Comparison of spinning trajectory designing methods for products with noncircular cross-section

Rotational shaping processes are divided into three main categories: metal spinning, shear forming, and flow forming [1]. The main principle of rotational processes is to make the blank rotate around the spindle axis. Then, by using the designed tools, a stress between yield point and tensile strength is applied to the workpiece [2]. The implementation and development of computerized numerical control (CNC) and stepper motors were key factors in developing an innovative method for spinning noncircular shapes.

The feature that distinguishes noncircular spinning from conventional spinning is the geometric pattern. The cross-sectional geometry of a circle has an infinite number of symmetry axes. This geometric feature allows for the conventional spinning process to be carried out by using the principle of maintaining a constant volume and uniform strain distribution on the cross-section of the blank during the process.

In the case of conventional rotational forming, distribution of strains and stresses is not affected by the position of a forming roller, because the distance between roller and mandrel is always the same. Uniform distribution of stresses by a spin roller in conventional rotational shaping is presented on the left side of Figure 1.

Fig. 1

The rotational forming of products with a non-circular cross-section, due to the lack or a limited number symmetry axes, takes place under condition of inhomogeneously arising stresses in the material during the process. The size of the stress heterogeneity depends on the degree of axial asymmetry of the mandrel, as shown on the right side of Figure 1, where different values of stresses will arise depending on the point of contact of the spinning roller with the material. It will cause inhomogeneous strains as: ɛ₁ ≠ ɛ₂ ≠ ɛ₃ ≠ ɛ₄.

The presented mandrel is a square in cross-section, so it has only four axes of symmetry. This means that the material distribution resulting from its flow due to stresses exceeding R_e in the blank is not the same in all directions. It depends on the degree of asymmetry of the mandrel's geometry. The material flow will occur in privileged directions, which will depend on several conditions, such as the geometry of the blank, type of material, and strain hardening.

An additional factor that hinders the analyses of the material flow in the semi-finished product during the axially asymmetric rotational forming is the complexity of the kinematics of the spinning process, in which two opposing phenomena occur simultaneously: material compression in the circumferential direction and stretching in the radial direction.

Publication [3] from 1975 indicates that experiments involving spinning of axially asymmetrical products were conducted as early as during the 1970s. The probable reason why this technology was not propagated was the lack of technical capabilities, particularly with regard to CNC control and the drives applied. The spinning process shown in Figure 2 is performed using a mandrel with a square cross-section and a spinning tool being a negative of the mandrel.

Fig. 2

Analysis of the literature indicates that, for the purposes of developing asymmetrical spinning, work on designing a spinning lathe adapted to this process was started. The condition for performing effective spinning was to ensure that the roll would not collide with the mandrel, which had a non-circular cross-section. Arai [4] described the design of an innovative spinning lathe designed for spinning of axially asymmetrical products with the application of control via the force generated on the spinning roll. Studies indicate that a substantial step change in the pressing force of the forming roll occurs at the site where the mandrel's geometry changes from curvilinear to planar. A different concept of a spinning lathe for axially asymmetrical products can be found in Ref. [5], where the process kinematics involve synchronization of the moving spinning roll in one direction (left–right) and of the moving template in the direction perpendicular to the roll's direction (front–back). During tests, the influence of asymmetry of the spun shape's geometry on the distribution of stresses during the process was noted. It was determined that radial stresses change with the angle of rotation of the elliptical mandrel. Stresses grow as the mandrel's angle of rotation changes and the spinning tool approaches the longer axis of the ellipse, and decreases when the spinning tool approaches the shorter axis of the ellipse. A similar phenomenon was observed in studies of spinning an axially asymmetrical cone in die-less spinning. Jia et al. [6] noted a significant effect of the half-cone angle. Forming a smaller half-cone angle resulted in a more uniform material hardening. According to the authors, this was due to the fact that when forming a smaller half-cone angle, the pressure exerted by the roller increased. While forming the largest half-cone angle leads to the largest differences in material hardening of up to 15%. A similar composition and its results were published in their next article [7]. Instead of the surface hardening effect, the article this time analyzed the phenomenon of nonuniform deformation during spinning of axially unsymmetrical products. The authors conducted FEM studies which they compared with real trials. Research has shown that the greatest deformation of the material takes place in the 0° area, and the smallest takes place in the 180° area. This confirms the strong correlation between the asymmetry of the product and the deformation of the material.

Another approach to spinning lathe design was presented in article [8], where a constant pressing force was applied with a constant gap. It was noted that the system of spinning control via spinning roll pressing force has flaws when applied to axially asymmetrical spinning, due to differing forming conditions in the case of convex and concave mandrel geometries. It was indicated that applying the axially asymmetrical spinning method with a constant distance between the mandrel and spinning roll not only eliminates problems arising from differing forming conditions between convex and concave geometries but also enables the researcher to adjust the spinning trajectory. Sugita and Arai [9] used a spinning lathe equipped with a force meter mounted on the spinning tool, which was used to generate the trajectory of the spinning tool via force measurement. During spinning of an axially symmetrical shape, 5% wall thinning occurred, but during spinning of an axially asymmetrical shape with a square cross-section, the thinning amounted to as much as 50% of the initial thickness, with a measured tendency of material accumulation in the right angles (corners) of the detail.

Advances in technology and CNC control afforded researchers with the appropriate laboratory equipment with the opportunity to study axially asymmetrical spinning, and they began to focus more on studying the spinning trajectory in axially asymmetrical products, with article [10] being evidence of this. Focus was placed on the theory concerning designing of the spinning roll's trajectory in the process of spinning without a mandrel in easily deformable 1050-grade aluminum, with a thickness of 2 mm. The applied algorithm for designing and generating the spinning tool's trajectory was made using the MATLAB® software. Drawpieces with wall thinning of ≈ 15% were produced, where the greatest scatter in thickness measurement was noted in the corners of the drawpiece. Also, in 2020, Arai and Gondo [11] described the results of their research in the scope of designing spinning trajectories.

Designing product trajectories for axially unsymmetrical products is an important stage in production. Loukaides and Russo [12], in their analysis of the design of trajectories for metal spinning, indicated that most studies and recommendations concern shear forming, and not metal spinning. This is due to the very difficult nature of metal spinning. Numerous studies on trajectory design for axially symmetric products indicate that the material should be formed in multiple steps to prevent folding. The authors’ analysis also shows that the spinning trajectory will largely depend on the feed per revolution parameter. In the current state of knowledge, it should be assumed that the recommendations for the design of the spinning trajectory for the spinning of axially symmetrical products can only partially be applied to axially unsymmetrical products. Many works indicate that designing a toolpath for metal spinning can be supported by FEM analyses, especially in such cases as multipass forming [13], rotational shaping of stainless steel [14], and rotational shaping without using a die [15]. Although the acquired results can be very accurate, conducting FEM analyses is time-consuming.

Due to the low popularity and research nature of axially asymmetric spinning, no extensive knowledge base about the theoretical foundations of the process was established. Therefore, for the analysis of shaping conditions, reference was made to the related literature describing rotational shaping in terms of the analysis of the kinematics of the process. The analyzed literature [16] distinguishes two methods of defining stresses and strains in rotational shaping: analytical and numerical. Analytical methods are based on four basic models: (1) deformation energy method [17], (2) the upper bound method [18], (3) prediction of failure by wrinkling [19], and (4) predictions of strains in spinning [20]. Analytical methods for describing the forces in rotational shaping have been described and developed at least since the 1950s, while numerical methods were developed only in the early 1990s [21]. Due to the limitations of the computing power of modern computer units, the first models were very simplistic. The vast differences in the FEM analyses result from the division into implicit [22] and explicit methods [23]. The analyzed literature in the aspect of predicting the stress distribution in the spinning of axially symmetrical products shows that hoop stresses are the smallest and have the lowest impact on the shaped detail. The carried out tests of axially unsymmetrical spinning indicate that hoop stresses have a much greater influence on the process than in axially symmetrical spinning. However, this issue requires further research.

Analysis of the literature indicates that many authors, in their works [4, 5, 7, 8, 24], refer to the rotary forming process of axially asymmetrical products as spinning, while the trajectory and character of the process applied by them have more features similar to shear forming than metal spinning. A characteristic feature of shear forming is that it occurs in one motion, which forms the side wall to the planned thickness arising from the formula. Shear forming introduces only tensile stress. The spinning process takes place in several movements and may consist of movements introducing both compressive and tensile stresses or solely tensile stresses. In effect, the obtained thickness of the drawpiece will be a resultant of the stresses introduced, while the side wall thickness reduction is an unintended effect. A comparison is shown in Figure 3. It should be emphasized that this linguistic error does not arise from the bad faith of the authors, but from the fact that spinning of products with a noncircular shape has been the subject of research for a relatively short time. Designing a trajectory that introduces only tensile stresses is easier to do as it does not require such expansive CNC code.

Fig. 3

The goal of the tests presented in this article is to develop innovative methods of designing spinning trajectories for noncircular products and to determine the influence of trajectory on the height of the drawpiece obtained, with particular differentiation between spinning and shear forming of a product with a noncircular cross-section. Two mandrels were used for tests with the purpose of designing a spinning trajectory: (1) in the shape of an ellipse with dimensions of 60 mm × 80 mm and (2) in the shape of a square with dimensions of 80 mm × 80 mm. CAD models are presented in Figures 4 and 5. Designed trajectories were tested by metal spinning blanks made from aluminum Al 1050 A. The strength of the material was measured at three angles to the rolling directions of aluminum sheet. The properties are presented in Table 1.

Fig. 4

Fig. 5

The first step in designing a spinning trajectory using CNC code controlling the position of the spinning tool is to acquire a set of points coordinating the position of the spinning tool according to the mandrel's outline as a function of the mandrel's angle of rotation as: f (α) = x_i, z_i, where α is the angle of the mandrel's rotation in degrees, and x_i and z_i are the positions of the spinning tool. During tests, three methods were used for this purpose: (1) using a spreadsheet and mathematical formulas, (2) using 2D CAD software, and (3) using 3D CAD software and an algorithm generating the trajectory. Conducted tests indicated that all the three methods make it possible to generate the mandrel's outline as a function of the mandrel's angle of rotation around the spindle's axis. The number of control commands depends directly on the complexity of the mandrel's shape and the required resolution. It should be accepted that the minimum number of points required for generating the trajectory of a single movement is 1 g-code command per 1° of the mandrel's rotation. To perform a full 360° rotation, 360 commands synchronizing the roll's position with that of the mandrel are required.

Method 1, utilizing mathematical formulas and spreadsheets to describe the mandrel's outline, is the most difficult and time-consuming method due to the fact that the trajectory must consist of an appropriately high resolution of manually generated coordinating points. During spinning of axially asymmetrical products, it is necessary to perform multiple mandrel revolutions synchronized with the advance rate of the spinning roll on the x and z axes. The complexity of the spinning trajectory's CNC code increases as per the product: 360 commands × number of revolutions. This product means that a single movement of the spinning tool requires ≈ 75,000 g-code lines to obtain a draw-piece with a noncircular cross-section in the shape of an ellipse on mandrel no. 1 from Figure 4. Over 300 000 g-code lines were used in total to obtain the drawpiece. Due to its complexity, this method requires the creation of five separate trajectories of the spinning tool's motion, in which the spinning tool performs spinning movements that stretch the material and position the piece's side wall at angles of 18°, 30°, 45°, 68°, and 90°, according to Figure 6. The goal of these tests was to produce a drawpiece with a height of 30 mm.

Fig. 6

The second method of designing the spinning trajectory was to apply the 2D CAD software. This method requires the application of a model in which the cross-section of a noncircular mandrel, having precisely one degree of freedom, namely, its rotation around its axis, which, under real-life conditions, will be co-linear with the axis of the spinning lathe's spindle. The mandrel's outline must be found in a relation of continuous contact with the model of the spinning roll. Next, the x_i and z_i position parameters must be noted manually depending on the mandrel's angle of rotation. This is a time-consuming method, but in contrast to the method based on the use of spreadsheets, it is more flexible and easier to apply to cross-sections with more geometrically complex shapes. The method was applied to produce the piece on mandrel no. 2, with a square cross-section according to the model in Figure 5. Over 168 000 g-code lines were used in total to obtain the drawpiece. Due to its complexity, this method requires the creation of five separate trajectories of the spinning tool's motion, in which the spinning tool performs spinning movements that stretch the material and position the piece's side wall at angles of 25°, 30°, 45°, 68°, and 90° according to Figure 7. The goal of these tests was to produce a drawpiece with a height of 30 mm.

Fig. 7

Method 3, utilizing 3D CAD software, is the most advanced method of obtaining the set of points describing the contour of points as a function of the mandrel's rotation. This method was used to design a spinning trajectory consisting of both movements stretching the material and upsetting the material. Introducing such a solution will make it possible to obtain drawpieces of a greater height. Methods 1 and 2 made it possible to obtain drawpieces with a height of 30 mm, and the application of Method 3 made it possible to obtain drawpieces with a height >40 mm.

The application of the method utilizing the outline of 3D CAD mandrel models made it possible to increase the number of spinning movements from 5 to 17, while simultaneously reducing the spinning trajectory to ≈ 1,000 commands in g-code. An additional advantage of this method is that it allowed for programming of movements stretching the material (marked in Figure 7 in red) and also movements compressing the material (marked in Figure 7 in green). The movements marked in Figure 7 from 1 to 8 consist of stretching and upsetting movements, while the final movement, 9, is a movement pressing the material to the mandrel. The previous methods required the creation of separate programs for performing a single movement and took up hundreds of thousands of lines, while this method makes it possible to perform more movements of the spinning tool with a much lesser volume of CNC code.

Tests of spinning products with noncircular cross-sections were performed on a spinning lathe MWS-200, equipped with step motors and a spindle allowing for precise control of the mandrel's rotations. The control system of the MWS-200 synchronizes the position of the spinning roll, making it possible to avoid collision between the roll and the mandrel.

Tests were performed on two mandrels with the use of three methods of designing the spinning trajectory. The geometry of the produced drawpieces was tested using a micrometer for measurement of the thickness of the drawpiece walls. At least 10 drawpieces were made by each method. The thickness of the blanks was from 1.5 mm to 2.5 mm.

Mandrel no. 1 – ellipse, on which spinning was performed with the spinning trajectory generated by Method 1. The dimensions of the ellipse-shaped blank were 120 mm × 95 mm. The thickness of the ellipse drawpiece was measured at three sites: the semi-minor axis – point A and the semi-major axis – point C of the ellipse, and at the center between them – point B. Measurements were taken after every spinning operation at angles 18°, 30°, 45°, 68°, and 90° at a distance of 15 mm from the frontal area of the drawpiece.

Mandrel no. 2 – the square shown in Figure 5, on which spinning tests were performed using Methods 2 and 3. The scheme of wall thickness measurements consistent with Figure 8 was applied to the square drawpiece.

Fig. 8

Measurements were taken at two sites: measurement A – on the flat wall and measurement B – on the rounded corner of the drawpiece. The height at which measurements were taken was based on the diagram in Figure 8; side wall thickness measurement was performed at the following distances from the face of the drawpiece: 5 mm, 15 mm, and 30 mm. The dimensions of the square-shaped blank were: 140 mm × 140 mm for Methods 2 and 3.

Based on the performed thickness measurements of the side walls of the drawpieces obtained, the relative percentage reduction of wall thickness (PRT) following each spinning process was calculated. Thinning was calculated based on Eq. (1) as (1) PRT=(1−gg0)×100% PRT = \left( {1 - {g \over {{g_0}}}} \right) \times 100\%

The spun drawpieces were scanned on the ATOS COMPACT SCAN 5M mobile optical scanner. In the dedicated GOM INSPECT V8 Professional software, the scanned shapes of the drawpieces were compared with the CAD models and the deviation was shown in the form of a figure.

Conducted tests of designing and generating a spinning trajectory for axially asymmetrical products led to the following conclusions:

It is possible to spin simple, axially asymmetrical shapes using Method 1; however, this is a time-consuming and complicated process. This means that, in laboratory conditions of testing, it is very difficult to implement and can only be applied in the case of simple shapes whose geometry can easily be described with a single mathematical formula in a Cartesian coordinate system. Also, this method was not suitable to apply compressive moves.