# Vibration Characteristics of Framed SUV Cab Based on Coupled Transfer Path Analysis

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## Abstract

The vibration transmission paths in a sport-utility vehicle with a frame structure were used to evaluate the coupled vibration of each vibration transmission link. This method was based on the transmission path of an “engine-powertrain mount system-frame-vehicle body suspension-body-driver seat rail,” and the research objective was to improve the vibration characteristics of the cab. This coupled transfer path analysis combined analysis and experiment to establish the vehicle vibration transmission path model and a finite element simulation model. With this method, the vibration level of the driver’s seat rail was reduced and engineering practice was effectively used to improve the vibration characteristics of the cab. This method was applied to a framed SUV cabin.

## Keywords

Framed SUV SUV cabin Vibration characteristics Coupling Transfer path## Abbreviations

- BIW
Body-in-white

- DOF
Degree of freedom

- SUV
Sport-utility vehicle

## 1 Introduction

With the progress of engineering technology and the improvement of living standards, people’s performance expectations for passenger cars have gradually increased. While pursuing power and economy performance, more and more attention is paid to ride comfort in sport-utility vehicles (SUVs). The vibration characteristics of the cab gradually become a key index to evaluate the quality of the vehicle [1].

In SUVs, the frame-to-body mount increases the vibration transfer linkage between the engine and the cab. In the target response analysis, each transmission link has an impact on the vibration characteristics of the cab. Also, there is a coupling effect between each transmission link, and the vibration coupling between transmission links is very complex. Therefore, it is important to study the vibration characteristics of a framed SUV cab.

Research into the vibration characteristics in the cab is mainly focused on improving vehicle vibration performance by means of transfer path analysis. Reference [2] used mechanical-acoustic transfer path analysis, where the contribution of each body panel to the vibration in the cab is analyzed, to diagnose the structural transmission noise. In Ref. [3], transfer path analysis and the experimental modal technique were combined to optimize the noise vibration harshness of the vehicle suspension. Reference [4] proposed a powertrain mounting system based on improved transfer path analysis to optimize the mount transfer characteristics of a car. In Ref. [5], coordinate transformation was used to solve the coupling problem of vibration force between partial transfer paths and analyze the vibration of the vehicle body.

Existing research, combined with an engineering example of a specific type of SUV, was used to explore the significant influence of all transfer paths on the cab vibration in an “engine-power train mount system-frame-body mount-body-driver seat guide.” According to the theory of vibration source coupling transfer path analysis, the coupling effect between each transmission link is analyzed, and the vehicle frame structure and powertrain mounting system are optimized. The combination of simulation, analysis, calculation, and experiment verified the effectiveness of the optimization results and proved the practicability of the method, which is especially useful for assessing vibration of the SUV cab.

## 2 Multistage Coupling Transfer Path Analysis Method

### 2.1 Basic Principles of Path Analysis of Vibration Source Transfer

*x*,

*y*, and

*z*directional components, were assumed, and each excitation component corresponds to

*n*transfer paths. Therefore, the excitation force component and corresponding transfer path produce a response component of the system. With the target point vibration as the system response, the vibration component can be expressed as:

*i*on the target point

*t*, \( H_{t/i} \left( \omega \right) \) is the frequency response function of the section

*i*path, and \( f_{i} \left( \omega \right) \) is the working load of the section

*i*path.

*n*transfer paths, the total response at the target point is a linear superposition of each component on each path, that is:

### 2.2 Analysis of Substructure Multistage Coupling Model

*c*), (2) the self-excited coordinate (hereinafter denoted

*i*), and (3) the self-response coordinate (hereinafter denoted

*o*). The degrees of freedom of the substructure are shown in Fig. 3.

The vibration transmission link from the engine to the cab of a framed SUV is increased by linkages between the substructures, that is, powertrain (A) → frame (B) → body (C). According to the theory of substructure coupling, the coupled vibrations of A, B, and C superpose; the transfer paths increase; and the coupling between the transfer links becomes more complicated. In contrast, the vibration characteristics between the SUV load-supporting structure and secondary substructure are much simpler. Therefore, to improve the vibration characteristics of the whole vehicle, it is necessary to fully consider the multistage vibration coupling relations between powertrain, frame, and body, so as to effectively improve the vibration characteristics in multiple coupling links.

## 3 An Example of Analysis and Optimization

### 3.1 Optimum Design of Body Structure Size

The excitation frequency of the SUV engine covers a range of 26.7–116.7 Hz. The natural frequency of the frame and the body-in-white (BIW) cannot completely avoid this excitation range, and the distribution of the natural frequency of the body is dense, as shown in Table 1. There is a coupling relationship between the structural modal frequency of the body before optimization and the excitation frequency of the engine idling speed. The first three natural frequencies of the BIW are coupled with the others to varying degrees, and the vibration excitation at these three frequencies has a strong impact on cab vibration.

*f*(

*x*) is the objective function and

*f*

_{1},

*f*

_{2}, and

*f*

_{3}are the natural values of the first-, second-, and third-order frequencies of the BIW, respectively.

Optimization of body structure modal frequency and engine idling excitation frequency before and after optimization

Order | The natural frequency of the frame (Hz) | The natural frequency of the body (before optimization) (Hz) | The natural frequency of the body (after optimization) (Hz) | Engine excitation frequency (Hz) |
---|---|---|---|---|

1 | 23.4 | 26.4 | 25.2 | 26.7 |

2 | 29.0 | 29.1 | 28.1 | 26.7 |

3 | 34.7 | 33.9 | 31.5 | 26.7 |

4 | 49.0 | 35.7 | 33.5 | 26.7 |

5 | 52.7 | 42.0 | 35.9 | 26.7 |

Optimization results of plate thickness

Variable | Initial value (mm) | Optimization result (mm) | Variable | Initial value (mm) | Optimization result (mm) |
---|---|---|---|---|---|

Roof | 0.7 | 0.4 | Right panel | 1.2 | 0.5 |

Front beam on the roof | 0.7 | 0.7 | Left panel | 1.2 | 0.4 |

Upper beam on the front window | 0.7 | 0.7 | Front panel | 1.0 | 1.0 |

Middle beam on the roof | 1.2 | 1.2 | Firewall | 1.2 | 0.7 |

Reinforcing plate | 1.6 | 1.2 | Reinforcing plate on the left A-pillar | 1.5 | 1.5 |

Front right side on the fender | 0.7 | 0.6 | Reinforcing plate on the right A-pillar | 1.5 | 1.5 |

Front left side on the fender | 0.7 | 0.6 | Lower beam on the front window | 1.0 | 1.0 |

Left side beam on the roof | 1.2 | 0.8 | Lower inner plate on the right A-pillar | 1.5 | 0.5 |

Right side beam on the roof | 1.2 | 0.8 | Lower inner plate on the left A-pillar | 1.5 | 0.5 |

Inner plate on the left B-pillar | 1.2 | 0.8 | Inner plate on the front window | 1.5 | 1.5 |

### 3.2 Analysis and Optimization of Powertrain Mounting System

The influence of the powertrain mounting system on the vibration characteristics of the cab is mainly controlled by two aspects: the design defect of the mounting support and the insufficient decoupling rate of the mounting system. In the suspension bracket design, the stiffness and first modal frequency of the front and rear suspension brackets are in accordance with the requirements of the engineering for the mounting bracket, and vibration isolation is achieved to a certain extent.

*RXX*,

*Y*, and

*Z*direction modes of the mounting system. The main methods for improving the vibration characteristics of the cab and the decoupling rate of the mounting system are to optimize the mounting stiffness and adjust the mounting angle of the mount [10]. The relevant parameters for powertrain and mount modeling are shown in Tables 3 and 4.

Powertrain basic parameters

Mass (kg) | Barycenter coordinate (mm) | Moment of inertia (kg m | |||||
---|---|---|---|---|---|---|---|

| | | | | | ||

270.8 | (− 5.6, 7.2, 203.2) | 9.32 | 26.21 | 23.3 | 0.46 | 0.12 | 2.81 |

Suspension point position and angle

Hard spot coordinate (mm) | Static stiffness (N/mm) | Tilt angle (deg) | |
---|---|---|---|

Front left | (− 95.2, − 229.1, 96.6) | (106, 128, 470) | 45 |

Front right | (− 142.4, 229.8, 93.2) | (106, 128, 470) | 45 |

Rear | (692.8, 4.9, − 115.8) | (52, 50, 270) | 45 |

- (1)
Objective function

- (2)
Design variable

*Y*-direction coordinate of the front and rear mounts are selected as design variables. There are 11 design variables, including front-mount three-direction coordinates (

*k*

_{u1},

*K*

_{v1},

*K*

_{w1}), rear-mount three-direction coordinates (

*K*

_{u2},

*K*

_{v2},

*K*

_{w2}), front-mount tilt angle (

*θ*

_{1},

*θ*

_{2}), front left and right suspension

*Y*coordinates (

*Y*

_{1},

*Y*

_{2}), and rear suspension

*Y*coordinate (

*Y*

_{3}).

- (3)
Constraint conditions

*f*:

*f*

_{i}and

*f*

_{j}are the

*i*th- and

*j*th-order natural frequencies of the powertrain mounting system and \( i \ne j \).

Comparison the value of each suspension stiffness and installation angle before and after optimization

Point | Isotropic stiffness (N/mm) | Tilt angle | ||||||
---|---|---|---|---|---|---|---|---|

| | | ||||||

Before | After | Before | After | Before | After | Before | After | |

Front left | 148.4 | 142.5 | 179.2 | 166.9 | 658.0 | 580.7 | 45.0 | 20.4 |

Front right | 148.4 | 142.5 | 179.2 | 166.9 | 658.0 | 580.7 | 45.0 | 20.4 |

Rear | 72.8 | 21.4 | 70.0 | 26.2 | 378.0 | 83.3 | 45.0 | 23.2 |

### 3.3 Simulation of Optimization Results

Comparison of natural frequency and decoupling rate of the suspension system before and after optimization

Order | Natural frequency (Hz) | Model kinetic energy symbol | Decoupling rate (%) | |||
---|---|---|---|---|---|---|

Before | After | Before | After | Difference | ||

1 | 6.13 | 5.27 | | 95.96 | 95.49 | 0.47 |

2 | 8.93 | 6.86 | | 73.27 | 96.92 | 23.65 |

3 | 9.51 | 7.73 | | 56.66 | 99.62 | 42.96 |

4 | 9.86 | 9.6 | | 45.91 | 93.54 | 47.63 |

5 | 16.45 | 10.69 | | 83.15 | 89.45 | 6.30 |

6 | 18.23 | 11.94 | | 60.29 | 97.61 | 37.32 |

## 4 Test Scheme and Validation

*j*th measuring point of the

*i*th working condition and \( v_{ij}^{X} ,\;v_{ij}^{Y} , \) and \( v_{ij}^{Z} \) are the total vibrational value in the

*X*,

*Y*, and

*Z*directions, respectively.

*a*

_{1}and

*a*

_{2}represent the total vibration values of the active and passive sides, respectively.

^{2}and 0.273 m/s

^{2}, respectively, which is 42.2% and 32.9% lower than that before optimization, indicating that the vibration characteristics of the cab are improved.

Comparison of the total vibration of each measuring point before and after optimization

Measuring position | Speed (rpm) | 800 | 1000 | 1250 | 1500 | 2000 | 2500 |
---|---|---|---|---|---|---|---|

Left mount | Before | 6.352 | 4.451 | 4.211 | 6.105 | 9.665 | 15.265 |

After | 4.148 | 4.800 | 3.798 | 5.300 | 8.827 | 10.495 | |

Right mount | Before | 6.293 | 4.477 | 4.779 | 6.031 | 9.250 | 18.492 |

After | 5.392 | 4.817 | 5.462 | 5.588 | 7.097 | 12.701 | |

Rear mount | Before | 7.327 | 3.754 | 3.387 | 5.844 | 9.573 | 15.100 |

After | 4.172 | 3.829 | 3.362 | 6.957 | 9.405 | 14.452 | |

Steering wheel | Before | 0.421 | 0.781 | 1.275 | 1.285 | 0.919 | 0.814 |

After | 0.356 | 0.484 | 0.745 | 0.544 | 0.647 | 0.831 | |

Seat guide | Before | 0.219 | 0.389 | 0.158 | 0.227 | 0.198 | 0.407 |

After | 0.216 | 0.225 | 0.152 | 0.156 | 0.200 | 0.273 |

Comparison of vibration isolation ratios of each suspension before and after optimization

Measuring position | Speed (rpm) | 800 | 1000 | 1250 | 1500 | 2000 | 2500 |
---|---|---|---|---|---|---|---|

Left mount | Before | 15.68 | 11.58 | 13.12 | 21.46 | 21.01 | 20.57 |

After | 19.33 | 17.23 | 16.32 | 22.04 | 21.88 | 21.02 | |

Right mount | Before | 16.47 | 13.81 | 18.30 | 20.23 | 20.43 | 27.41 |

After | 20.02 | 16.88 | 19.88 | 24.71 | 21.31 | 28.31 | |

Rear mount | Before | 13.17 | 12.66 | 11.90 | 12.85 | 10.86 | 15.04 |

After | 18.29 | 13.29 | 16.40 | 22.06 | 17.85 | 19.12 |

## 5 Conclusions

- 1.
On the basis of the dynamic characteristic parameters of the body structure, the coupling between the modal frequency of the body structure and the excitation frequency of the engine idling speed was analyzed. Thereafter, the partial plate thickness parameters were optimized, the weight of the body was reduced, and the influence of low-order frequency coupling on cab vibration characteristics was essentially eliminated.

- 2.
Decoupling of the power assembly suspension system was optimized. The finite element model simulation proved that the decoupling rate of each degree of freedom was increased to more than 89%.

## Notes

### Acknowledgements

The research was conducted under a grant from the Guangdong Province Science and Technology Planning Project (2015B010137002/2016A05053021).

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