# Optimization of Torsional Stiffness for Heavy Commercial Vehicle Chassis Frame

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## 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

- 1.
Weight of the body, passengers, and cargo loads

- 2.
Vertical and twisting load owing to uneven road surfaces

- 3.
Lateral forces caused by the road camber, side wind, and steering of the vehicle

- 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.

## 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).

*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.

*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:

*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.

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 | |

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

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/m |

4 | Poisonous ratio | 0.3 |

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, Ro_{x}, Ro_{y}, and Ro_{z} 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

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 |

### 4.4 Stiffness Analysis of Existing Chassis Frame

Constraints for load cases

Symbol | Degrees of freedom |
---|---|

1, 2, 3, 4, 5, 6 |

*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.

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 |

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 |

*a*is the displacement in

*z*-direction,

*b*is the distance between the two nodes where load is applied.

*k*

_{T}is the torsional stiffness,

*T*is the torque, \(\theta'\) is the angular deformation,

*k*

_{L}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

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

## 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.

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