 Surface - MapleSim Help

Tire Surface Options Description All tire components share similar options for defining the operating surface. These options are listed in the Surface section of the tire component properties. The main use of these options is to define the surface the tire is interacting with to ultimately calculate the surface normal vector, ${\stackrel{^}{e}}_{n}$ and tire center distance from the surface, $\mathrm{rz}$. There are three options for defining the surface: as a flat surface, with data points, and externally. Flat Surface

The Flat surface check box in the Surface section of the tire component properties determines whether the tire is operating on a flat surface.  When selected, the plane passing through [0,0,0] with the normal of ${\stackrel{^}{e}}_{g}$  is taken as the flat operating surface, where ${\stackrel{^}{e}}_{g}$ is the direction of gravity defined in the Multibody Settings tab of the MapleSim model. In other words, depending on the chosen ${\stackrel{^}{e}}_{g}$, one of the planes $\mathrm{yz}=0$, $\mathrm{xz}=0$, $\mathrm{xy}=0$ is taken as the flat surface. Below are examples of a tire sitting on the xy plane with choices of x and y as the spin axis. Spin axis is y Direction of gravity Tire spin axis  Spin axis is x Direction of gravity Tire spin axis The surface normal vector, ${\stackrel{^}{e}}_{n}$, and the tire center distance from the surface, $\mathrm{rz}$, is straightforward for the case of a flat surface:

${\stackrel{^}{e}}_{n}=-{\stackrel{^}{e}}_{g}$

$\mathrm{rz}={\stackrel{&conjugate0;}{r}}_{c}·{\stackrel{^}{e}}_{n}$

where ${\stackrel{&conjugate0;}{r}}_{c}$ is the tire center position vector. Defined using Data Points

With the Flat surface option not selected, the surface geometry can be defined either using data points (discussed here) or externally (discussed in the next section). The Data source drop-down in the tire component properties provides three options to define the surface data points: inline, using a file, or using an attachment. In each case, data points are given as a matrix in which the first column and first row represent discrete points on two of the global coordinate axes.

With the inline option, the matrix is entered in the MapleSim GUI. To change the matrix dimensions, right-click on the text input field and select Edit Matrix Dimensions. Alternatively, a CSV, XLS, or XLSX file can be used to define the matrix by choosing file or attachment for the Data source parameter and selecting the file or attachment as the Surface data parameter.

The interpretation of the data points matrix depends on the selected vector for direction of gravity, ${\stackrel{^}{e}}_{g}$, in the Multibody Settings. Different interpretations are summarized below Gravity parallel to x-axis  Gravity parallel to y-axis  Gravity parallel to z-axis For the given surface data points, an iterative algorithm calculates the surface normal vector, ${\stackrel{^}{e}}_{n}$, and tire center distance from the surface, $\mathrm{rz}$

The integer ${n}_{\mathrm{iter}}$ in the properties specifies the number of iterations. The recommended value is from 1 to 5 to get a reasonable trade-off between accuracy and performance.

To clarify the employed algorithm, the following describes the steps of the algorithm for ${n}_{\mathrm{iter}}=2$:

1. Iteration 1:

1) Project the tire center point onto the given surface to find ${\stackrel{&conjugate0;}{p}}_{1}$.  This requires interpolation of the provided surface data points. The interpolation smoothness is determined by the smoothness drop-down in the properties, as shown below. We suggest using the cubic splines to interpolate smoothly between the surface data points. 2) Create a tangent plane to the surface directly below the tire center. The radius of this tangent plane is controlled by the ${\mathrm{\delta }}_{L}$ parameter in the properties.

3) Project the vector from the surface point to the tire center point onto the surface normal vector to get the distance. 2. Iteration 2a:

1) Replace tire center with an intermediate point, ${\stackrel{&conjugate0;}{r}}_{2}$.

2) Project ${\stackrel{&conjugate0;}{r}}_{2}$ onto the given surface to obtain ${\stackrel{&conjugate0;}{p}}_{2}$. Again, this requires interpolation with smoothness defined by the smoothness drop-down in the properties.

3) Repeat the tangent plane calculation with the vertical projection of this point.  Again, the radius of this tangent plane is controlled by ${\mathrm{\delta }}_{L}$. 3. Iteration 2b:

1) Project the vector from the surface point to the tire center point onto the surface normal vector to get the distance. After these steps for ${n}_{\mathrm{iter}}=2$ are completed, the $\mathrm{n2}$  unit vector shown in the figure above is chosen as the surface normal vector, ${\stackrel{^}{e}}_{n}$, and ${d}_{2}$ is taken as the tire center distance from the surface, $\mathrm{rz}$. Defined Externally This option is enabled if the Flat surface check box is not selected and Defined externally selected in the surface properties. In this case, two inputs and one output appear on the tire component: en_in is a 3-vector input for the surface normal vector, ${\stackrel{^}{e}}_{n}$, to the tire component. rz_in is a scalar input that assigns the center distance from the surface, $\mathrm{rz}$. r_c is a 3-vector output of the tire center position with respect to the inertial frame which can be utilized by the user to calculate ${\stackrel{^}{e}}_{n}$ and $\mathrm{rz}$ externally.