4.1. GEAR PAIR MESHING IMPACT RESPONSE ANALYSIS 57
Considering v
1a
D v
2a
C v
a
; v
0
1a
D v
0
2a
C v, Eq. (4.17) can be written as
.
M
1
C M
2
/
v
2a
.
M
1
C M
2
/
v
2a
D M
1
v
a
M
1
v: (4.19)
Denote M D
M
1
M
2
M
1
CM
2
as the equivalent mass of the gear system, one can obtain
t
c
Z
0
f
a
.t/dt D M v
a
Mv: (4.20)
Assuming that the two gear enters normal meshing after the impact, then the relative
speed of the meshing point v will be 0, which means
t
c
Z
0
f
a
.t/dt D M v
a
: (4.21)
Replace Eq. (4.13) and !
c
D =t
c
in the type (4.21), we can obtain
t
c
Z
0
f
a
.t/dt D
t
c
Z
0
F
m
sin !
c
t dt D
2F
m
!
c
D
2F
m
t
c
: (4.22)
en, the time of gear meshing impact t
c
can be expressed as following:
t
c
D
2
M v
a
F
m
: (4.23)
4.1.2 CALCULATION OF IMPACT ACCELERATION SOUND PRESSURE
e acceleration noise produced by gear impacting at a certain point in the process of gear
grinding can be viewed as the acceleration noise produced by two cylinders with variable radius
of curvature impacting each other. Since the near sound field is difficult to be calculated, We
compute the sound pressure of the far sound field as [37]:
When 0 t
0
t
c
,
p.r; ; t/ D A
B cos !
c
t
0
C D sin !
c
t
0
C E cos l
1
t
0
e
t
2
t
0
C F
1
sin l
1
t
0
e
t
2
t
0
: (4.24)
When t
0
> t
c
,
p.r; ; t/ DA
˚
G cos
.
!
c
C l
1
/
t
c
l
1
t
0
H sin
.
!
c
C l
1
/
t
c
l
1
t
0
C X cos
.
!
c
l
1
/
t
c
l
1
t
0
C Y sin
.
!
c
l
1
/
t
c
l
1
t
0
e
t
2
.t
0
t
c
/
C
E cos l
1
t
0
C F sin l
1
t
0
e
t
2
t
0
o
; (4.25)
58 4. TRANSMISSIONSYSTEM PARAMETERSAND MESHING STIFFNESS CALCULATION
where l
1
D
p
95c
16a
; l
2
D
7c
16a
; t
0
D t
ra
c
, and c is the velocity of sound.
A D
r
a
r
a
2
cos
r
a
m
0
B D
1
p
95
8r
a
7
3
.
A
1
C B
1
/
!
c
1
3
.
C
1
C D
1
/
!
c
D D 1 C
1
p
95
8r
a
7
3
.
C
1
D
1
/
!
c
1
3
.
A
1
C B
1
/
!
c
E D
1
p
95
8r
a
7
3
.
E
1
C F
1
/
C
1
3
.
C
1
C D
1
/
!
c
F D
1
p
95
8r
a
7
3
.
C
1
D
1
/
!
c
C
1
3
.
E
1
C F
1
/
G D
1
p
95
8r
a
7
3
F
1
C
1
3
D
1
!
c
H D
1
p
95
8r
a
7
3
D
1
!
c
1
3
F
1
X D
1
p
95
8r
a
7
3
E
1
1
3
C
1
!
c
Y D
1
p
95
8r
a
7
3
C
1
!
c
1
3
E
1
:
Inside,
A
1
D
!
c
l
1
.
!
c
l
1
/
2
C l
2
2
B
1
D
!
c
C l
1
.
!
c
C l
1
/
2
C l
2
2
C
1
D
l
2
.
!
c
l
1
/
2
C l
2
2
D
1
D
l
2
.
!
c
C l
1
/
2
C l
2
2
E
1
D
!
c
l
1
l
2
1
l
2
2
.
!
c
l
1
/
2
C l
2
2
F
1
D
!
c
l
1
C l
2
1
C l
2
2
.
!
c
C l
1
/
2
C l
2
2
:
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