51
C H A P T E R 4
Transmission System
Parameters and Meshing
Stiffness Calculation
In this section, the meshing stiffness is first computed according to the Ishikawa formula [37],
and the meshing noises of the gear are then derived. In this chapter, the gear width is set as b,
the tooth surface normal load on the gear is F
N
, the tooth width of the gear unit is !, and the
total teeth deformation is defined as ı.
Based on the above definitions, the stiffness k of the individual tooth of the gear can be
defined by [37]:
k D
F
N
ı b
: (4.1)
e comprehensive meshing stiffness K of any gears pair can be described by:
K D
k
1
k
2
k
1
C k
2
; (4.2)
where k
1
and k
2
are the tooth stiffnesses of both the drive and driven gears.
e gear teeth number in the hybrid powertrain is shown in Table 4.1. e inertia and
material properties of the drive train components are tabulated in Table 4.2.
Table 4.1: Gear teeth quantity in the hybrid transmission
Name Number of Teeth Serial Number Name Number of Teeth
1 Small sun gear 23 6 Outer ring gear 41
2 Big sun gear 31 7 Reducer gear 75
3
Short planetary
gear
25 8 Reducer pinion 38
4
Long planetary
gear
18 9 Diff erential gear 85
5 Inner ring gear 73
52 4. TRANSMISSIONSYSTEM PARAMETERSAND MESHING STIFFNESS CALCULATION
Table 4.2: Inertia and material properties of the driveline components
Part Name Parameter Value
1 Engine rotating component assembly moment of inertia 0.28 kg·m
2
2 Planet carrier and motor assembly moment of inertia 0.0661 kg·m
2
3 Diff erential assembly moment of inertia 0.015 kg·m
2
4 Wheel moment of inertia 1.83 kg·m
2
5 Planetary frame assembly quality 2.53 kg
6 Motor 1 moment of inertia 0.027 kg·m
2
7 Motor 2 moment of inertia 0.037 kg·m
2
8 Diff erential assembly quality 4.43 kg
9 Damping shock absorber TS 618 Nm/rad
10 Left half shaft TS 5520 Nm/rad
11 Right half shaft TS 4222 Nm/rad
12 Tire TS 780 Nm/rad
13 Vehicle quality 1250 kg
Ishikawa Formula is mainly applied for gear meshing stiffness calculation. is formula
regards the gear tooth end face as a combination of a rectangle and a trapezoid. e total meshing
deformation is the sum of the rectangular part bending deformation, trapezoidal part deforma-
tion, shear deformation, the base part inclination deformation, and contact deformation. e
graphical representation of this formula is shown in Fig. 4.1.
e deformation ı of the load that is acting along the meshing line can be calculated by
the following equation [37]:
ı D ı
Br
C ı
Bt
C ı
S
C ı
G
; (4.3)
where ı
Br
refers to the deformation of the rectangular part [37]:
ı
Br
D
12F
N
cos
2
!
x
Ebs
2
F
h
x
h
r
.
h
x
h
r
/
C
h
3
r
3
: (4.4)
ı
Bt
is the amount of bending deformation of the trapezoidal part [37]:
ı
Bt
D
6F
N
cos
2
!
x
Ebs
3
F
h
i
h
x
h
i
h
r
4
h
i
h
x
h
i
h
r
2 ln
h
i
h
x
h
i
h
r
3
.
h
i
h
r
/
3
: (4.5)
ı
S
is the amount of deformation caused by shear:
ı
Br
D
12F
N
cos
2
!
x
Ebs
2
F
h
x
h
r
.
h
x
h
r
/
C
h
3
r
3
: (4.6)
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