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The transport sector is increasing day by day to satisfy the global market requirement. The bus is still the main mode of intercity transportation in Canada. Despite, an essentially unchanged conception, the total weight of the bus has increased by over 25% during the last three decades. To solve this problem, industrialists have moved to the use of light metals in the transportation field. Therefore, use of lightweight materials, such as aluminum is essential to reduce the total weight of bus. In this study, the focus is on the bus frame as it represents 30% of the total weight and it is the most stressed part of the bus. Its life duration is more important compared to that of all other elements. Thus, a study of the static and vibratory behavior would be very decisive. In this article, two types of analysis are carried out. First is the modal analysis to determine the natural frequencies and the mode shapes using a developed dynamic model of the bus. Because if any of the excitation frequencies coincides with the natural frequencies of the bus frame, then resonance phenomenon occurs. This may lead to excessive deflection, high stress concentration, fatigue of the structure and vehicle discomfort. In this case, the results analysis shows that the natural frequencies are not affected by the change of material. The second type of analysis is the linear static stress analysis to consider the stress distribution and deformation frame pattern under static loads numerically. For the numerical method, the frame is designed using SolidWorks and the analysis is made using Ansys WorkBench. The maximum Von Mises stress obtained for the static loading is in the same order for the three chassis frames studied. But in the case of the aluminium frame, the weight of 764 kg was reduced.

A bus frame represents the most stressed section in terms of excitation from the road or in terms of its main function of supporting structure. There have been several recent studies carried out at the level of this supporting structure, whether for car, truck, or bus. The focus of this different study was on design, geometry, static analysis, modal, and dynamic analysis. As for the work on design, different digital tools were used as Abaqus, Ansys, Catia, and SolidWorks. The most recent analyses were applied using the Ansys Workbench interface. The use of such finite element tools helps in accelerating design by minimizing the number of physical tests, thereby reducing the cost and the time.

Several static and modal studies have been established to evaluate the performance of the chassis. Among these works, M. Chandrasekar et al. [

Regarding the modal analysis [

The variation of chassis member thickness was also used [

This study focuses on the static and vibration analysis of aluminium and steel chassis of the bus. The frame or chassis is the most significant part used for supporting the bus structure as it is subjected to several of both dynamic and static forces. In this section, the chassis specification, the frame loading and the different frame motion are presented.

The bus frame model specified for this study consists of a single axle in front and tandem axles at the back with total length of 10.02 meters.

The dimensions of the longitudinal and the transversal beams constituting the frame chassis are presented in

To be able to reduce the weight of the existing standard steel frame (steel 1018-HR, steel 710C), the 6061-T6 aluminum alloy material was selected for this study. The characteristics of this aluminum alloy made it useful in the automotive field. The properties of the three materials are shown in

Regarding the loading, Quebec ministry of transportation [

Properties | Aluminium 6061-T6 | Steel 1018-HR | Steel 710C |
---|---|---|---|

Young’s modulus | 7.31 × 10^{10} N/m^{2} | 210 × 10^{10} N/m^{2} | 207 × 10^{10} N/m^{2} |

Density | 2700 kg/m^{3} | 7800 kg/m^{3} | 7800 kg/m^{3} |

Poisson ratio | 0.33 | 0.28 | 0.30 |

Tensile strength | 310 MPa | 475 MPa | 620 MPa |

Elastic limit | 275 MPa | 275 MPa | 550 Mpa |

of axles. The mass of the major considered elements for this study are presented in

For the case of an aluminum frame, the total static loading Q_{s} is equal to:

Q s = 18000 − ( Q 3-1 + Q 4 + Q 5 + Q 6 ) = 15087 kg (1)

Q s = 148003.5 N

For the tank and engine loads, they are applied separately then,

Q s 1 = Q s − ( Q 1 + Q 2 ) = 13 0 81 kg = 128324 . 64 N (2)

This static loading is applied on the longitudinal beam. There are two longitudinal beams, then Q s 1 is divided by two and it is uniformly distributed on each beam.

Load acting on the single beam:

128324.64 2 = 64162.32 N / beam (3)

・ Beam pressure

P beam = Q beam S beam = 100253.62 N / m 2 (4)

・ Tank pressure

P tank = Q tank S tank = 4248.92 N / m 2 (5)

・ Engine pressure

P engine = Q engine S engine = 5299.89 N / m 2 (6)

For the steel frame, the load acting on the single frame is equal to 60,419.80 N/beam and the beam pressure is equal to 94,217.50 N/m^{2}.

The frame is subjected to different motions as shown in

Elements | Mass (kg) |
---|---|

Filled tank (Q_{1}) | 476 |

Engine (Q_{2}) | 1530 |

Aluminum frame (Q_{3-1}) | 404 |

Steel frame (Q_{3-2}) | 1167 |

Front axle (Q_{4}) | 724 |

Rear axle 1 (Q_{5}) | 1224 |

Rear axle 2 (Q_{6}) | 561 |

the transverse axis; it is a top downward motion. The yaw angle represents the motion along the vertical axis. This yaw angle is not predominant compared to the pitch and roll angles. Therefore, in this study the focus was set on pitch and roll angles only. The vertical motion was also studied.

To be able to evaluate the motion of the bus frame, a three-dimensional dynamic model of the frame was developed. This model is presented in

The different parameters involved in this model are presented as follows:

Y 1 , 2 , 3 , 4 , 5 , 6 : Vertical motion of the six suspensions.

Y 7 : Vertical motion of the bus.

θ 7 : Pitch bus rotating angle.

∅ 7 : Roll bus rotating angle.

U i : Input excitation at the wheel i.

The different parameters values of this model are shown in

Definition | Symbol (Unit) | Value |
---|---|---|

Bus mass | m 7 ( kg ) | 15,491.5 |

Pitch moment | I θ ( kg ⋅ m 2 ) | 149,951.42 |

Roll moment | I ∅ ( kg ⋅ m 2 ) | 20,000.64 |

Distance (center gravity-wheel 1) | l 1 ( m ) | 2.25 |

Distance (center gravity-wheel 2) | l 2 ( m ) | 0.81 |

Distance (center gravity-wheel 3) | l 3 ( m ) | 2.25 |

Lateral distance | l 4 ( m ) | 1.25 |

Suspension rigidity for 1 and 4 | k 1 , 4 ( N / m ) | 374,000 |

Suspension rigidity for 2, 3, 5 and 6 | k 2 , 3 , 5 , 6 ( N / m ) | 435,000 |

Suspension damping i | b i ( N ⋅ s / m ) | 12,850 |

Tire rigidity i | k r i ( N / m ) | 2,800,000 |

Suspension mass for 1 and 4 | m 1 , 4 ( kg ) | 362 |

Suspension mass for 2 and 5 | m 2 , 5 ( kg ) | 611.83 |

Suspension mass for 3 and 6 | m 3 , 6 ( kg ) | 280.42 |

The equations of motion of the bus frame are written separately for the six wheel assemblies and later for the total frame.

1) Wheel assembly 1: equation of motion

This case represents a single degree of freedom, because there is only vertical motion possible. Then, the equation of motion can be written using Newton’s second law as follows, where i is the number of axle.

∑ F = m i y ¨ i (7)

For positive displacement of the masses 1 and 7 and for positive rotation by pitch angle θ 7 and roll angle ∅ 7 , the forces acting on the front side of the frame at the wheel 1 are represented in

・ Tire equation

F k r 1 = k r 1 ( y 1 − U 1 ) (8)

・ Suspension equation

F k 1 = k 1 [ y 1 − ( y 7 + l 1 θ 7 + l 4 ∅ 7 ) ] (9)

F b 1 = b 1 [ y ˙ 1 − ( y ˙ 7 + l 1 θ ˙ 7 + l 4 ∅ ˙ 7 ) ] (10)

All the forces opposing the motion are negative.

m 1 y ¨ 1 = − k r 1 ( y 1 − U 1 ) − k 1 [ y 1 − ( y 7 + l 1 θ 7 + l 4 ∅ 7 ) ] − b 1 [ y ˙ 1 − ( y ˙ 7 + l 1 θ ˙ 7 + l 4 ∅ ˙ 7 ) ] (11)

The same procedure as the wheel assembly 1 was used to develop the different equations of motion for the wheel assemblies 2, 3, 4, 5 and 6.

2) Total frame: equation of motion

The frame of the bus, shown in

∑ F = m 7 y ¨ 7 , ∑ M θ = I θ 7 θ ¨ 7 , ∑ M ∅ = I ∅ 7 ∅ ¨ 7 (12)

・ Bounce motion of the frame

For a positive vertical motion of the bus, all the suspensions elements act against it. Therefore, these forces are negative and the equation of bounce motion can be given by:

m 7 y ¨ 7 = − k 1 [ ( y 7 + l 1 θ 7 + l 4 ∅ 7 ) − y 1 ] − b 1 [ ( y ˙ 7 + l 1 θ ˙ 7 + l 4 ∅ ˙ 7 ) − y ˙ 1 ] − k 2 [ ( y 7 − l 2 θ 7 + l 4 ∅ 7 ) − y 2 ] − b 2 [ ( y ˙ 7 − l 2 θ ˙ 7 + l 4 ∅ ˙ 7 ) − y ˙ 2 ] − k 3 [ ( y 7 − l 3 θ 7 + l 4 ∅ 7 ) − y 3 ] − b 3 [ ( y ˙ 7 − l 3 θ ˙ 7 + l 4 ∅ ˙ 7 ) − y ˙ 3 ] − k 4 [ ( y 7 + l 1 θ 7 − l 4 ∅ 7 ) − y 4 ] − b 4 [ ( y ˙ 7 + l 1 θ ˙ 7 − l 4 ∅ ˙ 7 ) − y ˙ 4 ]

− k 5 [ ( y 7 − l 2 θ 7 − l 4 ∅ 7 ) − y 5 ] − b 5 [ ( y ˙ 7 − l 2 θ ˙ 7 − l 4 ∅ ˙ 7 ) − y ˙ 5 ] − k 6 [ ( y 7 − l 3 θ 7 − l 4 ∅ 7 ) − y 6 ] − b 6 [ ( y ˙ 7 − l 3 θ ˙ 7 − l 4 ∅ ˙ 7 ) − y ˙ 6 ] (13)

・ Pitch motion of the frame

For a positive pitch motion of the bus, all the suspension elements act against it. Therefore, these forces are negative and the equation of pitch motion can be given by:

I θ 7 θ ¨ 7 = − l 1 k 1 [ ( y 7 + l 1 θ 7 + l 4 ∅ 7 ) − y 1 ] − l 1 b 1 [ ( y ˙ 7 + l 1 θ ˙ 7 + l 4 ∅ ˙ 7 ) − y ˙ 1 ] − l 2 k 2 [ ( y 7 − l 2 θ 7 + l 4 ∅ 7 ) − y 2 ] − l 2 b 2 [ ( y ˙ 7 − l 2 θ ˙ 7 + l 4 ∅ ˙ 7 ) − y ˙ 2 ] − l 3 k 3 [ ( y 7 − l 3 θ 7 + l 4 ∅ 7 ) − y 3 ] − l 3 b 3 [ ( y ˙ 7 − l 3 θ ˙ 7 + l 4 ∅ ˙ 7 ) − y ˙ 3 ]

− l 1 k 4 [ ( y 7 + l 1 θ 7 − l 4 ∅ 7 ) − y 4 ] − l 1 b 4 [ ( y ˙ 7 + l 1 θ ˙ 7 − l 4 ∅ ˙ 7 ) − y ˙ 4 ] − l 2 k 5 [ ( y 7 − l 2 θ 7 − l 4 ∅ 7 ) − y 5 ] − l 2 b 5 [ ( y ˙ 7 − l 2 θ ˙ 7 − l 4 ∅ ˙ 7 ) − y ˙ 5 ] − l 3 k 6 [ ( y 7 − l 3 θ 7 − l 4 ∅ 7 ) − y 6 ] − l 3 b 6 [ ( y ˙ 7 − l 3 θ ˙ 7 − l 4 ∅ ˙ 7 ) − y ˙ 6 ] (14)

・ Roll motion of the frame

For a positive roll motion of the bus, all the suspension elements act against it. Therefore, these forces are negative and the equation of roll motion can be given by:

I ∅ 7 ∅ ¨ 7 = − l 6 k 1 [ ( y 7 + l 1 θ 7 + l 4 ∅ 7 ) − y 1 ] − l 6 b 1 [ ( y ˙ 7 + l 1 θ ˙ 7 + l 4 ∅ ˙ 7 ) − y ˙ 1 ] − l 6 k 2 [ ( y 7 − l 2 θ 7 + l 4 ∅ 7 ) − y 2 ] − l 6 b 2 [ ( y ˙ 7 − l 2 θ ˙ 7 + l 4 ∅ ˙ 7 ) − y ˙ 2 ] − l 6 k 3 [ ( y 7 − l 3 θ 7 + l 4 ∅ 7 ) − y 3 ] − l 6 b 3 [ ( y ˙ 7 − l 3 θ ˙ 7 + l 4 ∅ ˙ 7 ) − y ˙ 3 ]

− l 6 k 4 [ ( y 7 + l 1 θ 7 − l 4 ∅ 7 ) − y 4 ] − l 6 b 4 [ ( y ˙ 7 + l 1 θ ˙ 7 − l 4 ∅ ˙ 7 ) − y ˙ 4 ] − l 6 k 5 [ ( y 7 − l 2 θ 7 − l 4 ∅ 7 ) − y 5 ] − l 6 b 5 [ ( y ˙ 7 − l 2 θ ˙ 7 − l 4 ∅ ˙ 7 ) − y ˙ 5 ] − l 6 k 6 [ ( y 7 − l 3 θ 7 − l 4 ∅ 7 ) − y 6 ] − l 6 b 6 [ ( y ˙ 7 − l 3 θ ˙ 7 − l 4 ∅ ˙ 7 ) − y ˙ 6 ] (15)

By making the change of variables as presented below:

x 1 = y 1 , x 2 = y ˙ 1 , x 3 = y 2 , x 4 = y ˙ 2 , x 5 = y 3 , x 6 = y ˙ 3 , x 7 = y 4 , x 8 = y ˙ 4 , x 9 = y 5 , x 10 = y ˙ 5 , x 11 = y 6 , x 12 = y ˙ 6 , x 13 = y 7 , x 14 = y ˙ 7 , x 15 = θ 7 , x 16 = θ ˙ 7 , x 17 = ∅ 7 , x 18 = ∅ ˙ 7 (16)

The state system of the three-dimensional frame dynamic model has been developed. It is composed of eighteen unidentified variables. This system was solved using the Matlab software and the transfer functions were calculated. The parameters x 1 , x 3 , x 5 , x 7 , x 9 and x 11 represent the vertical motion of the six suspensions of the frame. The vertical, the pitch and roll motions of the frame corresponding to the transfer functions are related to the parameters x 13 , x 15 and x 17 . The corresponding matrix is presented below.

( x ˙ 1 x ˙ 2 x ˙ 3 x ˙ 4 x ˙ 5 x ˙ 6 x ˙ 7 x ˙ 8 x ˙ 9 x ˙ 10 x ˙ 11 x ˙ 12 x ˙ 13 x ˙ 14 x ˙ 15 x ˙ 16 x ˙ 17 x ˙ 18 ) = [ 0 1 0 0 0 0 ( − k r 1 − k 1 ) / m 1 ( − b 1 ) / m 1 0 0 0 0 0 0 0 1 0 0 0 0 ( − k r 2 − k 2 ) / m 2 ( − b 2 ) / m 2 0 0 0 0 0 0 0 1 0 0 0 0 ( − k r 3 − k 3 ) / m 3 ( − b 3 ) / m 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ( k 1 ) / m 7 ( b 1 ) / m 7 ( k 2 ) / m 7 ( b 2 ) / m 7 ( k 3 ) / m 7 ( b 3 ) / m 7 0 0 0 0 0 0 ( k 1 l 1 ) / I 7 ( b 1 l 1 ) / I 7 ( k 2 l 2 ) / I 7 ( b 3 l 3 ) / I 7 ( k 3 l 3 ) / I 7 ( b 3 l 3 ) / I 7 0 0 0 0 0 0 ( k 1 l 4 ) / I 8 ( b 1 l 4 ) / I 8 ( k 2 l 6 ) / I 8 ( b 2 l 4 ) / I 8 ( k 3 l 4 ) / I 8 ( b 3 l 4 ) / I 8 ] [ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 ( − k r 4 − k 4 ) / m 4 ( − b 4 ) / m 4 0 0 0 0 0 0 0 1 0 0 0 0 ( − k r 5 − k 5 ) / m 5 ( − b 5 ) / m 5 0 0 0 0 0 0 0 0 0 0 0 0 ( − k r 6 − k 6 ) / m 6 ( − b 6 ) / m 6 0 0 0 0 0 0 ( k 4 ) / m 7 ( b 4 ) / m 7 ( k 5 ) / m 7 ( b 5 ) / m 7 ( k 6 ) / m 7 ( b 6 ) / m 7 0 0 0 0 0 0 ( k 4 l 1 ) / I 7 ( b 4 l 1 ) / I 7 ( k 5 l 1 ) / I 7 ( b 5 l 1 ) / I 7 ( k 6 l 1 ) / I 7 ( b 6 l 1 ) / I 7 0 0 0 0 0 0 ( k 4 l 4 ) / I 8 ( b 4 l 4 ) / I 8 ( k 5 l 4 ) / I 8 ( b 5 l 4 ) / I 8 ( k 6 l 4 ) / I 8 ( b 6 l 4 ) / I 8 ]

| 0 0 ( k 1 ) / m 1 ( b 1 ) / m 1 0 0 ( k 2 ) / m 2 ( b 2 ) / m 2 0 0 ( k 3 ) / m 3 ( b 3 ) / m 3 0 0 ( k 4 ) / m 4 ( b 4 ) / m 4 0 0 ( k 5 ) / m 5 ( b 5 ) / m 5 0 0 ( k 6 ) / m 6 ( b 6 ) / m 6 0 1 ( − k 1 − k 2 − k 3 − k 4 − k 5 − k 6 ) / m 7 ( − b 1 − b 2 − b 3 − b 4 − b 5 − b 6 ) / m 7 0 0 ( − k 1 l 1 − k 2 l 2 − k 3 l 3 − k 4 l 1 − k 5 l 2 − k 6 l 3 ) / I 7 ( − b 1 l 1 − b 2 l 2 − k 3 l 3 − b 4 l 1 − b 5 l 2 − b 6 l 3 ) / I 7 0 0 ( − k 1 l 4 − k 2 l 4 − k 3 l 4 − k 4 l 4 − k 5 l 4 − k 6 l 4 ) / I 8 ( − b 1 l 4 − b 2 l 4 − b 3 l 4 − b 4 l 4 − b 5 l 4 − b 6 l 4 ) / I 8 |

| 0 0 ( k 1 l 1 ) / m 1 ( b 1 l 1 ) / m 1 0 0 ( − k 2 l 2 ) / m 2 ( − b 2 l 2 ) / m 2 0 0 ( − k 3 l 3 ) / m 3 ( − b 3 l 3 ) / m 3 0 0 ( k 4 l 1 ) / m 4 ( b 4 l 1 ) / m 4 0 0 ( − k 5 l 2 ) / m 5 ( − b 5 l 2 ) / m 5 0 0 ( − k 6 l 3 ) / m 6 ( − b 6 l 3 ) / m 6 0 0 ( − k 1 l 1 + k 2 l 2 + k 3 l 3 − k 4 l 1 + k 5 l 2 + k 6 l 3 ) / m 7 ( − b 1 l 1 + b 2 l 2 + k 3 l 3 − b 4 l 1 + b 5 l 2 + b 6 l 3 ) / m 7 0 1 ( − k 1 l 1 2 + k 2 l 2 2 + k 3 l 3 2 − k 4 l 1 2 + k 5 l 2 2 + k 6 l 3 2 ) / I 7 ( − b 1 l 1 2 + b 2 l 2 2 + b 3 l 3 2 − b 4 l 1 2 + b 5 l 2 2 + b 6 l 3 2 ) / I 7 0 0 ( − k 1 l 1 l 4 + k 2 l 2 l 4 + k 3 l 3 l 4 − k 4 l 1 l 4 + k 5 l 2 l 4 + k 6 l 3 l 4 ) / I 8 ( − b 1 l 1 l 4 + b 2 l 2 l 4 + b 3 l 3 l 4 − b 4 l 1 l 4 + b 5 l 2 l 4 + b 6 l 3 l 4 ) / I 8 |

Generally, the range of frequencies in the field of road vehicles varies between 1 and 20 Hz. In the case of this study, by using the developed 3D model of the bus frame, the resonant frequencies were obtained. These frequencies are obtained with the bode diagram for the case of materials shown in

・ Aluminum 6061-T6 bus frame

The results of the resonance frequencies obtained in the case of the aluminum frame are presented in this section.

Figures 7-9 show the bode diagrams obtained for the total frame respectively in the case of bounce, pitch, and roll motion. For all three cases, the resonance frequency is equal to 1.80 Hz. These frequency results are less than 20 Hz, which corresponds to what is found in the literature [

・ Steel 1018-HR and 710C bus frame

The comparison of the frequencies’ resonance results obtained for the designed frame with different materials presented in

A structural analysis of the frame chassis is presented in this section. This analysis includes a static study as well as a vibratory study. The materials used for this study are aluminum 6061-T6, steel 1018-HR and steel 710C. This analysis is

necessary to know the capacities of the aluminum chassis in comparison with those made of steel. The use of aluminum in the transport sector would make it possible to have a great advantage in terms of weight reduction, energy consumption and even durability [

Frequency | Aluminum 6061-T6 | 1018-HR | 710C |
---|---|---|---|

Wheel assembly 1 (Hz) | 14.35 | 14.40 | 14.40 |

Bounce (Hz) | 1.80 | 1.75 | 1.75 |

Pitch (Hz) | 1.80 | 1.75 | 1.75 |

Roll (Hz) | 1.80 | 1.75 | 1.75 |

tool of ANSYS Workbench. Many recent structural studies have been done using this software [

・ Frame mushing

In simulations, the first step consists in the choice of the material, subsequently the generation of the mesh followed by the boundary conditions and the loading part. It is the same mesh that is used for the three materials to be able to compare the results at the end.

The total frame is mushed with a tetrahedral element (Tet 10). In total, there is 1025281 elements and the number of nodes is equal to 1,738,446.

・ Loading and boundary conditions

The loading and boundary conditions of the aluminum and steel frames are presented in

two longitudinal beams obtained from the maximum admissible loading of the Quebec Ministry of transportation for this frame category. There are six boundary conditions in this model. All these boundary conditions are applied on the well axles of the frame. Two are on the front and the four others in the rear.

This study was carried out to compare the mechanical strengths due to the static loading of the aluminum frame with those designed in steel. For this, an analysis of the maximum stresses undergone by the chassis; evaluations of the total displacement as well as the stresses due to the shearing were realized.

・ Aluminum 6061-T6

The static analysis of 6061-T6 aluminum frame is presented in this section. The values of the loads applied on the aluminum frame are presented in the section 2.2. For this static analysis, the maximum Van Mises stress equals to 195.30 MPa as shown in

・ Steel 1018-HR and 710C frames

The static analysis results obtained for the 1018-HR steel frame are presented in _{s} is considered for the 6060-T6 aluminum and 1018-HR steel, the results will be:

F s = Elastic limit σ e Maximum stress σ max (18)

For aluminum and steel frames, the safety factor is eqal respectively to 1.41 and 1.39. This means that there no a big difference between the capacity of these two material in case of the static loading.

In this section, the static analysis of the frames made by the three different materials was presented to evaluate the capacity of the aluminum frames compared to those made of steel that is used now in transportation. Another important case to evaluate, is the modal analysis. For this modal analysis, all degrees of

Static analysis | 6061-T6 | 1018-HR | 710C |
---|---|---|---|

Equivalent stress (MPa) | 195.30 | 197.00 | 197.00 |

Total displacement (m) | 0.038 | 0.013 | 0.013 |

Shear stress (MPa) | 102.50 | 103.03 | 103.03 |

freedom are free to be able to evaluate the natural response of chassis frame. If one of the natural frequencies coincides with the frequency of the excitation rod, then resonance phenomena may occur with system breaks.

The comparison of the frequency results for the four first vibration modes of the total frame for the three materials is given in

Static and vibratory comparisons were made for a bus frame designed using three materials that are 6061-T6 aluminum, 1018-HR steel and 710C steel. The results analysis of the static study shows that the aluminum frame presents

Vibration modes | Frequency (Hz) | ||
---|---|---|---|

6061-T6 | 1018-HR | 710C | |

Torsion-1^{st} mode | 1.44 | 1.46 | 1.46 |

Bending-1^{st} mode | 9.10 | 9.18 | 9.18 |

Torsion-2^{nd} mode | 11.71 | 11.83 | 11.83 |

Bending-2^{nd} mode | 23.27 | 23.51 | 23.51 |

stresses in the same order as those of steel. The generated shear and Von Mises stresses are less than the permissible value so the design is safe for all three materials. Knowing that the 6061-T6 aluminum has the same elastic limit stress as the 1018-HR steel which is equal to 275 MPa, both frames will have the same behavior. Then, it is possible to replace the steel frame with that of aluminum, knowing that the latter can fulfill functions equivalent to that of steel in addition to bringing many more advantages such as flexibility, lightness, a gain at the level of the energy consumption in addition to a high resistance to corrosion.

As for the vibratory study, the results also show a very great similarity between the frames designed in aluminum in comparison with those made of steel. This study was carried out dynamically and numerically. So, the change of material does not really affect the vibratory behavior in the design of a frame.

The financial support of the Aluminium Research Center (REGAL) is greatly appreciated.

Rebaïne, F., Bouazara, M., Rahem, A. and St-Georges, L. (2018) Static and Vibration Analysis of an Aluminium and Steel Bus Frame. World Journal of Mechanics, 8, 112-135. https://doi.org/10.4236/wjm.2018.84010