Ride comfort analysis of vehicle seat suspension systems: A co-simulation study

Abstract

In this study, the vehicle seat suspension system installed with a semi-active magnetorheological (MR) damper is excited by the power spectral density (PSD) and its vibration control performance is evaluated using finite element analysis (FEA). The control system receives the velocity of the sprung and unsprung mass from the seat mounting locations and calculates the desired controllable damping forces available from MR damper. The effectiveness of the control systems is demonstrated by adopting ride quality evaluation method. To predict a better ride comfort and ride quality, co-simulation methodology is utilized considering the dynamic behavior of the real-world seat system. In this case, the multi-body dynamics and control system are coupled by solving the mechanical equations and the control logic. Then, the computed damping force is exchanged between the dynamics and controller in an iterative manner by passing state variables. The simulation results achieved from co-simulation methodology associated with the controller are analyzed by comparing with ISO 2631-1. The co-simulation results studied using vibration dose value (VDV), crest factor (CF) and seat effective amplitude transmissibility (SEAT) in terms of percentage improvement were found to be 44.33%, 26.66% and 17.65% respectively which were better than that for the passive suspension for a random rough road profile. Modified skyhook controller delivers superior performance for vibration suppression of the vehicle seat suspension as compared to other control policies. The application of co-simulation methodology can reduce time and cost for the development of a semi-active seat suspension system.

Keywords

Automotive seating system semi-active seat suspension damper co-simulation methodology ride comfort control strategy ride quality

Introduction

The degree of ride comfort of the driver and the occupant depends on the seat system which is an essential component in a passenger car. A good seat should have both instantaneous and long-lasting comfort after a prolonged period of seat usage as studied in.¹ The major parameters that affect the ride comfort are seat stiffness, seat geometry, seat height, seat width, occupant’s sitting posture, occupant’s pressure distribution, occupant’s eye focus, occupant’s reachability to clutch, brake and accelerator pedals, position of steering wheel and its orientation, head room and knee room availability and transmission type.² The seating system is a major sub-system through which vibration enters the automotive occupants. The ride comfort of the driver plays a vital role in safety, fatigue along with drivability on irregular road surfaces and during heavy traffic. Therefore, the road profile, mannequin mass distribution criteria, human disorders, fatigue, the critical zone of the seat system, etc., are to be considered for attenuating the vibration transfer to the body of the occupant. The vibrations transfer to the seat occupant of the vehicle from the irregular surface of the road, the source to the receiver as follows: road excitation-tire/wheel-chassis-seat mount-seat cushion and back rest. The whole body vibration (WBV) affects the ride comfort of both the driver and the occupant, creating physical pain with fatigue during their prolonged period of travel. The frequencies of parts of human body which are different play an important role in the ride comfort assessment. The frequency ranges of the various hazards while travelling are given as follows: motion sickness (0.1–1 Hz), fatigue (0.2–15 Hz), blurred vision (2–20 Hz), speech disturbance (1–20 Hz) and interference with various tasks (0.5–20 Hz). The seat effective amplitude transmissibility (SEAT) value is used to quantify the vibration isolation efficiency of the seat. Furthermore, the FEA can be used by exciting the PSD of chassis acceleration (random smooth and rough road profile) and the root-mean-square (RMS) acceleration at seat-mounting locations can be found.

The vibration control systems such as passive, active and semi-active are used to control the vibration transfer to the seated occupant. Among these control systems, the semi-active one is the most attractive because its performance is almost same as active one with less energy consumption. When integrating the semi-active suspension system and suitable control policies like proportional integral derivative (PID), skyhook on-off (SHO), skyhook continuous (SHC) and modified skyhook (MSH) system controllers with VSSS, estimates the desired damping (DD) force and the damper controller (Signum function) finds the current to be applied to MR damper and thus the controllable damping (CD) force is computed.³ Then, the results are compared with ISO 2631-1: 1997, which is given in Table 1, to assess the ride comfort of the driver and the occupant.⁴

Table 1.

ISO 2631-1: 1997 comfort index.

Vibration range (RMS)	Condition for comfort
<0.315 m/s²	Extremely comfortable
0.325 to 0.63 m/s²	Comfortable
0.5 to 1 m/s²	Fairly comfortable
0.8 to 1.6 m/s²	Uncomfortable
1.25 to 2.5 m/s²	Very uncomfortable
>2.0 m/s²	Extremely uncomfortable

The research works on the semi-active control for vibration control of vehicle sus-pension systems have been carried out by many scholars. Levesley et al⁵ proposed a two-state switchable (TSS) controller and used MatLAB/Simulink for predicting the dynamic response of the vehicle suspension with MR damper comparing the root-mean-square (RMS) acceleration of co-simulation between the passive and semi-active control strategies. Lu Yong-jie et al.⁶ presented a multi-body virtual prototype of heavy truck using co-simulation approach with the help of ADAMS/Control and MatLAB/Simulink software. The skyhook on-off controller for the semi-active MR damper was implemented to minimize the RMS seat vertical acceleration, suspension deflection and dynamic tire force. Faisal Shahzad and Qiu Yi et al.⁷ have demonstrated a proof of concept of developing a co-simulation method between multi-body dynamics (MBD) and finite element model, and Du et al.⁸ have proposed an integrated vehicle seat suspension system and control strategies (state feedback, robust static output feedback and multi-objective controllers) for a quarter car with 4-DOF (degree of freedom) driver model to minimize the driver head acceleration under regular dump and random. H. Metered and Z. Sika⁹ have introduced a fuzzy logic controller for a truck seat MR damper with 2-DOF seat model along with signum function as damper controller and simulated using MatLAB/Simulink showing a significant improvement in the ride comfort while comparing with passive system. Segla Stefan et al.¹⁰ have dealt with modelling, control and optimization of semi-active seat suspension with pneumatic spring and MR damper focusing on the isolating vibration excitation from cabin of a bucket-wheel excavator. Devdutt et al.¹¹ have designed a fuzzy logic controller integrated with MR suspension system of quarter car model and evaluated RMS acceleration and peak acceleration in terms of percentage improvement compared with passive suspension system. Choi et al.¹² have carried out the hardware-in-the-loop simulation (HILS) for MR seat suspension system considering a full-vehicle model. A.M. Abdel Ghany et al.¹³ have proposed a PID controller to determine the desired damping force of the seat suspension and evaluated vibration dose value (VDV) and crest factor (CF) in terms of percentage improvement over the passive seat system. S Gad et al.¹⁴ have designed the PID system controller tuned by genetic algorithm (GA) to achieve the desired damping force for the seat suspension and evaluated vibration control performance showing driver head acceleration and seat travelled distance in time and frequency domains. S M. Savaresi, et al¹⁵ have developed an ideal skyhook control system which can easily be implemented in a real-time application, and M Ramalingam et al.¹⁶ have investigated several control policies for MR damper based seat suspension system including PID controller and fuzzy logic controller. They also studied 3-DOF seat suspension system installed with MR damper focusing on the minimization of the vibration transfer from the road to the seat cushion and backrest.¹⁷ In this work, they have demonstrated that an appropriate choice of a controller to adapt MR damper is very significant to minimize RMS acceleration, peak to peak (PTP) acceleration and frequency weighted (FW) RMS acceleration evaluated by ISO 2631-1: 1997 (Table 1).

The above literature review reveals that the semi-active vehicle seating system installed with MR damper needs to be integrated with an appropriate controller to achieve or/and to predict the ride comfort, ride quality and health of the occupants. Consequently, the technical contribution of this work is to present a novel approach for better prediction of the ride comfort and ride quality of the seat occupant. The proposed approach includes three main methodologies: finite element analysis methodology, control system method-ology and co-simulation methodology. The evaluation parameters for vibration control are chosen by displacement, velocity, acceleration, stiffness, damping co-efficient, mass, and vibration transmissibility. Vibration responses of these parameters are presented in time domain and compared with and without control action for the semi-active MR damper.

Methodology

The complex dynamic characteristics of ASS were studied for predicting the behaviour of the seat’s natural frequency, mode shape, transmissibility, SEAT and random response. Finite element analysis using Altair HyperMesh and OptiStruct software was used in this study to modify the stiffness and damping properties of the seat structure for reducing the magnification and also for attenuation of vibration. In order to improve the ride comfort of the driver and the occupant, the seat damper system was further integrated with ASS and simulated to attenuate the vibration transfer to the seat cushion and backrest. Thus, the FEA demonstrates that the degree of ride comfort of driver and occupant are maximized.

As per ISO 5982: 2019,¹⁸ 73% of the 95^th percentile mannequin mass (73% of 102 kg) is distributed on the seat cushion and 27% on the seat backrest as illustrated in Figure 1. Modal analysis, frequency response analysis and random vibration study were carried out for reducing the transfer of vibration to the seated occupant

Figure 1.

Schematic representation of the mass distribution of the 95^th percentile mannequin (102 kg).

The design of the ASS must ensure that the fundamental natural frequency is more than 20 Hz and not creating the resonance condition that matches with the natural frequencies of the human body. The RMS acceleration of 1.0 m/s² was excited at the seat-mounting locations of ASS along the three directions separately for computing the vibration transmissibility of the seat system. The transmissibility value must be less than one to avoid occupant discomfort while driving a vehicle. The random vibration was carried out by exciting the PSD measured at the seat mounting¹⁹ locations (E₁, E₂, E₃ & E₄) for understanding the dynamic characteristics of the seat system. The calculated FW RMS acceleration values were compared with Table 1 for predicting the degree of ride comfort of the seat occupant.

Experimental validation

The seat system was mounted on a vibration shaker table as shown in Figure 2 and an RMS acceleration of 1.0 m/s² was excited in the vertical direction. The output response was measured using a single-axis accelerometer in the vertical direction. Since Shoulder & Neck are the most critical zone in the seat structure, the output response was measured at Shoulder on the seat backrest.
Figure 2.
Experimental test set-up of ASS.

The natural frequency of the seat system needs to be correlated by considering the experimental result and the FEA result to ensure that the correlation level is closer and not creating the resonance condition.

The accuracy of the FEA results can be further validated using “Modal Assurance Criterion (MAC)”. The MAC defined by equation (1) can be used for comparing the similarities of the two obtained mode shapes, Pastor, M et al.²⁰
${MAC}_{(1,2)} = \frac{{({ϕ_{1}}^{T} * {ϕ_{2}})}^{2}}{({ϕ_{1}}^{T} * {ϕ_{1}}) * ({ϕ_{2}}^{T} * {ϕ_{2}})}$
(1)

The MAC value is calculated using the simulation (HyperWorks software) result and experimental result. The value of MAC is zero (0) when the two vectors are orthogonal (mode shapes are not at all consistent) and unity (1) when the two vectors are equal (mode shapes are fully consistent).

Based on the literature survey, a 3-DOF mathematical model was selected for the present study. The governing equations of motion were derived by assuming that the tyre of the Quarter Car Model (QCM) was always in contact with the road surface. The parameters of the QCM specified in Table 2 were used for computing the transfer of vibration to the seated occupant.
Table 2.
Seat with QCM – Data used.¹¹

Parameter - seat with quarter car model

Mass (Kg) Damping (Ns/m) Spring stiffness (N/m)

m₁ 75 c₁ 1400 k₁ 24,000

m₂ 350 c₂ 750 k₂ 7500

m₃ 45 c₃ 0 k_t 160,000

Mathematical model of MR Damper - Modified Bouc-wen Model

The modified Bouc–Wen model and its equation was adopted to calculate the controlled damping force, Ambhore et al.¹⁹ with the help of the parameters given in Table 3.
Table 3.
Modified Bouc-wen model – Data used.¹³

Parameters - modified bouc-wen model

Parameter Units Values Parameter Units Values

C_oa Ns/m 784 k_p N/m 840

C_ob Ns/m 183 α_a N/m 12,441

k_o N/m 3610 α_b N/m 38,430

p_1a Ns/m 14,649 Γ 1/m² 136,320

p_1b Ns/m 34,622 B 1/m² 2,059,020

A — 58 H 1/s 2

x_o — 0.0245 N — 190

Methodology for estimating the controlled damping force

MR damper uses two con-trollers namely system and damper controllers for computing the CD force which is re-quired for attenuating the vibration transfer to the seated occupant. The system controller is used to calculate the DD force and the damper controller is used to estimate the command voltage required as input to MR damper for calculating the CD. The real-time system controllers like PID, PID+GA, SHO, SHC and MSH have been used for estimating the DD force.

The PID controller is chosen by considering its efficiency, simplicity and the extended capabilities in changing the system response. The PID controller takes relative displacement as an error signal across the damper and calculates the DD force using equation (2). As the damping force is proportional to the error, the integral function eliminates the steady-state error and the differential function compensates for any rapid changes in the error.
$U (t) = K_{p} e (t) + K_{I} \int e (t) d t + K_{D} \frac{d}{d t} e (t)$
(2)
Where, U(t) is the output of PID controller, K_P is the Proportional gain, K_I is the integral gain, K_D is the derivative gain, and e(t) is the error signal defined as the relative displacement across the damper. In semi-active MR damper, the PID signal U(t) is sent directly to a damper controller. However, in the case of active control systems, the signal U(t) is fed directly into the system.

The SH controller is extensively used to control the vibration transfer to the seat occupant. The skyhook is referred to as a pure skyhook control policy derived from the passive damper hooked to an imaginary inertial reference point.²⁰ The equation (3) is used for calculating the DD force.
$F_{d} = C_{\max} {\overset{`}{x}}_{1}$
(3)
Where, ${\overset{`}{x}}_{1}$ is the absolute velocity of seat system, C_max is the maximum damping coefficient and F_d is the DD force.

The SHO control policy is introduced by Cebon et al.²⁰ and is called as classical and comfort-oriented control policy. When the multiplication of relative velocity and absolute velocity of the seat system is greater than or equal to zero, a high damping coefficient (C_max) is preferred [eq. (4)]. If the product is less than zero, then a low damping coefficient (C_min) is preferred for calculating the DD force [eq. (5)]²⁰
$When {\overset{`}{x}}_{1} ({\overset{`}{x}}_{1} - {\overset{`}{x}}_{2}) \geq 0, C_{1} = C_{\max}$
(4)
$When {\overset{`}{x}}_{1} ({\overset{`}{x}}_{1} - {\overset{`}{x}}_{2}) < 0, C_{1} = C_{\min}$
(5)
Where, $({\overset{`}{x}}_{1} - {\overset{`}{x}}_{2})$ is the relative velocity between the seat and sprung mass, ${\overset{`}{x}}_{1}$ is the absolute velocity of the seat and C₁ is the damping coefficient of the seat.

The SHC is an extension of the SHO control policy. When the multiplication of relative velocity and absolute velocity of the seat system is greater than or equal to zero then the equation (6) is preferred for calculating the DD force. If the products is less than zero then a low damping coefficient (C_min) is preferred [eq. (7)].²⁰
$When {\overset{`}{x}}_{1} ({\overset{`}{x}}_{1} - {\overset{`}{x}}_{2}) \geq 0, C_{1} = C_{\max} {C_{\min} \cdot \min [(C_{sky} \cdot {\overset{`}{x}}_{1}) / (({\overset{`}{x}}_{1} - {\overset{`}{x}}_{2})) \cdot C_{\max}]}$
(6)
$When {\overset{`}{x}}_{1} ({\overset{`}{x}}_{1} - {\overset{`}{x}}_{2}) < 0, C_{1} = C_{\min}$
(7)

The MSH controller is derived by combining the SH and passive controllers and it computes the DD force using the control laws given by equations (8) and (9)²¹
$F_{d} = C_{1} ({\overset{`}{x}}_{1} - {\overset{`}{x}}_{2}) + C_{s} {\overset{`}{x}}_{1}$
(8)
where, C₁ is the passive damping ratio, C_S is the Skyhook damping ratios, ${\overset{`}{x}}_{1}$ is the absolute velocity, $({\overset{`}{x}}_{1} - {\overset{`}{x}}_{2})$ is the relative velocity between the seat and sprung mass and $F_{d}$ is the DD force

The ratio between the passive damping and maximum damping coefficients (C₁/C_max), can be substituted in equation (8) to derive the control law (9) for MSH controller^20,21
$F_{d} = {\begin{cases} C_{\max} (α ({\overset{`}{x}}_{1} - {\overset{`}{x}}_{2}) + (1 - α) {\overset{`}{x}}_{1}) w h e n F_{d} ({\overset{`}{x}}_{1} - {\overset{`}{x}}_{2}) > 0 \\ C_{\min} ({\overset{`}{x}}_{1} - {\overset{`}{x}}_{2}) w h e n F_{d} ({\overset{`}{x}}_{1} - {\overset{`}{x}}_{2}) \leq 0 \end{cases}$
(9)

When $α = 1, F_{d} = C_{\max} ({\overset{`}{x}}_{1} - {\overset{`}{x}}_{2})$ , works as passive control

When $α = 0, F_{d} = C_{\max} {\overset{`}{x}}_{1}$ , works as pure skyhook control

Damper controller

The damper controller estimates the command voltage and gives as input to the MR damper which is essential for calculating the CD force. Therefore, the Signum function damper controller was integrated with semi-active seat suspension system for calculating the command voltage using the equations (10)–(13).
$v = v_{s i g n 1} * v_{s i g n 2}$
(10)
$v_{s i g n 1} = \frac{V_{\max}}{N} \sum_{j = 0}^{N - 1} w_{j}$
(11)
$w_{j} = \frac{1 + s g n [{F_{d} - (1 + j K) {f_{a}} f}_{a}]}{2}$
(12)
$v_{s i g n 2} = 1 - {[\frac{1 + s g n (v_{s i g n 1} - V_{\max})}{2}] \cap [\frac{1 - s g n (f_{a} \overset{`}{f_{a}})}{2}]}$
(13)
where, sgn (.) is the Signum function, taking values either 1 or −1, $\cap$ is the Logical AND operator, V_max is the applied voltage, F_d is the DD force, f_a is the controlled damping force, $\overset{`}{f_{a}}$ is the time derivative of f_a, N is a positive number, K is a small negative constant and w_j is the weighing factor.

When F_d >> f_a, $v_{s i g n 1}$ = V_max and w_j = 1;

When F_d << f_a, $v_{s i g n 1}$ = 0 and w_j = 0;

When F_d $\approx$ f_a, $v_{s i g n 1}$ = some fraction of V_max and w_j = 1

Small and Large Bump Road Profile: Small and large bump road profiles are studied in this research work. The equation (14) is used to generate the small and large bump road profiles¹²
$x_{r} = {\begin{cases} a {1 - \cos (ω_{r} (t))}, & f o r 0 \leq t \leq \frac{d_{b}}{V_{c}} \\ 0, & o t h e r w i s e \end{cases}$
(14)
Where, x_r is the bump road profile; a is half of the bump amplitude, $ω_{r} = 2 π V_{c} / d_{b}$ , d_b is the bump width and V_c is the vehicle velocity. In this study, a = 0.02 m for small bump road profile and 0.04 m large bump road profile, db= 2.4 m and V_c= 0.856 m/s were taken from.¹²

Random road profile

The random road profile “PSD versus Frequency” has been converted into “Displacement versus Time” profile. This time domain signal is exited at the seat-mounting locations and simulated to predict the ride comfort and ride quality of the seat system. The seat dynamic model with passive damper is simulated for smooth and rough road conditions to calculate the RMS acceleration of ASS at different locations.

Ride Quality Evaluation

The FW RMS acceleration, SEAT value, VDV value and CF value were calculated and the ride quality was evaluated. The degree of ride comfort of the occupant was assessed by comparing the simulated results with Table 1.⁴ Also, the crest factor is used to choose the vibration evaluation method for assessing the ride quality of the seat system. CF values less than six indicate that the RMS acceleration is sufficient to evaluate the ride quality. When CF = 6 ≥ CF ≤ 9, the RMS acceleration and VDV should be used together to avoid the health disorder to the driver and occupant. When CF > 9, VDV value is sufficient to evaluate the ride quality. As per the ‘health guidance’ suggested by ISO 2631-1: 1997, the VDV values must lie between 8.5 and 17 m/s^1.75.

Where, aw(t) is the time history of the FW RMS acceleration and T is the period of the test.

“Altair Activate” software was used to solve the control system equations of the physical system. It also, provides an open integration platform for modeling, simulating and optimizing multi-disciplinary systems-of-systems using inherent 1D block diagrams.

Co-simulation methodology

The actual seat system cannot be modeled in 1D simulation software like Activate, etc. wherein the bodies in the system are approximated to blocks of masses instead of their actual structure. Therefore, the accuracy level of the results obtained from Activate may be lower than the results obtained from the actual system. To overcome this situation, “co-simulation” (co-operative simulation) methodology was used by coupling the Activate and the “MotionView & MotionSolve” software. This advanced virtual prototyping and control strategies offer a novel approach to investigate the dynamic behaviour of the real-world seat system. This approach involves the actual finite element mesh model and produces results much closer to the real system.⁵ The multi-body dynamic model of the seat was modelled in “MotionView” whereas the semi-active damper control systems were modelled in “Activate”. The data between MotionSolve and Activate were exchanged by passing state variables between each other. MotionSolve solves the mechanical system equations and Activate solves the control system equations. Activate receives the velocity of the sprung and unsprung masses from MotionSolve and the system controller estimates the DD force. The damper controller computes the command voltage and is sent to the magnetorheological damper for calculating the controllable damping force. This force is sent to the MotionSolve and cycle repeats.

Results and discussion

Finite element studies

The fundamental natural frequency of the ASS without mannequin mass was found to be greater than 30 Hz and this avoids resonance conditions with the seat occupant. Further, the RMS acceleration of 1.0 m/s² was excited at the seat-mounting locations of ASS along the three directions separately and computed the vibration transmissibility of the seat system.

The simulation result (Table 4) shows that the vibration transfer to the seat is more in the lateral direction when the seat is having no mannequin mass in the absence or presence of passive damper. Both in the presence and absence of a passive damper, the seat structure transfers more vibration to the seated occupant in the fore-aft direction. The result trend agrees with the Finite element study of²³ with magnitude change in transmissibility.
Table 4.
Maximum acceleration transmissibility (dB) [shoulder & neck].

Maximum acceleration transmissibility (dB) [shoulder & neck]

Mode No. Without passive damper With passive damper Mode shape

Without mannequin Mass With mannequin Mass Without mannequin Mass With mannequin Mass

1 17.49 5.47 17 5.4 Lateral mode (Y-axis)

2 9.5 11.98 8.82 10.3 Fore-aft mode (X-Axis)

3 4.28 5.49 4.49 4.8 Twist mode (Z-Axis)

The FW RMS accelerations were calculated using the FEA results for the seat without and with mannequin mass in the absence and presence of a passive damper. The vibration transferred to the human body was measured at the cushion and backrest of the seat system. The calculated FW RMS accelerations were compared with ISO 2631-1: 1997 (Table 1) and the ride comfort zone of the occupant is shown in Table 5. The result trend agrees with the Finite element study of²³ with magnitude change in RMS acceleration.
Table 5.
RMS acceleration of ASS

Base excitation Seat conditions RMS acceleration (m/s²)

Without damper Comfort index With damper Comfort index

Smooth road Seat without mannequin Mass 0.25 Extremely comfortable 0.23 Extremely comfortable

Seat with mannequin Mass 0.28 Extremely comfortable 0.27 Extremely comfortable

Rough road Seat without mannequin Mass 0.45 Comfort 0.44 Comfort

Seat with mannequin Mass 0.645 Fairly comfortable 0.62 Fairly comfortable

For the seat with and without mannequin mass under the smooth road condition, the RMS acceleration of ASS fell in the “extremely comfortable” ride index zone. For the seat with no mass of mannequin under rough road condition, the ASS exhibits the RMS acceleration that lies in the “comfortable” ride index zone. However, for the seat with mannequin mass under rough road condition, the RMS acceleration of ASS fell in the “fairly comfortable” ride index zone. To avoid this situation, the semi-active seat suspension system and suitable control policy needs to be integrated with ASS.

Correlation

The natural frequencies obtained by FEA and physical test (Table 6) results are compared and the correlation level (difference) was found to be 11.99% in the fore-aft mode, 1.56% in the lateral mode and 3.91% in the twist mode. Since the FEA predicted natural frequencies and experimental natural frequencies are >30 Hz i.e., above the targeted natural frequency of >20 Hz, the ASS will not create resonance condition.
Table 6.
Frequency and mode shape correlation (without passive damper).

Frequency and mode shape correlation

Mode shapes FEA - natural frequency (Hz) Physical test result (Hz) Gap (%) MAC

Fore-aft 33.80 30.18 11.99% 0.94

Lateral 35.97 36.54 1.56% 0.91

Twist 54.70 52.64 3.91% 0.93

The computed MAC value (Table 6) is closer to unity. Hence, the natural frequency correlation level is found to be acceptable. Therefore, the established “Finite element methodology” can be implemented in regular applications for controlling the vibration transfer to the seat cushion and seat backrest.

Integration with control system

The acceleration of ASS was computed for time domain using semi-active seat suspension system and control policies like PID, PID+GA, SHO, SHC and MSH. Figure 3(a) explains the PTP acceleration of ASS under small and large bump road profile excitations.
Figure 3.
(a) PTP Acceleration-Time graphs: Small and Large bump road profile.¹⁷ (b) PTP Acceleration-Frequency graphs: Small and Large bump road profile.¹⁷

RMS acceleration

The predicted RMS accelerations through “control system methodology” were compared with ISO 2631-1:1997 (Table 1) to categorize the human comfort ride index zone. The result of skyhook continuous and modified skyhook control policies shows that the RMS acceleration of 0.302 m/s² 0.296 m/s² falling in ”Extremely comfortable” ride index zone for large bump excitation. The Passive, MR passive off, PID and Skyhook on/off control policies shows that the RMS acceleration of 0.390 m/s², 0.372 m/s², 0.332 m/s² and 0.326 m/s² falling in “Comfortable” ride index zone for large bump excitation.

PTP acceleration

The computed PTP acceleration results using MR passive off, PID, SHO, PID+GA, SHC and MSH in terms of percentage improvement were found to be 4.99%, 14.40%, 20.17%, 23.46%, 29.53% and 32.53%, respectively which are better than passive suspension results of small bump road profile and 4.8%, 14.41%, 20.22%, 23.44%, 28.25% and 32.83%, respectively which are better than passive suspension results of large bump road profile.

Ride quality evaluation

The SEAT, VDV and CF values were computed and compared with ISO 2631-1: 1997 for assessing the degree of ride quality. The effectiveness of the MSH controller was evaluated in terms of SEAT, VDV and CF values for enhancing the degree of ride quality. The simulated results of SEAT, VDV and CF in terms of percentage improvement were found to be 30.41, 52.84%, and 11.62%, respectively which are better than that of passive suspension for small bump road profile and 31.76%, 53.27%, and 11.02% respectively which are better than that of passive suspension for a large bump road profile.¹⁷ Since, the actual 3D geometry of the seat system cannot be modelled in 1D Activate, MatLAB, etc., software, the co-simulation methodology was used to predict more realistic understanding of the ride comfort and this work makes an effort in this direction.

The acceleration of ASS was computed for frequency domain using semi-active seat suspension system and control policies. Figure 3(b) explains the PTP acceleration of ASS under small and large bump road profile excitations. The frequency plot agrees as seen in literature,¹³ with change in magnitude of acceleration. According to Figure 3(b), the modified skyhook controller can dissipate the energy better than the passive system and can improve the ride comfort effectively.

Results of co-simulation

The computed RMS acceleration of the seat system using various system controllers such as MR passive off (zero voltage applied to the damper coil), PID, SHO, SHC and MSH were correlated with those of the passive seat damping system. The simulation results of control policies are discussed below.

Time domain – small and large bump road profile

PTP acceleration of small bump road profile

The computed displacement and acceleration of the ASS for small bump road profile excitations are shown in Figure 4. The time history graph trend agrees with the “Control model” result of¹⁷ with magnitude change in displacement and acceleration. The MSH controller shows 33.33% performance improvement in PTP acceleration of the seat system when compared with that of the passive suspension system.
Figure 4.
Displacement versus time and acceleration versus time – small bump profile (co-simulation).

PTP acceleration of large bump road profile

The computed displacement and acceleration of the ASS for small bump road profile excitations are shown in Figure 5. The time history graph trend agrees with the result of¹⁷ with magnitude change in displacement and acceleration. The MSH controller shows 33.27% performance improvement in PTP acceleration of ASS when compared with that of a passive suspension system.
Figure 5.
Displacement versus time and acceleration versus time – large bump profile (co-simulation).

In summary, the simulation result of the seat system with MSH control policy reveals that the PTP acceleration is reduced by 33.33% and 33.27% for small bump road profile and large bump road profile excitations, respectively.

Ride quality evaluation – small and large bump road profile

Small bump road profile

The small bump road profile excited at seat-mounting locations of ASS and the effectiveness of the MSH control policy was studied using SEAT value, VDV value and CF value and the same were shown in Figure 6. The results showed that the values of SEAT, VDV, and CF in terms of percentage improvement were found to be 25.37%, 30.55% and 11.84%, respectively which were better than that of other control policies described in this work. The RMS accelerations of all the control policies were compared with Table 1 and were found to be fallen in the “Extremely comfortable” ride index zone for small bump road profile excitation.
Figure 6.
Percentage of ride quality improvement with passive damper (pd) – small bump profile (co-simulation).

Large bump road profile

The large bump road profile was excited at the seat-mounting locations of ASS and the effectiveness of the MSH control policy was studied using SEAT value, VDV value and CF value which are listed in Figure 7. The results revealed that the values of SEAT, VDV, and CF in terms of percentage improvement were found to be 25.61%, 28.41% and 14.27%, respectively which were better than that of other control policies discussed in this work.
Figure 7.
Percentage of ride quality improvement with PD – large bump profile (co-simulation).

The RMS acceleration of MSH control policy was 0.309 m/s² and fall in the “Extremely comfortable” ride index zone. For the Passive, MR passive off, PID, SHO and SHC control policies, the RMS acceleration values were 0.50 m/s², 0.478 m/s², 0.415 m/s² and 0.368 m/s², respectively indicating a “Comfortable” ride index zone.

Time-domain – random road profile

Smooth road profile

The smooth road profile was excited at the seat-mounting locations of ASS and simulated using co-simulation approach. The computed displacement and acceleration of ASS are shown in Figure 8(a) and 8(b). The trend of the response curve agrees with the literature¹⁴ with magnitude change in displacement and acceleration.
Figure 8.
(a) Displacement versus time – smooth road profile (co-simulation). (b) Acceleration versus time – smooth road profile (co-simulation).

The co-simulation results were correlated with “Activate” result¹⁷ and found that the RMS acceleration (maximum 0.04 m/s²) of ASS fell in “extremely comfortable” ride index zone.

Rough road profile

The rough road profile was excited at the seat-mounting locations of ASS and simulated using co-simulation approach. The computed displacement and acceleration of ASS are shown in Figure 9(a) and 9(b). The trend of the response curve agrees with the literature¹⁴ with magnitude change in displacement and acceleration.
Figure 9.
(a) Displacement versus time – rough road profile (co-simulation). (b) Acceleration versus time – rough road profile (co-simulation).

The co-simulation results were correlated with “Activate” result¹⁷ and found that the RMS acceleration (maximum 0.566 m/s2) of ASS fell in “Comfortable” ride index zone. Also, the RMS acceleration of the co-simulation result found 13.8% better than Activate result (control model result). The MSH controller provides the lowest vibration transfer to the seat system under the smooth and rough road profile excitations when compared with other control policies described in this study.

Ride quality evaluation – random road profile

Smooth road profile

The smooth road profile was excited at the seat-mounting locations of ASS and the effectiveness of the MSH control policy was evaluated using FW RMS acceleration, SEAT value, and VDV value. The values of FW RMS acceleration, SEAT and VDV in terms of percentage improvement were found to be 28.24%, 28.81% and 32.70%, respectively as shown in Figure 10 which were better than that of other control policies.
Figure 10.
Acceleration versus time – smooth road profile and rough road profile (co-simulation).

The RMS accelerations of all the control policies were compared with Table 1 and were found to be fallen in the “Extremely comfortable” ride index zone for random smooth road profile.

Rough road profile

The rough road profile excited at seat-mounting locations of ASS and the effectiveness of the MSH control policy was evaluated using FW RMS acceleration, SEAT value. It was observed that the values of FW RMS acceleration, SEAT and VDV in terms of percentage improvement were found to be 37.78%, 26.66% and 44.33%, respectively as shown in Figure 10 which were better than that of other control policies.

The RMS acceleration of MSH control policy was 0.314 m/s² and fall in the “Extremely comfortable” ride index zone. For the Passive, MR passive off, PID, SHO and SHC control policies, the RMS acceleration values were 0.4329 m/s², 0.4029 m/s², 0.3864 m/s² and 0.3821 m/s², 0.3142 m/s², respectively indicating a “Comfortable” ride index zone.

The PTP acceleration of “Activate” and “co-simulation” were compared with FE study of¹⁷ and the correlation levels were found to be 2.46% and 1.34%, respectively for small and large bump profile. The correlation levels of SEAT were 20.10% and 23.98%, respectively¹⁷ for small and large bump profile. The co-simulation results of VDV, SEAT and CF in terms of percentage improvement were found to be 32.7%, 28.81% and 18.89%, respectively which was better than that for the passive suspension for a random smooth road profile and 44.33%, 26.66% and 17.65%, respectively which were better than that for the passive suspension for a random rough road profile. The RMS accelerations of all the control policies were compared with Table 1 and were found to be fallen in the “Extremely comfortable” ride index zone for random smooth road profile. Since the actual 3D geometry of the seat system was considered for dynamic model and control model, the co-simulation approach predicted better ride comfort than the results obtained from “Activate” software.

Conclusion

The finite element analysis results reveal that the RMS acceleration of random rough road condition only is falling in “fairly comfortable” ride index zone. Therefore, to improve, the semi-active seat suspension system with suitable control policy needs to be integrated with ASS for enhancing the degree of ride comfort of the occupant.

The computed PTP acceleration results using MR passive off, PID, SHO, PID+GA, SHC and MSH in terms of percentage improvement were found to be 4.99%, 14.40%, 20.17%, 23.46%, 29.53% and 32.53%, respectively which are better than passive suspension results of small bump road profile and 4.8%, 14.41%, 20.22%, 23.44%, 28.25% and 32.83%, respectively which are better than passive suspension results of large bump road profile. The PTP acceleration reveals that the MSH controller delivers superior performance than other control policies studied in this work.

The SEAT, VDV and CF values were computed and compared with ISO 2631-1: 1997 for assessing the degree of ride quality. The effectiveness of the MSH controller was evaluated in terms of SEAT, VDV and CF values for enhancing the degree of ride quality. The simulated results of SEAT, VDV and CF in terms of percentage improvement were found to be 30.41, 52.84%, and 11.62%, respectively which are better than that of passive suspension for small bump road profile and 31.76%, 53.27%, and11.02% respectively which are better than that of passive suspension for a large bump road profile. Since, the actual 3D geometry of the seat system cannot be modeled in 1D Activate, MatLAB, etc., software; co-simulation methodology is preferred to better predict the ride comfort and ride quality of the seat occupant.

The “co-simulation” results of RMS accelerations of all the control policies were fell in “Extremely comfortable” ride index zone for small bump road profile excitation. RMS accelerations of MSH controller fell in “Extremely comfortable” and others fell in “Comfortable” ride index zone for large bump road profile excitation. The PTP acceleration value of “Activate” and “Co-simulation” were compared and the correlation levels were found to be 2.46% and 1.34%, respectively for small and large bump profile. The correlation levels of SEAT were 20.10% and 23.98%, respectively for small and large bump profile. The co-simulation results of VDV, SEAT and CF in terms of percentage improvement were found to be 32.7%, 28.81% and 18.89%, respectively which was better than that of passive suspension for a random smooth road profile and 44.33%, 26.66% and 17.65%, respectively which were better than that for the passive suspension for a random rough road profile. Since the actual 3D geometry of the seat system was considered for dynamic model and control model, the co-simulation approach predicted better ride comfort than the results obtained from “Activate” software. The co-simulation result concluded that the MSH controller delivers superior performance than other control policies studied in this work. This study finds that the application of co-simulation methodology in industry could meet the time-to-market, reduction in development cycle time, reduction in cost and improvement in performance of seat system than carrying out design iterations and studies using 1D simplified study.

Parameter - seat with quarter car model
m₁	75	c₁	1400	k₁	24,000
m₂	350	c₂	750	k₂	7500
m₃	45	c₃	0	k_t	160,000

Parameters - modified bouc-wen model
C_oa	Ns/m	784	k_p	N/m	840
C_ob	Ns/m	183	α_a	N/m	12,441
k_o	N/m	3610	α_b	N/m	38,430
p_1a	Ns/m	14,649	Γ	1/m²	136,320
p_1b	Ns/m	34,622	B	1/m²	2,059,020
A	—	58	H	1/s	2
x_o	—	0.0245	N	—	190

Maximum acceleration transmissibility (dB) [shoulder & neck]
1	17.49	5.47	17	5.4	Lateral mode (Y-axis)
2	9.5	11.98	8.82	10.3	Fore-aft mode (X-Axis)
3	4.28	5.49	4.49	4.8	Twist mode (Z-Axis)

Base excitation	Seat conditions	RMS acceleration (m/s²)
Smooth road	Seat without mannequin Mass	0.25	Extremely comfortable	0.23	Extremely comfortable
Seat with mannequin Mass	0.28	Extremely comfortable	0.27	Extremely comfortable
Rough road	Seat without mannequin Mass	0.45	Comfort	0.44	Comfort
Seat with mannequin Mass	0.645	Fairly comfortable	0.62	Fairly comfortable

Frequency and mode shape correlation
Fore-aft	33.80	30.18	11.99%	0.94
Lateral	35.97	36.54	1.56%	0.91
Twist	54.70	52.64	3.91%	0.93

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iD

Davidson Jebaseelan

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Parameter - seat with quarter car model
Mass (Kg)		Damping (Ns/m)		Spring stiffness (N/m)
m₁	75	c₁	1400	k₁	24,000
m₂	350	c₂	750	k₂	7500
m₃	45	c₃	0	k_t	160,000

Parameters - modified bouc-wen model
Parameter	Units	Values	Parameter	Units	Values
C_oa	Ns/m	784	k_p	N/m	840
C_ob	Ns/m	183	α_a	N/m	12,441
k_o	N/m	3610	α_b	N/m	38,430
p_1a	Ns/m	14,649	Γ	1/m²	136,320
p_1b	Ns/m	34,622	B	1/m²	2,059,020
A	—	58	H	1/s	2
x_o	—	0.0245	N	—	190

Maximum acceleration transmissibility (dB) [shoulder & neck]
Mode No.	Without passive damper		With passive damper		Mode shape
Mode No.	Without mannequin Mass	With mannequin Mass	Without mannequin Mass	With mannequin Mass	Mode shape
1	17.49	5.47	17	5.4	Lateral mode (Y-axis)
2	9.5	11.98	8.82	10.3	Fore-aft mode (X-Axis)
3	4.28	5.49	4.49	4.8	Twist mode (Z-Axis)

Base excitation	Seat conditions	RMS acceleration (m/s²)
Base excitation	Seat conditions	Without damper	Comfort index	With damper	Comfort index
Smooth road	Seat without mannequin Mass	0.25	Extremely comfortable	0.23	Extremely comfortable
Smooth road	Seat with mannequin Mass	0.28	Extremely comfortable	0.27	Extremely comfortable
Rough road	Seat without mannequin Mass	0.45	Comfort	0.44	Comfort
Rough road	Seat with mannequin Mass	0.645	Fairly comfortable	0.62	Fairly comfortable

Frequency and mode shape correlation
Mode shapes	FEA - natural frequency (Hz)	Physical test result (Hz)	Gap (%)	MAC
Fore-aft	33.80	30.18	11.99%	0.94
Lateral	35.97	36.54	1.56%	0.91
Twist	54.70	52.64	3.91%	0.93