## 1 Introduction  
A grommet is typically made from hyper-elastic materials, such as the ethylene propylene diene monomer (EPDM), and is used to secure the position of cables embedded in a vehicle [1; 2; 3; 4; 5; 6; 7]. Because EPDM materials boast excellent elasticity-recovery properties and a high friction coefficient, they are utilized in research on bonded and dustproof parts [8; 9; 10].  
The existing grommet parts are joined to cables through a bonding process. There have also been other problems, such as the generation of hazardous substances during manufacturing or in the process of separating the cable. Accordingly, recent studies have investigated a grommet structure that is physically bonded with the cable.  
Physical bonding is more environmentally friendly than chemical bonding and allows for easier dismantling; however, it has the disadvantage of having a low bonding force. In a related study, the bonding force was enhanced by approximating the physical properties of the parts and modifying their shape through finite element analysis (FEA). However, the process of approximating EPDM or rubber depends only on the strain-stress properties and does not consider the interaction with other parts.  
Physical properties related to the elasticity of rubber can generally be derived by standard test methods, such as ASTM D412-16 and KS M 6518 [11; 12]. In addition, strain-stress data can be approximated through mathematical models, such as the [PERSON] model [13], Yeoh model [14],Gent model [15], and Ogden model [16; 17; 18; 19; 20]. The mathematically defined physical properties are applied to FEA and compared with the experimental results by using the mean square error technique. If the mean square error does not satisfy the reference value, the design of experiments (DOE) or genetic algorithms can be utilized to modify the parameters of the mathematical model, thereby changing the results of the FEA. The technique of repeating this process to reduce the error in the experimental results is referred to as the inverse method and is used to improve the reliability of FEA results. The inverse method is generally used for curve fitting the strain-stress curve for tensile specimens [21; 22; 23; 24]. By defining the property values used in FEA through the inverse method, the thickness, geometry, and analysis conditions of the finite element model can be varied to enhance product performance [25]. However, the performance of rubber parts cannot be sufficiently expressed by elasticity alone. Because not only grommets but also rubber parts are commonly bound to other parts, their interaction with other parts must be considered. By using the inverse method to approximate the elasticity and interaction relationship that affects the bonding force, an accurate prediction of grommet performance can be obtained through FEA.  
This paper proposes an experiment and inverse analysis method to approximate the bonding force of a grommet part with a hollow shaft structure. A tensile experiment was performed on the EPDM material, and the inverse method was applied to the displacement-force data. The physical properties of the finite element model are defined through the Ogden model, and the Ogden coefficient values are used as parameters in the inverse method. The bonding force of the grommet was tested, and the inverse method was applied to the displacement-force data. A contact condition was assumed for the relationship between the grommet and cable forming the bonding force. The correlation was assumed to be a scale factor of the bonding force and used as a parameter in the inverse method. Additionally, the Box-Behnken DOE, for approximating the bonding force according to the geometry variables, was used to derive a regression equation. Based on the predicted values of the derived regression equation and the FEA results, as well as the comparison of the experimental results, the bonding force approximation model was validated.