Chapter 10 | Reading Kudlich-Slibar Impulse Data

Introduction

In this chapter, we’ll review how to interpret collision data contained in the auto-ees and ees object data containers. To make the process straightforward, we’ll work through a simple collinear and inline impact case that can be easily compared to hand calculations.

Initial Set-up

Begin by setting up two vehicles in your Virtual CRASH environment. Press [P] to pause physics during initial set-up to make things a little easier.

The figure below illustrates an inline collision between a Kia K5 (white) and a Lucid Air (brown). Both vehicles are positioned with a yaw orientation of 0 degrees and a y-coordinate of 0 feet.

Kia K5: placed at x = -20 feet
Lucid Air: placed at x = 0 feet

Initial speeds are defined as follows:

The Lucid travels at 5 mph as it approaches the stop sign.
The Kia travels at 20 mph from behind.

The simulation is staged on the x–y plane. No sequences have been added, so no additional lateral or longitudinal tire forces are introduced from driver inputs.

Press [P] again to unpause physics.

As you set the initial speeds for your vehicles, Virtual CRASH immediately updates the simulation to display the resulting motion. You can use the time slider in the lower-right corner of the screen to scroll backward or forward in time and focus on the moment of impact. Remember that Virtual CRASH is an impulse-based simulator, which models impulses as being delivered instantaneously to objects during collisions.

The Auto-EES Data Container

Now that you’ve set up a collision, let’s take a look at the associated collision data. Left-click on “auto-ees” in the left-side control panel (see below). EES objects in this panel provide direct control over the inputs to the Kudlich-Slibar impulse-momentum model (see Appendix 1) and allow you to instantly collect results related to specific impulse exchanges.

Next, open the “defaults,” “misc,” and “selection” menus to display various auto-ees features. In the “selection” menu, left-click “previous contact” to select the impulse exchange. If the contact interaction between the vehicles required more than one impulse exchange to resolve, you can cycle through each exchange by using the “next contact” button. Below we used [Ctrl+1] to switch our display to Contours view mode.

In the “defaults” menu of the auto-ees object, you’ll find parameters that affect the calculations of all impulses contained in the auto-ees object. These parameters are reviewed below.

Depth of Penetration

Impulse-based collision models such as Kudlich-Slibar do not rely on force–deflection relationships to resolve contact interactions. Instead, crush damage is represented through direct user input. The “depth of penetration” parameter effectively specifies the approximate total system crush. The depth of penetration, $\Delta t_{p}$, is defined in the time domain. Starting from the initial contact time $t_i$, the equal and opposite impulses are delivered to the vehicles at $ t_i + \Delta t_p $. The specific location of the impulse (force) centroid within each vehicle will be discussed later. For more information on depth of penetration, see this blog post.

Friction

The friction input value acts as a threshold. Kudlich-Slibar first solves for the impulse exchange required to bring the vehicles to a common velocity at the effective point of contact (impulse centroid). However, the tangential component of the resulting impulse vector cannot exceed the product of the input friction value and the normal impulse component. If the tangential impulse needed to fully satisfy the common-velocity condition is greater than this product, post-impact sliding contact will result. When physical evidence indicates post-impact sliding contact, lowering the friction input value can help ensure the simulation reflects this condition.

Restitution

Once the impulse calculation is completed to bring the vehicles to a common velocity and friction is accounted for, the impulse vector magnitude is increased by an amount proportional to restitution. This setting specifies the coefficient of restitution used by the collision model, with values ranging from -1 to 1. A value of 0 corresponds to a fully inelastic collision where all available collision energy is lost to inelastic effects, while a value of 1 generally corresponds to a perfectly elastic collision with no energy loss (subject to frictional effects). Negative values represent cases where the contact surfaces do not reach a common velocity, such as when components break off at the area of contact during the collision. In most vehicle collisions, realistic values typically fall between 0 and 0.5.

Pitch

Under “pitch” you will see the pitch angle of the normal axis of the collision model. This can be useful in cases of extreme front-end underride.

Selecting an Impulse Exchange

Use the “previous contact” and “next contact” buttons in the “selection” menu to cycle through the impulse exchanges within a contact interaction, or across multiple contact interactions.

Once you press “next contact,” the user environment will display the impulse vectors, the friction cones (blue), and the plane orthogonal to the normal collision axis (red). The left-side control panel will also show detailed data summarizing the collision event (see below). The tangent impulse component lies within the red friction plane. The friction cone represents the upper limit of the volume in which the impulse vector must fall for the collision. If an impulse vector lies on the surface of the cone, the tangent component may be at its upper limit, which can imply post-impact sliding motion. As the maximum coefficient of friction allowed in the simulation is reduced, the cone decreases in size, showing that the allowable volume is also reduced. In the extreme case where the coefficient of friction is set to 0, the cone collapses to a line along the normal axis projection, meaning only normal impulse components act on the vehicles.

In the “contact” menu, you’ll find several useful outputs for each impulse exchange, including the separation speed at the impulse centroid, the impulse vector magnitude, and the deformation energy (the change in system kinetic energy resulting from the impulse exchange).

Left-click on “object 1” and “object 2” in the left-side control panel to display the resulting values for each vehicle associated with the selected impulse exchange.

Next, open “position-local,” “rotation-local,” and “timing” to view the position of the impulse centroid (in the global frame), the orientation of the impulse normal axis (in the global frame), and the simulation time prior to depth of penetration when the impulse exchange begins.

User Defined Contacts

Scroll to the bottom of the auto-ees menu in the left-side control panel and left-click on “create user contact.” Creating a user contact allows you to modify the inputs to the collision model for the selected impulse exchange, as well as reposition the impulse centroid and adjust the normal axis orientation.

Simulated Vehicle Deformation

Select the new “ees” object at the top of the project list. This represents the custom user contact. Each time you left-click “create user contact,” a new ees object is extracted from the auto-ees object and added to the project or layers list.

Next, open the “contact” menu for the new ees object. You will see that the “deform” option is disabled by default. Left-click the box next to “deform” to enable simulated deformation.

Adjust Impulse Centroid Position

Now we will customize the impulse centroid position. This is the point in three-dimensional space where the equal and opposite impulse vectors act on each vehicle. Click the box to the left of “auto-position” to disable automatic positioning of the impulse vectors (see below). By default, Virtual CRASH sets the centroid position using the overlap of the vehicle bounding boxes at the instant of momentum exchange.

Once “auto-position” is disabled, both position-local (x, y, z) and rotation-local (yaw, pitch, roll) become unlocked and can be adjusted manually.

Adjust the $z$-position of the impulse centroid. For illustration purposes, we will align this $z$-position with the vehicle centers of gravity to eliminate rotational effects from the simulation by ensuring the impulse vectors pass directly through the centers of gravity. Under “position-local,” set $z$ = 1.772 feet.

Shift the $x$ position of the impulse centroid to $x$ = -5 ft to simulate a case where the bullet vehicle’s front-end stiffness is much greater than the target vehicle’s rear-end stiffness. Next, scroll up and set the “depth of penetration” value to 0.06 seconds to exaggerate the crush damage. Note that by scrolling down the left-side control panel and left-clicking on “timing,” you can see the time at which the vehicles first come into contact.

As you advance the time slider forward, you’ll notice that at times greater than 0.225 seconds (the initial contact time) + 0.06 seconds (the depth of penetration setting), the impulses and crush damage will have been imparted to both vehicle meshes.

Finally, scroll up and left-click to expand “object 1” and “object 2” in the left-side control panel to display the vehicle data for the selected impulse exchange. Then open the “contact” menu. We will now compare this data with our expectations from hand calculations.

The Impulse

Let’s define “vehicle 1” as the Lucid (rear impacted vehicle) and “vehicle 2” as the Kia. In this simple inline and collinear scenario, (65) in Appendix 1 reduces to:

$$ \bar{J}_1 = -(1+\varepsilon)\left[\left(\frac{1}{\bar{m}}\right)\mathbf{1}_{3\times 3} - \mathbf{0}_{3\times 3}\right]^{-1} \cdot \bar{v}_{\text{Rel,i}}^{P} $$

or

$$\bar{J}_1 = -(1+\varepsilon)\cdot \bar{m} \cdot \bar{v}_{\text{Rel,i}}^{P} $$

where the system’s reduced mass is given by:

$$ \bar{m} = {155.75~\text{slugs} \cdot 100.38~\text{slugs} \over 155.75~\text{slugs} + 100.38~\text{slugs}} = 61.04~\text{slugs} $$ and the closing-velocity vector at impact is given by:

$$\bar{v}_{Rel,i}^P = 7.33~\text{fps}~\hat{x}- 29.33~\text{fps}~\hat{x} = -22~\text{fps}~\hat{x} $$

Plugging these values into our expression for impulse gives:

$$\bar{J}_1 = (1+0.1)\cdot 61.04~\text{slugs} \cdot 22~\text{fps}~\hat{x} = 1477.21 ~\text{lbs-s} ~\hat{x} = 6571.96 ~\text{N-s} ~\hat{x}$$

This is in agreement with the reported value in the contact menu.

The orientation of the impulse vector is reported as “impulse ni” (azimuth angle) and “impulse nz” (polar angle), available in both global and local frames. The “impulse pdof” value gives the azimuth expressed using the traditional SAE J670 convention (see this post).

Delta-V

The $|\Delta \bar{v}|$ values associated with this impulse exchange are simply given by the ratio of impulse magnitude to object mass. $|\Delta \bar{v}_1|$ is found in the “object 1” menu and $|\Delta \bar{v}_2|$ is found in the “object 2” menu. We can estimate their values by:

$$ |\Delta \bar{v}_1| = {|\bar{J}_1| \over m_1 }= {1477.21 ~\text{lbs-s} \over 155.75~\text{slugs}} = 6.47~\text{mph} $$

$$| \Delta \bar{v}_2| = {|-\bar{J}_1| \over m_2} = {1477.21 ~\text{lbs-s} \over 100.38~\text{slugs}} = 10.03 ~\text{mph} $$

Both of these estimates are in agreement with the values displayed in the left-side control panel.

Note: a contact interaction between vehicles may take numerous impulse exchanges to fully resolve, and therefore the $|\Delta \bar{v}|$ associated with one of potentially many impulse exchanges may not fully characterize a vehicle’s full $|\Delta \bar{v}|$. It is preferable to estimate the “cumulative” $|\Delta \bar{v}|$ using the dynamics info tool to account for multiple impulse exchanges as well as external forces acting on the vehicles during a contact interaction.

Deformation Energy

For two vehicles undergoing a contact interaction via Kudlich–Slibar impulse exchange, the deformation energy is defined as the absolute value of the difference between the system’s final kinetic energy (just after impact) and initial kinetic energy (just prior to impact).

The system’s kinetic energy is the sum of translational and rotational kinetic energy terms for both vehicles:

$$ E_{Deformation} = |KE_f - KE_i| $$

Since there is no pre- or post-impact rotation in this inline collision example, we only need to consider translational kinetic energy.

$$ KE_{1,i} = {1 \over 2}\cdot (155.75~\text{slugs})\cdot(7.33~\text{ft/s})^2 = 4,187.95~\text{ft-lbs}$$

$$ KE_{1,f} = {1 \over 2}\cdot (155.75~\text{slugs})\cdot(16.82~\text{ft/s})^2 = 22,026.11~\text{ft-lbs}$$

$$ KE_{2,i} = {1 \over 2}\cdot (100.38~\text{slugs})\cdot(29.33~\text{ft/s})^2 = 43,187.66~\text{ft-lbs}$$

$$ KE_{2,f} = {1 \over 2}\cdot (100.38~\text{slugs})\cdot(14.62~\text{ft/s})^2 = 10,725.11~\text{ft-lbs}$$

Therefore:

$$ E_{Deformation} = |(22,026.11~\text{ft-lbs} + 10,725.11~\text{ft-lbs}) - (4,187.95~\text{ft-lbs} + 43,187.66~\text{ft-lbs})| $$

$$ E_{Deformation} = 14,624.38~\text{ft-lbs} \approx 19,828~\text{J}$$

This is in agreement with the reported value in the contact menu.

Deformation

The deformation value for a given vehicle is determined by the distance between the vehicle’s bounding box and the impulse centroid position, measured along the normal collision axis. This distance is generally influenced by the depth of penetration time as well as the pre-impact orientations and positions of the vehicles. In our example, the auto-position feature of the ees object was disabled so that the centroid could be moved further into the Lucid’s rear. As a result, the Lucid shows a larger deformation value compared to the Kia. In typical cases, the impulse centroid and corresponding deformation estimates will be based on known crush profiles of the subject vehicles involved.

Objects connected by joints

The Kudlich-Slibar model is used automatically for collisions between simulated vehicle objects. When vehicles are coupled by joints to other simulated objects, such as objects connected by the rope tool, or tractors being coupled to trailers, care must be taken to obtain estimates for Delta-V values. This is because the Kudlich-Slibar model will impart impulses between objects directly undergoing contact ignoring the effect of joint coupling, and joint coupling forces will be accounted for after the initial Kudlich-Slibar calculation. This means the Delta-V value displayed in the EES object for a joint coupled vehicle undergoing contact with another vehicle will not account for the additional effective mass of the connected object. In these cases, it is best to obtain cumulative Delta-V values either from the diagram tool, dynamics report data, or the dynamics info tool.

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