Pulse Index
During the early stages of vehicle development, it can be useful to understand occupant acceleration without needing to include a complex and computationally expensive occupant model.
The Pulse Index Workflow allows you to estimate the acceleration that would be experienced by a vehicle occupant in a crash test scenario.
The tool assumes a virtual single-degree-of-freedom mass-spring system in which the occupant is represented by a mass and the seatbelt is represented by a spring. See below for more details of the pulse index calculation.
This virtual mass-spring system is effectively attached to a selected node moving with a set initial velocity.
The tool optionally takes a slack input to account for seatbelt engagement.
How to use the Pulse Index tool in PRIMER
Access the Pulse Index tool from the Workflows menu in PRIMER. Upon selecting the Pulse Index tool, the following menu will appear:
Units System
Select the appropriate units system for your model. All of the input will be expecting an input in the selected units system. When the selected unit system is changed, all existing inputs are automatically converted to the new units system.
Initial velocity
Enter the initial velocity of the vehicle.
Restraint stiffness
The Pulse Index can either be calculated with constant or variable restraint stiffness (must be a non-zero positive value). The model assumes a unit mass therefore the restraint stiffness must be scaled accordingly based on the expected mass of the occupant. For stiffness, enter a non-zero stiffness value. For stiffness, select a *DEFINE_CURVE keyword that defines the variable stiffness in terms of the model units (you may need to create a new keyword before making the selection). If a constant stiffness is provided, the time period \(T\) for the mass spring system will be displayed to the right of the Select Curve button (this allows the user to ensure the given stiffness is reasonable).
Slack (optional)
You can choose to add slack to the seatbelt. This option allows the virtual vehicle occupant to move freely for a specified distance before the restraint stiffness begins to take effect. Slack works with both constant and variable stiffness options.
Measurement node
Select a *DATABASE_HISTORY_NODE that will be used as the node on the vehicle structure to which the virtual single-degree-of-freedom mass-spring system will be attached.
Display Units
Select time (Seconds or Milliseconds) and displacement units (Metres, Millimetres or Feet) to use on the graphs using the dropdowns. For the acceleration graph use the radio buttons to calculate in g or the display units. Please note if the Unit System is changed, the Time and Displacement Units will default to the matching ones for the Unit System, for example changing to U5 would default the Time units to Seconds and the Displacement units to Feet.
Acceleration Filter
Select the filter which is applied to the vehicle acceleration data before calculation. You can choose from three options, C60, C180, and C600.
Read Velocity
If desired, vehicle velocity can be used in the calculation rather than vehicle acceleration. This is done by differentiating the velocity curve with respect to time and using the resulting curve in place of direct vehicle acceleration data.
Save
You can save the Workflow Definition to a .json file or to the model (as post-*END data). When saving to the model, you will need to write the model from PRIMER in order to save the changes to the keyword file.
How to use the Pulse Index tool in T/HIS
Access the Pulse Index tool from the Workflows menu in T/HIS. Upon selecting the Pulse Index tool, the same menu appears as in PRIMER. This allows you to adjust some of the input parameters when performing the pulse index calculation. The Measurement Node and Variable Stiffness settings can only be modified in PRIMER.
Calculate
If the input parameters are valid, the button will become active. Clicking executes the pulse index calculation and produces a four-graph layout comparing Vehicle and Virtual Occupant results, such as in this example:
Pulse Index Calculation
Initial Conditions
The vehicle and virtual occupant both start with zero initial displacement:
\(s_t^{veh} = s_t^{occ} = 0\)
The vehicle and the virtual occupant are both given the same initial velocity, defined by you in PRIMER. In PRIMER, you also specify the restraint system stiffness \(k\) and the measurement node for the vehicle acceleration \(a_t^{veh}\).
Iterative Calculation
The Pulse Index Workflow performs an iterative calculation to determine the displacement \(s_t^{occ}\), velocity \(v_t^{occ}\) and acceleration \(a_t^{occ}\) experienced by the virtual occupant over time. First, the vehicle's velocity \(v_{t+1}^{veh}\) and displacement \(s_{t+1}^{veh}\) at time \(t+1\) are calculated from its acceleration \(a_t^{veh}\):
\(v_{t+1}^{veh} = v_t^{veh} + a_t^{veh} * dt\)
\(s_{t+1}^{veh} = s_t^{veh} + v_t^{veh} * dt\)
Then the displacement \(x\) between the vehicle and virtual occupant is calculated and the effective spring displacement \(x_{eff}\) is found:
\(x = s_t^{occ} - s_t^{veh}\)
\(x_{eff} = (|x| - slack) \ge 0\)
The occupant acceleration is then calculated from the spring displacement, and the restraint stiffness \(k\). Occupant mass \(m\) has been included in the below equation for clarity, however, since a unit mass is taken it can effectively be ignored:
\(a_t^{occ} = \frac{k}{m}x_{eff}\)
Finally, the occupant's resultant velocity and displacement are calculated, ready for the next time iteration:
\(v_{t+1}^{occ} = v_t^{occ} + a_t^{occ} * dt\)
\(s_{t+1}^{occ} = s_t^{occ} + v_t^{occ} * dt\)