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Automotive Innovation

, Volume 1, Issue 4, pp 352–361 | Cite as

Optimization of Torsional Stiffness for Heavy Commercial Vehicle Chassis Frame

  • S. H. GawandeEmail author
  • A. A. Muley
  • R. N. Yerrawar
Article
  • 224 Downloads

Abstract

The chassis frame is the backbone of a heavy commercial vehicle (HCV). Its main purpose is to securely carry the determined load under all designed operative situations. Thus, it should be rigid enough to withstand the various forces acting on it. The objective of this study was to develop a stiffness model to select an optimum cross section with determined torsional stiffness. Johnson's method of optimization was adapted to develop a stiffness equation and select a section with a determined torsional stiffness and a required mass constraint. The stiffness obtained from the developed stiffness model and finite element analysis (FEA) is a close match, which proves the validity of the proposed model. The section with the maximum torsional stiffness was used for frame-level optimization to improve the torsional and lateral stiffness of the overall chassis frame. The strain energy absorption capacity of the cross member improved by changing the section of the cross member. By using the optimized section, the torsional stiffness of the frame improved by 44% and a lateral stiffness of 10% was obtained. The Creo software was used for modeling and FEA was performed with the Hypermesh software.

Keywords

Chassis frame Torsional stiffness FEA Cross members Deformation 

1 Introduction

The chassis frame of a vehicle is an auxiliary member, both in structural and in functional terms, to all other chassis aggregate systems such as the suspension, steering, and braking systems. It consists of two side members called the long members, which are joined by a series of cross members. In addition to strength, an important consideration in the chassis frame design is adequate bending and torsion stiffness. Adequate torsional stiffness is necessary to ensure good handling characteristics. According to the conventional design procedure, the stiffness of the chassis is increased by adding cross members. This results in the overall increase in the chassis weight. Hence, it is necessary to design the chassis with adequate stiffness and strength. The frame is always subjected to the following loads:
  1. 1.

    Weight of the body, passengers, and cargo loads

     
  2. 2.

    Vertical and twisting load owing to uneven road surfaces

     
  3. 3.

    Lateral forces caused by the road camber, side wind, and steering of the vehicle

     
  4. 4.

    Torque transmitted from engine and transmission.

     

A limited amount of studies has been conducted on torsional stiffness optimization for the chassis frame of heavy commercial vehicles (HCVs). The available literature was collected from technical periodicals, research articles, and industrial surveys (Metalsa India Pvt. Ltd., Pune, India). Kilimnik and Korbin [1] have investigated the calculation of fatigue caused by higher stresses at the end parts of the chassis during torsion and considered the influence exerted by the position of the transverse axis along the frame on the state of stress in the structure. Seyfried et al. [2] have highlighted the lightweighting opportunities in the HCV frame structure by changing the sections that keep the section modulus at the same level. With this approach, the U-shaped profile can reduce the weight by up to one third of the existing weight.

Oskar and Alejandro [3] investigated the torsional, lateral, and bending stiffness of the Volvo car chassis frame, and Weerawut and Supasit [4] investigated the design of the space frame racing car front clip and rear clip for torsional rigidity. Lonny et al. [5] have designed a twist fixture to measure the torsional stiffness of a Winston cup chassis. Ojo and Pakharuddin [6] have investigated the optimization of the Hino model truck chassis frame for high torsional stiffness with shape modifications. The torsional stiffness depends on the property of the structure, but is independent of the applied load’s magnitude. The torsional stiffness of the chassis depends on the types of cross section used and the material of the chassis frame. Kurisetty et al. [7] have studied the effect of various frame parameters, such as the frame width, wheel base, and height and thickness of a long member, on the chassis frame stiffness to acquire the optimum stiffness. Rahul et al. [8] have investigated torsional stiffness optimization for a truck frame by providing the X-type member of minimum thickness. Finite element analysis (FEA) was performed for the root model and optimized model using ANSYS workbench, and a 17% improvement in torsional stiffness was obtained. Goel et al. [9] have investigated the chassis frame of the Ashok Leyland Vikings model by replacing the existing C-section cross member with an I-section and a rectangular box type section. Their results revealed that the I-section cross member had the maximum strength; thus, they concluded that changing the cross section of the cross member did not significantly affect the natural frequency of the chassis frame. Devaraj and Raghu [10] investigated the effect of stiffness parameters on the crashworthiness of the ladder frame. The optimized cross section of the chassis’ side member was obtained by considering the specific energy. Patel and Chitransh [11] have reported the design and analysis of the TATA 2518 TC chassis frame with constraints of maximum stress induction and the deflection of chassis under maximum load. Prabakaran and Gunasekar [12] optimized the chassis frame of the Eicher E2 model by varying the section of a long member for three different cases with maximum shear stress constraints and the deflection of the chassis under maximum load. Divyesh et al. [13] investigated the AMW 2523TP truck chassis with maximum shear stress constraints and the deflection of the chassis under maximum load. The analysis was performed using C, I, and rectangular box type cross sections. Gawande [14] have reported the design and performance investigation of metal expansion bellows, wherein Johnson’s method of optimum design [23] was used to select the optimum material for bellows, with the objective of minimizing the weight and cost. Sahu et al. [15] have conducted static load analysis with different cross sections and two different materials (i.e., structural steel and Al alloy).

Prakash and Prabhu [16] have investigated the improvement in torsional stiffness based on the obtained FEA results. Improvement in terms of torsional stiffness was achieved by providing a stiffener in the front and rear portion of the frame. Patil and Deore [17] optimized the TATA 912 Diesel bus chassis frame with maximum shear stress constraints and chassis deflection under maximum load and observed that the rectangular box section provided more strength than the C- and I-section. Siva Nagaraju et al. [18] investigated the analysis of the Innova car chassis with different cross sections. The analysis results revealed that the stresses induced in the C-section were concentrated in the box type section, but were within the ultimate strength limit. The C-type cross section weighs less than the rectangular section and provides operational benefits. Sharma et al. [19] have designed and analyzed the TATA LPS 2515 EX truck chassis, for which they observed that a box type cross section was best in terms of deflections, although the overall weight of the chassis was higher than that of other cross members. Vijaykumar and Patel [20] modified the design of the existing cross section by changing the dimension to optimize the chassis weight. Singh et al. [21] have analyzed the TATA LP 912 with higher strength as the main criterion by applying the vertical loads acting on different cross sections. Rakesh et al. [22] have investigated the Ashok Leyland chassis using three different materials, namely, Al-360, cast iron, and glass fiber-reinforced plastic, GFRP, to select the best one.

Because the handling characteristics of a vehicle are mostly related to the torsional stiffness of the chassis, the torsional stiffness of the chassis frame is one of the most important factors from a design viewpoint. Increased chassis torsional rigidity improves the vehicle handling characteristics. Higher torsional stiffness allows the suspension components to control a larger percentage of vehicle kinematics. The chassis frame’s lack of torsional stiffness tends to magnify the effect under the steering and over steering of the vehicle. Considering single wheel bump conditions owing to uneven road surfaces, the front and rear axle portion of the chassis frame becomes twisted around its x-axis. Studies and industrial surveys have reported that the torsional load case is one of the worst load cases. Hence, the torsional stiffness optimization of the chassis frame is required. Based on this study, Johnson’s optimization method can be modified to select the optimum dimensions for the required weight constraints based on torsional stiffness, when the numbers of different sections with variable thickness are available.

2 Problem Formulation and Research Scope

This paper reports the stiffness analysis of an HCV chassis frame for different cross sections, which was conducted to improve the torsional stiffness. Johnson’s method of optimum design was used to select the optimum section with the objective of maximizing the torsional stiffness under a given weight condition. The torsional stiffness of the chassis is a function of the torsional stiffness of the individual cross members in the chassis frame. The front and rear torsional stiffness is influenced by the type of cross member present at the front and rear side of the chassis. If it is difficult to replace the engine cross member; the third cross member for the front torsion and the seventh cross member for the rear torsion should be selected for replacement. The existing chassis frame consists of eight cross members, all of which are C-sections, and the overall frame weight is 610 kg. The third and seventh cross members are 30 kg in total. Hence, with regard to optimization, it is useful to design cross members with a weight of 15 kg each. The cross member is connected to long members using a gusset or brackets on each side. Considering that the bracket weight for the cross member is 4.5 kg on each side, the cross member section must be less than 6 kg to maintain the original weight of the chassis frame.

The benchmarking data of various truck chassis frames reveal that C-sections, hollow square sections, and tubular sections are typically used as cross members in the truck chassis frames. Approximately 65% of HCV chassis frames have C-sections to ensure good resisting bending forces. Hollow sections are better in resisting torsional forces in comparison with the existing C-section. Hence, to optimize the torsional stiffness of a chassis frame, the existing C-section cross members in the third and seventh position should be replaced with hollow type cross members. Hence, these three sections were compared with respect to torsional and lateral stiffness and weight as a constraint. Figures 1 and 2 show the existing third and seventh C-section cross members, respectively.
Fig. 1

Existing third cross member

Fig. 2

Existing seventh cross member

3 Analytical Method

Selecting a cross section for a cross member is very important from a design, weight, and stiffness viewpoint. The stiffness of the chassis frame depends on the material and type of sections used. Because the chassis frame material is kept constant, it is necessary to select the best suitable cross section from a torsional stiffness viewpoint. In this study, Johnson’s method of optimization was modified and implemented to develop an objective function for torsional stiffness and weight. In the optimization, the individual sections used as cross members in the chassis frame were considered. The torsional stiffness of the individual sections was obtained using Johnson’s method [23]. Then, the section with maximum torsional stiffness was used in the chassis frame to improve the frame’s overall torsional stiffness. Johnson’s method comprises the formulation of the primary design equation (PDE), subsidiary design equation (SDE), and limit equation (LE).

The PDE is the most important design equation and expresses the most significant functional requirement to be maximized or the most significant undesirable effect to be minimized. The PDE expresses the quantity upon which the particular optimum design is based. The most significant desirable effect to maximize is the torsional stiffness of the section, which is expressed as follows:
$$S = \frac{GJ}{L}$$
(1)
where L is the length of the section, J is the section’s polar moment of inertia, G is the section’s modulus of rigidity, and S is the section’s torsional stiffness. The SDE expresses either the functional requirement or the undesirable effects according to Eqs. 2 and 3.
$$J = \frac{\pi }{32}\left( {D^{4} - d^{4} } \right)$$
(2)
$$M = \frac{\pi }{4}\left( {D^{2} - d^{2} } \right) \times L \times \rho$$
(3)
where D is the external diameter, d is the internal diameter, L is the section’s thickness, and ρ is the density of the material. In the optimum design, satisfactory ranges are available for the values of certain parameters. These ranges can be expressed mathematically by an equation known as the limit equation, which is always rigid or loose. Moreover, it is always beneficial to take the advantage of a loose limit, because a slight change in the value of a parameter may result in substantial improvement in the optimum design. The mass limit of the section is expressed as follows:
$$M \le 6\,{\text{kg}}$$
(4)
By combining Eqs. 1, 2 and 3 we obtain the following relationship:
$$S = \frac{{G\left[ {\frac{\pi }{32}\left( {D^{4} - d^{4} } \right)} \right]}}{{\frac{M}{{\frac{\pi }{4}\left( {D^{2} - d^{2} } \right) \times \rho }}}}$$
(5)
By combining Eqs. 4 and 5, to maximize the torsional stiffness S, the value of the geometry selection factor (GSF), i.e., \(S = 8.147 \times 10^{12} \left( {D^{4} - d{}^{4}} \right)\left( {D^{2} - d^{2} } \right)\), should be maximum. Table 1 presents the estimation of the various geometric parameters of bellows. From Table 1, we can conclude that the tubular section with a thickness of 4 mm has the maximum torsional stiffness in comparison with the other sections of the same weight. Therefore, this tubular section was selected for further analysis.
Table 1

Geometry selection parameter

Sr. no.

Section

Mass (kg)

Outside dimension (mm)

Inside dimension (mm)

Torsional stiffness (kN·m/rad)

1

Tubular (4 mm thickness)

6

104

96

417,793.8

2

Tubular (5 mm thickness)

6

85

75

268,003.71

3

Hollow square

6

82

74

282,933.06

4 Numerical Simulation of Sections

4.1 Specifications of Existing Chassis Frame

In this study, a 25 tonnage capacity truck chassis frame with a weight of 610 kg was used for optimization. The existing chassis material was BSK46 steel with a yield strength of 410 MPa. The side members of the existing chassis frame were made from C-channels with a section size of 290 mm × 90 mm × 7 mm. Table 2 shows the physical properties of BSK46, and Table 3 shows the specifications of the existing chassis frame.
Table 2

Physical properties of BSK46 [8]

Sr. no.

Parameter

Values

1

Modulus of elasticity

210 GPa

2

Modulus of rigidity

80.76 GPa

3

Density

7850 kg/m3

4

Poisonous ratio

0.3

Table 3

Specifications of existing chassis frame

Sr. no.

Parameter

Values (mm)

1

Overall length of frame

9250

2

Front width of frame

890

3

Rear width of frame

793

4

Wheel base

5405

4.2 Solid Modeling of Sections

A tubular section with an external diameter of 104 mm, internal diameter of 96 mm, and length of 611 mm was created using the Creo software to perform FEA. Similarly, a hollow square section with an external dimension of 82 mm, internal dimension of 74 mm, and length of 611 mm was created. The same sections were meshed using the Hypermesh 14.0 software. For all sections, a two-dimensional (2D) mesh with an element size of 10 mm was used. One end of the section was completely constrained (i.e., Ux, Uy, Uz, Rox, Roy, and Roz were blocked). At the other end, a torque of 10 kN m was applied to produce a twisting moment.

4.3 Angular Deformation and Torsional Stiffness

The sections’ angular deformation was measured, and the torsional stiffness of the section was calculated. The angular deformation of the tubular cross member with a thickness of 4 mm was 0.0000243 rad, which is the minimum value among the three sections. The angular deformation of the tubular cross member with a thickness of 5 mm was 0.0000381 rad, which is approximately 36% higher than the 4-mm thickness section. The angular deformation of the hollow square cross member was 0.000039379 rad and is the maximum value among the three sections. Table 4 shows the angular deformation and torsional stiffness of the tubular and hollow square section. The torsional stiffness of the tubular section with a thickness of 4 mm was the highest (i.e., 411,522.6337 kN m/rad). The torsional stiffness of the tubular section with a thickness of 5 mm and that of the hollow square section with a thickness of 4 mm were 262,329.48 kN m/rad and 251,319.4270 kN m/rad, respectively.
Table 4

Angular deformation and torsional stiffness

Section

Tubular section

Tubular section

Hollow square section

Outer dimension

104 mm

85 mm

82 mm

Inner dimension

96 mm

75 mm

74 mm

Length

611 mm

611 mm

611 mm

Thickness

4 mm

5 mm

4 mm

Mass

6 kg

6 kg

6 kg

Torque applied [A]

10 kN·m

10 kN·m

10 kN·m

Angular deformation [B]

0.0000243 rad

0.0000381 rad

0.00003979 rad

Torsional stiffness \(\left( {\frac{A}{B}} \right)\)

411,522.6337 kN·m/rad

262,329.48 kN·m/rad

251,319.4270 kN·m/rad

Johnson’s method of optimum design gives various geometry selections for the considered application, because the difference between the stiffness values of the individual sections, which were obtained using the analytical method and FEA, was within the limit. Figure 3 shows the comparison of torsional stiffness obtained by the analytical method and FEA for the individual sections. In Fig. 3, it can be seen that the tubular section with a thickness of 4 mm had higher torsional stiffness (i.e., 417,793.80 kN m/rad). Thus, the tubular section with a thickness of 4 mm was stiffer than the other hollow tubular section with a thickness of 5 mm and the square section in terms of resisting torsional loads. The torsional stiffness of the tubular section with a thickness of 4 mm was 36% higher than that of the tubular section with a thickness of 5 mm, and 32% higher than that of the hollow square section. Hence, the tubular section with a thickness of 4 mm was selected for frame-level optimization.
Fig. 3

Stiffness by analytical method and FEA for individual sections

4.4 Stiffness Analysis of Existing Chassis Frame

For stiffness analysis, 2D meshing with an element size of 10 mm was used. The deformation of the chassis was measured by applying a load of 10 kN at the location of the shear center. The stiffness was calculated by measuring the deformation of the chassis frame in various load cases. Four different load cases were considered, namely, the front torsion load case, rear torsion load case, front lateral load case, and rear lateral load case, to compare the overall stiffness of the chassis frame. Figure 4 shows the top view of the existing chassis frame. Figure 5 shows the loads and boundary conditions used in the FEA. Table 5 shows the constraints for the various load cases.
Fig. 4

Top view of existing chassis frame

Fig. 5

Loads and boundary conditions

Table 5

Constraints for load cases

Symbol

Degrees of freedom

Open image in new window

1, 2, 3, 4, 5, 6

Owing to the load applied at the front shear center in the front torsion load case, the chassis frame deformed in the z-direction. One side of the frame was displaced in the positive z-direction, while the other side was displaced in the negative z-direction. The deformation value was measured at the point where the load was applied. Figure 6 shows the chassis frame deformed by 268 mm in the front torsion load case. Similarly, Fig. 7 shows the chassis deformed at the rear side by 208 mm in the rear torsion load case. In the front and rear lateral load case, the chassis frame deformed in the y-direction and the deformation was measured at the point where the load was applied. Table 6 and Figs. 8 and 9 show the deformation of the existing chassis frame by 158 mm and 264 mm in the front and rear lateral load case, respectively. Table 7 shows the stiffness obtained for the existing chassis frame.
Fig. 6

Front torsion load case

Fig. 7

Rear torsion load case

Table 6

Stiffness analysis for existing chassis frame

Sr. no.

Parameter

Deformation (mm)

Weight (kg)

1

Front torsional deformation

268

610

2

Rear torsional deformation

208

3

Front lateral deformation

264

4

Rear lateral deformation

158

Fig. 8

Front lateral load case

Fig. 9

Rear lateral load case

Table 7

Stiffness for existing chassis frame

Sr. no.

Parameter

Stiffness

1

Front torsional stiffness

17.46 kN·m/rad

2

Rear torsional stiffness

17.10 kN·m/rad

3

Front lateral stiffness

0.076 kN/mm

4

Rear lateral stiffness

0.127 kN/mm

$${\text{tan }}\theta \,= \, {\frac{a}{b/2}}$$
(6)
where a is the displacement in z-direction, b is the distance between the two nodes where load is applied.
$${k_T} \, = \, \frac{{T}}{\theta'}$$
(7)
$${k_L} \, = \, \frac{{F}}{c}$$
(8)
where kT is the torsional stiffness, T is the torque, \(\theta'\) is the angular deformation, kL is the lateral stiffness, F is force, and c is the displacement in y-direction. The torsional stiffness and lateral stiffness can be evaluate by above formulas, and the specific values are shown in Table 7.

4.5 FEA of Chassis Frame with Tubular Cross Member

According to the results obtained by the analytical method and FEA for the individual sections, the tubular section with a thickness of 4 mm provided the highest torsional stiffness. Hence, the same section with a casting bracket was used for optimization. Because the front and rear torsional stiffness of the chassis depends on the type of cross member provided at the front and rear side of the chassis frame, the third and seventh cross members were replaced by a tubular cross member with the dimension listed in Table 1. Figure 10 shows the computer-aided design (CAD) model of the tubular cross member with a casting bracket and an overall cross member weight of 15 kg. Additionally, Fig. 11 shows the meshed frame with the third and seventh tubular cross members. Similar analysis was performed by applying the loads and boundary conditions as shown in Fig. 5. Table 8 shows the deformation and stiffness of the optimized chassis frame.
Fig. 10

CAD model of tubular cross member

Fig. 11

Meshed frame with tubular cross member

Table 8

Deformation and stiffness of optimized chassis frame

Sr. no.

Load case

Deformation (mm)

Stiffness

Weight (kg)

1

Front torsion

135

32.259 kN·m/rad

610

2

Rear torsion

105

31.980 kN·m/rad

3

Front lateral

234

0.085 kN/mm

4

Rear lateral

141

0.142 kN/mm

5 Results and Discussion

From Tables 6 and 8, it was found that, in the optimized truck chassis frame, the front torsional deformation and rear torsion deformation of the chassis frame were reduced by approximately 49%. The lateral deformation of the chassis frame in the front and rear lateral load case was reduced by 11% and 10%, respectively. Figure 12 shows the reduction in the deformation of the chassis.
Fig. 12

Deformation of optimized frame in various load cases

Figure 13 shows the improvement in torsional stiffness by changing the existing C-section cross member with a tubular cross member. The torsional stiffness improved because the section became stiffer in resisting torsional loads as the material concentrated farther away from the section’s center of gravity. The tubular cross member had more material concentrated away from the section’s center of gravity in comparison with the existing C-section. Therefore, it achieved a better result.
Fig. 13

Comparison of torsional stiffness

Figure 14 shows the improvement in lateral stiffness, respectively, when the existing C-section cross member is replaced with a tubular cross member. The lateral stiffness of the chassis depends on the spread of the gusset or bracket, which connects the long member and cross members. In the existing chassis frame, the C-section cross member was connected with the help of a gusset. The spread of the gusset over the cross-member web portion was less than the casting bracket of the tubular cross member in the optimized chassis frame. Therefore, the lateral stiffness in the optimized frame was improved.
Fig. 14

Comparison of lateral stiffness

Figure 15 shows the frame’s improvement in terms of natural frequency, when the C-section cross member was replaced with a tubular cross member. To avoid resonance and excessive vibrations, the first five modes are very important. In the existing chassis frame, the weakest mode is torsion with a natural frequency of 4.28 Hz, which improved by 1.81 Hz in the optimized frame. Figures 16 and 17 show the strain energy contribution of the existing C-section cross member and the tubular cross member, respectively, in the front and rear torsion load cases. The strain energy contribution of the cross member demonstrates its ability to absorb strain energy. In the existing C-section, the cross member does not absorb the strain energy, while a portion of the strain energy is absorbed by the long member section. In the optimized chassis frame, the strain energy is absorbed by the cross member. The section highlighted in blue and orange color on the cross member shown in Figs. 16 and 17 shows the higher strain energy absorption capacity for the front and rear torsion load cases, respectively. Hence, the tubular sections contribute more in the torsional load case, in comparison with the existing C-section.
Fig. 15

Natural frequency at first five modes

Fig. 16

a, b Strain energy contribution of existing third cross member and tubular cross member in front torsion load case

Fig. 17

a, b Strain energy contribution of existing seventh cross member and tubular cross member in rear torsion load case

6 Conclusion

The primary objective of this study was to develop an optimum design model for torsional stiffness. Johnson’s method of optimum design was modified such that it provided the optimum value of torsional stiffness for a mass constraint to select the best section among the number of available sections. However, the torsional stiffness model is limited to closed sections only because the torsion of an open section causes warping and has difficulty in cogitating the effect of warping. The tubular section with a thickness of 4 mm was found to be better than the hollow square section with a thickness of 4 mm and the tubular section with a thickness of 5 mm. The front and rear torsional stiffness of the chassis frame is influenced by the type of cross member used at the front and rear side of the chassis. Hence, to optimize the torsional stiffness of the chassis frame, the third and seventh cross members were replaced with a tubular section, whose dimensions were obtained by the modified Johnson’s method.

The FEA results revealed that for same chassis weight, the front and rear torsional stiffness was improved by 44%, while the front and rear lateral stiffness was improved by 10%. The modal analysis results for the existing and optimized chassis frame indicate an improvement in terms of natural frequency for the first five modes. In the existing frame, the weakest mode is torsion and is improved by using the proposed tubular cross member with a thickness of 4 mm. The strain energy contribution indicates that the tubular section absorbs more strain energy than the existing C-section cross member in the front and rear torsion load cases. The results of this study can be used to modify the well-established Johnson optimization method to select the optimum dimensions for the required weight constraints based on the determined torsional stiffness, when the numbers of the diverse sections with variable thickness are available.

References

  1. 1.
    Kilimnik, L.S., Korbin, M.M.: Torsional stiffness of tractor trailer chassis. Sov. Appl. Mech. 2(5), 82–85 (1966)CrossRefGoogle Scholar
  2. 2.
    Seyfried, P., Taiss, E.J.M., Calijorne, A.C., et al.: Light weighting opportunities and material choice for commercial vehicle frame structures from a design point of view. Adv. Manuf. 3(1), 19–26 (2015)CrossRefGoogle Scholar
  3. 3.
    Oskar, D., Alejandro, G.: Influence of body stiffness on vehicle dynamics characteristics in passenger cars. Master’s Thesis in Automotive Engineering, Chalmers University of Technology Goteborg, Sweden (2015)Google Scholar
  4. 4.
    Weerawut, C., Supasit, R.: Design of the space frame racing car front clip and rear clip for torsional rigidity. In: The 18th Conference on Mechanical Engineering Network October 18–20, 2004. Province-Khon Kaen (2004)Google Scholar
  5. 5.
    Lonny, T., Jon, L., Harry, L.: Design of a twist fixture to measure the torsional stiffness of a Winston cup chassis. In: Motorsports Engineering Conference and Exposition, Dearborn, Michigan November 16–19 (1998)Google Scholar
  6. 6.
    Ojo, K., Roslan, A.R., Pakharuddin, M.S.: Optimization of heavy duty truck chassis design by considering torsional stiffness and mass of the structure. Appl. Mech. Mater. 554(2014), 459–463 (2014)Google Scholar
  7. 7.
    Kurisetty, P., Sukumar, N., Gupta, U.: Parametric study of ladder frame chassis stiffness. SAE Technical Paper 2016-01-1328Google Scholar
  8. 8.
    Rahul, V., Nirmal, R., Aniket, N.: Structural analysis of pick-up truck chassis using FEM. Int. J. Chemtech Res. 9(6), 384–391 (2016)Google Scholar
  9. 9.
    Goel, G., Garg, R., Ranjan, T., et al.: Structural and modal analysis of a ladder frame chassis. ARPN J. Eng. Appl. Sci. 11(23), 13599–13603 (2016)Google Scholar
  10. 10.
    Devaraj, S., Raghu, V.: Parametric analysis of factors influencing stiffness and crashworthiness of a ladder frame. In: Proceedings of the ASME 2016 International Mechanical Engineering Congress and Exposition. November 11–17 (2016)Google Scholar
  11. 11.
    Patel, A.S., Chitransh, J.: Design and analysis of TATA 2518TC truck chassis frame with various cross sections using CAE tools. Int. J. Eng. Sci. Res. Technol. 5(9), 692–714 (2016)Google Scholar
  12. 12.
    Prabakaran, S., Gunasekar, K.: Structural analysis of chassis frame and modification for weight reduction. Int. J. Eng. Sci. Res. Technol. 3(5), 595–600 (2014)Google Scholar
  13. 13.
    Divyesh, N., Vinod, M., Dharmeet, P.: Strength and rigidity analysis of heavy vehicle chassis for different frame cross section by analytically and FEA under various loading condition. Int. J. Adv. Res. Eng. Sci. Technol. 3(5), 411–420 (2016)Google Scholar
  14. 14.
    Gawande, S.H.: A combined numerical and experimental study on metal expansion bellows for STHE. J. Braz. Soc. Mech. Sci. Eng. 40(9), 465 (2018)CrossRefGoogle Scholar
  15. 15.
    Sahu, R.K., Sahu, S.K., Behera, S., et al.: Static load analysis of a ladder type chassis frame. Imp. J. Interdiscip. Res. 2(5), 1404–1409 (2016)Google Scholar
  16. 16.
    Prakash, V., Prabhu, M.: Design and analysis of heavy vehicle frame. Int. J. Adv. Sci. Eng. Res. 1(1), 486–494 (2016)Google Scholar
  17. 17.
    Patil, K.Y., Deore, E.R: Stress analysis of ladder chassis with various cross sections. IOSR J. Mech. Civ. Eng. (IOSR-JMCE) 12(4), 111–116 (2015)Google Scholar
  18. 18.
    Siva Nagaraju, N., Sathish Kumar, M.V.H., Koteswarao, U.: Modeling and analysis of an innova car chassis frame by varying cross section. Int. J. Eng. Res. Technol. 2(12), 1868–1875 (2013)Google Scholar
  19. 19.
    Sharma, A., Kumar, P., Jabbar, A., et al.: Structural analysis of heavy vehicle chassis made of different alloys by different cross section. Int. J. Eng. Res. Technol. 3(6), 1778–1785 (2014)Google Scholar
  20. 20.
    Patel, V.V., Patel, R.I.: Structural analysis of automotive chassis frame and design modification for weight reduction. Int. J. Eng. Res. Technol. 1(3), 1–6 (2012)Google Scholar
  21. 21.
    Singh, A., Soni, V., Singh, A.: Structural analysis of ladder chassis for higher strength. Int. J. Emerg. Technol. Adv. Eng. 4(2), 1–7 (2014)Google Scholar
  22. 22.
    Rakesh, N.L., Kumar, G.K., Hussain, J.H.: Design and analysis of Ashok Leyland chassis frame under 25 ton loading condition. Int. J. Innov. Res. Sci. Eng. Technol. 3(11), 17546–17551 (2014)Google Scholar
  23. 23.
    Johnson, R.C.: Method of optimum design. J. Mech. Des. 101, 667–673 (1979)CrossRefGoogle Scholar

Copyright information

© China Society of Automotive Engineers (China SAE) 2018

Authors and Affiliations

  1. 1.Department of Mechanical Engineering, M.E.S. College of Engineering PuneS. P. Pune UniversityPuneIndia

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