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Automotive Innovation

, Volume 1, Issue 3, pp 263–271 | Cite as

Investigation and Application on the Vertical Vibration Models of the Seated Human Body

  • Xiong ShaoEmail author
  • Nan Xu
  • Xiang Liu
Article
  • 524 Downloads

Abstract

Investigation of the vertical vibration characteristics of the seated human body is beneficial for the design and development of vehicle ride comfort. In this study, we first established models of the seated human body with two, three and four degrees of freedom (DOF). Then, the vibration characteristics of 30 volunteers were tested under standard conditions with a vibration test rig to obtain data for the apparent mass, driving point mechanical impedance, and seat-to-head transfer function. Based on the experimental data, the parameters of these models are identified and the results show that the four-DOF model can simulate the vertical vibration characteristics of the seated human body more comprehensively. Then, different seated human body models were applied to optimize the damping of shock absorber. The results show that the optimized damping with the four-DOF Chinese seated human body model is 27% more than that with rigid mass and 7% less than that with ISO 5982:2001 seated human body model.

Keywords

Seated human body model Apparent mass Driving point mechanical impedance Seat-to-head transfer function Optimization design of damping 

Abbreviations

AM

Apparent mass

DOF

Degrees of freedom

DPM

Driving point mechanical impedance

STH

Seat-to-head transfer function

\( {\text{AM}}\left( \omega \right) \)

Spectrum of the AM

\( {\text{DPM}}\left( \omega \right) \)

Spectrum of the DPM

\( {\text{STH}}\left( \omega \right) \)

Spectrum of the STH

\( F\left( \omega \right) \)

Spectrum of exciting force between the seat panel and seated human body

\( a_{0} \left( \omega \right) \)

Spectrum of acceleration of the force-measuring panel

\( v_{0} \left( \omega \right) \)

Spectrum of velocity of the force-measuring panel

\( a_{1} \left( \omega \right) \)

Spectrum of acceleration of the volunteer’s head

\( F \)

Exciting force between the seat panel and the seated human body

\( F_{\text{t}} \)

Force sensor signal under the force-measuring panel

\( m_{\text{plate}} \)

Mass of the force-measuring plate

\( a_{0} \)

Acceleration signal of the force-measuring panel

\( g \)

Acceleration of gravity

mu

Unsprung mass

ms

Sprung mass

mc

Cushion mass

cs

Shock absorber damping

cc

Cushion damping

kt

Tire stiffness

ks

Spring stiffness

kc

Cushion stiffness

krl

Suspension rebound limit stiffness

kcl

Suspension compression limit stiffness

Arl

Suspension rebound limit stroke

Acl

Suspension compression limit stroke

r

Leverage ratio

\( \sigma_{\text{fd}} \)

Root-mean-square of the suspension dynamic travel

\( \left[ {f_{\text{d}} } \right] \)

Stroke limit of suspension

\( \varsigma \)

Root-mean-square of the dynamic wheel load

1 Introduction

With continued economic development and improvement in the Chinese standard of living, consumers are paying increased attention to vehicle ride comfort. At present, ride comfort is improved mainly by optimizing the parameters for the suspension, tire and seat. However, kinetics of the human body is seldom considered, or it is regarded as a rigid mass. When the frequency is larger than 2 Hz, the dynamic response characteristics between the human body and a rigid mass are different [1]. This indicates that the ride comfort of the vehicle is related not only to the parameters for suspension, tire and seat but also to the vibration characteristics of the seated human body [2]. Therefore, the vertical vibration characteristics of the seated human body are studied, and a dynamic model of human–vehicle–road system has been established to contribute to the development of vehicle ride comfort.

Seated human body models mainly include the centralized mass parameter model [3], the finite element model [4, 5], the multi-body dynamics model [6] and the neural network model [7]. As the centralized mass parameter model is simple and practical, it has been studied often.

In 1962, Coermann [1] was the first to study the vibration characteristics of the seated human body and establish a model with a single degree of freedom (DOF) using the mechanical impedance data of eight volunteers. In 1969, Suggs et al. [8] proposed a parallel two-DOF model to simulate the mechanical impedance of the seated human body. In 1981, standard ISO 5982:1981 [9] was promulgated, and it included the same two-DOF model proposed by Suggs and summarized the relevant research results available at that time. The standard was later revised as ISO 5982:2001 [10], and the revision included a three-DOF model that can simulate the apparent mass (AM), driving point mechanical impedance (DPM) and seat-to-head transfer function (STH) characteristics of the seated human body. In addition to the above models, other researchers also proposed a 4-DOF model [11, 12], 6-DOF model [13], 7-DOF model [14, 15], 9-DOF model [16], 11-DOF model [17] and 15-DOF model [18]. In 2005, Maeda and Mansfield [19] found that there was a clear difference between the AM of Japanese subjects and ISO 5982:2001 data and that it was not sufficient to apply the ISO 5982 standard to Japanese vehicle design or crash-test dummy design.

In 1986, Feng [20] studied the vertical vibration characteristics of the Chinese seated human body by testing the mechanical impedance of 11 volunteers and establishing a parallel two-DOF model. In 1996, Chinese standard GB/T 16440 [21] was established using the average DPM vibration characteristics of 60 subjects, and it used a parallel three-DOF model. However, this standard has not yet been revised or updated. In 2008, Zhang et al. [22] established a four-DOF model, and the model parameters were identified based on the AM, DPM and STH data published in various non-Chinese studies. Zhang et al. [23] and Liu et al. [24], respectively, established five-DOF and seven-DOF models; however, the model parameters were identified only from STH characteristics. In 2011, Hou and Gao et al. [25, 26] obtained the AM characteristics of 28 subjects and identified the parameters of the two-DOF and three-DOF models. However, the STH characteristics were not obtained due to inadequate test conditions, and the vertical vibration characteristics of the seated human body were not studied comprehensively [27].

In summary, European and American researchers have studied the seated human body continuously and comprehensively. However, Chinese researchers have studied only single vertical vibration characteristics of the seated human body, which makes it difficult to establish a comprehensive vertical vibration model for the Chinese seated human body. Therefore, it is necessary to carry out a comprehensive study of the vertical vibration characteristics of the seated human body using Chinese subjects.

2 Vertical Vibration Models of the Seated Human Body

Because the finite element, multi-body dynamics and neural network models are complex, they have high computational burdens. Therefore, this study used the centralized mass parameter model to simulate the vertical vibration characteristics of the seated human body.

The AM, DPM and STH are usually used to simulate the vertical vibration characteristics of the seated human body, and their original definitions are as follows [5]:
$$ {\text{AM}}\left( \omega \right) = {{F\left( \omega \right)} \mathord{\left/ {\vphantom {{F\left( \omega \right)} {a_{0} \left( \omega \right)}}} \right. \kern-0pt} {a_{0} \left( \omega \right)}} $$
(1)
$$ {\text{DPM}}\left( \omega \right) = {{F\left( \omega \right)} \mathord{\left/ {\vphantom {{F\left( \omega \right)} {v_{0} \left( \omega \right)}}} \right. \kern-0pt} {v_{0} \left( \omega \right)}} $$
(2)
$$ {\text{STH}}\left( \omega \right) = {{a_{1} \left( \omega \right)} \mathord{\left/ {\vphantom {{a_{1} \left( \omega \right)} {a_{0} \left( \omega \right)}}} \right. \kern-0pt} {a_{0} \left( \omega \right)}}, $$
(3)
where \( {\text{AM}}\left( \omega \right) \) is the spectrum of the AM, \( {\text{DPM}}\left( \omega \right) \) is the spectrum of the DPM, \( {\text{STH}}\left( \omega \right) \) is the spectrum of the STH, \( F\left( \omega \right) \) is the spectrum of the excitation force between the seat panel and seated human body, \( a_{0} \left( \omega \right) \) is the spectrum of acceleration of the force-measuring panel, \( v_{0} \left( \omega \right) \) is the spectrum of velocity of the force-measuring panel, and \( a_{1} \left( \omega \right) \) is the spectrum of acceleration of the volunteer’s head.

2.1 Vertical Vibration Models of the Seated Human Body

This section describes the equations for centralized mass parameter models of the seated human body with two, three and four DOF.

2.1.1 Two-DOF Model

The two-DOF model established by Suggs [3] is shown in Fig. 1. The model can simulate AM and DPM characteristics of the seated human body.
Fig. 1

Two-DOF model of the seated human body

The differential equations of vibration for the two-DOF model are as follows:
$$ F = m_{0} \ddot{z}_{0} + m_{1} \ddot{z}_{1} + m_{2} \ddot{z}_{2} $$
(4)
$$ m_{1} \ddot{z}_{1} = \left( {z_{0} - z_{1} } \right)k_{1} + \left( {\dot{z}_{0} - \dot{z}_{1} } \right)c_{1} $$
(5)
$$ m_{2} \ddot{z}_{2} = \left( {z_{0} - z_{2} } \right)k_{2} + \left( {\dot{z}_{0} - \dot{z}_{2} } \right)c_{2} . $$
(6)
The Laplacian transformation of the above formulas yields the following equations:
$$ F\left( s \right) = m_{0} s^{2} z_{0} \left( s \right) + m_{1} s^{2} z_{1} \left( s \right) + m_{2} s^{2} z_{2} \left( s \right) $$
(7)
$$ \left( {m_{1} s^{2} + k_{1} + c_{1} s} \right)z_{1} \left( s \right) = \left( {k_{1} + c_{1} s} \right)z_{0} \left( s \right) $$
(8)
$$ \left( {m_{2} s^{2} + k_{2} + c_{2} s} \right)z_{2} \left( s \right) = \left( {k_{2} + c_{2} s} \right)z_{0} \left( s \right). $$
(9)
The AM and DPM of the two-DOF model of the seated human body are calculated by the following formulas:
$$ {\text{AM}}\left( s \right) = {{F\left( s \right)} \mathord{\left/ {\vphantom {{F\left( s \right)} {a_{0} \left( s \right)}}} \right. \kern-0pt} {a_{0} \left( s \right)}} $$
(10)
$$ {\text{DPM}}\left( s \right) = {{F\left( s \right)} \mathord{\left/ {\vphantom {{F\left( s \right)} {v_{0} \left( s \right)}}} \right. \kern-0pt} {v_{0} \left( s \right)}}, $$
(11)
where a0 is the acceleration of m0, \( a_{0} \left( s \right) = s^{2} z_{0} \left( s \right) \), v0 is the velocity of m0, \( v_{0} \left( s \right) = sz_{0} \left( s \right) \), and \( s = \omega j \). After substituting these parameters into formula (10) and formula (11), the expressions of AM and DPM are as follows:
$$ {\text{AM}}\left( \omega \right) = m_{o} + \frac{{\left( {k_{1} + c_{1} \omega j} \right)m_{1} }}{{\left( {k_{1} - m_{1} \omega^{2} + c_{1} \omega j} \right)}} + \frac{{\left( {k_{2} + c_{2} \omega j} \right)m_{2} }}{{\left( {k_{2} - m_{2} \omega^{2} + c_{2} \omega j} \right)}} $$
(12)
$$ {\text{DPM}}\left( \omega \right) = {\text{AM}}\left( \omega \right) \cdot \omega j. $$
(13)

2.1.2 Three-DOF Model

The ISO 5982:2001 standard [5] established the three-DOF model of the seated human body. In this model, \( m_{2} \) represents the head, as shown in Fig. 2. The model can simulate AM, DPM and STH characteristics of the seated human body.
Fig. 2

Three-DOF model of the seated human body

The derived mathematical expressions for the AM, DPM, and STH are as follows:
$$ \begin{aligned} &{\text{AM}}\left( \omega \right) = m_{o} + \frac{{\left( {k_{3} + c_{3} \omega j} \right)m_{3} }}{{\left( {k_{3} - m_{3} \omega^{2} + c_{3} \omega j} \right)}} \\ & \quad + \frac{{\left( {k_{2} - m_{2} \omega^{2} + c_{2} \omega j} \right)\left( {k_{1} + c_{1} \omega j} \right)m_{1} + \left( {k_{1} + c_{1} \omega j} \right)\left( {k_{2} + c_{2} \omega j} \right)m_{2} }}{{\left[ {k_{1} + k_{2} - m_{1} \omega^{2} + \left( {c_{1} + c_{2} } \right)\omega j} \right]\left( {k_{2} - m_{2} \omega^{2} + c_{2} \omega j} \right) - \left( {k_{2} + c_{2} \omega j} \right)^{2} }} \\ \end{aligned} $$
(14)
$$ {\text{DPM}}\left( \omega \right) = {\text{AM}}\left( \omega \right) \cdot \omega j $$
(15)
$$ \begin{aligned} & {\text{STH}}\left( \omega \right) \\ & = \frac{{\left( {k_{1} + c_{1} \omega j} \right)\left( {k_{2} + c_{2} \omega j} \right)}}{{\left[ {k_{1} + k_{2} - m_{1} \omega ^{2} + \left( {c_{1} + c_{2} } \right)\omega j} \right]\left( {k_{2} - m_{2} \omega ^{2} + c_{2} \omega j} \right) - \left( {k_{2} + c_{2} \omega j} \right)^{2} }}. \\ \end{aligned} $$
(16)

2.1.3 Four-DOF Model

This paper presents a new four-DOF model of the seated human body, where \( m_{4} \) represents the head, as shown in Fig. 3. This model is different from the four-DOF models proposed by other scholars [6, 7].
Fig. 3

Four-DOF model of the seated human body

The derived mathematical expressions of the AM, DPM and STH in the four-DOF model are as follows:
$$ \begin{aligned} &{\text{AM}}\left( \omega \right) = m_{o} + \frac{{\left( {k_{1} + c_{1} \omega j} \right)m_{1} }}{{\left( {k_{1} - m_{1} \omega^{2} + c_{1} \omega j} \right)}}\frac{{\left( {k_{2} + c_{2} \omega j} \right)m_{2} }}{{\left( {k_{2} - m_{2} \omega^{2} + c_{2} \omega j} \right)}} \\ & \quad + \frac{{\left( {k_{4} - m_{4} \omega^{2} + c_{4} \omega j} \right)\left( {k_{3} + c_{3} \omega j} \right)m_{3} + \left( {k_{3} + c_{3} \omega j} \right)\left( {k_{4} + c_{4} \omega j} \right)m_{4} }}{{\left[ {k_{3} + k_{4} - m_{3} \omega^{2} + \left( {c_{3} + c_{4} } \right)\omega j} \right]\left( {k_{4} - m_{4} \omega^{2} + c_{4} \omega j} \right) - \left( {k_{4} + c_{4} \omega j} \right)^{2} }} \\ \end{aligned} $$
(17)
$$ {\text{DPM}}\left( \omega \right) = AM\left( \omega \right) \cdot \omega j $$
(18)
$$ \begin{aligned} & {\text{STH}}\left( \omega \right) \\ & = \frac{{\left( {k_{1} + c_{1} \omega j} \right)\left( {k_{2} + c_{2} \omega j} \right)}}{{\left[ {k_{1} + k_{2} - m_{1} \omega ^{2} + \left( {c_{1} + c_{2} } \right)\omega j} \right]\left( {k_{2} - m_{2} \omega ^{2} + c_{2} \omega j} \right) - \left( {k_{2} + c_{2} \omega j} \right)^{2} }}. \\ \end{aligned} $$
(19)

2.2 Vertical Vibration Experiments of the Seated Human Body

The vertical vibration test rig of the seated human body shown in Fig. 4 was based on the schemes of both domestic and foreign scholars and existing hardware. The operating principle of the test rig is as follows: the host computer generates a random white noise signal to control the linear motor and produce a corresponding excitation displacement through the digital-to-analog (D/A) port of the data acquisition card. Then, the signals of head acceleration, seat panel acceleration and seat panel force are acquired through the analog-to-digital (A/D) port of the data acquisition card during the vibration process. The data are saved on the host computer.
Fig. 4

Overall scheme of the test rig

The vibration test rig was used to conduct vertical vibration tests with 30 male volunteers who were healthy and free of physical handicaps. The values for age, height, seated weight, seated weight proportion of body weight and body mass index of the volunteers are listed in Table 1.
Table 1

Volunteer’s physical characteristics

No.

Age (year)

Height (cm)

Weight (kg)

Seated weight (kg)

Seated weight/body weight

Body mass index (kg/m2)

1

26

179

79.63

61.94

0.78

24.85

2

35

174

70.31

55.79

0.79

23.22

3

25

173

64.40

49.34

0.77

21.52

4

24

175

76.70

61.73

0.80

25.05

5

24

174

64.56

51.12

0.79

21.32

6

23

173

59.09

47.61

0.81

19.74

7

23

180

78.37

59.87

0.76

24.19

8

23

177

77.53

61.88

0.80

24.75

9

24

166

51.23

40.63

0.79

18.59

10

25

165

59.13

45.89

0.78

21.72

11

22

170

73.67

61.10

0.83

25.49

12

30

173

75.10

56.69

0.75

25.09

13

28

177

87.62

73.07

0.83

27.97

14

28

178

80.11

67.82

0.85

25.28

15

23

173

67.14

54.14

0.81

22.43

16

24

180

96.74

80.63

0.83

29.86

17

29

173

63.55

50.43

0.79

21.23

18

19

190

77.71

58.02

0.75

21.53

19

19

184

65.11

48.41

0.74

19.23

20

19

175

66.12

51.40

0.78

21.59

21

19

170

57.25

41.76

0.73

19.81

22

20

181

71.58

55.93

0.78

21.85

23

19

180

69.44

54.94

0.79

21.43

24

20

172

56.63

44.26

0.78

19.14

25

20

173

61.67

45.05

0.73

20.60

26

25

170

72.21

53.58

0.74

24.99

27

28

172

68.45

59.53

0.87

23.14

28

24

175

65.29

52.40

0.80

21.32

29

25

172

67.71

55.14

0.81

22.89

30

23

179

91.98

75.39

0.82

28.71

Mean

24

175

70.53

55.85

0.79

22.95

Max

35

190

96.74

80.63

0.87

29.86

Min

19

165

51.23

40.63

0.73

18.59

Deviation

3.8

5.2

10.43

9.55

0.03

2.83

Based on standard ISO 5982:2001 [5], the standard position of the seated human body is as follows: hands are on the thighs, thighs are parallel to the seat panels, lower legs are perpendicular to the thighs, the body sits naturally, the head is upright, and eyes look straight ahead.

During each test, the volunteers wore a helmet with an acceleration sensor, and the helmet was adjusted to ensure that the sensor was vertical. The height of the footrest was adjusted to make the thighs parallel to the seat panel. The buttocks position was adjusted so that the center of gravity of the body was centered over the seat panel. Volunteers were asked to relax as much as possible after positioning. The standard seated position of a volunteer is shown in Fig. 5.
Fig. 5

Volunteer in standard seated position

The excitation frequency was 0.5–20 Hz, and the vibration intensity (root-mean-square acceleration) was set to 1.0 m/s2, which matches the test conditions of most non-Chinese studies [28]. Each volunteer was tested twice under the same test conditions and each test lasted for 30 s. After the first successful test, each volunteer was asked to relax for about 5 min before being tested a second time.

The impact of the mass of the force-measuring panel on the test results can be eliminated according to formula (20) [29]:
$$ F = F_{\text{t}} , - m_{\text{plate}} \cdot a_{0} - m_{\text{plate}} \cdot g $$
(20)
where \( F \) is the excitation force between the seat panel and the seated human body, \( F_{\text{t}} \) is the signal of the force sensor under the force-measuring panel, \( m_{\text{plate}} \) is the mass of the force-measuring panel (7.6 kg), \( a_{0} \) is the acceleration signal of the force-measuring panel, and \( g \) is the acceleration of gravity (9.8 m/s2).
The minimum frequency was set to 2 Hz due to the limitation of the acceleration sensor band range in the data processing. The mean curves of the AM, DPM and STH at each frequency of vertical vibration characteristics of 30 seated volunteers are shown in Fig. 6.
Fig. 6

Mean curves of vertical vibration characteristics of 30 seated volunteers. a Amplitude–frequency characteristics of AM, b phase–frequency characteristics of AM, c amplitude–frequency characteristics of DPM, d phase–frequency characteristics of DPM, e amplitude–frequency characteristics of STH, f phase–frequency characteristics of STH

According to the experimental data, the first resonant frequency f1-AM of the AM amplitude–frequency characteristics of the measured volunteers is between 3.66 Hz and 5.37 Hz, with an average value of 4.52 Hz. The second resonant frequency f2-AM of the AM amplitude–frequency characteristics is between 8.55 Hz and 11.96 Hz, with an average value of 10.55 Hz. The first resonant frequency f1-DPM of the DPM amplitude–frequency characteristics is between 4.64 Hz and 6.84 Hz, with an average value of 5.08 Hz. The second resonant frequency f2-DPM of the DPM amplitude–frequency characteristics is between 9.03 Hz and 14.65 Hz, with an average value of 11.3 Hz. The first resonant frequency f1-STH of the STH amplitude–frequency characteristics is between 2.93 Hz and 6.1 Hz, with an average value of 4.8 Hz. The second resonant frequency f2-STH of the STH amplitude–frequency characteristics is between 8.79 Hz and 14.4 Hz, with an average value of 10.99 Hz. The results are shown in Table 2.
Table 2

Resonant frequencies of AM, DPM and STH

 

f1-AM (Hz)

F2-AM (Hz)

f1-DPM (Hz)

f2-DPM (Hz)

f1-STH (Hz)

f2-STH (Hz)

Min

3.66

8.55

4.64

9.03

2.93

8.79

Max

5.37

11.96

6.84

14.65

6.1

14.4

Mean

4.52

10.55

5.08

11.3

4.8

10.99

2.3 Parameter Identification of Models

The required vehicle seat load in standard GB/T 4970-2009 [30] is for a person with a body weight of 65 kg, which is 0.92 times the mean body weight of volunteers in this experiment. Based on preliminary findings that the amplitudes of AM and DPM are positively correlated with body weight, the amplitudes of AM and DPM of the standard seated human body can be obtained by weight conversion. Other vibration characteristics do not need to be converted.

The identified parameters are mass, stiffness and damping. Because the seated human body weight was 0.79 times the human body weight on average in this study, the standard seated human body weight is set to 52 kg (65 kg × 0.79). The constraints are as follows: the total mass of the model is 52 kg and the parameters of the model’s mass, stiffness and damping are greater than zero. The optimization goal is to minimize the sum of squares of deviations between tests and simulations. The optimization problem was solved using the optimization function fmincon in MATLAB software.

Figure 7 shows the comparison of simulations of different seated human body models and the mean of converted test data.
Fig. 7

Comparison of simulation of different seated human body models and test data. a Amplitude–frequency characteristics of AM, b phase–frequency characteristics of AM, c amplitude–frequency characteristics of DPM, d phase–frequency characteristics of DPM, e amplitude–frequency characteristics of STH, f phase–frequency characteristics of STH

The fitting accuracy of the model is calculated according to formula (21).

$$ {\text{Accuracy}} = 1 - \sqrt {\frac{{\sum\limits_{i = 1}^{n} {[{\text{test}}(f_{i} ) - {\text{sim}}(f_{i} )]^{2} } }}{{\sum\limits_{i = 1}^{n} {{\text{test}}(f_{i} )^{2} } }}} , $$
(21)
where test(fi) are the experimental data at the frequency fi and sim(fi) are the simulation data at the frequency fi.
The identified parameters and fitting accuracies of different seated human body models are listed in Table 3 and Table 4, respectively.
Table 3

Identified parameters of different seated human body models

Parameters

Two-DOF model

Three-DOF model

Four-DOF model

m0/(kg)

6.7

6.6

5.5

m1/(kg)

29.1

29.3

27

m2/(kg)

16.2

1

18

m3/(kg)

15.1

0.77

m4/(kg)

1.16

c1/(N s/m)

456.5

503.2

399.1

c2/(N s/m)

850.6

36.8

965.3

c3/(N s/m)

798.6

0.0046

c4/(N s/m)

38.1

k1/(N/m)

31,463.6

32,837.1

29,429.4

k2/(N/m)

58,587.1

16,796.1

61,243.2

k3/(N/m)

57,288.9

20,602.4

k4/(N/m)

1259.3

Table 4

Fitting accuracies of different seated human body models

Evaluation index

Two-DOF model (%)

Three-DOF model (%)

Four-DOF model (%)

Amplitude of AM

95.52

95.51

94.45

Phase of AM

92.45

92.04

91.54

Amplitude of DPM

96.41

96.33

94.41

Phase of DPM

89.58

89.32

88.08

Amplitude of STH

69.68

89.80

Phase of STH

59.04

85.87

The identification results show that the two-DOF, three-DOF and four-DOF models all can simulate the vertical vibration characteristics of the AM and DPM of the Chinese seated human body. Further, all of them can be used as a dynamic load to simulate the relationship of force transmission between the seated human body and vehicle seat. But only the four-DOF model can simulate the vertical vibration characteristics of the STH to simulate the head vibration of the human body.

3 Application of the Seated Human Body Models

In this section, we describe how the three seated human body models were applied as the load on a vehicle seat to optimize the damping action of a shock absorber. Figure 8 shows the quarter-vehicle dynamic model with the three seated human body models. The parameters of the human body models and vehicle model are listed in Tables 5 and 6, respectively.
Fig. 8

Quarter-vehicle dynamic model with different seated human body models. a Two-DOF model, b three-DOF model, c four-DOF model for Chinese body type

Table 5

Parameters of human body models

Parameter

Rigid mass

ISO 5982 human model

Chinese four-DOF human model

m0/(kg)

52

2

5.5

m1/(kg)

6

27

m2/(kg)

2

18

m3/(kg)

45

0.77

m4/(kg)

1.16

c1/(N s/m)

387

399.1

c2/(N s/m)

234

965.3

c3/(N s/m)

1390

0.0046

c4/(N s/m)

38.1

k1/(N/m)

9990

29,429.4

k2/(N/m)

34,400

61,243.2

k3/(N/m)

36,200

20,602.4

k4/(N/m)

1259.3

Table 6

Parameters of quarter-vehicle model

Description

Symbol

Value

Unit

Unsprung mass

m u

36

kg

Sprung mass

m s

261.5

kg

Cushion mass

m c

1

kg

Shock absorber damping

c s

2250

N s/m

Cushion damping

c c

400

N s/m

Tire stiffness

k t

220e3

N/m

Spring stiffness

k s

32.5e3

N/m

Cushion stiffness

k c

20e3

N/m

Suspension rebound limit stiffness

k rl

80e3

N/m

Suspension compression limit stiffness

k cl

80e3

N/m

Suspension rebound limit stroke

A rl

0.04

m

Suspension compression limit stroke

A cl

0.04

m

Leverage ratio

r

0.82

To optimize shock absorber damping to improve vehicle ride comfort, the goal is to minimize the root-mean-square of the weighted acceleration at the vehicle seat. At the same time, the dynamic travel of the suspension and the dynamic load of the wheel are constrained to maintain the vehicle’s handling, stability and safety characteristics. The selected constraints are [31, 32]:
$$ \sigma_{\text{fd}} \le \frac{1}{3}\left[ {f_{\text{d}} } \right]\quad {\text{and}}\quad \varsigma \le \frac{1}{3}, $$
(22)
where \( \sigma_{\text{fd}} \) is the root-mean-square of the dynamic suspension travel, \( \left[ {f_{\text{d}} } \right] \) is the stroke limit of the suspension, and \( \varsigma \) is the root-mean-square of the wheel dynamic load.

The damping of the shock absorber with different seated human body models was optimized using MATLAB software. The results show that the optimized damping with the four-DOF Chinese seated human body model is about 27% more than that with rigid mass and about 7% less than that with ISO 5982:2001 seated human body model under the same travel conditions. Because the Chinese four-DOF seated human body model is established based on the vertical vibration characteristics of the Chinese seated human body, it is more suitable for optimizing damping behavior in Chinese vehicles.

4 Conclusions

In this study, models of the seated human body with two,three, and four degrees of freedom (DOF) were established and mathematical expressions for the AM, DPM, and STH were derived firstly.

Then the vibration characteristics of 30 volunteers were tested under standard test conditions, and data for the AM, DPM, and STH were obtained with a vibration test rig. The average value of first and second resonant frequency of the AM amplitude-frequency characteristics of the measured volunteers are 4.52 Hz and10.55 Hz respectively. The average value of first and second resonant frequency of the DPM amplitude-frequency characteristics are 5.08 Hz and 11.3 Hz respectively. The average value of first and second resonant frequency of the STH amplitude-frequency characteristics are 4.8 Hz and 10.99 Hz respectively. Based on the experimental data, the parameters of the two-DOF, three-DOF, and four-DOF model were identified and the results show that the four-DOF model can simulate the vertical vibration characteristics of the seated human body more comprehensively with an average accuracy of 90.69%.

Further, different seated human body models were applied to optimize shock absorber damping, and the optimized damping with the four-DOF Chinese seated human body model is 27% more than that with rigid mass and 7% less than that with ISO 5982:2001 seated human body model.the results showed that the four-DOF Chinese seated human body model is more suitable for the improvement of ride comfort in Chinese vehicles.

In the future, the vibration characteristics of different occupant types, such as different age groups and sexes, will be tested and combined with the research results reported here. This will lead to a unified vertical vibration model for the Chinese seated human body so it can be applied to the improvement of ride comfort.

Notes

Acknowledgements

This work could not have been achieved without the voluntary participation of the test subjects who took part in the experiments. Also, we gratefully acknowledge the financial and test equipment support provided by KH Automotive Technologies (Changchun) Co., Ltd.

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Copyright information

© China Society of Automotive Engineers (China SAE) 2018

Authors and Affiliations

  1. 1.Advanced Product Development DepartmentDongfeng Commercial Vehicle Technical CenterWuhanChina
  2. 2.College of Automotive EngineeringJilin UniversityChangchunChina

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