Numerical and Experimental Study on cold rolling process of 5B02 aluminum alloy tubes

Taking the rolling of 5B02 aluminum alloy tubes in Pilger LG50 mill as an example, the finite element analysis of the tube rolling process was carried out by using ABAQUS software. The effects of rolling speed, rotary angle and feeding amount on the inner wall stress of the tubing and the dimensional accuracy and ellipticity of the finishing section in the forming process of Pilger rolling of 5B02 aluminum alloy tubes were investigated through the orthogonal test. The optimal process parameters were preferably selected for the experimental validation. The results show that the stresses in the inner wall of the wall-reduced section of the billet are the highest during the whole rolling process. The average stresses in the inner wall of the reduced wall section of the billet are in the following order: feed>rotary angle>rolling speed. The feed and rolling speed have a greater influence on the dimensional accuracy and ovality of the finishing section. Excessive rotary angle can lead to grid distortion in the reduced-wall section of the billet. The 5B02 aluminum alloy tubes rolled at a rolling speed of 1989mm/s, a rotary angle of 57°, and a feed of 2.5mm meet the requirements of dimensional accuracy, internal surface quality, and metallurgical structure, and improve production efficiency.


Introduction
With the development of aerospace industry, the performance and precision of piping systems are constantly improved.The realization of fine production is the future research direction in the processing field [1] .Two roll Pilger cold rolling technology is an important technology for the preparation of high precision tubes.In the rolling process, the pipes undergo a local incremental loading process dominated by compressive stress, so they have the characteristics of large deformation, high dimensional accuracy and high surface quality [2] .This process is widely used to manufacture seamless steel tubes of various alloys [3] .
The current research on two-roll pilger cold rolling is mainly in the mold and process design.In the mold design, Huang [4] and others optimized the structure by the method of orthogonal test, taking the shape quality as the evaluation criterion.In the process design, the stress and strain characteristics under different process parameters were analyzed by numerical simulation and experimental verification.An excellent rolling process was obtained based on these characteristics.Martin et al. [5] obtained the distribution law of rolling force and stress in the rolling process by simulating the rolling process of one cycle.Wang et al. [6] studied the cold rolled 304 stainless steel feeding volume, slewing angle and Q value on the change rule of pipe mechanics and dimensions.Li et al. [7] and Chu et al. [8] studied the feed rate of cold-rolled stainless-steel pipe.At present, there are few analyses of the aluminum alloy cold rolling process and process parameter optimization, the lack of stress and dimensional accuracy as a benchmark for the evaluation of the form.
The factors such as rolling speed, rotation Angle and feeding amount are directly related to the quality and production efficiency of the finished product.In this paper, taking Pilger LG50 mill rolling 5B02 aluminum alloy pipe as an example, ABAQUS software was used to carry out finite element analysis on the rolling process of 5B02 aluminum alloy pipe, and the effects of rolling speed, rotation Angle and feeding amount on the inner wall stress, dimensional accuracy and ellipticity of the finishing section of the pipe were studied by orthogonal test.The optimum process parameters were selected for experimental verification.This paper has important reference significance for the optimization of process parameters and process application of two-roll Pilger cold rolling aluminum alloy.

The Numerical Model
Table 1 shows the chemical composition of 5B02 aluminum alloy.Figure 1a shows the finite element model of two-roll Pilger cold rolling, consisting of upper and lower rolls, tubes and mandrels.The position corresponding to the roll is the open end. Figure 1b shows the true stress-strain curve of the material and is used to establish the material model for finite element analysis.The Young's Modulus is 68900MPa and the Poisson's Ratio is 0.33.The initial billet size is Φ75×5mm and the finished pipe size is Φ53×2mm.

Determination of contact type and boundary conditions
In order to ensure the accuracy of the simulation process, the contact, boundary conditions and load conditions are as close as possible to the actual pipe rolling process.In terms of contact type, hard contact is used in the normal direction and no penetration behavior between contact pairs is allowed.Since it is a rolling problem, the tangential contact is calculated using the frictional contact mode of the penalty function method with the friction coefficient set to 0.1 [9] .The rolls and mandrels are set as rigid bodies, the billet is set as elastic-plastic, and the mandrels are fixed during the rolling process, in which the roll speed loading amplitude curve is approximated to be applied as a sinusoidal curve.The methodology for this simulation is based on the modified Lagrange multipliers and the material model follows Von Mises yield criterion [10] .

Evaluation criteria establishment
From Fig. 2a, it can be seen that the region of higher stress is the inner wall in the wall reduction section, the value of which is in the range of 200~220 MPa, and the other parts are in the range of 100~160 MPa.
The area where the stress concentration will produce defects.The stress of the wall reduction section should be as an indicator.In the inner wall of the wall reduction section (400 mm from the tail section) (e.g., Fig. 2b), the average stress of the 37 nodes (e.g., Fig. 2c) is equally spaced and selected as one of the criteria for evaluating the process parameters,  ̅ .While ensuring the quality of the inner wall, it is also necessary to ensure the dimensional accuracy of the finished pipe.Finished tube size of the outer diameter and wall thickness, distribution uniformity is an important criterion for evaluating the dimensional accuracy.The average radius ̅ and wall thickness  ̅ of 37 positions in the finishing section (630 mm from the end) are obtained from the coordinate positions, and the difference with the standard radius r and wall thickness t is mean deviation of radius r and the mean deviation of wall thickness t, which are used as a measure of the dimensions.The distribution uniformity is expressed by the variance   2 .The ellipticity is expressed by the difference of the maximum value and the minimum value of the outer diameter.The difference between the maximum and minimum values of the outer diameter is represented by .In this way, the evaluation criteria of the "5 indicators" were established.

Orthogonal test design
Rolling process of the mill's important parameters are rolling speed, rotary angle and feed.these three parameters of different matching on the quality of the finished pipe will have a different impact.According to the actual production situation, the important parameters of the LG50 mill can be adjusted range of: rolling speed of 1790~2188mm/s, rotary angle of 51 °72 °, the amount of feed in the 2~3mm.The production of most of the selection of the rolling speed of 1790mm/s, rotary angle of 51 ° and the amount of 2mm feed.In order to study the effect of these three parameters on the quality of the finished product, orthogonal tests as shown in Table 2 were carried out.The angle of rotation in current production is based on the number of rotations required for one cycle.For 5, 6 or 7 rotations, the actual angle of rotation is 51°, 57° and 72°.Six rotations of 60° were not used because a 60° rotation would cause the pipe to go through the open end twice in one cycle, which result in roll mark defects on the surface.The nine sets of test parameters were simulated in ABAQUS and the corresponding simulation results were obtained.Taking  ̅ 、r、t、  2 and  as the evaluation criteria.The smaller the numerical results are, the better the quality and the higher the dimensional accuracy of the product.

Analysis of simulation result
Figure 3 shows the stress cloud after rolling, of which Fig. 3c, Fig. 3f and Fig. 3i, the mesh distortion phenomenon occurs at the end of the wall reduction section, which can't be completely simulated.
Removing these three groups of tests, the other simulation tests are able to simulate the finishing section, and the overall stress range of the finishing section is in the range of 40~225 MPa.In order to explore the characteristics of the rolling process stress-strain, Figure 4 test 1 reduction section, wall section and finishing section stress-strain cloud diagrams are analyzed.The stress of the whole process is less than 225MPa, wall section and finishing section strain is periodically distributed.From Fig. 4a stress cloud diagram of diameter reduction section and Fig. 4e strain cloud diagram, it can be seen that mainly the ridge is stressed, the ridge stress is greater than the opening, the equivalent strain is overall smaller, and the equivalent strain of the upper side is slightly larger than that of the lower side.From Fig. 4b stress cloud diagram of the wall reduction section and Fig. 4e strain cloud diagram, it can be seen that the lower side of the inner wall of the stress is greater than that of other parts of the wall, and the strain of the inner wall is slightly larger than that of the outer wall.From Fig. 4c stress cloud diagram of finishing section and Fig. 4f strain cloud diagram, it can be seen that the overall stress is less than 225MPa, and the overall stress and strain of the reduction section and finishing section are cyclically distributed.Cloud can be seen that the overall stress is relatively uniform, and the inner wall strain is more than one order of magnitude larger than that of the outer wall.Through the polar analysis to find the factors in the order of priority, to find out the optimal level to carry out the optimal combination, to get the optimal process parameters.Remove the simulation results of factor 2 level 3. Table 3 shows the orthogonal test results of the three indicators, and the results of the polar analysis of the five indicators.The results are shown in Table 4, where   ̅̅̅̅ (i=1,2, j=1,2,3) indicates the average value of the corresponding indicator j factor i level, and Rj is the corresponding polar deviation.From Table 4, it can be seen that except for r, factor C, i.e., feed volume, has the greatest influence on the other four indicators, in which the influence on the average stress of the inner wall is more than two times that of the other two factors.For r, factor A, i.e., rolling speed, has the greatest influence.Analysis of Table 4 reveals that A2, B2 and C2 appear most frequently, so the optimal combination is chosen as A2B2C2, i.e., the rolling speed is 1989 mm/s, the rotary angle is 57°, and the feed amount is 2.5 mm.Compared with the initial process parameters, the rolling efficiency is improved.

Experimental validation
Rolled with preferred A2B2C2 process parameters.Measurements and analyses of the dimensions, internal surface quality and organisation of the rolled tubes were carried out.Table 5 shows the finished pipe sampling size, which meets the production requirements of high-precision grade pipe in GB/T4436 (the deviation of outer diameter is less than 0.15mm, and the deviation of wall thickness is less than 0.1mm).The internal surface quality was detected by endoscope, and it can be seen from Fig. 5a that there is no obvious defects such as scratched channels.Figure 5b shows the metallographic organisation after annealing, and it can be seen that the crystalline grains are equiaxed, and the grain size is in the range of 32~139 μm, which meets the requirement of first-grade grain size.

Conclusion
By analyzing the stress-strain diagram, the stress concentration in the whole rolling process is located in the inner wall of the wall reduction section, and the equivalent strain of the wall reduction section and the finishing section is cyclic, and the strain of the inner wall is larger than that of the outer wall.
The influence of each factor on the stress distribution of the inner wall of the wall-reducing section of the billet is in the following order: feeding volume > rotary angle > rolling speed.Among them, the feeding volume and rolling speed also have a greater impact on the dimensional accuracy of the finishing section and the degree of ellipticity, when the rotary angle of 72°, it will lead to the billet wall reduction section of the prism and cracking phenomenon.
According to the results of extreme difference analysis, the optimal combination of process parameters is selected as follows: rolling speed of 1989mm/s, rotary angle of 57°, feed amount of 2.5mm.the quality and size of the rolled pipe under this process meet the requirements, and at the same time improve the efficiency.

Fig. 2
Fig. 2 Inner wall stress selection process: (a) longitudinal interface stress distribution; (b) location of the point; (c) the way to take points

Fig. 4
Fig. 4 Stress-strain distribution: (a) Reduced diameter section stress; (b) Reduced wall section stress; (c) Finished section (d) Reduced diameter section equivalent strain; (e) Reduced wall section equivalent strain; (f) Finished section equivalent strain