbols(\"m_nac, g, m_hub\")\n", + "R_nac = -m_nac * g * D.z\n", + "R_hub = -m_hub * g * G.z\n", + "\n", + "F1 = v_U_1.dot(R_nac) + v_P_1.dot(R_hub)\n", + "F2 = v_U_2.dot(R_nac) + v_P_2.dot(R_hub)\n", + "F3 = v_U_3.dot(R_nac) + v_P_3.dot(R_hub)\n", + "\n", + "Fr = sm.Matrix([F1, F2, F3])\n", + "Fr" + ] + }, + { + "cell_type": "code", + "execution_count": 93, + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle \\left[\\begin{matrix}- L_{overhang}^{2} m_{hub} \\cos^{2}{\\left(\\theta_{tilt} \\right)} \\dot{u}_{yaw} + Nx m_{nac} \\left(- Nx \\dot{u}_{yaw} - Nz u_{yaw}^{2}\\right) - Nz m_{nac} \\left(- Nx u_{yaw}^{2} + Nz \\dot{u}_{yaw}\\right) - \\left(Nac_{YIner} - m_{nac} \\left(Nx^{2} + Ny^{2}\\right)\\right) \\dot{u}_{yaw} + \\left(- \\left(Hub_{Iner} - hub_{cm}^{2} m_{hub}\\right) \\left(- \\left(u_{drtr} + u_{geaz}\\right) u_{yaw} \\sin{\\left(q_{drtr} + q_{geaz} \\right)} \\cos{\\left(\\theta_{tilt} \\right)} + \\cos{\\left(\\theta_{tilt} \\right)} \\cos{\\left(q_{drtr} + q_{geaz} \\right)} \\dot{u}_{yaw}\\right) + \\left(Hub_{Iner} - hub_{cm}^{2} m_{hub}\\right) \\left(u_{drtr} + u_{geaz} + u_{yaw} \\sin{\\left(\\theta_{tilt} \\right)}\\right) u_{yaw} \\sin{\\left(q_{drtr} + q_{geaz} \\right)} \\cos{\\left(\\theta_{tilt} \\right)}\\right) \\cos{\\left(\\theta_{tilt} \\right)} \\cos{\\left(q_{drtr} + q_{geaz} \\right)} + \\left(- \\left(Hub_{Iner} - hub_{cm}^{2} m_{hub}\\right) \\left(\\sin{\\left(\\theta_{tilt} \\right)} \\dot{u}_{yaw} + \\dot{u}_{drtr} + \\dot{u}_{geaz}\\right) - \\left(Hub_{Iner} - hub_{cm}^{2} m_{hub}\\right) u_{yaw}^{2} \\sin{\\left(q_{drtr} + q_{geaz} \\right)} \\cos^{2}{\\left(\\theta_{tilt} \\right)} \\cos{\\left(q_{drtr} + q_{geaz} \\right)}\\right) \\sin{\\left(\\theta_{tilt} \\right)}\\\\- \\left(Hub_{Iner} - hub_{cm}^{2} m_{hub}\\right) \\left(\\sin{\\left(\\theta_{tilt} \\right)} \\dot{u}_{yaw} + \\dot{u}_{drtr} + \\dot{u}_{geaz}\\right) - \\left(Hub_{Iner} - hub_{cm}^{2} m_{hub}\\right) u_{yaw}^{2} \\sin{\\left(q_{drtr} + q_{geaz} \\right)} \\cos^{2}{\\left(\\theta_{tilt} \\right)} \\cos{\\left(q_{drtr} + q_{geaz} \\right)}\\\\- \\left(Hub_{Iner} - hub_{cm}^{2} m_{hub}\\right) \\left(\\sin{\\left(\\theta_{tilt} \\right)} \\dot{u}_{yaw} + \\dot{u}_{drtr} + \\dot{u}_{geaz}\\right) - \\left(Hub_{Iner} - hub_{cm}^{2} m_{hub}\\right) u_{yaw}^{2} \\sin{\\left(q_{drtr} + q_{geaz} \\right)} \\cos^{2}{\\left(\\theta_{tilt} \\right)} \\cos{\\left(q_{drtr} + q_{geaz} \\right)}\\end{matrix}\\right]$" + ], + "text/plain": [ + "⎡ 2 2 ⎛ 2⎞ ↪\n", + "⎢- L_overhang ⋅m_hub⋅cos (θₜᵢₗₜ)⋅u_ẏaw + Nx⋅m_nac⋅⎝-Nx⋅u_ẏaw - Nz⋅u_yaw ⎠ - Nz ↪\n", + "⎢ ↪\n", + "⎢ ↪\n", + "⎢ ↪\n", + "⎢ ↪\n", + "⎢ ↪\n", + "⎣ ↪\n", + "\n", + "↪ ⎛ 2 ⎞ ⎛ ⎛ 2 2⎞⎞ ⎛ ↪\n", + "↪ ⋅m_nac⋅⎝- Nx⋅u_yaw + Nz⋅u_ẏaw⎠ - ⎝Nac_YIner - m_nac⋅⎝Nx + Ny ⎠⎠⋅u_ẏaw + ⎝- ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "\n", + "↪ ⎛ 2 ⎞ ↪\n", + "↪ ⎝Hub_Iner - hub_cm ⋅m_hub⎠⋅(-(u_drtr + u_geaz)⋅u_yaw⋅sin(q_drtr + q_geaz)⋅c ↪\n", + "↪ ↪\n", + "↪ ⎛ ↪\n", + "↪ - ⎝Hub_Iner - ↪\n", + "↪ ↪\n", + "↪ ⎛ ↪\n", + "↪ - ⎝Hub_Iner - ↪\n", + "\n", + "↪ ⎛ 2 ↪\n", + "↪ os(θₜᵢₗₜ) + cos(θₜᵢₗₜ)⋅cos(q_drtr + q_geaz)⋅u_ẏaw) + ⎝Hub_Iner - hub_cm ⋅m_h ↪\n", + "↪ ↪\n", + "↪ 2 ⎞ ⎛ 2 ↪\n", + "↪ hub_cm ⋅m_hub⎠⋅(sin(θₜᵢₗₜ)⋅u_ẏaw + u_dṙtr + u_gėaz) - ⎝Hub_Iner - hub_cm ⋅m ↪\n", + "↪ ↪\n", + "↪ 2 ⎞ ⎛ 2 ↪\n", + "↪ hub_cm ⋅m_hub⎠⋅(sin(θₜᵢₗₜ)⋅u_ẏaw + u_dṙtr + u_gėaz) - ⎝Hub_Iner - hub_cm ⋅m ↪\n", + "\n", + "↪ ⎞ ↪\n", + "↪ ub⎠⋅(u_drtr + u_geaz + u_yaw⋅sin(θₜᵢₗₜ))⋅u_yaw⋅sin(q_drtr + q_geaz)⋅cos(θₜᵢₗ ↪\n", + "↪ ↪\n", + "↪ ⎞ 2 2 ↪\n", + "↪ _hub⎠⋅u_yaw ⋅sin(q_drtr + q_geaz)⋅cos (θₜᵢₗₜ)⋅cos(q_drtr + q_geaz) ↪\n", + "↪ ↪\n", + "↪ ⎞ 2 2 ↪\n", + "↪ _hub⎠⋅u_yaw ⋅sin(q_drtr + q_geaz)⋅cos (θₜᵢₗₜ)⋅cos(q_drtr + q_geaz) ↪\n", + "\n", + "↪ ⎞ ⎛ ⎛ 2 ⎞ ↪\n", + "↪ ₜ)⎠⋅cos(θₜᵢₗₜ)⋅cos(q_drtr + q_geaz) + ⎝- ⎝Hub_Iner - hub_cm ⋅m_hub⎠⋅(sin(θₜᵢ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "\n", + "↪ ⎛ 2 ⎞ 2 ↪\n", + "↪ ₗₜ)⋅u_ẏaw + u_dṙtr + u_gėaz) - ⎝Hub_Iner - hub_cm ⋅m_hub⎠⋅u_yaw ⋅sin(q_drtr ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "\n", + "↪ 2 ⎞ ⎤\n", + "↪ + q_geaz)⋅cos (θₜᵢₗₜ)⋅cos(q_drtr + q_geaz)⎠⋅sin(θₜᵢₗₜ)⎥\n", + "↪ ⎥\n", + "↪ ⎥\n", + "↪ ⎥\n", + "↪ ⎥\n", + "↪ ⎥\n", + "↪ ⎦" + ] + }, + "execution_count": 93, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# 惯性力\n", + "\n", + "# 机舱惯性\n", + "Nac_YIner = sm.symbols(\"Nac_YIner\")\n", + "Inertia_nac = (Nac_YIner - m_nac * (N_x**2 + N_y**2)) * me.outer(D.y, D.y)\n", + "Inertia_nac\n", + "\n", + "# hub惯性\n", + "Hub_Iner, hub_cm = sm.symbols(\"Hub_Iner, hub_cm\")\n", + "Inertia_hub = (Hub_Iner - m_hub * hub_cm**2) * me.outer(G.x, G.x) + (Hub_Iner - m_hub * hub_cm**2) * me.outer(G.y, G.y)\n", + "Inertia_hub\n", + "\n", + "T_nac = -(D.ang_acc_in(A).dot(Inertia_nac) + me.cross(D.ang_vel_in(A), Inertia_nac).dot(D.ang_vel_in(A)))\n", + "T_hub = -(G.ang_acc_in(A).dot(Inertia_hub) + me.cross(G.ang_vel_in(A), Inertia_hub).dot(G.ang_vel_in(A)))\n", + "\n", + "F1s = v_U_1.dot(-m_nac * U.acc(A)) + v_P_1.dot(-m_hub * P.acc(A)) + w_D_1.dot(T_nac) + w_C_1.dot(T_hub)\n", + "F2s = v_U_2.dot(-m_nac * U.acc(A)) + v_P_2.dot(-m_hub * P.acc(A)) + w_D_2.dot(T_nac) + w_C_2.dot(T_hub)\n", + "F3s = v_U_3.dot(-m_nac * U.acc(A)) + v_P_3.dot(-m_hub * P.acc(A)) + w_D_3.dot(T_nac) + w_C_3.dot(T_hub)\n", + "\n", + "Frs = sm.Matrix([F1s, F2s, F3s])\n", + "Frs" + ] + }, + { + "cell_type": "code", + "execution_count": 94, + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle \\left\\{q_{drtr}, q_{geaz}\\right\\}$" + ], + "text/plain": [ + "{q_drtr, q_geaz}" + ] + }, + "execution_count": 94, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "me.find_dynamicsymbols(Fr)" + ] + }, + { + "cell_type": "code", + "execution_count": 95, + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle \\left\\{q_{drtr}, q_{geaz}, u_{drtr}, u_{geaz}, u_{yaw}, \\dot{u}_{drtr}, \\dot{u}_{geaz}, \\dot{u}_{yaw}\\right\\}$" + ], + "text/plain": [ + "{q_drtr, q_geaz, u_drtr, u_geaz, u_yaw, u_dṙtr, u_gėaz, u_ẏaw}" + ] + }, + "execution_count": 95, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "me.find_dynamicsymbols(Frs)" + ] } ], "metadata": { diff --git a/多体+耦合求解器/sympy_test.ipynb b/多体+耦合求解器/sympy_test.ipynb new file mode 100644 index 0000000..d263c40 --- /dev/null +++ b/多体+耦合求解器/sympy_test.ipynb @@ -0,0 +1,16 @@ +{ + "cells": [], + "metadata": { + "kernelspec": { + "display_name": "MinerU", + "language": "python", + "name": "python3" + }, + "language_info": { + "name": "python", + "version": "3.10.16" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/多体+耦合求解器/资料收集/FAST 中耦合叶片模态.md b/多体+耦合求解器/资料收集/FAST 中耦合叶片模态.md new file mode 100644 index 0000000..0f143f6 --- /dev/null +++ b/多体+耦合求解器/资料收集/FAST 中耦合叶片模态.md @@ -0,0 +1 @@ +https://forums.nrel.gov/t/coupled-blade-modes-in-fast/314/9 \ No newline at end of file diff --git a/多体+耦合求解器/风机模型.excalidraw.md b/多体+耦合求解器/风机模型.excalidraw.md index 28eae37..8e9c2be 100644 --- a/多体+耦合求解器/风机模型.excalidraw.md +++ b/多体+耦合求解器/风机模型.excalidraw.md @@ -10,6 +10,9 @@ tags: [excalidraw] # Excalidraw Data ## Text Elements +Q1： yaw 主动力为何如此计算？ +由控制计算，作为一个外力直接施加 ^enHSE5Ed + ## Embedded Files c0166535889251fc00499757c5d32377c8fd6767: [[Pasted Image 20250120103502_252.png]] @@ -1562,560 +1565,496 @@ lqlKnKa84GMCXbT+alNIP8vm8vGppA7SwMm9iK3cTB0l8I66tWWqkFldRPZbawWOkBHQxq1NaoCa48DR QNLM3k/Vcyg5RS3SmsPyCIgDYi8yllj3mkVXBF8Sq0kno/MNGf5mtNqaZ3o95pdEj/JFGWUpSXBoq1p+QxfBGkbngUcjrUFpkxS7Imi+O06WjNemomzdZWkVNMCSd10xoYIJ19vaQe3DacDsakB1XS75RRJNdaS5kPLp9xs5ulRJOPqWyoYCwLUscAguWNPUS92PIEmKQ1fzWULT7GPgEv0iOxVqgzHSUUnU4FryXpo9zhpNTXwcZEDUx0oDwtLK -CKNKb/U12J/9SNynU8M3/kEMf7c89dFMnleL5FKJQsUhcljiqCkRRFOGMcW2WFJT/uEQOJWaYtE4Oe4e5JuH48EFvqrwXYBnUT9aSN4KgXuAnCla6x1+q5MNNEac6018xtvsQzGseJw0c9PRIu1TccW6xmK9yZ7ohMx4kAv/b5c3uiZYIaYCGV5POwhEEzwPoSZIR5EheBEUsho6HXlC0pM848yCEMEpkGvpCROybsILzMyVOsRlCQJid49EQmis 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+1,10 @@ { "nodes":[ {"id":"b698e88ca5fb9c51","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":-96,"y":80,"width":456,"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\nP1 多体原理学习 YouTube课程 018\nP1 气动模块联合调试，跑通 no\nP1 稳态工况多体动力学求解方法\nP1 使用python搭建风电机组多体模型\nP1 叶片模态叠加法算法\n\n","x":-620,"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\nP1 多体原理学习 YouTube课程 018\nP1 气动模块联合调试，跑通 no\nP1 稳态工况多体动力学求解方法\nP1 使用python搭建风电机组多体模型 刚性部件主动力、惯性力计算\nP1 柔性部件 叶片、塔架主动力惯性力算法\n\n","x":-620,"y":-307,"width":450,"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 （6.8/10）\n\n关键结果：对标Bladed模块完成 （7.2/10）\n\n关键结果：风机多体动力学文献调研情况完成 （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":"1ebeabaf5c73ddbb","x":-440,"y":520,"width":440,"height":340,"type":"text","text":"# 本月已完成\n\n多体原理学习 YouTube课程 018"} + {"id":"1ebeabaf5c73ddbb","type":"text","text":"# 本月已完成\n\n多体原理学习 YouTube课程 018","x":-440,"y":520,"width":440,"height":340} ], "edges":[] } \ No newline at end of file diff --git a/工作总结/周报/~$71-郭翼泽.docx b/工作总结/周报/~$71-郭翼泽.docx new file mode 100644 index 0000000000000000000000000000000000000000..53c1f3478a8c2cd6637a0f7398bead0a34231bd7 GIT binary patch literal 162 zcmZQ}RnTJ~889=rGAJ;BH2OL_P2ylYA3Wp8@+Ipy8duA$3y5iczS4w0E;E#KKC@6z z!IQVE%EY4T{SCRUS=zfRO)&G96TSS*GFN7bxxR~M!0WvxHjcb%E)V0nl~Yo>-!Pp0 S`h@vE5c~*v!@%6p&kO)tqbpwk literal 0 HcmV?d00001 diff --git a/工作总结/周报/周报71-郭翼泽.docx b/工作总结/周报/周报71-郭翼泽.docx index b6c4fc914f9c5baf35ad701e948aea897f362061..6c2bef3b3461a0d3f2eafaa226db227b231b9cdd 100644 GIT binary patch delta 14582 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