Mathematical Model for the Rotation of a Door Including Vehicle Inclination

The analysis presented in this document demonstrates the mathematical model approach for determining the rotation of a door about the hinge axis. Additional results from the model are the torque due to gravity about the axis, opening force, and the door hold open check link force. Vector mechanics, equations of a plane, and parametric equations were utilized to develop this model, which only requires coordinate points as inputs. This model allows for various hinge axis angles and door rotation angles to quickly be analyzed. Vehicle pitch and roll angles may also be input along with door mass to determine the torque about the hinge axis. The vector calculations to determine the moment arm of the door check link and its resulting force are demonstrated for both a standard check link design and an alternate check link design that has the link connected to a slider translated along a shaft. This math model may be implemented using commonly available programs such as Microsoft Excel VBA or MATLAB. This paper will showcase some inputs and results from the calculations that were coded into Excel VBA. To validate the model’s accuracy, computer-aided design (CAD) software NX was employed to confirm the rotation points determined by the model. It is shown that the coded program results for the door check link moment arm (perpendicular distance between the hinge axis and the line of action of the check link) match the dimensions measured in NX after rotating the input points in the CAD file. Torque measurements were also taken on the vehicle at various pitch and roll angles to confirm the calculation for torque.