Translational Spring, Damper, Actuator - MapleSim Help

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Translational Spring, Damper, Actuator

Applies stiffness, damping, and actuation between two frames

 Description A spring, damper, and force actuator, acting in parallel between two end frames, is shown in the diagram below.  These three elements are combined into a single translational spring-damper-actuator (TSDA).   Assuming that the translation vector, $\mathbf{r}$, is directed from frame_a, $[{x}_{1},{y}_{1},$${z}_{1}],$to frame_b, $[{x}_{2},{y}_{2},$${z}_{2}]$,  the resultant forces are ${\mathbf{f}}_{1}=\frac{f}{‖\mathbf{r}‖}\mathbf{\cdot }\left(\left(\mathbf{r}\mathbf{\cdot }{\mathbf{e}}_{\mathrm{x1}}\right)\mathbf{\cdot }{\mathbf{e}}_{\mathrm{x1}}+\left(\mathbf{r}\mathbf{\cdot }{\mathbf{e}}_{\mathrm{y1}}\right)\mathbf{\cdot }{\mathbf{e}}_{\mathrm{y1}}+\left(\mathbf{r}\mathbf{\cdot }{\mathbf{e}}_{\mathrm{z1}}\right)\mathbf{\cdot }{\mathbf{e}}_{\mathrm{z1}}\right)$ ${\mathbf{f}}_{2}=-\frac{f}{‖\mathbf{r}‖}\mathbf{\cdot }\left(\left(\mathbf{r}\mathbf{\cdot }{\mathbf{e}}_{\mathrm{x2}}\right)\mathbf{\cdot }{\mathbf{e}}_{\mathrm{x2}}+\left(\mathbf{r}\mathbf{\cdot }{\mathbf{e}}_{\mathrm{y2}}\right)\mathbf{\cdot }{\mathbf{e}}_{\mathrm{y2}}+\left(\mathbf{r}\mathbf{\cdot }{\mathbf{e}}_{\mathrm{z2}}\right)\mathbf{\cdot }{\mathbf{e}}_{\mathrm{z2}}\right)$   where ${\mathbf{f}}_{1}$ and ${\mathbf{f}}_{2}$ are the reaction forces applied to frame_a and frame_b, respectively and      where $s=‖\mathbf{r}‖$ is the instantaneous length of the TSDA, $L$ is the undeformed spring length, $\mathrm{D}$ is the viscous damping coefficient, and ${f}_{\mathrm{act}}$ is the prescribed force in the actuator. Also, ${\mathbf{e}}_{\mathrm{x1}},{\mathbf{e}}_{\mathrm{y1}},{\mathbf{e}}_{\mathrm{z1}}$ are the unit vectors along the frame_a coordinate frame and ${\mathbf{e}}_{\mathrm{x2}},{\mathbf{e}}_{\mathrm{y2}},{\mathbf{e}}_{\mathrm{z2}}$ are the unit vectors along the frame_b coordinate frame.

Connections

 Name Description ${\mathrm{frame}}_{a}$ Force driver inboard frame ${\mathrm{frame}}_{b}$ Force driver outboard frame $\mathrm{TSDAInput}$ Real signal input specifying the magnitude of the actuation force ${\mathrm{flange}}_{a}$ Inertial reference frame for 1-D translational components ${\mathrm{flange}}_{b}$ Displacement between ${\mathrm{frame}}_{a}$ and ${\mathrm{frame}}_{b}$. Connects to 1-D translational components

Parameters

 Symbol Default Units Description Modelica ID ${K}_{\mathrm{spring}}$ $0$ $\frac{N}{m}$ Spring constant Kspring ${l}_{0}$ 0 $m$ Unstretched spring length L0 ${K}_{ⅆampⅇr}$ $0$ $\frac{N\cdot s}{m}$ Damping constant Kdamper true $-$ Controls whether the input signal force port is displayed. useForcePort