# Performance Enhancement of Vehicle Mechatronic Inertial Suspension, Employing a Bridge Electrical Network

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Model Building

#### 2.1. Seven-Degree-of-Freedom Vehicle Model

_{a}is the sprung mass. m

_{1}, m

_{2}, m

_{3}, and m

_{4}are the unsprung mass of the four suspensions, respectively. K

_{t}is the equivalent stiffness of the tire. k

_{f}and c

_{f}are the spring stiffness and the damping coefficient of the front suspensions, respectively. k

_{r}and c

_{r}are the spring stiffness and the damping coefficient of rear suspensions, respectively. Z

_{10}, Z

_{20}, Z

_{30}, and Z

_{40}are the vertical displacements of the connection between the vehicle body and the four suspensions. F

_{10}, F

_{20}, F

_{30}, and F

_{40}are the forces of the four suspensions, respectively. Z

_{1}, Z

_{2}, Z

_{3}, and Z

_{4}are the vertical displacements of four unsprung masses, respectively. Z

_{b}

_{3}and Z

_{b}

_{4}are the vertical displacements of the mechatronic inerter of the left rear suspension and the right rear suspension. Q

_{1}, Q

_{2}, Q

_{3}, and Q

_{4}are the displacement inputs of the four wheels. Z

_{a}is the vertical displacement of the sprung mass. θ is the body roll angle, and I

_{x}is the body roll moment of inertia. φ is the body pitch angle, and I

_{y}is the body pitch moment of inertia. l

_{1}and l

_{2}are the distance from the front axle and rear axle to the body centroid, respectively. d is the wheelbase, b is the inertial coefficient of the mechatronic inerter, and v is the vehicle speed. k

_{t}and k

_{e}are the inductive torque constant and the inductive voltage constant of the rotating motor, respectively. Z is the impedance of the external circuit of the rotating motor. u

_{3}and u

_{4}are the forces of the series branch of the mechatronic inerter and the damper, respectively. P is the lead of the ball screw.

#### 2.2. Bridge Network

_{1}, R

_{2}, R

_{3,}R

_{4}, and R

_{5}are resistors, T

_{1}, T

_{2}, and T

_{3}are equivalent impedances.

#### 2.3. Series-Parallel Network

## 3. Optimization of the Inertial Suspension Parameters

_{1}and d

_{2}are non-negative constants, called acceleration factors, and the general range is between 0 and 4. r

_{1}and r

_{2}are random numbers between (0, 1). P

_{id}and P

_{gd}are the individual extremum and global extremum, respectively.

_{1}, R

_{2}, R

_{3}), one capacitor (C

_{1}), and one inductor (L

_{1}) of the external electrical circuit are taken as individuals to be solved. Moreover, the performance indicators have different units and orders of magnitude, so it is necessary to establish a unified objective function. The performance indexes of the mechatronic inertial suspension are divided by the corresponding indexes of the passive suspension, and the sum of their quotients is taken as the objective function. In this paper, f is the objective function of optimization, which is obtained by weighting the following parameters. The influence of different units of evaluation indexes is ignored; meanwhile, the improvement of suspension performance is studied by quantifying the objective function Therefore, the optimization of evaluation indexes of the ride comfort and the road friendliness is transformed into the minimum value problem of the unified objective function. The smaller the value of the optimization objective function, the better the optimization effect, and the performance improvement is obvious. In the optimization process, the road condition and running speed are set as C grade and 20 km/h, respectively, and the number of iterations is 100. Due to the mechatronic inertial suspension being used to replace the rear suspension system, the relevant evaluation indexes of the rear suspension are mainly used as the optimization objectives. The expression of the unified objective function and constraint conditions are as follows:

_{pas}, LRSWS

_{pas}, LRDTL

_{pas}, RRSWS

_{pas}, and RRDTL

_{pas}are the RMS of the corresponding performance indexes of the traditional passive suspension. P is the set of parameters to be optimized. LM and UM are the upper and lower bounds of these parameters, and these parameters will affect the handling stability of the vehicle.

## 4. Discussion

#### 4.1. Road Input

_{r}(t) is the vertical displacement of the random road input, w(t) is the white noise with mean value of 0, and G

_{q}(n

_{0}) is the road roughness (2.56/10

^{4}m

^{3}).

#### 4.2. Performance Analysis of Mechatronic Inertial Suspension

## 5. Experimental Research

#### 5.1. Structure Selection and Real Vehicle Installation

#### 5.2. Random Road Input

#### 5.3. Pulse Road Input

^{−2}) to 7.1722 (m·s

^{−2}), which is only 0.5% and helped to improve the vehicle ride comfort. However, for the vehicle body roll angular acceleration, the improvement was apparent, from 4.9686 (rad·s

^{−2}) to 4.5532 (rad·s

^{−2}), and the degree of reduction was 8.4%. For the vehicle body pitch angular acceleration, the peak to peak of the mechatronic inertial suspension was relatively higher than that of the passive suspension, which increased from 9.6225 (rad·s

^{−2}) to 10.1903 (rad·s

^{−2}) (5.9%), and there was no improvement in the vehicle handling stability. The peak to peak values of the suspension working space and dynamic tire load of the left front suspension, comparing the passive suspension with the mechatronic inertial suspension based on a bridge network (a), were reduced by 2.3% and 2.2%, respectively. The performance improvement of the left rear suspension was obvious compared to the left front suspension. The suspension working space decreased from 0.1234 (m) to 0.1008 (m) (18.3%), and the dynamic tire load decreased from 7047 (N) to 6568 (N) (6.8%). These improvements helped to improve the vehicle ride comfort and road friendliness.

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 3.**(

**a**). bridge network consists of five resistance elements. (

**b**). Equivalent network of the bridge network.

Parameters | Symbol | Unit | Value |
---|---|---|---|

Sprung mass | m_{a} | k_{g} | 1659 |

Unsprung mass of left and right front wheels | m_{1}, m_{2} | k_{g} | 47.5 |

Unsprung mass of left and right rear wheels | m_{3}, m_{4} | k_{g} | 42.5 |

Spring stiffness of front axle suspension | k_{f} | kN·m^{−1} | 25 |

Spring stiffness of rear axle suspension | k_{r} | kN·m^{−1} | 22 |

Damping coefficient of front axle suspension | c_{f} | kN·s·m^{−1} | 1.8 |

Damping coefficient of rear axle suspension | c_{r} | kN·s·m^{−1} | 1.5 |

Equivalent stiffness of tire | K_{t} | kN·m^{−1} | 192 |

Distance from front axle to body centroid | l_{1} | m | 1.28 |

Distance from rear axle to body centroid | l_{2} | m | 1.43 |

Wheelbase | d | m | 1.62 |

Inertance of rear suspension | b | k_{g} | 308 |

Body roll moment of inertia | I_{x} | k_{g}·m^{2} | 1088 |

Body pitch moment of inertia | I_{y} | k_{g}·m^{2} | 3032 |

Parameters | Bridge Network | Series-Parallel Network | ||||
---|---|---|---|---|---|---|

(a) | (b) | (c) | (d) | (e) | (f) | |

Capacitance C_{1} (mF) | 8 | 3 | 8.4 | 6.3 | 2.5 | 7.5 |

Inductance L_{1} (mH) | 18.8 | 17.5 | 3.5 | 16 | 13.7 | 15 |

Resistance R_{1} (Ω) | 2908 | 2553 | 857 | 2976 | 2856 | 2598 |

Resistance R_{2} (Ω) | 2984 | 2824 | 3000 | 2768 | 2708 | 2714 |

Resistance R_{3} (Ω) | 2992 | 2996 | 1350 | 2748 | 2158 | 2944 |

Suspension Performance Index | Passive Suspension | Bridge Network | ||
---|---|---|---|---|

(a) | (b) | (c) | ||

RMS of centroid acceleration (m·s^{−2}) | 1.8792 | 1.7902 | 1.8023 | 1.8010 |

RMS of body roll angular acceleration (rad·s^{−2}) | 0.1059 | 0.1044 | 0.1037 | 0.1037 |

RMS of body pitch angular acceleration (rad·s^{−2}) | 1.3827 | 1.3440 | 1.3532 | 1.3539 |

RMS of working space of left front suspension (m) | 0.0266 | 0.0256 | 0.0257 | 0.0257 |

RMS of dynamic tire load of left front wheel (kN) | 1.9287 | 1.8665 | 1.8781 | 1.8781 |

RMS of working space of left rear suspension (m) | 0.0271 | 0.0201 | 0.0202 | 0.0203 |

RMS of dynamic tire load of left rear wheel (kN) | 1.8907 | 1.7389 | 1.7497 | 1.7495 |

Suspension Performance Index | Passive Suspension | Series-Parallel Network | ||
---|---|---|---|---|

(d) | (e) | (f) | ||

RMS of centroid acceleration (m·s^{−2}) | 1.8792 | 1.8354 | 1.8378 | 1.8446 |

RMS of body roll angular acceleration (rad·s^{−2}) | 0.1059 | 0.1131 | 0.1125 | 0.1125 |

RMS of body pitch angular acceleration (rad·s^{−2}) | 1.3827 | 1.4571 | 1.4591 | 1.4642 |

RMS of working space of left front suspension (m) | 0.0266 | 0.0253 | 0.0252 | 0.0254 |

RMS of dynamic tire load of left front wheel (kN) | 1.9287 | 1.8444 | 1.8441 | 1.8528 |

RMS of working space of left rear suspension (m) | 0.0271 | 0.0229 | 0.0233 | 0.0230 |

RMS of dynamic tire load of left rear wheel (kN) | 1.8907 | 1.7855 | 1.7897 | 1.7935 |

Parameter | Value | Parameter | Value |
---|---|---|---|

Nominal shaft diameter d_{0} (mm) | 16 | Rated power P (W) | 2000 |

Lead P (mm) | 5 | Rated speed n_{e} (r·min^{−1}) | 3000 |

Center distance of balls on both sides d_{p} (mm) | 16.75 | Maximum speed n_{m} (r·min^{−1}) | 6000 |

Groove diameter d_{c} (mm) | 13.5 | Rated torque T_{e} (N·m) | 5.88 |

Number of columns × Number of turns | 1 × 2.65 | Rated voltage U_{e} (V) | 310 |

Effective stroke l_{0} (mm) | 120 | Rated current I_{e} (A) | 6 |

Lead screw stiffness k_{l} (N·μm^{−1}) | 130 | Inductive torque constant k_{t} (N·m/A) | 0.98 |

Dynamic rated load c_{a} (kN) | 5.4 | Inductive voltage constant k_{e} (V·s/rad) | 0.98 |

Static rated load c_{oa} (kN) | 13.3 | Allowable stress σ_{p} (N·mm^{−2}) | 150 |

Dynamic load coefficient k_{s} | 2 | Radius of flywheel r (mm) | 30 |

Static load coefficient k_{d} | 3 | Thickness of flywheel h (mm) | 20 |

Performance Index | RMS of Passive Suspension | Bridge Network (a) | |
---|---|---|---|

RMS | Improvement (%) | ||

Centroid acceleration (m·s^{−2}) | 1.2656 | 1.2428 | 1.8 |

Vehicle body roll angular acceleration (rad·s^{−2}) | 1.1139 | 1.0526 | 5.5 |

Vehicle body pitch angular acceleration (rad·s^{−2}) | 0.4426 | 0.4643 | −4.9 |

Working space of left front suspension (m) | 0.0142 | 0.0138 | 2.5 |

Dynamic tire load of left front wheel (N) | 1022 | 1000 | 2.2 |

Working space of left rear suspension (m) | 0.0145 | 0.0114 | 21.1 |

Dynamic tire load of left rear wheel (N) | 981 | 919 | 6.3 |

Performance Index | Peak to Peak of Passive Suspension | Bridge Network (a) | |
---|---|---|---|

Peak to Peak | Improvement (%) | ||

Centroid acceleration (m·s^{−2}) | 7.2110 | 7.1722 | 0.5 |

Vehicle body roll angular acceleration (rad·s^{−2}) | 4.9686 | 4.5532 | 8.4 |

Vehicle body pitch angular acceleration (rad·s^{−2}) | 9.6225 | 10.1903 | -5.9 |

Working space of left front suspension (m) | 0.1128 | 0.1102 | 2.3 |

Dynamic tire load of left front wheel (N) | 7200 | 7038 | 2.2 |

Working space of left rear suspension (m) | 0.1234 | 0.1008 | 18.3 |

Dynamic tire load of left rear wheel (N) | 7047 | 6568 | 6.8 |

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## Share and Cite

**MDPI and ACS Style**

Zhang, T.; Yang, X.; Shen, Y.; Liu, X.; He, T.
Performance Enhancement of Vehicle Mechatronic Inertial Suspension, Employing a Bridge Electrical Network. *World Electr. Veh. J.* **2022**, *13*, 229.
https://doi.org/10.3390/wevj13120229

**AMA Style**

Zhang T, Yang X, Shen Y, Liu X, He T.
Performance Enhancement of Vehicle Mechatronic Inertial Suspension, Employing a Bridge Electrical Network. *World Electric Vehicle Journal*. 2022; 13(12):229.
https://doi.org/10.3390/wevj13120229

**Chicago/Turabian Style**

Zhang, Tianyi, Xiaofeng Yang, Yujie Shen, Xiaofu Liu, and Tao He.
2022. "Performance Enhancement of Vehicle Mechatronic Inertial Suspension, Employing a Bridge Electrical Network" *World Electric Vehicle Journal* 13, no. 12: 229.
https://doi.org/10.3390/wevj13120229