Incremental forming of solid cylindrical components using flow forming principles

Journal of Materials Processing Technology 153–154 (2004) 60–66

Incremental forming of solid cylindrical components using flow forming principles C.C. Wong∗ , T.A. Dean, J. Lin Mechanical and Manufacturing Engineering, School of Engineering, University of Birmingham, Edgbaston, Birmingham B15 2TT, UK

Abstract The flow forming process has been used to produce a range of engineering components, with reduced forming loads and enhanced mechanical and surface quality for a finished part, compared with press formed parts. However, studies on the flow forming of solid cylindrical components have not been documented. In this paper, test facilities were established in order to study the effects of roller geometry and feed rate on forming load and material flow when flow forming a simple solid cylindrical component with uniform diameter, using lead as the material. Experiments are carried out to study the effects of feed rates and roller geometry on material flow. A finite element (FE) model is proposed to simulate the process using ABAQUS implicit and explicit. The difficulties in simulating flow forming are outlined and the model using different formulations are compared for their efficiency in analysing the process. © 2004 Elsevier B.V. All rights reserved. Keywords: Flow forming; Roller geometry; Machine deflection; Finite element

1. Introduction In last two decades or so, flow forming has gradually matured as a metal forming process for the production of engineering components in small to medium batch quantities. Due to its inherent advantages such as flexibility, simple tooling and low forming loads, flow forming has enabled customers to optimise designs and reduce weight and cost, all of which are vital, especially in the automotive industries. The flow forming process, including shear forming, which grew out of spinning, is a process whereby the workpiece is rotated while the tool, which rotate about its own axis, may move axially or radially to the axis of rotation of workpiece, manipulating it to the final desired shape. It is most widely used to produce thin walled, high precision tubular products where the tubular workpiece is held onto the mandrel, the material being displaced axially by one or more rollers moving axially along a mandrel, as shown in Fig. 1. Over the past decade, several researchers [1–4] have conducted experimental and theoretical analysis in flow forming of tubes to evaluate power and load requirements as well as the effects of process variables such as feed rate, ∗ Corresponding author. Tel.: +44-121-4143542; fax: +44-121-4143958. E-mail address: [email protected] (C.C. Wong).

0924-0136/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2004.04.102

approach angle and percentage reduction on surface finish and forming load. In addition, finite element simulation has been performed by Xu et al. [5] and Xue et al. [6] to analyse the material displacement and accuracy in diameter, respectively. As the rapidly emerging trend nowadays is geared towards near net-shape and net-shape manufacturing, flow forming appears to be an attractive alternative to press formed parts especially with its lower forming load requiring considerable smaller equipment and more flexible tooling as compared to conventional presses. However, despite the flexibility and many advantages of flow forming process, investigation of the possibility of the flow forming of solid cylindrical component has not been documented. In this work, a preliminary investigation into flow forming of a simple solid cylindrical components with uniform diameter were conducted in order to gain an understanding as well as assessing the feasibility of this process when forming solid cylindrical components. These include establishing test facilities for conducting experiments. In addition, an FE model is proposed to analyse the process. In order to select the most cost effective and yet reliable FE analysis code, both the implicit and explicit code were reviewed and a small part of the flow forming process was simulated using both codes to compare the CPU cost of each method.

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Roller feed Roller

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Flow formed tube Fig. 1. Flow forming of tubular products.

2. Experimentation 2.1. Testing apparatus Fig. 3. Roller geometry.

In flow forming of tubes, the workpiece is held onto the mandrel as the forming roller moves along the workpiece axially to reduce the diameter. Therefore, in order to successfully conduct the experiment, an NC lathe machine was chosen as it has the same working principles as that of a flow forming machine. A roller tool was designed and built to accommodate the lathe tool post. In addition, electric strain gauges were mounted on the surface of the tool in order to measure separately the axial and radial forces. The strain gauges were calibrated with a conventional press and two RDP transducer indicators amplify the acquired voltage signals of the forming forces in the axial and radial directions. The final data was then processed with a computerised data-logging system. Fig. 2 shows the experimental set-up for the flow forming process. 2.2. Method Lead was chosen as the workpiece material and EN8 for the roller material. Since the cylindrical lead workpiece was cast from solid blocks, circularity of the workpiece was ensured by machining it on the same NC lathe used to carry out the experiments. The starting diameter for the workpiece was 48 mm. Four different roller geometries were used as shown in Fig. 3. The reduction was set at 2 mm, which should give a total diameter reduction of 4 mm. The rotational speed of

the workpiece was fixed at 250 rpm and different axial feed rates were used.

3. FE simulation procedure 3.1. Difficulties in FE modelling and simulation The flow forming process by nature, like other incremental forming processes, is very difficult to model due to the following factors: (i) As it involves only localised deformation, only a small portion of the workpiece is in contact with the roller at any given time and due to the cyclic character in the application of forces, only a small surface of the workpiece comes repeatedly into contact with the roller. (ii) Rotating the workpiece in an FE analysis tends to result in volume change due to repeated projection of nodes along the tangential velocities [7] and also increases computational time. (ii) Only a 3D model can be adopted and fine mesh discretisation is necessary in order to allow continuity of contact as nodal forces transfer from one element to the next. Thus modelling of incremental forming processes is inherently very time consuming and involves large computational resources.

Fig. 2. Set-up for flow forming experiments on an NC lathe.

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Thus, considering the above factors, suitable FE methods to analyse the flow forming process is necessary. Normally, the static implicit FE code is adopted to analyse metal forming processes. However in recent years, the dynamic explicit FE code, which is normally used to solve high-speed dynamic events, has become increasingly prevalent in the solving of manufacturing processes, especially sheet metal forming, because of the numerical robustness and computational efficiency in the case of highly non-linear and large-scale applications.

on the use of the diagonal mass matrix, which can reduce computational time significantly when it comes to large 3D models. The major disadvantage of the explicit code is that it is conditionally stable and the time step is subjected to a limitation. Therefore, in order to reduce the number of increments when the natural time is quite large, e.g. flow forming process, one can reduce the number of increments by either artificially increasing the material density or the loading speed. However, such an attempt may results in an increase in the inertial effects, which consequently affects the accuracy of the solution.

3.2. Implicit and explicit solution procedure Generally, there are two types of FE code available for metal forming simulations: implicit and dynamic codes. The implicit method solves for static equilibrium using the following form: Ku = P − I where K is the tangent stiffness matrix, u is the displacement increment, P is the static external load vector and I is the internal force vector. In non-linear problems like metal forming processes, iterations are necessary to achieved equilibrium. These iterations include the formation and solution of the linear system of equations and will continue to iterate until contact, force, displacement corrections, etc. are within the prescribed tolerances. However, with the increase in model size, especially 3D models where the process is highly discontinuous, the analysis is required to solve a large number of system equations, requiring many more iterations, resulting in higher computational time, disk space and memory. The explicit method system of equations is in the following form: M u¨ + Du˙ = P − I where M and D are the mass and damping matrices, u the nodal displacement, P is the external load vector and I is the internal load vector. One of the significant features in the explicit method is the lack of the tangent stiffness matrix, which is required with implicit method. Instead, it is based

3.3. Proposed FE model The initial meshes and model set-up are shown in Fig. 4. The workpiece was considered as an elastic–plastic model and the roller was modelled as a rigid surface. The workpiece was fixed and the roller was chosen to rotate around the axis of the workpiece at the same rotational speed as that of the rotating workpiece in the actual process. By adopting this method, not only can volume be controlled, but also a significant reduction in computational time can be achieved. The friction between the roller and the workpiece interface was assumed to be quite low so a frictionless condition was prescribed at the contact interface. The model was discretised with about 20 000 brick elements. For the explicit analysis, since using the natural time period of the flow forming process will result in even longer computational time than the implicit code, the density of the material is increased by a factor of 10 000 and 1000 times in order to speed up the analysis. In order to make sure that the explicit analysis produces essentially a quasi-static response, the ratio of the kinetic energy to the internal energy is used to measure the dynamic effects. In forming analysis, most of the internal energy is due to plastic deformation. Since the roller is a rigid surface with no mass, the workpiece is the only body with mass and the kinetic energy is solely due to the motion of the workpiece. Typically, the kinetic energy should not exceed 5–10% of the internal energy to indicate an acceptable quasi-static analysis. In

Fig. 4. Proposed FE model.

C.C. Wong et al. / Journal of Materials Processing Technology 153–154 (2004) 60–66

this study, apart from evaluating the energies to ensure that the density scaling factors were appropriate, forming loads obtained from the explicit analysis were compared to that obtained from the implicit analysis.

4. Results and discussions 4.1. FE results In order to achieve a qualitative assessment for comparison, the analysis was run for only 1 s as simulating the whole flow forming process will required very long CPU time. Fig. 5 shows the results of the kinetic, internal energies and CPU time for the explicit analysis. From the plots, it can be seen that both the density-scaling factors shown results of kinetic energy that is only about 1% of the internal energy, which confirms that even the highest factor yielded an essentially quasi-static response. In addition, the axial

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and radial forming forces were compared to the static analysis, as shown in Fig. 6, and are in good agreement. For all three cases, fluctuation of forming forces can be seen, the highest for the explicit analysis with a density scaling factor of 10 000. The reason is that for the highest density scaling factor, kinetic energy is considerably larger than that with a factor of 1000 and the static implicit case, where the kinetic energy is essentially zero. The fact that the kinetic energy is slightly fluctuating after 0.5 s may suggest slightly higher plasticity as compared to the other two cases [9]. Moreover, this fluctuation of kinetic energy may be the cause of the decrease of radial force after 0.6 s. The fluctuation of forces for all three cases may also be due to the nature of localised deformation where the elements were repeatedly contacting and separating as the roller feeds outwards over the edges of elements [8]. Scaling the density by a factor of 10 000 using explicit analysis produce results with the shortest CPU time (10 h) and the implicit analysis took the longest (96 h). Although, the comparison

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Fig. 7. Deformed shape of predicted by explicit analysis (factor = 10 000) and that produced from experiment.

results was only for the initial 1 s, with cost-effectiveness in mind, the highest density scaling factor was chosen for the analysis in this preliminary study. 4.2. Experimental results

On the other hand, roller 4 that has an approach angle of 30◦ and a radiused edge caused material flow predominantly in the axial direction causing a bulge just in front of the roller. This bulge gradually increased with the axial feeding of the roller.

4.2.1. Deformed shape Fig. 7 shows the results predicted from explicit analysis (factor = 10 000) for roller 1 and that produced from experiment using roller 1 and 4 at a feed rate of 0.24 mm/rev. During the initial forming stage, some of the material actually flowed in the opposite direction to the axial feed of the roller resulting in the formation of a crater at the free end of the workpiece. As the roller moved further axially, material is displaced predominantly in the radial direction producing a flange, ultimately resulting in edge splitting due to excessive circumferential tensile stress. The shape predicted by FE generally agreed with the experimental results except the fact that the flange wrinkled instead of being straight. Also since no failure criteria were incorporated into the FE analysis, edge splitting was not predicted. Using a roller with the same flat surface, i.e. rollers 2 and 3, but with a larger diameter also produce the same phenomenon.

4.2.2. Forming forces and diameter profile Fig. 8 shows the diameter profile obtained at different feed rates using rollers 2–4. For roller 2 at a feed rate of 0.24 mm/rev, reduction only occurs until about 20 mm. Even at the initial 20 mm, reduction seems to be deviating away from the ideal reduction, suggesting severe tool deflection. The problem encountered with roller 2 was partly dealt with, using roller 3 with a smaller width. Reduction achieved at 0.24 and 0.12 mm/rev was more although actual reduction was still nowhere near the nominal reduction, as can be seen from Fig. 8a, and similar to roller 2, reduction achieved was decreasing as roller displacement increased. However, the slowest reduction at 0.06 mm/rev tends not only to achieve more reduction but also achieves an almost constant diameter after 20 mm displacement. The reason for the non-uniform reduction for feed rate at 0.24 and 0.12 mm/rev may be due

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Fig. 8. Radius profile for (a) rollers 2 and 3 and (b) roller 4.

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C.C. Wong et al. / Journal of Materials Processing Technology 153–154 (2004) 60–66

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Fig. 9. Experimental axial and radial forces using roller 3.

to the fact that at a higher feed rate, more material tends to escape underneath the roller, flowing in the opposite direction to the roller axial displacement. Due to the higher reduction achieved with slower feed rate, more material was displaced forward in front of the roller, resulting in a more rigid flange with thicker width. In addition, it can be seen from Fig. 9 that the axial forces recorded were higher with reducing feed rate because more material was displaced resulting in higher real reduction. For roller 4, axial force at different feed rates, shown in Fig. 10, can be seen to increase because of the gradual material pile-up in front of the roller. Comparing with roller 3 at the same feed rate of 0.06 mm/rev, this roller seems to achieve a lower diameter reduction, as can be seen from Fig. 8b, although it has a smaller radial contact. Similar to

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roller 3, the forces recorded for roller 4 increases with slower feed rate because real reduction was higher. However, only a slight increase in diameter reduction was achieved for the slower feed rate. The forming forces obtained from the FE analysis in Fig. 6, at the initial 1 mm displacement appears to be higher than the ones obtained from the experiment. However, due to the fact that nominal reduction was not achieved, comparison cannot be conclusive.

5. Conclusions 1. With regards to the process itself, the static implicit code seems to be the ideal choice for simulating the flow forming process. However, due to the nature of the flow forming processes, using the implicit code will invariably lead to extremely high computational cost and furthermore convergence of solution are not guaranteed. Explicit code appears to be the better alternative but extreme care must be taken to ensure that the explicit analysis produce an essentially quasi-static response. 2. Results from the explicit analysis with the both density-scaling factors (10 000 and 1000) showed that kinetic energy is less than 1% of the internal energy. In addition, the forming forces for both cases are in good agreement with the implicit analysis. Although the deformed using the highest scaling factor was fairly reasonable compared to the experiment, more comparative analysis and verification needs to be carried out.

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3. The roller with an approach angle (roller 4) resulted in material flowing predominantly in the axial direction that causing a build-up in front of the roller, whereas rollers with flat approach surfaces normal to the axis resulted in material flow predominantly in the radial direction causing a flange of increasing diameter eventually resulting in edge splitting. 4. The axial force recorded was higher with reducing feed rate because of higher real reduction achieved. In addition, smaller feed rate produced more constant diameter reduction but machine and tool deflection needs to be compensated in order to achieve a higher accuracy in diameter reduction. Comparison of forming forces between FE and experiment cannot be conclusive because nominal reduction was not achieved during the experiment. 5. This study shows the possibility of utilising flow forming not only to reduce the diameter of solid cylindrical components but also produce flange-type components. However, more studies need to be conducted in order to understand the underlying science of this process.

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