Repository: petrobras/ross

Issue:
Error when trying to save rotor with coupling element
As mentioned in #1134, an error was encountered when saving a rotor with coupling element:
```
File d:\ProgramData\Anaconda3\Lib\site-packages\spyder_kernels\py3compat.py:356 in compat_exec
exec(code, globals, locals) File ..\wvc_insideshafting\ross10v01_inside_coupling.py:107
rotor.save('rotor.toml')
File d:\ProgramData\Anaconda3\Lib\site-packages\ross\rotor_assembly.py:3132 in save
el.save(file)
File d:\ProgramData\Anaconda3\Lib\site-packages\ross\shaft_element.py:411 in save
"name": self.material.name,
AttributeError: 'CouplingElement' object has no attribute 'material'
```

Hints from issue comments:
@ross-bott: Hi there!
I have marked this issue as stale because it has not had activity for 45 days.
Consider the following options:
- If the issue refers to a large task, break it in smaller issues that can be solved in
less than 45 days;
- Label the issue as `wontfix` or `wontfix for now` and close it.

Solution patch:
diff --git a/docs/user_guide/tutorial_part_1.ipynb b/docs/user_guide/tutorial_part_1.ipynb
index 111580e8..37bc71ee 100644
--- a/docs/user_guide/tutorial_part_1.ipynb
+++ b/docs/user_guide/tutorial_part_1.ipynb
@@ -630,6 +630,195 @@
     "```"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### 2.3 Creating coupling element (CouplingElement Class)\n",
+    "\n",
+    "Here, we introduce the `CouplingElement` class, a subclass of the `ShaftElement` class, designed to model the interaction between two rotor shafts. This element is implemented in a general form in ROSS. The coupling plays a crucial role in mechanical systems by transmitting forces, vibrations, and motion between rotating shafts. It is primarily characterized by adding stiffness, mass, and inertia to the system, which are essential for simulating the real-world behavior of coupled rotors.\n",
+    "\n",
+    "__Steps:__\n",
+    "- Create two shafts: Start by defining two rotor shafts using the `ShaftElement` class. Each shaft can have its own properties like material, length, and diameter.\n",
+    "- Join shafts with coupling: Use the `CouplingElement` class to connect the two shafts by inserting the elements in a list following a certain order."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "#### 2.3.1 Define the shafts with their respective dimensions and properties"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Shaft 1 - Left\n",
+    "L1 = [300, 92, 200, 200, 92, 300]  # Segment lengths (in mm)\n",
+    "r1 = [61.5, 75, 75, 75, 75, 61.5]  # Segment radii (in mm)\n",
+    "shaft1 = [\n",
+    "    rs.ShaftElement(\n",
+    "        L=L1[i] * 1e-3,  # Convert length to meters\n",
+    "        idl=0.0,  # Inner diameter in meters\n",
+    "        odl=r1[i] * 2e-3,  # Outer diameter in meters\n",
+    "        material=steel,  # Material used for the shaft\n",
+    "        shear_effects=True,\n",
+    "        rotary_inertia=True,\n",
+    "        gyroscopic=True,\n",
+    "    )\n",
+    "    for i in range(len(L1))\n",
+    "]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Shaft 2 - Right\n",
+    "L2 = [80, 200, 200, 640]  # Segment lengths (in mm)\n",
+    "r2 = [160.5, 160.5, 130.5, 130.5]  # Segment radii (in mm)\n",
+    "shaft2 = [\n",
+    "    rs.ShaftElement(\n",
+    "        L=L2[i] * 1e-3,  # Convert length to meters\n",
+    "        idl=0.0,  # Inner diameter in meters\n",
+    "        odl=r2[i] * 2e-3,  # Outer diameter in meters\n",
+    "        material=steel,  # Material used for the shaft\n",
+    "        shear_effects=True,\n",
+    "        rotary_inertia=True,\n",
+    "        gyroscopic=True,\n",
+    "    )\n",
+    "    for i in range(len(L2))\n",
+    "]"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "#### 2.3.2 Define the coupling element that connects the two shafts"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "In this example, only the torsional stiffness is adopted. However, you can pass any of the following arguments (if not provided, the default value is zero):\n",
+    "- kt_x, \n",
+    "- kt_y,\n",
+    "- kt_z (axial stiffness), \n",
+    "- kr_x, \n",
+    "- kr_y,\n",
+    "- kr_z (torsional stiffness),\n",
+    "\n",
+    "considering that the stiffness matrix $\\mathbf{K}$ will be assembled like this:\n",
+    "\n",
+    "$\n",
+    "\\mathbf{K} = \n",
+    "\\begin{bmatrix}\n",
+    "k_{t_x} & 0 & 0 & 0 & 0 & 0 & -k_{t_x} & 0 & 0 & 0 & 0 & 0 \\\\\n",
+    "0 & k_{t_y} & 0 & 0 & 0 & 0 & 0 & -k_{t_y} & 0 & 0 & 0 & 0 \\\\\n",
+    "0 & 0 & k_{t_z} & 0 & 0 & 0 & 0 & 0 & -k_{t_z} & 0 & 0 & 0 \\\\\n",
+    "0 & 0 & 0 & k_{r_x} & 0 & 0 & 0 & 0 & 0 & -k_{r_x} & 0 & 0 \\\\\n",
+    "0 & 0 & 0 & 0 & k_{r_y} & 0 & 0 & 0 & 0 & 0 & -k_{r_y} & 0 \\\\\n",
+    "0 & 0 & 0 & 0 & 0 & k_{r_z} & 0 & 0 & 0 & 0 & 0 & -k_{r_z} \\\\\n",
+    "-k_{t_x} & 0 & 0 & 0 & 0 & 0 & k_{t_x} & 0 & 0 & 0 & 0 & 0 \\\\\n",
+    "0 & -k_{t_y} & 0 & 0 & 0 & 0 & 0 & k_{t_y} & 0 & 0 & 0 & 0 \\\\\n",
+    "0 & 0 & -k_{t_z} & 0 & 0 & 0 & 0 & 0 & k_{t_z} & 0 & 0 & 0 \\\\\n",
+    "0 & 0 & 0 & -k_{r_x} & 0 & 0 & 0 & 0 & 0 & k_{r_x} & 0 & 0 \\\\\n",
+    "0 & 0 & 0 & 0 & -k_{r_y} & 0 & 0 & 0 & 0 & 0 & k_{r_y} & 0 \\\\\n",
+    "0 & 0 & 0 & 0 & 0 & -k_{r_z} & 0 & 0 & 0 & 0 & 0 & k_{r_z}\n",
+    "\\end{bmatrix}\n",
+    "$\n",
+    "\n",
+    "__Note:__ Although not demonstrated here, the same logic used for stiffness coefficients can also be applied to damping coefficients (ct_x, ct_y, ct_z, cr_x, cr_y, cr_z)."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 14,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "CouplingElement(m=151.0, Ip=3.48, n=None)"
+      ]
+     },
+     "execution_count": 14,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "# Mass at each station (e.g., hub mass of the coupling)\n",
+    "mass_left_station = 151 / 2\n",
+    "mass_right_station = 151 / 2\n",
+    "\n",
+    "# Polar moment of inertia of the coupling\n",
+    "Ip = 3.48\n",
+    "\n",
+    "# Torsional stiffness\n",
+    "torsional_stiffness = 3.04e6\n",
+    "\n",
+    "# Create the coupling element\n",
+    "coupling = rs.CouplingElement(\n",
+    "    m_l=mass_left_station,  # Mass on the left station (in kg)\n",
+    "    m_r=mass_right_station,  # Mass on the right station (in kg)\n",
+    "    Ip_l=Ip\n",
+    "    / 2,  # Polar moment of inertia on the left station (assuming equal distribution in kg·m²)\n",
+    "    Ip_r=Ip\n",
+    "    / 2,  # Polar moment of inertia on the right station (assuming equal distribution in kg·m²)\n",
+    "    kr_z=torsional_stiffness,  # Torsional stiffness (in N·m/rad)\n",
+    ")\n",
+    "coupling"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "#### 2.3.3 Coupling all elements\n",
+    "\n",
+    "Combine all elements into a single list for the rotor model.\n",
+    "The elements must be in order."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 15,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[ShaftElement(L=0.3, idl=0.0, idr=0.0, odl=0.123,  odr=0.123, material='Steel', n=None),\n",
+       " ShaftElement(L=0.092, idl=0.0, idr=0.0, odl=0.15,  odr=0.15, material='Steel', n=None),\n",
+       " ShaftElement(L=0.2, idl=0.0, idr=0.0, odl=0.15,  odr=0.15, material='Steel', n=None),\n",
+       " ShaftElement(L=0.2, idl=0.0, idr=0.0, odl=0.15,  odr=0.15, material='Steel', n=None),\n",
+       " ShaftElement(L=0.092, idl=0.0, idr=0.0, odl=0.15,  odr=0.15, material='Steel', n=None),\n",
+       " ShaftElement(L=0.3, idl=0.0, idr=0.0, odl=0.123,  odr=0.123, material='Steel', n=None),\n",
+       " CouplingElement(m=151.0, Ip=3.48, n=None),\n",
+       " ShaftElement(L=0.08, idl=0.0, idr=0.0, odl=0.321,  odr=0.321, material='Steel', n=None),\n",
+       " ShaftElement(L=0.2, idl=0.0, idr=0.0, odl=0.321,  odr=0.321, material='Steel', n=None),\n",
+       " ShaftElement(L=0.2, idl=0.0, idr=0.0, odl=0.261,  odr=0.261, material='Steel', n=None),\n",
+       " ShaftElement(L=0.64, idl=0.0, idr=0.0, odl=0.261,  odr=0.261, material='Steel', n=None)]"
+      ]
+     },
+     "execution_count": 15,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "shaft_elements = [*shaft1, coupling, *shaft2]\n",
+    "shaft_elements"
+   ]
+  },
   {
    "cell_type": "markdown",
    "metadata": {},
@@ -666,7 +855,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 12,
+   "execution_count": 16,
    "metadata": {
     "execution": {
      "iopub.execute_input": "2023-05-04T01:05:09.852258Z",
@@ -682,7 +871,7 @@
        "DiskElement(Id=0.329, Ip=0.178, m=32.58, color='Firebrick', n=0, scale_factor=1.0, tag='Disk')"
       ]
      },
-     "execution_count": 12,
+     "execution_count": 16,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -703,7 +892,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 13,
+   "execution_count": 17,
    "metadata": {
     "execution": {
      "iopub.execute_input": "2023-05-04T01:05:09.858420Z",
@@ -720,7 +909,7 @@
        " DiskElement(Id=0.17809, Ip=0.38373, m=35.8, color='Firebrick', n=4, scale_factor=1.0, tag=None)]"
       ]
      },
-     "execution_count": 13,
+     "execution_count": 17,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -746,7 +935,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 14,
+   "execution_count": 18,
    "metadata": {
     "execution": {
      "iopub.execute_input": "2023-05-04T01:05:09.865480Z",
@@ -763,7 +952,7 @@
        " DiskElement(Id=0.17809, Ip=0.38373, m=35.8, color='Firebrick', n=4, scale_factor=1.0, tag=None)]"
       ]
      },
-     "execution_count": 14,
+     "execution_count": 18,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -810,7 +999,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 15,
+   "execution_count": 19,
    "metadata": {
     "execution": {
      "iopub.execute_input": "2023-05-04T01:05:09.872858Z",
@@ -859,7 +1048,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 16,
+   "execution_count": 20,
    "metadata": {
     "execution": {
      "iopub.execute_input": "2023-05-04T01:05:09.878732Z",
@@ -876,7 +1065,7 @@
        " DiskElement(Id=5.5224, Ip=0.56007, m=128.38, color='Firebrick', n=4, scale_factor=1.0, tag=None)]"
       ]
      },
-     "execution_count": 16,
+     "execution_count": 20,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -903,7 +1092,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 17,
+   "execution_count": 21,
    "metadata": {
     "execution": {
      "iopub.execute_input": "2023-05-04T01:05:09.888469Z",
@@ -920,7 +1109,7 @@
        " DiskElement(Id=5.5224, Ip=0.56007, m=128.38, color='Firebrick', n=4, scale_factor=1.0, tag=None)]"
       ]
      },
-     "execution_count": 17,
+     "execution_count": 21,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -963,7 +1152,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 18,
+   "execution_count": 22,
    "metadata": {
     "execution": {
      "iopub.execute_input": "2023-05-04T01:05:09.898793Z",
@@ -985,7 +1174,7 @@
        " DiskElement(Id=0.025, Ip=0.048, m=6.96, color='Firebrick', n=35, scale_factor=1, tag=None)]"
       ]
      },
-     "execution_count": 18,
+     "execution_count": 22,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1048,7 +1237,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 19,
+   "execution_count": 23,
    "metadata": {
     "execution": {
      "iopub.execute_input": "2023-05-04T01:05:09.933249Z",
@@ -1100,7 +1289,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 20,
+   "execution_count": 24,
    "metadata": {
     "execution": {
      "iopub.execute_input": "2023-05-04T01:05:09.939716Z",
@@ -1181,7 +1370,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 21,
+   "execution_count": 25,
    "metadata": {
     "execution": {
      "iopub.execute_input": "2023-05-04T01:05:09.949823Z",
@@ -1242,7 +1431,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 22,
+   "execution_count": 26,
    "metadata": {
     "execution": {
      "iopub.execute_input": "2023-05-04T01:05:09.956539Z",
@@ -2187,7 +2376,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 23,
+   "execution_count": 27,
    "metadata": {
     "execution": {
      "iopub.execute_input": "2023-05-04T01:05:10.022418Z",
@@ -3203,7 +3392,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 24,
+   "execution_count": 28,
    "metadata": {
     "execution": {
      "iopub.execute_input": "2023-05-04T01:05:10.032332Z",
@@ -4159,7 +4348,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 25,
+   "execution_count": 29,
    "metadata": {
     "execution": {
      "iopub.execute_input": "2023-05-04T01:05:10.043025Z",
@@ -4184,7 +4373,7 @@
        " frequency=None, tag=None)"
       ]
      },
-     "execution_count": 25,
+     "execution_count": 29,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -4209,7 +4398,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 26,
+   "execution_count": 30,
    "metadata": {
     "execution": {
      "iopub.execute_input": "2023-05-04T01:05:10.049684Z",
@@ -4223,18 +4412,18 @@
      "data": {
       "text/plain": [
        "BallBearingElement(n=0, n_link=None,\n",
-       " kxx=[46416883.847697675], kxy=[0.0],\n",
-       " kyx=[0.0], kyy=[100906269.23412538],\n",
-       " kzz=[0], cxx=[580.211048096221],\n",
+       " kxx=[np.float64(46416883.847697675)], kxy=[0.0],\n",
+       " kyx=[0.0], kyy=[np.float64(100906269.23412538)],\n",
+       " kzz=[0], cxx=[np.float64(580.211048096221)],\n",
        " cxy=[0.0], cyx=[0.0],\n",
-       " cyy=[1261.3283654265672], czz=[0],\n",
+       " cyy=[np.float64(1261.3283654265672)], czz=[0],\n",
        " mxx=[0], mxy=[0],\n",
        " myx=[0], myy=[0],\n",
        " mzz=[0],\n",
        " frequency=None, tag='ballbearing')"
       ]
      },
-     "execution_count": 26,
+     "execution_count": 30,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -4270,7 +4459,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 27,
+   "execution_count": 31,
    "metadata": {
     "execution": {
      "iopub.execute_input": "2023-05-04T01:05:10.057753Z",
@@ -4284,18 +4473,18 @@
      "data": {
       "text/plain": [
        "RollerBearingElement(n=0, n_link=None,\n",
-       " kxx=[272821927.4006065], kxy=[0.0],\n",
-       " kyx=[0.0], kyy=[556779443.6747072],\n",
-       " kzz=[0], cxx=[3410.2740925075814],\n",
+       " kxx=[np.float64(272821927.4006065)], kxy=[0.0],\n",
+       " kyx=[0.0], kyy=[np.float64(556779443.6747072)],\n",
+       " kzz=[0], cxx=[np.float64(3410.2740925075814)],\n",
        " cxy=[0.0], cyx=[0.0],\n",
-       " cyy=[6959.74304593384], czz=[0],\n",
+       " cyy=[np.float64(6959.74304593384)], czz=[0],\n",
        " mxx=[0], mxy=[0],\n",
        " myx=[0], myy=[0],\n",
        " mzz=[0],\n",
        " frequency=None, tag='rollerbearing')"
       ]
      },
-     "execution_count": 27,
+     "execution_count": 31,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -4335,7 +4524,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 28,
+   "execution_count": 32,
    "metadata": {
     "execution": {
      "iopub.execute_input": "2023-05-04T01:05:10.064205Z",
@@ -4350,18 +4539,18 @@
      "data": {
       "text/plain": [
        "MagneticBearingElement(n=0, n_link=None,\n",
-       " kxx=[-4640.623377181318], kxy=[0.0],\n",
-       " kyx=[0.0], kyy=[-4640.623377181318],\n",
-       " kzz=[0], cxx=[4.645268645827145],\n",
+       " kxx=[np.float64(-4640.623377181318)], kxy=[0.0],\n",
+       " kyx=[0.0], kyy=[np.float64(-4640.623377181318)],\n",
+       " kzz=[0], cxx=[np.float64(4.645268645827145)],\n",
        " cxy=[0.0], cyx=[0.0],\n",
-       " cyy=[4.645268645827145], czz=[0],\n",
+       " cyy=[np.float64(4.645268645827145)], czz=[0],\n",
        " mxx=[0], mxy=[0],\n",
        " myx=[0], myy=[0],\n",
        " mzz=[0],\n",
        " frequency=None, tag='magneticbearing')"
       ]
      },
-     "execution_count": 28,
+     "execution_count": 32,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -4419,7 +4608,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 29,
+   "execution_count": 33,
    "metadata": {
     "execution": {
      "iopub.execute_input": "2023-05-04T01:05:10.072303Z",
@@ -4447,7 +4636,7 @@
        "  837.75804096  942.47779608 1047.1975512  1151.91730632], tag=None)"
       ]
      },
-     "execution_count": 29,
+     "execution_count": 33,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -4474,7 +4663,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 30,
+   "execution_count": 34,
    "metadata": {
     "execution": {
      "iopub.execute_input": "2023-05-04T01:05:10.091977Z",
@@ -4509,7 +4698,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 31,
+   "execution_count": 35,
    "metadata": {
     "execution": {
      "iopub.execute_input": "2023-05-04T01:05:10.096377Z",
@@ -4527,7 +4716,7 @@
        "       [0., 0., 2.]])"
       ]
      },
-     "execution_count": 31,
+     "execution_count": 35,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -4540,7 +4729,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 32,
+   "execution_count": 36,
    "metadata": {
     "execution": {
      "iopub.execute_input": "2023-05-04T01:05:10.101806Z",
@@ -4558,7 +4747,7 @@
        "       [0., 0., 0.]])"
       ]
      },
-     "execution_count": 32,
+     "execution_count": 36,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -4594,7 +4783,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 33,
+   "execution_count": 37,
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-          18799.63787620342,
-          19067.0017878122
+          6916.878414881941,
+          6773.543052824832,
+          6650.504147140471,
+          6543.075819313423,
+          6447.901858226217,
+          6363.028661360778,
+          6287.732704590799,
+          6222.173997023632,
+          6166.960704715362,
+          6123.40390737707,
+          6092.1224942756635,
+          6071.976955577278,
+          6060.849795915919,
+          6056.2824720228045,
+          6056.339798333127,
+          6059.704257175552,
+          6065.491244414916,
+          6073.074798602869,
+          6081.862593306162,
+          6091.313103520541,
+          6101.019280199866,
+          6110.771805674974,
+          6120.441198284279,
+          6129.938632523526,
+          6139.143703064118,
+          6147.917877012829,
+          6156.173502424005,
+          6163.861466753642,
+          6170.959238136233,
+          6177.462389078369,
+          6183.37859930542
          ]
         },
         {
@@ -36481,7 +36597,6 @@
          ]
         },
         "legend": {
-         "itemsizing": "constant",
          "orientation": "h",
          "x": 0.5,
          "xanchor": "center",
@@ -37336,7 +37451,7 @@
         "yaxis": {
          "range": [
           0,
-          21232.460413614375
+          21232.46040459453
          ],
          "title": {
           "text": "Natural Frequencies (RPM)"
diff --git a/ross/coupling_element.py b/ross/coupling_element.py
index fbbf38e2..51cc5a13 100644
--- a/ross/coupling_element.py
+++ b/ross/coupling_element.py
@@ -1,9 +1,12 @@
 """Coupling Element module.
 
 This module defines the CouplingElement class which will be used to represent the coupling
-between two rotor shaft, which add mainly stiffness, mass and inertia to the system.
+between two rotor shafts, which add mainly stiffness, mass and inertia to the system.
 """
 
+import inspect
+import toml
+
 import numpy as np
 from plotly import graph_objects as go
 
@@ -205,6 +208,24 @@ class CouplingElement(ShaftElement):
             f"n={self.n})"
         )
 
+    def save(self, file):
+        signature = inspect.signature(self.__init__)
+        args_list = list(signature.parameters)
+        args = {arg: getattr(self, arg) for arg in args_list}
+
+        try:
+            data = toml.load(file)
+        except FileNotFoundError:
+            data = {}
+
+        data[f"{self.__class__.__name__}_{self.tag}"] = args
+        with open(file, "w") as f:
+            toml.dump(data, f)
+
+    @classmethod
+    def read_toml_data(cls, data):
+        return cls(**data)
+
     def M(self):
         """Mass matrix for an instance of a coupling element.
 


Test patch:
diff --git a/ross/tests/test_shaft_element.py b/ross/tests/test_shaft_element.py
index 8fe98551..63dcdb2c 100644
--- a/ross/tests/test_shaft_element.py
+++ b/ross/tests/test_shaft_element.py
@@ -9,6 +9,7 @@ from numpy.testing import assert_allclose, assert_almost_equal
 
 from ross.materials import steel
 from ross.shaft_element import ShaftElement
+from ross.coupling_element import CouplingElement
 
 
 @pytest.fixture
@@ -636,3 +637,123 @@ def test_gyroscopic_matrix_tim_6dof(tim_6dof):
 ])
     # fmt: on
     assert_almost_equal(tim_6dof.G() * 1e3, G0e_tim, decimal=5)
+
+
+@pytest.fixture
+def coupling():
+    mass_station = 151 / 2  # Assuming equal distribution of mass (in kg)
+    Ip_station = 1.74  # Polar moment of inertia, assuming equal distribution (in kg·m²)
+
+    return CouplingElement(
+        m_l=mass_station,
+        m_r=mass_station,
+        Ip_l=Ip_station,
+        Ip_r=Ip_station,
+        kt_x=1e6,
+        kt_y=2e6,
+        kt_z=3e6,  # Axial stiffness (in N/m)
+        kr_x=4e6,
+        kr_y=5e6,
+        kr_z=6e6,  # Torsional stiffness (in N·m/rad)
+    )
+
+
+def test_parameters_coupling(coupling):
+    assert coupling.m == 151
+    assert coupling.Ip == 3.48
+    assert coupling.Id_l == 0.87
+    assert coupling.Id_r == 0.87
+    assert coupling.kt_x == 1e6
+    assert coupling.kt_y == 2e6
+    assert coupling.kt_z == 3e6
+    assert coupling.kr_x == 4e6
+    assert coupling.kr_y == 5e6
+    assert coupling.kr_z == 6e6
+    assert coupling.ct_x == 0.0
+    assert coupling.ct_y == 0.0
+    assert coupling.ct_z == 0.0
+    assert coupling.cr_x == 0.0
+    assert coupling.cr_y == 0.0
+    assert coupling.cr_z == 0.0
+
+
+def test_mass_matrix_coupling(coupling):
+    # fmt: off
+    M0 = np.array([
+        [75.5 ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ],
+        [ 0.  , 75.5 ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ],
+        [ 0.  ,  0.  , 75.5 ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ],
+        [ 0.  ,  0.  ,  0.  ,  0.87,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ],
+        [ 0.  ,  0.  ,  0.  ,  0.  ,  0.87,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ],
+        [ 0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  1.74,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ],
+        [ 0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  , 75.5 ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ],
+        [ 0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  , 75.5 ,  0.  ,  0.  ,  0.  ,  0.  ],
+        [ 0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  , 75.5 ,  0.  ,  0.  ,  0.  ],
+        [ 0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.87,  0.  ,  0.  ],
+        [ 0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.87,  0.  ],
+        [ 0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  1.74]
+    ])
+    # fmt: on
+    assert_almost_equal(coupling.M(), M0, decimal=5)
+
+
+def test_stiffness_matrix_coupling(coupling):
+    # fmt: off
+    K0 = np.array([
+        [ 1.,  0.,  0.,  0.,  0.,  0., -1.,  0.,  0.,  0.,  0.,  0.],
+        [ 0.,  2.,  0.,  0.,  0.,  0.,  0., -2.,  0.,  0.,  0.,  0.],
+        [ 0.,  0.,  3.,  0.,  0.,  0.,  0.,  0., -3.,  0.,  0.,  0.],
+        [ 0.,  0.,  0.,  4.,  0.,  0.,  0.,  0.,  0., -4.,  0.,  0.],
+        [ 0.,  0.,  0.,  0.,  5.,  0.,  0.,  0.,  0.,  0., -5.,  0.],
+        [ 0.,  0.,  0.,  0.,  0.,  6.,  0.,  0.,  0.,  0.,  0., -6.],
+        [-1.,  0.,  0.,  0.,  0.,  0.,  1.,  0.,  0.,  0.,  0.,  0.],
+        [ 0., -2.,  0.,  0.,  0.,  0.,  0.,  2.,  0.,  0.,  0.,  0.],
+        [ 0.,  0., -3.,  0.,  0.,  0.,  0.,  0.,  3.,  0.,  0.,  0.],
+        [ 0.,  0.,  0., -4.,  0.,  0.,  0.,  0.,  0.,  4.,  0.,  0.],
+        [ 0.,  0.,  0.,  0., -5.,  0.,  0.,  0.,  0.,  0.,  5.,  0.],
+        [ 0.,  0.,  0.,  0.,  0., -6.,  0.,  0.,  0.,  0.,  0.,  6.]
+    ])
+    # fmt: on
+    assert_almost_equal(coupling.K() / 1e6, K0, decimal=5)
+
+
+def test_dynamic_stiffness_matrix_coupling(coupling):
+    Kst0 = np.zeros((12, 12))
+    assert_almost_equal(coupling.Kst(), Kst0, decimal=5)
+
+
+def test_damping_matrix_coupling(coupling):
+    C0 = np.zeros((12, 12))
+    assert_almost_equal(coupling.C(), C0, decimal=5)
+
+
+def test_gyroscopic_matrix_coupling(coupling):
+    # fmt: off
+    G0 = np.array([
+        [ 0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ],
+        [ 0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ],
+        [ 0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ],
+        [ 0.  ,  0.  ,  0.  ,  0.  ,  1.74,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ],
+        [ 0.  ,  0.  ,  0.  , -1.74,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ],
+        [ 0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ],
+        [ 0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ],
+        [ 0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ],
+        [ 0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ],
+        [ 0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  1.74,  0.  ],
+        [ 0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  , -1.74,  0.  ,  0.  ],
+        [ 0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ]
+    ])
+    # fmt: on
+    assert_almost_equal(coupling.G(), G0, decimal=5)
+
+
+def test_pickle_coupling(coupling):
+    coupling_pickled = pickle.loads(pickle.dumps(coupling))
+    assert coupling == coupling_pickled
+
+
+def test_save_load_coupling(coupling):
+    file = Path(tempdir) / "coupling.toml"
+    coupling.save(file)
+    coupling_loaded = CouplingElement.load(file)
+    assert coupling == coupling_loaded