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Abstract

Vehicle swing rig is a structure used for experimental study of moment of inertia of a 4-wheeler vehicle by loading and swinging a vehicle back and forth and measuring period of oscillation. For experimental results of be reliance and accurate, structural integrity of frame structure has to be high enough so that it can sustain the weight and at the same time, it should be lightweight so that system’s own mass does not add to vehicle’s and make moment of inertia determination erroneous. In the current study, finite element methods have been used in Abaqus to analyse a base structure of vehicle swing rig using different beam cross-sections such as I-beam, tube, C-section, Hollow Square and rectangular etc. A Modified design has been designed and analysed to meet required deformation, stress (Factor of safety) and weight requirements.

Keywords: Vehicle swing rig; Abaqus; bending stiffness for beam elements

1. Introduction

A vehicle swing rig is used to experimental study to measure moment of inertia of a vehicle in which a vehicle is loaded on to a structure which is suspended on a frame to a hinge. If the frame is lightweight, then most of the kinetic energy used in swinging would be from vehicle and very less part would be contributed by swing rig hence measurement would be precise and accurate. Different beam cross-sections provide different bending, tensile and compressive strength depending on their dimensions and design. In current study, different cross-sectional beam members are first accessed to make a base frame to analyse stiffness of each for proof load case and based on comparison, best performing cross-sectional member of I-beam is used to further modify the structure to reduce its deformation and stress within permissible limits. Several design proposals were generated and tested using ABAQUS CAE. Additional members with I-beam profile were added into the initial frame structure to meet the strength and stiffness demands.

1.1. Aims and objectives

In the current study, a base frame structure provided is analysed for

• To check deformation and stresses with different beam cross-sections.
• Aim is to reduce the maximum deformation to 2mm with AISI 1010 material.
• The yield stress factor of safety has to be greater than 10.
• Objective is keep the maximum weight limited to 180 Kg.

2. Finite Element Model

In the current section, use of Abaqus to assess frame structure using different beam element cross-sections and modified to meet design objectives. A base geometry used in current analysis is made as shown in Figure 1. Current FE model utilizes beam elements in Abaqus. A line skeleton geometry is created in Abaqus as shown in Figure 2 which is as per the base structure dimensions mentioned in Figure 1. Since geometry can only be developed in a plane, other swinging elements are developed in a separate part which will be assembled together as instances during assembly to get the overall structure.

Fig. 1 Vehicle swing rig base design dimensions used for geometry creation

 

Fig. 2 Vehicle swing rig line body skeleton as per base dimensions modelled in Abaqus

2.1. Geometry Details in Abaqus

Once the line skeleton geometry is prepared, it has to be assigned beam cross-section. A beam cross-section profile is created as shown in Figure 3 for I-beam cross-section dimensions for which are taken from [1]. Prepared cross-section geometry is then added to a section which contains which material as well as cross-sectional information. Prepared section is shown in Figure 4. Using a section definition, prepared beam cross-section is assigned to current model. Along with material, cross-section information, a beam required orientation also to be assigned so that the cross-section orientation can be determined. All the beam members are assigned with an orientation in such a manner so that web of I-beam cross-section can be kept vertically in the loading direction. After section assignment, cross-section can be visualized for entire frame as shown in Figure 5.

Fig. 3 I-beam cross-section dimension used in Abaqus

 

Fig. 4 Created I-beam cross-section in Abaqus used for base analysis

 

Fig. 5 Overall base structure of vehicle swing rig as used in current study

Similarly, 3 other different cross-sections are created so as to analyse base structure’s performance and stiffness. In the current study, one of the objective is to reduce maximum deformation to 2 mm, for which different cross-sectional members will perform differently. Figure 6 shows C-cross-section used in the current study and corresponding dimensions used to create profile. Figure 7 shows square hollow tube cross-section used in the current study and corresponding dimensions used to create profile. Figure 8 shows rectangular cross-section used in the current study and corresponding dimensions used to create profile.

Fig. 6 C Cross-section used for beam analysis with dimensions

 

Fig. 7 Square Cross-section used for beam analysis with dimensions

 

Fig. 8 Rectangular Cross-section used for beam analysis with dimensions

2.2. Material properties, element type, loading and boundary conditions

A static structural analysis is performed in the current study. Current study uses beam elements for all the beam member is frame as well as base structure. A global seed size of 10 mm was defined and meshing was performed. Used beam type element details are shown in Figure 9.

Fig. 9 Beam type element details as used in current analysis

 

Material used in current study is AISI 1010 for which material properties are defined in Table 1.

Young’s Modulus	Yield Strength	Ultimate Strength	Density
200	305	365	7872
GPa	MPa	MPa	Kg/m3

 

In the assembly mode, all the parts are brought together as instances. Rotation and translation of different instances is performed so as to make the assembly. As the assembly is made by joining 3 different parts together, tie constraints are defined at nodal junctions to constrain all 6 degrees of freedoms of the system together. An overall assembled geometry is shown in Figure 10 for I-beam cross-section.

Fig. 10 Assembly view of frame structure with swinging arms

After assigning material, creating assembly, creating mesh, and brining the elements together, loads and boundary conditions are applied onto the assembly structure. A total of 5000 N of load is to be applied on to the base structure in vertically downward direction at 4 different locations as also mentioned in Figure 1. As a boundary condition, 2 nodes on which entire swing rig is suspended, is applied with ‘ENCASTRE’ condition in Abaqus where in all 6 d.o.f are constrained.

Fig. 11 Loads applied on four beam arms of the structure

3. Design & Development

In this section, a modified design is proposed by adding few member on to the base structure so as to meet the design requirements on deformation, stress and weight requirements.

3.1. Analysis with I-beam cross-section

As discussed in previous section, I-beam cross-section model is prepared and analyzed, stress and deformation results are shown in Figure 12. Maximum stress observed is 271 MPa and maximum deformation is 8.63mm which are both out of the maximum permissible limit set for current study.

Fig. 12 Equivalent stresses and deformation using I-beam cross-section for frame structure

3.2. Analysis with Square beam cross-section

As discussed in previous section, Square-beam cross-section model is prepared and analysed, stress and deformation results are shown in Figure 13. Maximum stress observed is 586 MPa and maximum deformation is 21.5 mm which are both out of the maximum permissible limit set for current study.

Fig. 13 Equivalent stresses and deformation using Square-beam cross-section for frame structure

3.3. Analysis with Rectangular beam cross-section

As discussed in previous section, Rectangular beam cross-section model is prepared and analysed, stress and deformation results are shown in Figure 14. Maximum stress observed is 517 MPa and maximum deformation is 14.4 mm which are both out of the maximum permissible limit set for current study.

Fig. 14 Equivalent stresses and deformation using rectangular-beam cross-section for frame structure

3.4. Analysis with C-beam cross-section

As discussed in previous section, C-beam cross-section model is prepared and analysed, stress and deformation results are shown in Figure 15. Maximum stress observed is 1410 MPa and maximum deformation is 12.21 mm which are both out of the maximum permissible limit set for current study.

Fig. 15 Equivalent stresses and deformation using C beam cross-section for frame structure

Based on the study of different cross-sectional beams, I beam was found to be most stiff for same weight of the structure. Hence for further design modification, few beam members were added to base structure with I-beam cross-section so to bring down maximum stresses and deformation.

After a few iterations, a final structure as shown in Figure 16 is prepared where multiple beam members were added to the base structure so as to provide truss like stiffness to the system. Since total mass of the system (frame with structure) has to be kept less than 180 Kg., lighter I-beams were used from reference [1] as shown in Figure 17. Original base structure had total length of beam members as 7660 mm hence with 23.2 Kg/m mass distribution, total weight of the system was 177.7 Kg. With modification of added members for stiffness, total length of the system is approximately 12000 mm hence with 14 Kg/m linear weight of I-beam cross-section used, total mass of the system is kept limited to 168 Kg. Results for the designed frame are discussed in next section.

Fig. 16 Modified frame design after iterations obtained for required stiffness and stress values

 

Fig. 17 I-beam cross-section dimensions used in final structure with linear weight of 14 Kg/m

4. Results

Final reinforced design as shown in Figure 18 where in a truss like structure is added to the base structure. Since in the design requirements, maximum deformation is to be restricted to 2mm, and weight to 180 Kg, the I-beam cross-section was changed to lower linear weight of 14 Kg/m, so that the total mass can be restricted to below 180 Kg. which has already been shown in the previous section.

Figure 18. Deformation plot of modified design structure with added stiffness

 

Figure 19. Stress plot of modified design structure with added stiffness

As can be seen in Figure 18, deformation of the structure is reduced to <2 mm in the region of main frame where maximum load is applied. All the structural beam members are assumed to be connected through rigid joints, the stresses near the joints can be neglected. The maximum stress in the main frame structure is restricted to ~40 MPa as shown in figure 19. Since the material used in the current analysis is AISI 1010 steel, for which yield stress is 305 MPa, hence factor of safety for currently suggested designed structure is ~7.6. Since structure has already reached near the maximum required weight, reducing the stresses further will increase weight.

5. Discussion

In the current study, use of finite element analysis driven design approach is demonstrated. For a base structure of vehicle swing rig, different beam cross-sections were evaluated for their performances (stresses and deformation). For same linear weight of the elements, I-beam performs best for same load and C-section has maximum deformation and stresses compared to all others. Since the vertical load distributed over the blue patches of figure 1, the region of maximum deformation is on the same beam. To reduce the deformation, a truss like structure is designed and added below the beam carrying vertically downward loads. It reduced the vertical deformation of the horizontal load carrying beams. Also, load causes the vertical swing rods to bend vertically in Y-direction for which another truss structure was designed and added at the base. Finally, overall deformation of the main frame structure to <2 mm. Overall weight of the structure is restricted to 168 Kg. Further, for the main frame, the maximum equivalent stresses are restricted to 40 MPa, hence from 305 MPa yield strength of the material, calculated minimum yield stress factor of safety is 7.5.

6. Conclusions

In the current study, a design of vehicle swing rig is proposed which meets the design requirements of maximum deformation of less than 2mm, yield stress factor of safety to be 10, and weight of the frame structure to less than 180 Kg. For the vehicle swing rig moment of inertia measurements to be accurate, mentioned design requirements are necessary to be met. Current proposed design meets the weight requirements as explained in previous section. It can further be verified using experimental fabrication and moment of inertia measurement.

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