Investigation and Application on the Vertical Vibration Models of the Seated Human Body
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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 dampingAbbreviations
- 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
- m_{u}
Unsprung mass
- m_{s}
Sprung mass
- m_{c}
Cushion mass
- c_{s}
Shock absorber damping
- c_{c}
Cushion damping
- k_{t}
Tire stiffness
- k_{s}
Spring stiffness
- k_{c}
Cushion stiffness
- k_{rl}
Suspension rebound limit stiffness
- k_{cl}
Suspension compression limit stiffness
- A_{rl}
Suspension rebound limit stroke
- A_{cl}
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.
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
2.1.2 Three-DOF Model
2.1.3 Four-DOF Model
2.2 Vertical Vibration Experiments of the Seated Human Body
Volunteer’s physical characteristics
No. | Age (year) | Height (cm) | Weight (kg) | Seated weight (kg) | Seated weight/body weight | Body mass index (kg/m^{2}) |
---|---|---|---|---|---|---|
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.
The excitation frequency was 0.5–20 Hz, and the vibration intensity (root-mean-square acceleration) was set to 1.0 m/s^{2}, 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.
Resonant frequencies of AM, DPM and STH
f_{1-AM} (Hz) | F_{2-AM} (Hz) | f_{1-DPM} (Hz) | f_{2-DPM} (Hz) | f_{1-STH} (Hz) | f_{2-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.
The fitting accuracy of the model is calculated according to formula (21).
Identified parameters of different seated human body models
Parameters | Two-DOF model | Three-DOF model | Four-DOF model |
---|---|---|---|
m_{0}/(kg) | 6.7 | 6.6 | 5.5 |
m_{1}/(kg) | 29.1 | 29.3 | 27 |
m_{2}/(kg) | 16.2 | 1 | 18 |
m_{3}/(kg) | – | 15.1 | 0.77 |
m_{4}/(kg) | – | – | 1.16 |
c_{1}/(N s/m) | 456.5 | 503.2 | 399.1 |
c_{2}/(N s/m) | 850.6 | 36.8 | 965.3 |
c_{3}/(N s/m) | – | 798.6 | 0.0046 |
c_{4}/(N s/m) | – | – | 38.1 |
k_{1}/(N/m) | 31,463.6 | 32,837.1 | 29,429.4 |
k_{2}/(N/m) | 58,587.1 | 16,796.1 | 61,243.2 |
k_{3}/(N/m) | – | 57,288.9 | 20,602.4 |
k_{4}/(N/m) | – | – | 1259.3 |
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
Parameters of human body models
Parameter | Rigid mass | ISO 5982 human model | Chinese four-DOF human model |
---|---|---|---|
m_{0}/(kg) | 52 | 2 | 5.5 |
m_{1}/(kg) | – | 6 | 27 |
m_{2}/(kg) | – | 2 | 18 |
m_{3}/(kg) | – | 45 | 0.77 |
m_{4}/(kg) | – | – | 1.16 |
c_{1}/(N s/m) | – | 387 | 399.1 |
c_{2}/(N s/m) | – | 234 | 965.3 |
c_{3}/(N s/m) | – | 1390 | 0.0046 |
c_{4}/(N s/m) | – | – | 38.1 |
k_{1}/(N/m) | – | 9990 | 29,429.4 |
k_{2}/(N/m) | – | 34,400 | 61,243.2 |
k_{3}/(N/m) | – | 36,200 | 20,602.4 |
k_{4}/(N/m) | – | – | 1259.3 |
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 | – |
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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