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 |