^{1}

^{*}

^{1}

^{*}

^{2}

^{1}

In order to solve the problems of rolling forming accuracy and fillet thinning of alloy steel rim, a three-dimensional model of three pass rolling process was established, and the influence of different process parameters on forming quality was analyzed by using the finite element software, and the optimal process parameter combination was obtained. On this basis, the simulation results of wheel rim stress and strain for each pass rolling are analyzed, and the particle tracking technology is introduced to analyze the variation rule of stress in each incremental step. Finally, the simulation and experimental results show that the simulation thickness is basically consistent with the actual thickness, which improves the accuracy of rim rolling forming, and further verifies the correctness of rolling process simulation.

With the acceleration of automobile lightweight process, alloy steel has been widely used in the production of automobile parts [

With the maturity of finite element numerical simulation technology, through the rim rolling machining simulation, and according to the simulation results to analyze the deformation characteristics, it can improve the product design efficiency and forming quality. Deng, R., et al. [

During the multi-step rolling process of automobile rim, the blank undergoes elastic and plastic deformation, and is formed into the final workpiece with the loading movement of the roller. The elasto-plastic deformation process is accompanied by a high degree of nonlinearity, and structural nonlinearity has always been a difficult point in the finite element analysis process. The incremental method is used to deal with the nonlinear problem, and the evolution history of stress and strain during the loading process can be obtained, and the solution accuracy is high, Good stability [

There are many reasons for the non-linear problem of the blank, which can be divided into three main types: 1) The rim is geometrically nonlinear. The rim material undergoes a large deformation under the action of external load, which causes a large change in the force of the structure system. As the load continues to increase, the unit coordinates and structural rigidity in the workpiece change, causing the unit body to produce translation, torsion, elongation and compression deformation cause changes in geometric shapes, resulting in a nonlinear response of the structure, that is, the force-displacement relationship is no longer proportional. When analyzing the linear response problem, the small deformation of the workpiece geometry is ignored. The linear relationship can be used to express the relationship between deformation and displacement. However, in the nonlinear response, the workpiece geometry deforms greatly, and the linear relationship is no longer applicable. Through continuous iteration, it can obtain a convergent solution. 2) Non-linear rim material. In the process of the large strain of the blank, the stress-strain of the material no longer conforms to Hooke’s law, resulting in a complex nonlinear relationship. The influencing factors include (loading history, loading time, ambient temperature, etc.). 3) The boundary conditions of the rim are nonlinear. During the forming process of the blank, the contact area with the mold has been changing. With the continuous influence of load, material, constraints and other factors, it is difficult to perform linear analysis on the contact surface. At the same time, friction will also occur in the contact area, and the friction types are all Non-linear, its change process is more complicated, and the superposition of various factors makes the convergence of the contact area more difficult.

Therefore, it is necessary to numerically integrate the basic equation of infinitesimal increment form within the loading step time, and linearize the basic equation, so that the rim elastic-plastic nonlinear problem is simplified into a series of linear problems.

The essence of rim elastoplastic constitutive relationship is the stress-strain relationship of the blank, the elastoplastic constitutive equation is calculated by the Von-Mises yield criterion. The yield stress is expressed by and the Von-Mises yield function is as follows

f = J ′ 2 ( σ i j ) − 1 3 σ 2 ¯ = 1 2 σ ′ i j σ ′ i j − 1 3 σ 2 ¯ = 0 (1)

The total strain increment is the sum of elastic strain increment and plastic strain increment. The calculation formula is as follows:

d ε i j = d ε i j e + d ε i j p (2)

where, d ε i j is the total strain increment, d ε i j e is the elastic strain increment, and d ε i j e is the plastic strain increment.

The elastic stress conforms to Hooke’s law. The calculation formula is as follows:

d σ i j = D d ε i j e (3)

d σ i j = D ( d ε i j − d ε i j p ) (4)

where, D is the elastic stress-strain relationship matrix, which is determined by Young’s modulus and Poisson’s ratio.

The relationship between yield stress, plastic strain and work hardening coefficient is as follows:

H ′ = ∂ σ ¯ ∂ ε P ¯ (5)

The relationship between plastic strain increment and stress state under the relevant flow criterion is as follows:

d ε i j p = d λ ∂ f ∂ σ i j (6)

The subsequent yield state can be obtained from Equation (1) as follows:

d f = ∂ f ∂ σ i j d σ i j − 2 3 σ ¯ ∂ C ¯ ∂ ε P ¯ d ε P ¯ = 0 (7)

Among them ∂ f ∂ σ i j = ∂ ′ i j (8)

From Equation (5), the relationship between plastic strain increment and stress increment can be obtained as follows:

d ε p ¯ = 2 3 d ε i j p d ε i j p = 2 3 λ 3 2 σ ′ i j σ ′ i j = 2 3 λ σ ¯ (9)

Substituting formulas (4), (7) and (8) into (6), the relationship is as follows:

σ ′ i j d σ i j − ( 2 3 σ ¯ ) 2 H ′ λ = 0 (10)

Substituting formulas (5) and (7) into (3), the relationship is as follows:

d σ i j = D ( d ε i j − λ ∂ σ ′ i j ) (11)

Substituting formula (10) into formula (9), the relationship is as follows:

λ = σ ′ i j D d ε i j σ ′ i j D σ ′ i j + ( 2 3 σ ¯ ) 2 H ′ (12)

Substituting the above equation into Equation (10), the relationship between the rim elastic-plastic stress increment and strain increment can be obtained as follows:

d σ i j = [ D − σ ′ i j D d ε i j σ ′ i j D σ ′ i j + ( 2 3 σ ¯ ) 2 H ′ ] d ε i j (13)

In finite element analysis, isoparametric elements are used to discretize the solution domain, and the displacement of the element coordinates is expressed by node interpolation:

x 0 i = ∑ k = 1 n N k x 0 i k , x t i = ∑ k = 1 n N k x t i k , x t + Δ t i = ∑ k = 1 n N k x t + Δ t i k ( i = 1 , 2 , 3 , ⋯ ) (14)

u t i = ∑ k = 1 n N k u t i k , u i = ∑ k = 1 n N k u i k ( i = 1 , 2 , 3 , ⋯ ) (15)

where, X t i k is the coordinate component of node k in the i direction at time t, u t i k is the displacement component of node k in the i direction at time t, N k is the shape function associated with node k, and N is the number of nodes for unit interpolation.

The Piola Kirchhoff stress increment is related to the Green strain increment by the constitutive tensor, and the nonlinear equation described by T. L. can be obtained, Combining Equations (14) and (15) to calculate the displacement derivatives in the integral formulas of the full Lagrangian equation, the finite element matrix form of T. L. scheme is derived as follows [

( [ K L ] 0 t + [ K N L ] 0 t ) { U } = { Q } t + Δ t − { F } 0 t

( [ K L ] 0 t + [ K N L ] 0 t ) { U } = { Q } t + Δ t − { F } 0 t (16)

where, { Q } t + Δ t is the node load vector; { U } is the node displacement increment vector; [ K L ] 0 t , [ K N L ] 0 t and { F } 0 t respectively are ∫ 0 V D 0 i j r s e 0 r s δ e 0 i j 0 d V , ∫ 0 V S 0 t i j δ η 0 i j 0 d V and ∫ 0 V S 0 t i j δ e 0 i j 0 d V points integration, The expression is as follows:

[ K L ] 0 t = ∑ e ∫ 0 V B 0 t L T D 0 B 0 t L d 0 V (17)

[ K N L ] 0 t = ∑ e ∫ 0 V B 0 t N L T S 0 t B 0 t N L d 0 V (18)

[ F ] 0 t = ∑ e ∫ 0 V B 0 t L T S ^ 0 t d 0 V (19)

where, B 0 t L , B 0 t N L and B 0 t L are the conversion matrices of linear strain, nonlinear strain, and displacement, respectively, D 0 are the incremental material characteristic matrix, S 0 t and S ^ 0 t are the matrix formed by Piola-Kirchhoff stress.

Roll forming is an advanced cold forging process, The forming process is complex, including rounding, welding and slagging, flaring, one-pass rolling, two-pass rolling, three-pass rolling, expansion finishing and Inflatable door holes and other processes [

According to the rim rolling forming principle, the rim three pass rolling model is shown in

The function of the first roll forming is the pre-forming of the rim, which mainly rolls out the transition shape of the deep groove and rounded corners of the rim, and the flared parts on both sides are not deformed, the second pass of roll forming is mainly to shape the groove bottom and fillet part, and pre-shape the flange part at the same time, the third pass of roll forming accurately forms the rim so that its shape and size meet the standard requirements [

In order to ensure the accuracy of simulation and obtain the accurate mechanical properties parameters of the rim material, the tensile test machine was used

to conduct tensile tests on 3 specimens of the same type.

In the rolling process, almost no deformation occurs in the mold, which is defined as analytic rigid body [

In the actual processing, the regulating wheel is connected to the cylinder, and the blank is pressed by air pressure [

The rolling time includes feed forming time and progressive forming time, which are related to feed quantity, feed speed and blank rotation speed. The time step is calculated by

t = t 1 + t 2 (20)

t 1 = d v (21)

specimen | Density (kg/m^{3}) | Elastic Modulus(GPa) | Poisson’s ratio | tensile strength (MPa) | Plastic extension strength (MPa) | Elongation (%) | Yield Strength (MPa) |
---|---|---|---|---|---|---|---|

1 | 7830 | 210 | 0.3 | 468.46 | 321.92 | 32.88 | 468.13 |

2 | 7830 | 210 | 0.3 | 469.82 | 317.68 | 32.02 | 469.28 |

3 | 7830 | 210 | 0.3 | 468.08 | 324.53 | 32.48 | 467.87 |

t 2 = 2 n π w (22)

where, t is the time step, t_{1} is the feed forming time, t_{2} is the progressive forming time, v is the feed velocity, d is the feed quantity, n is the number of turns of the progressive forming workpiece, n is 1.

The billet rotation speed (w) is calculated based on the equal linear velocity of the rolling contact point.

v 1 = 2 π r 1 w 1 = 2 π r 2 w 2 (23)

where, v_{1} is the linear velocity of the contact point, r_{1} is the roll-down radius, w_{1} is the roll-down speed, r_{2} is the blank radius, andw_{2} is the blank speed.

The main process parameters that affect the quality of rim roll forming include friction coefficient, feed speed and wheel speed. In actual production, the process parameters are mainly selected by the researcher’s experience and cannot ensure the optimal combination of parameters. In order to study the relationship between process parameters and forming quality, a single parameter experiment method was used to simulate the rim.

1) The influence of friction on the forming quality

In rolling processing, the workpiece and the mold are rotated by friction, but due to the influence of lubrication conditions and the wear of the mold surface, it is difficult to determine the relationship between the friction and the workpiece. Combined with practical experience, keep the feed speed 21.89 mm/s and the speed 200 r/min unchanged, and explore the influence of the friction coefficient on the forming quality when the friction coefficient is 0.2, 0.3 and 0.4. The results in

2) The influence of feed speed on forming quality

In actual rolling, if the feed speed is too high, it will cause the blank to run off and the forming will be unstable, if the feed speed is too small, the rolling time will be prolonged and the processing efficiency will be reduced. Keep the friction coefficient at 0.3 and the speed of 200 r/min unchanged, and analyze the influence on the forming quality when the feed rate is 32.84 mm/s, 21.89 mm/s and 16.42 mm/s.

thickness of the workpiece is only 3.32 mm. As the feed rate increases, the thickness of the measuring point increases and the forming quality of the workpiece tends to be better, so it can be increased appropriately feed rate. However, in actual processing, the feed speed of the mold is too fast, which will cause the workpiece to produce lateral force and the workpiece will shift. As shown in

3) The influence of roller speed on forming quality

The speed ratio of the roller is matched inversely according to the diameter of the roller [

Simufact Forming software is used to perform finite element simulation on the rim. In the simulation, the feed distance is the translational distance of the roller, and the analysis results of the speed, feed speed, time step and feed distance are shown in

The analysis cloud diagram of the rolling stress and strain of each pass is shown in

Upper roller speed (r/min) | Lower roller speed (r/min) | Feed rate (mm/s) | Time step (s) | Feed distance (mm) | |
---|---|---|---|---|---|

The 1^{st} roll | 200 | 220 | 21.89 | 1.79 | 32.84 |

The 2^{nd} roll | 200 | 220 | 8.40 | 1.8 | 12.6 |

The 3^{rd} roll | 182 | 200 | 6.75 | 1.82 | 10.13 |

workpiece reaches 0.33, the equivalent strain value of the groove and the rounded area is larger, and the strain value of the flange area is smaller, indicating that the plastic deformation occurs in the groove area is larger.

The second pass roll forming shape, mainly preform the flange area, and further shape the groove and rounded corners.

The third pass rolls mainly shape the wheel flange accurately, and makes the groove fillet size meet the requirements of the workpiece.

In order to analyze in detail the rolling simulation process of each pass of the rim, the particle tracking technology is introduced into the rolling results to

track the stress change process of the workpiece at each time step.

The relationship curve between third rolling equivalent stress and forming time is shown in

In order to verify the correctness of the simulated rim forming, the actual production workpiece and the simulated formed workpiece were compared and analyzed in thickness. The rim rolling process is shown in

Through the rim rolling process, each pass roll forming workpiece is obtained.

It can be found from

large, and the thinning rate reached 10%, the flange is subjected to little compressive stress, and under the action of tensile stress, the material flows to the fillet to compensate for excessive thinning of fillet; The largest thickness thinning area of the second roll occurs at the wheel rim, mainly because of the preforming of the wheel rim, the stress is large, the deformation is large, and there is no material supplement in this area, the thinning rate reaches 10.8%, and the thinning rate of other positions is small; After three-roll forming, the thickness distribution is relatively uniform, and the largest thinning area occurs at the rounded corner, and the thinning rate is about 9.7%.

1) The increase of the friction coefficient is beneficial to the forming of the workpiece, but after the friction coefficient is increased to 0.3, the effect on the forming quality is not obvious. The increase of the feed speed will increase the thickness of the measuring point, which is conducive to forming, but if the feed speed is too high, the lateral force will increase, which will easily cause the workpiece to shift. The reduction of the speed is beneficial to control the thinning of the rim, but if the speed is too small, the formation of the rim will be uneven.

2) The simulation results show that first rolling rounded corner and groove produce greater stress and strain. Second rolling pre-formed flange, where the stress and strain are both large, and the maximum equivalent stress appears at the flange, and the groove and rounded corner also produce large stress. Third rolling rim is accurately formed, the stress distribution is more uniform, and the fillet deformation is relatively small.

3) Comparative analysis of experimental and simulation results. The simulated forming thickness is basically consistent with the experimentally measured thickness, which proves the feasibility of simulation. The design optimization of new products can be carried out on this basis, which has certain reference value for the production and processing of enterprises.

Conceptualization, W.L. and M.P.; methodology, W.L.; software, S.L.; validation, W.L., M.P. and S.L.; data curation, M.C.; writing-review and editing, W.L.; writing-review and editing, M.P. and M.C.; supervision, M.C.; All authors have read and agreed to the published version of the manuscript.

The research was supported by the natural science foundation of Zhejiang Province with the grant number (LQY19E050001), and the school enterprise cooperation project with the grant number (20193300102049).

The authors declare no conflicts of interest regarding the publication of this paper.

Lv, W.H., Pang, M., Li, S.P. and Cao, M.L. (2021) Simulation Analysis and Optimization of Rolling Process of Steel Rim. World Journal of Mechanics, 11, 34-51. https://doi.org/10.4236/wjm.2021.113004