5.3. NUMERICAL ANALYSIS OF NATURAL FREQUENCIES AND MODES 75
in the same direction, the twelfth and thirteenth orders are the TV of the short planets, and the
fourteenth order is the TV of the long and short planets in opposite directions.
It can be seen from Figs. 5.3–5.6 that the amplitude of the whole drive train is larger that
of in the first-order mode, the left-wheel amplitude is the largest in the second-order mode, and
the right wheel also has a large amplitude; the third-order mode has the largest amplitude and
the left wheel amplitude is larger; the fourth-order mode has the largest amplitude of the large
sun gear, and the amplitude of the small sun gear is obvious; the fifth-order mode corresponds
to the differential. e reducer also has large amplitude; the sixth-order mode corresponds to
the differential, but the ring gear and the reducer also have a large amplitude. e amplitude
of the reducer is the largest at the seventh-order natural frequency, and the differential and the
ring gear also have a large amplitude; the amplitude of the long planetary gear 2 is larger at
the eighth-order natural frequency, and the long planetary gear 3 has a larger reverse vibration.
e three long planetary gears at the tenth order mode has the largest amplitude, and the three
short planetary wheels also have a large amplitude, the eleventh natural frequency has the largest
amplitude of the short planetary gear 2, and the short planetary gear 3 also has a large ampli-
tude. At the twelfth-order mode, the short planetary gear 3 has the largest amplitude, and the
short planetary gear 1 and the long planetary gear 3 also have a large amplitude; the three short
planetary gears have the largest amplitude at the thirteenth natural frequency, and the three
long planetary gears also have large amplitude. Comparing with the experimental results, it can
be found that the fifth and sixth orders in pure electric working conditions are the important
reasons for the vibration and noise of the drive train. Figures 5.7–5.11 show the mode shapes of
the powertrain in hybrid driving mode.
As can be seen from Fig. 5.7, in the hybrid driving mode, the low orders of eigen modes
and frequencies are also referred to the vehicle and driving wheels. As shown from Fig. 5.8, the
sixth mode seems to be a coupled vibration corresponding to differential, carrier, reducer, and
ring, the seventh mode corresponds TV of the differential, the eighth mode represents TV of
the short and long planets, the ninth mode is referred to the TV of the long and short planets
and the differential, and the tenth to fifteenth modes are corresponding to higher frequency
TVs of short planets and long planets.
It can be concluded that the low-order frequencies are mainly relevant to the vehicle and
wheels, the middle frequencies are related to the TV of sun gears, differential and reducer, and
the high orders are concentrated on differential, reducer, and planets in both driving mode.
It can be seen from Figs. 5.7–5.11 that the amplitude of the entire drive train is larger
in the first mode, the amplitude of the engine and the left wheel is the largest at the second-
order natural frequency, the left and right wheels have the largest amplitude at the third-order
natural frequency. In the fourth-order mode, the amplitude of the planet carrier, the large sun
gear, the three long planetary gears, the three short planetary gears, the ring gear, the speed
reducer, and the differential are relatively large. In the fifth-order mode, the amplitude of the
differential is the largest, the amplitude of the carrier, the reducer, and the ring gear is large,
76 5. MATHEMATICAL MODELING AND TV ANALYSIS OFHYBRID ELECTRIC VEHICLES
f1 = 5.6
f2 = 17.3
f3 = 26.1
1.0
0.5
0.0
-0.5
-1.0
Components of Vibration
Relative Amplitude of Eigenvectors
? ?2 ?3 ???? ???? ?? ?? ?? ?2 ?1 ?2 ?3 ?1
Figure 5.7: e first, second, and third eigen modes of TVs of drivetrain in the hybrid driving
condition.
5.3. NUMERICAL ANALYSIS OF NATURAL FREQUENCIES AND MODES 77
f4 = 27.1
f5 = 836.1
f6 = 4441
1.0
0.5
0.0
-0.5
-1.0
Components of Vibration
Relative Amplitude of Eigenvectors
? ?2 ?3 ???? ???? ?? ?? ?? ?2 ?1 ?2 ?3 ?1
Figure 5.8: e fourth through sixth eigen modes of TVs of the drivetrain in the hybrid driving
condition.
78 5. MATHEMATICAL MODELING AND TV ANALYSIS OFHYBRID ELECTRIC VEHICLES
f7 = 3722
f8 = 4441
f9 = 10023
1.0
0.5
0.0
-0.5
-1.0
Components of Vibration
Relative Amplitude of Eigenvectors
? ?2 ?3 ???? ???? ?? ?? ?? ?2 ?1 ?2 ?3 ?1
Figure 5.9: e seventh through ninth eigen modes of TVs of the drivetrain in the hybrid driving
condition.
5.3. NUMERICAL ANALYSIS OF NATURAL FREQUENCIES AND MODES 79
f10 = 10023
f11 = 10508
f12 = 14641
1.0
0.5
0.0
-0.5
-1.0
Components of Vibration
Relative Amplitude of Eigenvectors
? ?2 ?3 ???? ???? ?? ?? ?? ?2 ?1 ?2 ?3 ?1
Figure 5.10: e tenth through twelfth eigen modes of TVs of the drivetrain in the hybrid
driving condition.
..................Content has been hidden....................
You can't read the all page of ebook, please click here login for view all page.