Mathematical Model for the Rotation of a Door Including Vehicle
Inclination 2024-01-5045
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.