## 5 Conclusions and Future Plans  
In this study, a multi-DOF modeling procedure for an automotive LED headlamp assembly was proposed. This technique was utilized to predict the force transmitted through the headlamp under severe conditions when a vehicle moves across uneven road surfaces. The major contributions of this paper are as follows:  
1. A new concept for the multi-DOF modeling of an automotive LED headlamp assembly was introduced. This type of study on vibration and dynamics has not been performed on an LED headlamp; thus, a vibration model for the headlamp module was proposed to simulate the system under the desired boundary conditions. Using LEDs in automotive lighting is an emerging concept that requires additional validation and standardization studies;
2. The proposed methodology provides an understanding of the dynamics of each component of the system. In the present work, an effort has been made to determine the dynamics of the LED headlamp module to determine whether the system can withstand the forcing conditions applied by the vehicle moving across an uneven road to ensure the reliability of the equipment. Linear and angular displacements of the components of the headlamp were determined using [PERSON]'s second law, and then the force transmitted through each body was calculated using MATLAB;
3. A 3D model of the system was developed. Each mass component was considered as a cube with realistic parameters, the same as the actual device. There were four main components considered in the system: projection unit, aiming unit, bracket unit, and outer housing. The motion of each component was considered in three dimensions including a rotation point for each. A vibration model with 23 DOFs was developed, and a system of equations of motion was obtained. These equations were solved in Simulink, and the linear and angular displacements were calculated using a GUI application in MATLAB;
4. The GUI was developed to simulate the system under several conditions. The GUI provides a user-friendly interface that can be used to solve the model with just one click. Even a basic knowledge of MATLAB is sufficient to obtain results. Simulink was linked with the GUIDE application of MATLAB to obtain a UI environment. Parameters such as stiffness, length, and mass were included in this application, which can be altered to observe the behavior of the system;
5. An experiment was conducted to apply the forcing conditions that actually occur in an automobile chassis. The acceleration data in each axis was obtained using an accelerometer mounted on the vehicle. Applying this data to the developed model provided the fluctuations of the system that occur on the road. Then, the forces transmitted from the automobile chassis to the headlamp components were compared for the two cases of automobile movement. In addition, using the real data from road provided approximately the real road conditions to the simulation; \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Component** &
\begin{tabular}{c} **Force Transmitted** \\ **(\(\pm\)5)** \\ \end{tabular} & **Case I** & **Case II** & **Increase** \\ \hline Projection Unit & FX1 & \(-\)29 & \(-\)94 & 65 (224\%) \\ \(M_{1}\) & FY1 & 6 & 9 & 3 (150\%) \\  & FZ1 & 23 & 65 & 42 (282\%) \\ \hline Aiming Unit & FX2 & \(-\)41 & \(-\)132 & 91 (321\%) \\ \(M_{2}\) & FY2 & \(-\)37 & \(-\)107 & 70 (289\%) \\  & FZ2 & 27 & 71 & 44 (262\%) \\ \hline Bracket Unit & FX3 & \(-\)67 & \(-\)222 & 155 (331\%) \\  & FY3 & 10 & 33 & 23 (330\%) \\  & FZ3 & 53 & 181 & 128 (341\%) \\ \hline Housing & FX4 & \(-\)47 & \(-\)155 & 108 (329\%) \\  & FY4 & \(-\)39 & \(-\)127 & 88 (325\%) \\  & FZ4 & 49 & 150 & 101 (306\%) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of force transmission results from GUI for case I and case II. hence, extensive experimental work could be avoided, and authentic anticipation of results can be achieved  
This analysis successfully identified the locations in the system with higher displacements and forces.