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. 2021 Sep 22;21(19):6328. doi: 10.3390/s21196328
cm Mesh damping of the gear pair
cc Contact damping of the cam-tappet pair
este(t) Static transmission error
fc Cam centrifugal force
km Mesh stiffness of the gear pair
kc Contact stiffness of the cam-tappet pair
mc The mass of the cam
mp The mass of the pinion
mg The mass of the gear
md The mass of the disc
mi The mass of ith element
q Displacement vector of the overall DOF
q i s Displacement vector of the shaft element
q s Displacement vector of arbitrary point on the shaft
q g Displacement vector of the meshing gear pair
q i d Displacement vector of node i on the rotor disc
q i k Displacement vector of node i on the beam element
q i b Displacement vector of node i on the bar element
q c Displacement vector of the cam-tappet pair
rbp The base radius of the pinion
rbg The base radius of the gear
ui The ith DOF of the dynamic model
A The cross-sectional area of the shaft element
B The half of gear backlash
C b Damping matrix of the bearing
C g Damping matrix of the gear pair
C c Damping matrix of the cam-tappet pair
C Overall damping matrix of the dynamic model
E Young’s modulus of the material
F i s Force matrix of the shaft element
F i d Force matrix of the rotor disc
F c Contact force of the cam-tappet pair
F c Force matrix of the cam-tappet pair
F Overall force matrix of the dynamic model
G Overall gyroscopic matrix of the dynamic model
G i s Gyroscopic matrix of the shaft element
G i d Gyroscopic matrix of the rotor disc
JDs Diameter mass moments of inertia of the shaft element
JPs Polar mass moments of inertia of the shaft element
JDd The moment of inertia about a diameter of the disc
JPd The polar moment of inertia of the disc
JPp The polar moment of inertia of the pinion
JDp The moment of inertia about a diameter of the pinion
JDg The moment of inertia about a diameter of the gear
JPg The polar moment of inertia of the gear
JPc The polar moment of inertia of the cam
JDc The moment of inertia about a diameter of the cam
K i s The stiffness matric of the shaft element
K b The stiffness matric of the ball bearing
K g Stiffness matrix of the gear pair
K c Stiffness matrix of the cam-tappet pair
K Overall stiffness matrix of the dynamic model
Li The length of ith element
M i s Mass matrix of the shaft element
M i d Mass matrix of the rotor disc
M g Mass matrix of the gear pair
M c Mass matrix of the cam-tappet contact
M Overall mass matrix of the dynamic model
N Shape function of the shaft element
αt Transverse pressure angle
βb Base helix angle
δm Dynamic displacement of the meshing gear pair
δc Dynamic deformation of the cam-tappet pair
μ Friction coefficient of the cam-tappet pair
ρ Material density of the shaft element
φ Phase angle of the cam
φ 0 Initial phase angle of the cam
Ω Spin speed of the shaft