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Lightweight frame is very important to engineering machinery. In this paper, a lightweight design method is proposed for a mechanical mowing truck frame. This method combines topological optimization with topology optimization to design the frame successfully. Based on the finite element simulation, the strength analysis of the two working conditions (bending condition and torsion condition) for the mowing vehicle frame is carried out on the basis of satisfying the requirements of the frame work strength. This paper makes a comparative analysis of the frame after the second optimization using the combined method proposed. The comparison results show that the optimized frame meets the strength requirement, and its quality is 34.3% lower than before. The lightweight effect is obvious.

Energy conservation and environmental protection are always the theme of world development. On a global scale, the total energy is limited. And with the rapid development of economy, energy consumption is also increasing. Foreign relevant research data indicate that the fuel consumption can be reduced by 6% - 8% for every 10% reduction in vehicle weight [

The paper optimizes the motorcycle frame, making its minimum quality, and the lightweight effect is remarkable [

The reliability of the frame directly affects the operation of the vehicle and the safety of the driver. Therefore, the lightweight design should be carried out under the condition that the intensity is met. The mower frame has both beam structure and slab structure. There is room for improvement in overall structure and unit size. So this paper combines the advantages of topology optimization and size optimization. Topology optimization is carried out first, and dimensional optimization is carried out on the basis of topology optimization. Finally, the required frame structure is obtained, and compared with the original frame. We examine the advantages and disadvantages of the optimization results and whether the results are more satisfactory than the single optimization.

Owing to its function, the mowing vehicle is different from the traditional passenger car. There is a big difference in the form of the frame. The whole frame is composed of 27 parts, such as the front plate of the baffle battery seat and the front and rear support beams. The frame model is built with Solid works software, and we simplify the unnecessary parts. The remaining parts are modeled according to the actual size. Each component is bound according to the actual situation. After the completion of the assembly model is shown in

Steel copper and aluminum and other plastic materials usually fail in the form of submission. In finite element analysis, the static strength of materials can be

judged by the size of the equivalent stress of Von Mises. The frame material is Q235 steel. Yield strength is σ s = 235 MPa . Elasticity modulus is E = 210 GPa. Poisson’s ratio is ν = 0.3 . The maximum stress is not exceeding the allowable stress of the material. The effect force can be expressed as.

σ r = 1 2 [ ( σ 1 − σ 2 ) 2 + ( σ 2 − σ 3 ) 2 + ( σ 3 − σ 1 ) 2 ] (1)

The condition of meeting strength should be established: σ r ≤ [ σ ] . There into, σ r is Equivalent stress, σ 1 , σ 2 , σ 3 respectively represent the first and second and third principal stresses. [ σ ] indicates the allowable stress of the material. And σ s / [ σ ] = n , n is safety factor.

Because of the different load, the frame can produce different deformation in the process of work. And bending deformation and torsional deformation is the most common deformation, corresponding bending working condition and twisting working condition, which are the two kinds of typical working condition. These two kinds of typical working conditions are the most basic conditions, and it is also the two important conditions that have a great affect on frame. Therefore, this article selects bending condition and twisting working condition which are the two kinds of typical working condition to check the frame strength.

Using the finite element simulation, we import the model established in Solid works for static analysis. The load and constraints of the frame are applied in accordance with the actual conditions. The main force of the frame is the force on the frame, the force of the driver on the frame, the force of the rear battery pack on the frame, and the weight of the frame. The driver’s quality is 90 kg , and the knife dish quality is 98 kg . Finally, quality of battery pack is 80 kg .

Under bending condition, the constraint condition is the four supporting points of fixed constraint of the whole frame. All parts of the frame are bound to each other. The specific load and constraints are shown in

It can be seen from

In the torsion condition, the degree of freedom of a front-end supporting vertical direction is released, and the other three supports are fixed. All parts of the frame are bound to each other. The specific load and constraints are shown in

As can be seen from

It can be seen from the analysis of two typical working conditions that the overall stress of the frame is small, and the frame strength has a large margin. There is a lot of waste in the utilization of materials, so it is necessary to carry out lightweight design. The object characteristics of topology optimization and size optimization are different. It is used for different occasions. The mower frame has both beam structure and slab structure, and there is room for improvement in overall structure and unit size. As a result, this paper adopts topology optimization and size optimization of two-stage optimization method to optimize design, in order to achieve better weight loss.

The purpose of topology optimization design is to find the optimal distribution

of shapes and materials within the specified design space, commonly used in concept design phase. The basic design idea of structural topology optimization is to transform the optimal topological structure of the search structure into the problem of finding the optimal material distribution in a given design area. In product concept design phase, it is not enough to through experience to design the structure. Only by analyzing the topology optimization design and combining with the rich design experience of the designer, can the reasonable scheme be obtained in the early stage of conceptual design. Finally, the design products meet the requirements. The essence of continuum topology optimization is the combination of 0 - 1 discrete variables, and the variable density method is commonly used.

In the process of topology optimization, the unit density is selected as the design variable, and the mathematical model can be written.

Minimize: f ( x ) = f ( x 1 , x 2 , ⋯ , x n ) (2)

Constraint condition { g j ( x ) ≤ 0 j = 1 , ⋯ , m h k ( x ) = 0 k = 1 , ⋯ , h x i L ≤ x i ≤ x i U i = 1 , ⋯ , n (3)

There into, X = x 1 , x 2 , ⋯ , x n is the design variable; f ( x ) is the target function; g ( X ) is inequality constraint function; h ( X ) is equality constraint function; x i is design variable; L is lower limit; U is upper limit.

Size optimization design is a target without changing topological structure under the premise of geometric shape and material properties, relying on dimension parameters as design variables, through specific mathematical model of the optimization algorithm to optimize the parameters of the structure to minimize the mass or volume. The size optimization design is used in the detailed design stage. It can meet certain design requirements (such as stress frequency displacement, etc.) by changing the properties of structural elements (such as the thickness of shell elements, pole of cross-sectional area, etc.). So using the method of finite element theory to calculate the structural displacement and stress, it does not change the target topology structure size parameters, such as attributes. It can directly optimize the existing structure size parameters, reduce the cost and improve the structure performance.

In the process of dimension optimization, the thickness of each part is selected as the design variable, and the mathematical model can be expressed as:

Minimize: M = ρ ∑ i = 1 n v i (4)

Constraint condition: { σ max ≤ σ e x i L ≤ x i ≤ x i U i = 1 , ⋯ , n (5)

There into, M is the overall quality of frame structure; is the material density; v i is the element volume; n is the number of units; σ max is the maximum stress value of element in finite element analysis; σ e is the material yield limit, x i is the design variable; L is lower limit; U is upper limit.

The lightweight design scheme of the frame is shown in

In this paper, the bending and torsion conditions are respectively selected to

optimize the topology, and the two conditions are basically same. The specific steps are as follows:

1) In the two working conditions, the static analysis of the frame was carried out. The frame model was imported into the workbench, and the material properties, load and constraints were set in the static analysis module, and the static force was solved after the network completed.

2) After the static analysis, we insert shape optimization module after static analysis module and enter the module for loading and restraint. The load applied is the same as the constraint and static analysis. We set a 30% reduction in target reduction. After the setting, the topology optimization is solved.

3) The model was modified according to the topological optimization results, and the modified model was then analyzed to verify whether the modified results met the requirements.

The overall topology optimization results are shown in

In the whole frame, the main parts are left and right long beam, front and rear cross beams, battery seat, rear baffle and front plate. So the main goal of topology optimization is to select these components. According to

According to the result of modification, the strength of bending and torsion condition is rectified, and the calculation results are shown in

It can be seen from

On the basis of topology optimization, we select the thickness of the large plate, the thickness of the battery seat, the thickness of the left and right beam, the thickness of the front beam, the thickness of the back beam, and the seven dimension parameters of the rear baffle as the design variables. The constraint conditions are selected as maximum equivalent stress without exceeding allowable stress. The constraint conditions are selected as maximum equivalent stress without exceeding allowable stress. The finite element simulation is used to optimize the target drive of bending and torsion.

The finite element simulation use the Design Explorer as the optimization tool, and this tool studies the output parameters through the design point parameters. But input design point is limited in general, so the response surface is usually studied by a finite number of design points. According to the selected 7

size parameters, 79 design points are generated by the software. By calculation, in both cases, recommended optimal design points are generated according to the set constraints and target functions. The two design points are inserted into the original finite element model for static calculation. The selection and calculation results of dimension values are shown in

According to the calculation results of two working conditions, we select the size values that can satisfy the requirements of both conditions. The final selection is shown in

Bending condition | Torsion condition | |
---|---|---|

Big board | 2.421 mm | 2.113 mm |

Battery seat | 3.3451 mm | 3.6637 mm |

Left long beam | 1.7374 mm | 1.6991 mm |

Right long beam | 1.5795 mm | 1.5357 mm |

Front cross beams | 1.6592 mm | 1.8848 mm |

Rear cross beams | 1.8094 mm | 2.5378 mm |

Rear baffle | 2.7284 mm | 2.3978 mm |

Maximum Equivalent Stress | 69.97 MPa | 42.356 kg |

Overall quality of the frame | 42.356 kg | 42.898 kg |

Component thickness | Unit (mm) |
---|---|

Big board | 2.4 |

Battery seat | 3.7 |

Left long beam | 1.7 |

Right long beam | 1.7 |

Front cross beams | 1.9 |

Rear cross beams | 2.6 |

Rear baffle | 2.4 |

It can be seen from

The following conclusions are drawn from the above analysis:

1) In this paper, Solid works software is used to model the parameterization of mowing frame. The strength analysis of bending condition and torsion working condition was conducted by the finite element simulation. The maximum equivalent stress of the two conditions is 39.5 MPa and 53.1 MPa respectively. The stress in most areas is not more than 20 MPa, which is less than the allowable stress of 78.3 MPa. This meets the intensity requirements. The overall frame has a lot of optimization space.

2) Topology optimization of frame is carried out. The maximum stress in the two conditions of the optimized frame is 43 MPa and 44 MPa, which is less than the allowable stress of 78.3 MPa. This meets the intensity requirements. There is still room for further refinement. The overall frame was reduced from 67.075 kg to 59.69 kg, which decreased by 7.385 kg and decreased by 11%. We’ve got a good weight loss effect initially.

3) Further dimensional optimization was carried out. The maximum stress is 60.37 MPa and 72.34 MPa in the two conditions of the optimized frame, which is less than the allowable stress of 78.3 MPa. This meets the intensity requirements. The overall frame weight was reduced from 59.69 kg to 44.053 kg and 15.637 kg. A total of 23.022 kg was alleviated through two-stage optimization, and 34.3% weight was finally reduced. The lightweight design effect is remarkable.

This work was supported by National Key Research and Development Program of China (2016YFD0700800).

Li, S.M., Xu, K. and Wang, J.R. (2018) The Light Weight Design of Mowing Vehicle Frame with a Combined Method. Modern Mechanical Engineering, 8, 192-203. https://doi.org/10.4236/mme.2018.83013