## 2 Proposed Method  
The headlamp is an essential part of the vehicle; hence, its proper functioning is vital. To achieve highly reliable products that can withstand various types of applied forces, the real-life conditions occurring in the headlamp assembly inside the system must be observed. In the past, research is done on the 3D models of headlamps and analyzed using ANSYS. Modal analysis and PSD results are commonly used for durability and deformation prediction inside the assembly. These studies have not briefly described the inner mounting conditions of different components and their stiffness. The proposed work has discussed the components separately and all the supports are modeled by considering three dimensional effects. It helps achieve better results close to the real conditions. As mentioned in the literature background, natural frequencies of the system are mostly calculated for dynamic study of the assembly. Then the obtained values are compared to the vibration frequency of the engine. Then resonance between the headlamp and engine is focused. However, in the presented article, the effect of road surface oscillations is studied which have higher magnitude as compared to the ones produced by the engine. Hence, the study provides more useful results for headlamp mountings design. A simulation technique is proposed based on the vibration analysis of the equipment. The system is modeled in terms of the equations of motion, and then the displacements of the components of the headlamp assembly are solved. Owing to the difficultly of conducting experiments on an actual model in the laboratory, the exact boundary conditions and real-life excitation force must be applied to obtain accurate displacement values.  
The headlamp model studied contains many small components, such as controller chips and wires; and thermal management equipment, such as a heat sink and fan. The major parts are the main projection unit, aiming unit, bracket unit, and outer housing. These four parts are considered in this analysis. The actual model could not be presented because of the manufacturer's copyright restrictions. Figure 1 shows the assembly of these components in three dimensions.  
The projection unit \(M_{1}\) is the main component, which consists of a semiconductor light source and an arrangement of lenses to aim the light beam toward the required area on the road. It is connected to three other components with fixed and rotational supports. Each contact point has a stiffness value in every axis. A total of four components are studied with three-dimensional stiffness supports, which contribute 12 DOFs.  
Figure 1 shows that each component has an origin of rotation. The points a, b, c, d, and e are the locations where the main projection unit, aiming unit, bracket unit, and housing have rotational DOFs, respectively. Because these are three-dimensional rational supports, there will be 12 additional DOFs included in the system, for a total of 24 DOFs; the developed model has 23 DOFs, only in the case of rotation where no moment was applied to the body. The equations of motion for each DOF were derived and modeled in Simulink. The obtained linear and angular displacements were used to calculate the transmitted force. The different parameters used in the analysis, such as mass, length, and angular moments of inertia, are listed in Table 1.  
Figure 1: Demonstration of four components.