TECHNICAL FIELD The present disclosure relates to a method of generating a toolpath for a spin forming process.

BACKGROUND Metal spinning is a metal forming process which has traditionally been used to produce hollow, axially symmetric (axisymmetric) items or articles from a metal blank. Figure 1 illustrates a traditional spin forming apparatus 1 . A workpiece 2, typically in the form of a metal blank, is secured to a mandrel 3 on a spinning lathe 4 and the workpiece 2 is gradually deformed into a desired shape by applying pressure, from a forming tool 6, onto an outer surface 8 of the workpiece 2, as it rotates. The workpiece 2 presses against the mandrel 3 as it deforms, such that one end of the mandrel 3 defines a base shape 10 of the article and longitudinal surfaces of the mandrel 3 define a length 12 of the article with an opening 14 at a free end. This process may, for example, be used to produce any of the axisymmetric articles shown in Figure 2 and may be completed in a single pass of the forming tool 6 over the workpiece 2 (shear spinning) or by multiple passes over the workpiece 2 (conventional spinning).

Metal spinning is advantageous in that there is minimal springback of the finished article and the initial tooling costs are relatively low. However, conventional spinning methods face challenges when producing re-entrant shapes, due to the need to remove the finished article from the underlying mandrel 3. As a result, the finished articles are generally axisymmetric with little complexity.

Further, a new mandrel 3 is required whenever the shape of the desired article changes. Accordingly, the costs associated with design variations are high and controlling the forming tool 6 requires technical expertise in order to avoid damaging the workpieces or the machinery.

The forming tool 6 may be controlled by manual inputs from an operator or by computer numeric control (CNC). When using CNC, the operator determines a suitable route (toolpath) for the forming tool 6 to follow and enters the route as a series of position adjustments that can be executed sequentially and repeated to allow some degree of automation. However, both control methods are inflexible and unaccommodating of design changes. Design changes require changes to the toolpath which may be extensive and time consuming. Traditional methods have also been unable to produce asymmetric articles and, as a result, the usefulness of metal spinning has been relatively limited compared to other metal forming methods.

More recently, metal spinning methods have been developed which are mandrel-free. WO 2012/042221 A1 describes a mandrel-free spinning apparatus 20 for spin forming both axisymmetric and non-axisymmetric articles. The mandrel-free spinning apparatus 20, illustrated in Figures 3 to 5, includes mobile support tools that support a workpiece 2 in key areas as the workpiece 2 rotates, replacing the functionality of the fully formed mandrel. Figure 3 illustrates the principle features of a mandrel-free spinning apparatus 20, wherein a metal workpiece 2 is secured to a spinning lathe 4 and the workpiece 2 can be gradually deformed into a desired shape by a forming tool 6 which acts on an inner 28 or an outer 30 surface of the workpiece 2 as it rotates. A first support tool 32, shown proximal to the lathe 4, contacts an opposing surface of the workpiece 2 and can be moved according to a predetermined toolpath as the workpiece 2 rotates to resist deformation of the workpiece 2 and define a bending location along a perimeter of the artefact's base.

As the process proceeds, the workpiece 2 may be deformed such that it includes a longitudinal length and eventually an inner or outer surface of the workpiece 2 may come into contact with a second support tool 34 and a third support tool 36 of the mandrel-free spinning apparatus 20. The second and third support tools 34, 36 may be positioned towards a distal end of the workpiece 2 and can be moved as the workpiece 2 rotates such that they resist deformation of the workpiece 2 and allow formation of the artefact's longitudinal shape. In some applications, the second and third support tools 34, 36 may be moved to mimic the motion of the forming tool 6 and further guide the workpiece's deformation.

Figure 4 illustrates an end view of the mandrel-free spinning apparatus 20 shown in Figure 3. In this embodiment the first, second and third support tools 32, 34, 36 are shown acting against an inner surface 28 of the workpiece 2 whilst the forming tool 6 acts against an outer surface 30 of the workpiece 2. Applying force to opposing surfaces of the workpiece 2, as described, creates bending moments that guide the deformation into the desired shape of the article.

Figure 5 shows a practical embodiment of the mandrel-free spinning apparatus 20, as depicted in WO 2012/042221 A1 and as illustrated conceptually in previous figures 3 and 4. The positions of the forming tool 6 and of the first, second and third support tools 32, 34, 36 are adjustable relative to the workpiece 2 by relevant actuators 38 that remove the need for a fully formed mandrel. The mandrel-free spinning apparatus 20 possess sufficient mobility to deform a metal workpiece 2 into a variety of both axisymmetric and non-axisymmetric shapes, such as those shown in Figure 6. The absence of a fully formed mandrel also enables the production of re-entrant shapes, as illustrated by the profile in Figure 6(a). In addition, the spinning process can be completed in a single pass of the forming tool 6 over the workpiece 2 (shear spinning) or in multiple passes over the workpiece 2 (conventional spinning) as practised on traditional spin forming machines.

However, despite its potential advantages the technology is immature and non- axisymmetric articles have not previously been produced using the mandrel-free spinning apparatus 20. Further, control methods have relied on toolpaths defined by manual inputs that correspond to specific article shapes. As a result, the metal forming process is currently inefficient, expensive and unsuitable for commercial exploitation.

The present invention has been developed to attend to at least some of the above- mentioned problems.

SUMMARY OF THE INVENTION

According to an aspect of the present invention there is provided a method of controlling a spin forming machine to produce an article from a workpiece, the article having a target shape, the spin forming machine comprising a rotatable mounting point for the workpiece and a forming tool capable of deforming the workpiece as it rotates, the method including: receiving a computerised representation of the target shape; determining a toolpath for the forming tool in dependence on the computerised representation, wherein the toolpath includes; one or more passes, wherein each pass relates to a route of the forming tool between a start point and an end point, each pass achieving an iterative deformation of the workpiece from a first shape towards the target shape; and whilst rotating the workpiece with respect to the forming tool, controlling the forming tool according to the toolpath to deform the workpiece into a second shape that substantially matches the target shape.

Advantageously, determining a toolpath for the forming tool in dependence on the computerised representation of the target shape allows the toolpath to be reconfigurable as the target shape changes. Consequently, the toolpath can be efficiently redesigned to accommodate changes to the design of the article by updating the computerised representation. The method also facilitates operation of the spin forming machine by a relatively unskilled operator since the toolpaths are generated based on the computerised representation.

Reference to the term 'target shape' is intended to mean the three dimensional shape of a desired article which comprises all of the article's visible surfaces. Accordingly by 'second shape', it is intended to mean the product of the workpiece's deformation from the first shape into a shape that substantially reproduces the three dimensional shape of the desired article, allowing for manufacturing tolerances. In this manner, the dimensions, curvatures and volumes of the second shape should match the dimensions, curvatures and volumes of the target shape, within allowable tolerances.

Optionally, the target shape is non-axisymmetric and/or asymmetric. Controlling the forming tool according to the toolpath enables the production of non-axisymmetric and/or asymmetric articles. In this manner, the method widens the capabilities of the spin forming process. In an embodiment, the route of each pass of the forming tool comprises a plurality of command positions, each command position is defined by a first distance along a first axis aligned with an axis of rotation of the workpiece, and a second distance along a second axis perpendicular to the first axis, wherein each command position is based on an angle of rotation of the workpiece and on a point on the target shape that corresponds to the angle of rotation of the workpiece.

For example, the first axis may take the form of a longitudinal axis of the spin forming machine and the second axis may take the form of a radial axis of the spin forming machine. In this manner, the rotation of the workpiece can be discretized into intervals of rotation and each toolpath can be defined by positions of, for example, radial and longitudinal distance for each interval of rotation. These positions may, for example, correspond to sequential points on the surfaces of the target shape. Thus, the forming tool can be moved dynamically, as the workpiece rotates, to deform the workpiece towards the target shape.

Optionally, the method further includes inputting a user input, wherein the toolpath for the forming tool is based on the computerised representation of the target shape and the user input. Advantageously, the user input allows recalibration of the toolpath. This may facilitate iterative improvements of the toolpath and provide the flexibility required to produce more complex target shapes.

Additionally, the user input may, for example, configure the toolpath to include a plurality of passes. At least one pass may, for example, be a finishing pass wherein the route of the forming tool includes the deformation of the workpiece into the second shape.

Reference to the term 'finishing pass' is intended to mean a pass of the forming tool relative to the workpiece which deforms at least a portion of the workpiece into the second shape during at least a section of the pass. Alternatively, the forming tool may, for example, deform the workpiece into the second shape during substantially the entirety of the finishing pass. For example, the command positions of the finishing pass may correspond to a sequence of points on the surfaces of the target shape and the sequence of points may be ordered in accordance with the angle of rotation of the workpiece to continually deform the workpiece towards the target shape as the workpiece rotates. In an embodiment, the user input may, for example, configure the toolpath such that the plurality of passes include one or more moulding passes, wherein the route of the forming tool during each moulding pass includes a predetermined deviation from the route of the forming tool during the finishing pass.

Reference to the term 'moulding pass' is intended to mean a pass of the forming tool relative to the workpiece that includes a deviation from the target shape which reduces the forces on the forming tool. In this manner, the deviation may, for example, position the forming tool further towards an edge of the workpiece than would be required to deform the workpiece into the target shape. The deviation may affect at least a portion of the moulding pass or substantially the entirety of the moulding pass. For example, the command positions of the moulding pass may correspond to a sequence of points that are offset from the surfaces of the target shape and the sequence of points may be ordered in accordance with the angle of rotation of the workpiece.

Optionally, the deviation is predetermined on the basis of the user input. Advantageously, this allows the user to adjust the command positions of the forming tool relative to the positions defined by the surfaces of the target shape. For example, the user input may adjust the command positions to allow for a series of moulding passes that gradually deform the workpiece towards the target shape.

Optionally, the deviation comprises a difference between a first location of the forming tool on the second axis during the moulding pass and a corresponding second location of the forming tool on the second axis during the finishing pass, wherein the first and second locations of the forming tool are considered at a matching location along the first axis. For example, when the forming tool is at a given longitudinal distance, the radial distance may, for example, be larger during the moulding pass than during the finishing pass. Additionally, the radial distance may be greater than a point on the target shape that corresponds to the angle of rotation of the workpiece. Advantageously, the tool forces during the moulding pass may, for example, be less than the tool forces during either the finishing pass or a pass of a shear spinning process.

Optionally, the deviation varies with distance, from the start point, along the first axis. In this manner, the resistance to deformation changes as the forming tool moves from the start point to the end point of the route. For example, the radial distance of the forming tool may increase with the longitudinal distance. Optionally, the deviation is defined by a parametric equation as a function of the distance, from the start point, along the first axis and the user input is configured to define parameters of the parametric equation. Advantageously, parametric equations can be used to plot the trajectory of the forming tool in a convenient manner and generate a relatively controlled forming tool route.

For each pass, the second distance of each command position of the forming tool may, for example, be given by: r _t (X) = r _p {X) + a. X ⁿ where r _t (X) is the distance of the command position along the second axis, X is the distance of the command position along the first axis, r _p (X) is a point on the target shape corresponding to the angle of rotation of the workpiece and the distance of the command position along the first axis, a. X ⁿ is the deviation, a is defined based on the user input and acts as a scalar coefficient and n is also defined based on the user input and n acts as an exponent. Advantageously, the equation adds the deviation term to the position of the forming tool dictated by the target shape. Therefore, in addition to being part agnostic, this method ensures that the forming tool does not collide with any other support tools.

Optionally, the plurality of passes are sequential and each pass deforms the workpiece closer towards the target shape than the preceding pass. Advantageously, this allows for gradual deformation of the workpiece that reduces spin forming effects such as cracking and wrinkling.

The toolpath may, for example, include returning the forming tool to the start point between passes. Optionally, the forming tool does not contact the workpiece during the return to the start point.

The end point of each pass may, for example, be adjustable by the user input.

Optionally, the start point of each pass is adjustable by the user input. In an embodiment, the thickness of the workpiece may, for example, be substantially unchanged by the iterative deformation of the workpiece from the first shape to the second shape. In this manner, the method is able to replicate conventional spinning techniques. Optionally, determining the toolpath for the forming tool is in dependence on at least one of a rate of rotation of the workpiece and a feed rate.

Additionally, the rate of rotation of the workpiece and/or the feed rate may, for example, be adjustable by the user input. This may, for example, allow greater control over the process and affect the quality of the surface finish of the deformed workpiece.

Optionally, the workpiece is metallic.

Optionally, the target shape may include a base portion at a first end of the target shape and a wall portion extending from the base portion. The base portion may, for example, be a central flat region used to mount the workpiece to the spin forming machine.

The wall portion may, for example, include a re-entrant surface. Optionally, the start point of at least one pass is located at the first end.

In an embodiment, the spin forming machine may, for example, comprise a mandrel-free spinning apparatus further including; a first support tool capable of supporting the workpiece such that the base portion of the target shape can be formed; wherein, in use, the spin forming machine is configured to rotate the workpiece with respect to the forming tool and the first support tool. Advantageously, the mandrel-free spinning apparatus is configured to produce asymmetric and non-axisymmetric shapes and replaces the need for a physical mandrel. Additionally, the method may, for example, further include; determining a second toolpath for the first support tool of the spin forming machine in dependence on the computerised representation, wherein the second toolpath relates to a route of the first support tool corresponding to the base portion of the target shape.

In this manner, the second toolpath is reconfigurable as the target shape changes. Consequently, the second toolpath can be efficiently redesigned to accommodate changes to the design of the article by updating the computerised representation. The method also facilitates operation of the spin forming machine by a relatively unskilled operator since the second toolpath is generated based on the computerised representation of the target shape.

Optionally, the second toolpath moves the first support tool in planar alignment with the forming tool.

The route of the first support tool may, for example, be arranged to resist deformation of the workpiece, in use, to form the base portion of the target shape. In this manner, the second toolpath may, for example, move the first support tool to define the shape of the base of the article.

In an embodiment, the spin forming machine may, for example, further include; a second support tool and a third support tool capable of supporting the workpiece such that the wall portion of the target shape can be formed as the workpiece is iteratively deformed from the first shape towards the second shape; wherein, in use, the spin forming machine is configured to rotate the workpiece with respect to the forming tool, the first support tool, the second support tool and the third support tool. Advantageously, supporting the workpiece in this manner may mitigate warping and wrinkling effects during the deformation.

Optionally, the method further includes; determining a third toolpath for the second and third support tools of the spin forming machine in dependence on the computerised representation, wherein the third toolpath substantially matches the first toolpath for the forming tool, further including suitable offsets to engage the second and third support tools with an opposing surface of the workpiece. Advantageously, the workpiece is supported on opposing surfaces during deformation, reducing stress concentrations. The computerised representation may, for example, include one or more of: a plurality of points corresponding to a surface of the target shape; a plurality of dimensions of the target shape; a two-dimensional angular plane of the target shape; a series of two-dimensional angular planes of the target shape; a three-dimensional model of the target shape; an equation defining a surface of the target shape. Within the scope of this application it is expressly intended that the various aspects, embodiments, examples and alternatives set out in the preceding paragraphs, in the claims and/or in the following description and drawings, and in particular the individual features thereof, may be taken independently or in any combination. That is, all embodiments and/or features of any embodiment can be combined in any way and/or combination, unless such features are incompatible. The applicant reserves the right to change any originally filed claim or file any new claim accordingly, including the right to amend any originally filed claim to depend from and/or incorporate any feature of any other claim although not originally claimed in that manner.

BRIEF DESCRIPTION OF THE DRAWINGS

One or more embodiments of the invention will now be described, by way of example only, with reference to the accompanying drawings, in which:

Figures 1 illustrates the operation of a traditional spin forming apparatus to form an article;

Figures 2 illustrates a range of articles, shown form a side view, that may be formed by the traditional spin forming apparatus, shown in Figure 1 ;

Figure 3 illustrates the operation of a mandrel-free spinning apparatus to form an article; Figure 4 illustrates an end view of the mandrel free spinning apparatus, shown in Figure 3;

Figure 5 illustrates a practical arrangement of the mandrel free spinning apparatus, shown in Figure 3;

Figures 6(a) to 6(c) illustrate a range of non-axisymmetric articles that may be formed by the mandrel free spinning apparatus, shown in Figure 5;

Figure 7 illustrates a system of devices that may be used to operate a spin forming machine in accordance with the method of the invention; Figures 8(a) and 8(b) illustrate an example of an article which may be formed in accordance with the method of the invention, the article taking the form of a square cup;

Figure 9 illustrates a cross-sectional view through an angular plane of the square cup shown in Figure 8;

Figure 10 shows a view of the square cup, shown in Figure 8, from a second end of the square cup; Figure 1 1 shows a plan view of the mandrel-free spinning apparatus, shown in Figure 5;

Figures 12(a) and 12(b) illustrate an initial operation of the spin forming process and a final operation of the spin forming process respectively. Figure 13(a) illustrates the motion of a first support tool of the mandrel-free spinning apparatus, shown in Figure 5, as it forms a base shape of the square cup, shown in Figure 8, and Figure 13(b) graphically illustrates the motion of the first support tool along a radial axis; Figure 14 illustrates the motion of a forming tool of the mandrel-free spinning apparatus, shown in Figure 5, as it forms the shape of the square cup shown in Figure 8;

Figure 15 illustrates an embodiment of the spin forming process from an initial design of the square cup, shown in Figure 8, to a spin formed reproduction of the square cup.

Figure 16 illustrates a computerised representation of the square cup, shown in Figure 8, that provides a target shape;

Figure 17 graphically illustrates a plurality of target shape points located within a first angular plane (solid line) and a plurality of target shape points located within a second angular plane (dashed line) of the target shape, shown in Figure 16;

Figure 18 illustrates the computerised representation of the square cup, shown in Figure 16, divided into twenty-eight angular planes; Figure 19 illustrates the motion of the first support tool as it forms the base shape of the square cup shown in Figure 8;

Figure 20 illustrates an embodiment of a first toolpath for the forming tool of the mandrel- free spinning apparatus, shown in Figure 5, which includes a plurality of moulding passes and a finishing pass.

DETAILED DESCRIPTION Embodiments of the present invention relate to a method of controlling a spin forming machine to produce an article from a workpiece 2. The workpiece may, for example, take the form of a blank sheet of ductile metal. The spin forming machine may take the form of a traditional spin forming apparatus 1 or of a mandrel-free spinning apparatus 20. In either case, the spin forming machine inevitably includes a rotatable mounting point, or lathe 4, for mounting and rotating a workpiece, as well as a forming tool 6 that is capable of deforming the workpiece 2 into the shape of the article as it passes relative to the workpiece 2. The control method requires a computerised representation of the article, which provides a target shape for determining a route of the forming tool 6, that route being known as a toolpath. The toolpath is determined based on the target shape, such that the toolpath can be efficiently redesigned, to accommodate article design changes, by updating the target shape.

During the spin forming process, the workpiece 2 rotates on the rotatable mounting point 4 and the forming tool 6 moves relative to the workpiece 2 in accordance with the predetermined toolpath. The forming tool moves along a first axis, aligned with an axis of rotation of the workpiece 2, and along a second axis, perpendicular to the first axis. In this manner, the forming tool 6 can deform the workpiece 2, as it rotates, into a shape that substantially matches the target shape. The toolpath may control the movement of the forming tool 6 along a plurality of passes relative to the workpiece 2, with each pass moving the forming tool 6 between a start point and an end point and achieving an iterative deformation toward the target shape.

For the sake of clarity, the 'plurality of passes' and the references to 'passes relative to the workpiece 2' are intended to mean that there is relative movement between the workpiece 2 and the forming tool 6 through position adjustments of the forming tool 6 and/or the lathe 4 and, during the relative movement, the forming tool 6 engages with a surface of the workpiece 2 and deforms the workpiece 2 towards the target shape.

Figure 7 provides an illustration of a system of devices 40 used to execute the spin forming method in accordance with the invention. The system of devices 40 includes a spin forming machine 1 , 20, a controller 42 for operating the spin forming machine 1 , 20, a computing device 44 and various sensors 46 that monitor the operation of the spin forming machine 1 , 20. The spin forming machine 1 , 20 may take various forms as described above. However, for most practical purposes, the spin forming machine 1 , 20 will also feature a support tool or a variety of support tools, against which the workpiece can be deformed. In a traditional spin forming apparatus 1 , the support tool may take the form of a mandrel 3. However, in a mandrel-free spinning apparatus 20, a variety of moveable support tools 32, 34, 36 may be used, substantially as described previously with reference to Figures 3 to 5.

The spin forming machine 1 , 20 is configured to receive control signals, from the controller 42, to rotate the workpiece 2 and move the forming tool 6 in accordance with the predetermined toolpath. Optionally, the control signals also move one or more of the support tools 32, 34, 36 in accordance with additional toolpaths.

The various sensors 46, which may include accelerometers, actuation sensors and force sensors, are arranged to monitor the operation of the spin forming machine 1 , 20 and determine, for example, the positions, motion and loading, or applied force, of the forming tool 6 and the support tools 32, 34, 36 and relay measurements back to the controller 42. The controller 42 may adapt the operation of the spin forming machine 1 , 20 based on feedback from these sensors 46.

The controller 42 is further configured to receive inputs from the computing device 44. The computing device 44 is configured to determine a set of computer readable instructions that the controller 42 can use to generate the control signals for operating the spin forming machine 1 , 20. The computer readable instructions may take the form of computer generated code which can be processed by the controller 42 to determine corresponding control signals. The computing device 44 may be further configured to receive inputs from a memory storage device (not shown) and/or a user in order to determine suitable instructions. In an embodiment of the invention, the computing device 44 is configured to receive a computerised representation of the article, which provides a target shape, in addition to one or more user inputs. The computing device 44 is further configured to determine toolpaths in the form of computer readable code based on the user inputs and the target shape.

The computer readable code is output to the controller 42 and used to determine real-time control signals that configure the operation of the spin forming machine 1 , 20 and deform the workpiece 2 into a shape that substantially matches the target shape. Optionally, the controller 42 may be configured to output signals to the computing device 44 to provide information feedback.

The formed article can be removed from the spin forming machine 1 , 20 upon completion of the spin forming process and the article should substantially retain its moulded shape with minimal springback.

The spin forming process is suitable for use producing articles that have a variety of shapes. Typically the articles will be metallic, though conceivably the workpiece could comprise any relatively ductile material. More specifically, ductile metals such as aluminium and stainless steel may be used as well as certain composites thereof. The articles formed may be axisymmetric, non-axisymmetric and even asymmetric and, advantageously, the same method of operation can be applied to each variation. By way of example, Figures 8(a) and 8(b) show an article 50 which may be formed in accordance with the invention. The article 50 consists of a single workpiece 2 that has been deformed into a hollow shape. The article 50 includes a base portion 52, at a first end 54; a rounded portion 56, which borders the base portion 52 and a body portion 58 that extends a short distance from the rounded portion 56 to a second end 60 of the article 50. The second end 60 features an opening which makes an interior volume of the article 50 accessible and the hollow shape defines interior surfaces 64 and exterior surfaces 66 of the article 50.

The subsequent description also considers Figure 9 which shows a cross-sectional view of the article 50 and Figure 10 which shows an end view of the article 50 from its second end 60. The cross-section in Figure 9 shows a base wall 68 at the base portion 52, filleted walls 70 at the rounded portion 56 and sidewalls 72 at the body portion 58. The base wall 68, filleted walls 70 and sidewalls 72 have substantially constant wall thickness.

In the example provided, the filleted walls 70 of the article 50 pass through an angle of approximately 90°, such that the sidewalls 72 extend from the filleted walls 70 approximately perpendicular to the base wall 68.

The base wall 68 features an inner base surface 74 facing the article's interior volume and an outer base surface 76 facing away from the article 50. Ends of the base wall 68 define perimeter edges 78 of the inner and outer base surfaces 74, 76.

The perimeter edges 78 define a base shape 80 of the article 50. In this example, the base shape 80 takes the form of a square with rounded corners, as best shown in Figure 10. The base shape 80 features a first 81 , a second 82, a third 83 and a fourth 84 straight edge and a first 85, a second 86, a third 87 and a fourth 88 rounded corner.

For the sake of clarity, the square cup is one such example of an article 50 that may be formed by the method of this invention. However, any article produced by this method will inevitably feature a base portion 52, including a base wall 68 and a base shape 80; a rounded portion 56, that borders the base portion 52; and a body portion 58, which features one or more sidewalls 72 that extend away from the base portion 52. The one or more sidewalls 72 may be inclined relative to the base portion 52 but do not need to extend perpendicularly. It should be understood that the base shape 80 will change depending on the geometry of the specific article considered.

The subsequent description describes a process of forming an article 50, such as the square cup shown in Figure 8, by application of an embodiment of the method to a spin forming machine, in the form of a mandrel-free spinning apparatus 20. Figure 1 1 shows a plan view of the mandrel-free spinning apparatus 20 shown in Figure 5. The plan view identifies a longitudinal axis 82 of the lathe 4 and a radial axis 84 which extends perpendicularly to the longitudinal axis 82. The positions of the forming tool 6 and of the first, second and third support tools 32, 34, 36 are adjustable relative to the workpiece 2 by relevant actuators 38 and these actuators 38 are arranged such that they can move the forming tool 6 and the first, second and third support tools 32, 34, 36, along the longitudinal axis 82 and the radial axis 84. In this manner, the longitudinal axis 82 acts as a first axis of movement for each of the tools 6, 32, 34, 36 and the radial axis 84 acts as a second axis of movement.

The fundamental operations of the mandrel-free spinning apparatus 20 are described with additional reference to Figures 12 to 14.

Initially, the workpiece 2 is mounted on the mandrel-free spinning apparatus 20 as indicated in Figure 12(a). The workpiece 2 is rotated on the lathe 4 and the forming tool 6 applies pressure to an outer surface 30 of the workpiece 2 to deform the workpiece 2 against the first, second and third support tools 32, 34, 36 to produce the desired article 50. At the same time, the first support tool 32 acts to resist deformation of the workpiece 2 at the inner surface 28 and the first support tool 32 remains engaged with the perimeter edges 78 of the base wall 68, throughout the spin forming process, to define the base portion 52 of the article 50. Similarly, the second and third support tools 34, 36 mimic the movement of the forming tool 6 to support an inner surface of the workpiece 2 and guide the deformation. Figure 12(b) illustrates the final operations of the spin forming process.

The operations of the forming tool 6 and the first, second and third support tools 32, 34, 36 will now be considered in more detail.

The plan view of the mandrel-free spinning apparatus 20, shown in Figure 1 1 , features the first support tool 32 attached to one end of a curved member 90 which is designed to allow insertion/removal of the first support tool 32 from the interior volume of the article 50, as the workpiece 2 takes its hollow shape. The first support tool 32 takes the form of a blending roller and radial position adjustments form the base shape 80 of the article 50. The position adjustments correspond to the changing orientation of the workpiece 2 and the non-axisymmetric form of the article's base shape 80.

More specifically, the first support tool 32 moves such that an outer surface of the forming tool 6 maintains contact with the edges 78 of the base shape 80 and resists deformation along these edges 78 to preserve the flatness of the base wall 68. Outside of the edges 78, the workpiece 2 is unsupported by the first support tool 32 and the forming tool 6 is able to deform the workpiece 2 towards the target shape.

Figures 13(a) and 13(b) illustrate the radial position adjustments that form the base shape 80 of the square cup. In a first position, shown by the solid lines, the first support tool 32 engages a mid-point of the first straight edge 81 of the base shape 80. As the workpiece 2 rotates the first straight edge 81 becomes inclined to the first support tool 32. Consequently, the first support tool 32 must move to a greater radial distance to remain in contact with the first straight edge 81 . Eventually, the workpiece 2 rotates such that the first rounded corner 85 of the base shape 80 moves into alignment with the first support tool 32. This second position is shown by the dashed lines. The first support tool 32 reaches a maximum radial distance in the second position.

As the workpiece 2 continues to rotate, the radial distance of the first support tool 32 subsequently reduces, reaching a minimum distance when the first support tool 32 engages a mid-point of the second straight edge 82. This third position (not shown) would appear substantially similar to the first position due to the symmetry of the square cup.

Thus, the first support tool 32 moves between maximum radial positions as it defines each rounded corner 85, 86, 87, 88 of the base shape 80 and minimum radial positions as the first support tool 32 engages the mid-points of each straight edge 81 , 82, 83, 84.

As a result, the first support tool 32 appears to oscillate as the workpiece 2 rotates about the longitudinal axis 82. The motion of the first support tool 32 is illustrated, in Figure 13(b), as a cyclic motion along the radial axis 84.

Referring back to Figure 1 1 , the plan view also shows the forming tool 6 supported at one end of an extending member 92. The forming tool 6 takes the form of a working roller which may be metallic and may feature a ceramic coating that can provide enhanced durability and minimise friction. The angle of the extending member 92 is adjustable relative to the workpiece 2 but generally remains constant during a single spin forming process.

Adjusting the radial and longitudinal positions of the forming tool 6 applies pressure to the outer surfaces of the workpiece 2 and can deform the workpiece 2 into the shape of the article 50. The position adjustments correspond to the changing orientation of the workpiece 2 and the geometry of the desired article 50.

More specifically, the forming tool 6 may be moved to engage the outer surface 30 of the workpiece 2 and reproduce the outer surfaces of the article 50 through radial and longitudinal position adjustments, as will be described in more detail through the example of the square cup. Figure 14 provides a graphical illustration of the motion of the forming tool 6 as it deforms the workpiece 2 into the target shape of the square cup. The longitudinal position adjustments describe the movement of the forming tool 6 along the length of the article 50, from the first end 54 to the second end 60. The radial position adjustments form the rounded portion 56 and the body portion 58 of the article 50. Notably, the radial position adjustments appear to be oscillatory. This motion pattern reproduces the radial variation of the rounded portion 56 and the body portion 58 that arise due to the non-axisymmetric shape of the article 50. The oscillatory motion is consistent with the cyclic oscillations of the first support tool 32 as the first support tool 32 engages the edges 78 of the base shape 80.

Returning to Figure 1 1 , the plan view additionally shows the second and third support tools 34, 36 in the form of support rollers which are mounted at the ends of respective extending members 94, 95. The extending members 94, 95 are similarly designed to allow insertion/removal of the second and third support tools 34, 36 from the opening 62 at the second end 60 of the article 50. Adjusting the radial and, optionally, the longitudinal positions of the second and third support tools 34, 36 can help to define the longitudinal shape of the article 50 by moving the second and third support tools 34, 36 to correspond with the changing orientation of the workpiece 2 and the geometry of the article 50. More specifically, the second and third support tools 34, 36 may act at a single longitudinal position and be moved in a similar manner to the first support tool 32, to define the interior surfaces 64 of the article 50. Alternatively, the second and third support tools 34, 36 may mimic the motion of the forming tool 6, with suitable offsets, such that the second and third support tools 34, 36 engage with the inner surface 28 of the workpiece 2 and support the sidewalls 72 against undesirable deformation.

Having established the capabilities of the mandrel-free spinning apparatus 20, the subsequent description describes determining suitable toolpaths that dictate the motion of the forming tool 6 and the first, second and third support tools 32, 34, 36 to produce the desired article 50 and details a method of controlling the mandrel-free spinning apparatus 20 to produce the square cup in accordance with the invention. Figure 15 provides a description of a production process 100 from an initial design of the desired article 50 to a spin formed reproduction of the article 50. In step 101 , the computing device 44 comprises a computerised representation of the desired article 50. The computerised representation may be produced on software of the computing device 44 or generated elsewhere and received at the computing device 44. For example, the computerised representation may be received at the computing device 44 from a memory storage device, a three-dimensional scanning device or a cloud storage system. The computerised representation provides a target shape for the subsequent control of the mandrel-free spinning apparatus 20.

Accordingly, the computerised representation of the article 50 may take various forms that provide sufficient detail to determine a first toolpath, which directs the motion of the forming tool 6; a second toolpath, which directs the motion of the first support tool 32; and a third toolpath, which directs the motion of the second and third support tools 34, 36.

The computerised representation of the article 50 may take the form of a CAD model, as shown in Figure 16. The CAD model provides a three-dimensional representation of the article 50.

In step 102, the computerised representation is discretized into a plurality of target shape points on a co-ordinate system. For example, a triangulated mesh can be created from the CAD model which discretizes the CAD model into such a plurality of points, as shown in Figure 16. The size of the triangulated mesh can be adjusted to create as many target shape points as necessary to provide an accurate representation of the article 50. These target shape points provide a coordinate based representation of the article 50 for use in determining the first, second and third toolpaths. The coordinate system may take the form of a cylindrical coordinate system with each point being defined by a radial position, V, an angular coordinate, 'θ', and a longitudinal position, 'z , such that each point, '/, is represented by the co-ordinates '(0,-, r ₇ -, z,-)'- Figure 17 shows a graphical plot of the target shape points located within a first angular plane (solid line) and the target shape points located within a second angular plane (dashed line). The target shape points located in the first angular plane have angular coordinates of '0-L' and the target shape points located in the second angular plane have angular coordinates of 'θ ₂ '.

In step 103, a user provides user inputs to the computing device 44. The user inputs include a feed rate; a number of angular planes; a number of passes; a start point for each pass; an end point for each pass; and a deviation for each pass.

The feed rate input, 'F', defines the movement of the forming tool 6 relative to the workpiece 2 in terms of a longitudinal position adjustment per revolution of the workpiece 2. The feed rate takes the form: dz . 2π

^{F =} ^r

Where 'dz' is a longitudinal movement of the forming tool 6 relative to the workpiece 2 and 'δθ' is the angle of rotation of the workpiece 2 as the forming tool 6 moves. The feed rate is used to determine the longitudinal positions of the forming tool 6, with respect to the rotation of the workpiece 2, when determining the first toolpath.

In step 104, the computing device 44 uses the number of planes input, which may take the form of an integer 'k', to determine 'k' angular planes through the target shape. These angular planes may be produced for equal angular divisions of the target shape or they may, for example, be distributed according to the regional complexity of the target shape.

In this manner, the three-dimensional model is converted into a plurality of two-dimensional cross-sections, each two-dimensional cross-section corresponding to a different angular plane and the cross-section extending along the radial and longitudinal axes.

For example, the user input may divide the target shape into thirty angular planes with each angular plane corresponding to a 12° interval around the target shape. Figure 18 shows the CAD model of the square cup divided into twenty-eight angular planes.

During the spin forming process, the workpiece 2 is rotated about the longitudinal axis 82 of the lathe 4, whilst the forming tool 6 and the first, second and third support tools 32, 34, 36 are controlled to move along the longitudinal axis 82 of the lathe and the radial axis 84, which extends in a single perpendicular direction. Thus, the rotation of the workpiece 2 can be divided into discrete intervals of rotation, such that each interval of rotation has a corresponding angular plane through the target shape. The computing device 44 discretizes the rotation of the workpiece 2 in this manner such that the first, second and third toolpaths can each be defined by positions of radial and longitudinal distance for each interval of rotation, , where 'i = 1 to N' and after 'N' intervals of rotation the spin forming process is complete. Accordingly, the computing device 44 determines a command position of the forming tool 6 in the first toolpath, a command position of the first support tool 32 in the second toolpath and command positions of the second and third support tools 34, 36 in the third toolpath for each interval of rotation, . These command positions are based on the target shape points that are located within the angular plane corresponding to the relevant interval of rotation. In this manner, the command positions of each toolpath are based on sequential angular planes through the target shape, as the workpiece 2 rotates. For example, referring back to Figure 17, initially ' i = V and the command positions of the forming tool 6 and the support tools 32, 34, 36 will be determined based on the target shape points having angular coordinates equal to 'θ^. As the workpiece 2 rotates to the second interval of rotation, 'i = 2', the command points of the forming tool 6 and the support tools 32, 34, 36 will be based on the target shape points having angular coordinates equal to 'θ ₂ '.

The second toolpath consists of a sequence of command points for moving the first support tool 32. The command positions consist of radial distances, ' rSiy, and longitudinal distances, zS , for each interval of rotation, , and the successive command positions are connected in the second toolpath to produce smooth and continuous motion of the first support tool 32 throughout the duration of the spin forming process.

In step 105, the computing device 44 determines the command positions that constitute the second toolpath. The longitudinal distance is determined such that the first support tool 32 engages with the inner surface of the workpiece 2. Thus the longitudinal distances, 'zSli ', for each interval of rotation, , are given by: ^z ^ -n ^z inner

Where 'z _inner ' is the longitudinal distance to the inner base surface 74 of the target shape.

The longitudinal distance, 'z _inner ', does not change throughout the spin forming process and in this configuration the first support tool 32 applies a resistance force to the inner surface of the workpiece 2 as the forming tool 6 applies pressure to the outer surface of the workpiece 2.

Throughout the spin forming process the radial distance of the first support tool 32 corresponds to the base shape 80 and thus the second toolpath adjusts the radial distance of the first support tool 32 as the workpiece 2 rotates through each interval of rotation, . Rotating the workpiece 2 changes the relevant angular plane through the target shape and as a result the radial distance to the edges 78 of the base shape 80 will vary for each interval of rotation, , as different angular planes pass into alignment with the first support tool 32. Thus the radial distances, 'rSiy, for each interval of rotation, , are given by: rSli = ΜΑΧ{γ{θ _{ίι Ζΰ} ))

Where 'r(0(, z _o )' is the radial distance to each target shape point located at the first end 54 of the article 50, with longitudinal distance 'ζ ₀ ', and located within the angular plane corresponding to the relevant interval of rotation , with angular coordinates 'θ . The position of the first support tool 32 is further offset to adjust for the nose radius of the first support tool 32.

Therefore the second toolpath consists of a sequence of command positions defined by the coordinates '(rSl^ Sl;)' for each interval of rotation, . A spline fit or similar fitting function between the command positions produces a continuous route for the first support tool 32 to follow.

Figure 19 graphically illustrates the variation of the radial distance of the first support tool 32 in the second toolpath. The 'commanded positions' 94 in the figure correspond to the command positions on the second toolpath determined for each interval of rotation, . The line 96 between the successive 'commanded positions' 94 illustrates the spline fitting. The longitudinal distance of the first support tool 32 remains constant throughout the spin forming process.

Similarly, the first toolpath consists of a sequence of command positions for moving the forming tool 6. The command positions consist of radial distances, ' rF , and longitudinal distances, 'zF , for each interval of rotation, , and the successive command positions are connected in the first toolpath to produce smooth and continuous motion of the forming tool 6 throughout each pass. In step 106, the computing device 44 determines the longitudinal distances of the forming tool, 'zFi , during each pass, for each interval of rotation of the workpiece, . The longitudinal positions, 'zF , are given by:

Where 'F' is the feed rate, defined in terms of a longitudinal movement of the forming tool 6 per revolution of the workpiece 2, and 'φ is the accumulated rotation of the workpiece 2 at the relevant interval of rotation, . In step 107, the computing device 44 determines the radial distances of the forming tool 6, 'rF , during each pass, for each interval of rotation of the workpiece, , based on the target shape and the user inputs. The number of passes and the corresponding start points, end points and deviations for each pass have a synergistic effect on the first toolpath.

When the user input includes a plurality of passes, the computing device 44 determines a first toolpath consisting of a plurality of moulding passes that iteratively deform the workpiece 2 towards the target shape, as well as a finishing pass which completes the deformation into the shape that substantially matches the target shape. Figure 20 illustrates such a form of first toolpath for the forming tool 6 which includes a first 171 , a second 172, a third 173 and a fourth 174 moulding pass, as well as a finishing pass 175.

Each pass has a start point and an end point that are defined by the user inputs. In this example, the start point for each pass it located at the first end 54 of the target shape with a longitudinal distance, and the end points of the first, second, third and fourth moulding passes 171 , 172, 173, 174 gradually increase with each successive pass.

The computing device 44 is configured to determine a first toolpath which moves the forming tool 6 from the start point of each pass to the end point of each pass and, upon reaching the end point of each pass, the first toolpath moves the forming tool 6 to the start point of the subsequent pass, without contacting the workpiece 2. Thus between passes, the first toolpath moves the forming tool 6 to the first end 54 of the article 50 without causing further deformation of the workpiece 2.

The deviation input also causes the computing device 44 to include a deviation from the finishing pass and hence a deviation from the target shape for each of the first 171 , second 172, third 173 and fourth 174 moulding passes. For each moulding pass 171 , 172, 173, 174, the deviation increases the radial distances of the command positions compared to the radial distances of the command positions determined for the finishing pass 175, when considering command positions with matching longitudinal distances. Thus, during each moulding pass 171 , 172, 173, 174, the radial distances of the command positions do not match the radial distances of the target shape points for each interval of rotation. Instead, the deviation input defines an additional radial distance for each command position which may, for example, vary as a function of the longitudinal distance. The additional radial distance means that for each command position the forming tool 6 is positioned further from the axis of rotation of the workpiece 2 and hence the bending moments are larger and deformation forces are reduced. This helps to maintain the thickness of the workpiece 2 during the deformation process.

In Figure 20, the computing device 44 determines the deviations by using a polynomial equation, wherein the radial distances of the forming tool 6 vary with the longitudinal distance along the target shape. In this case, the coefficients of the polynomial equation are defined by the deviation inputs.

Thus, in the embodiment of the invention shown in Figure 20, which includes a deviation for each pass defined in terms of a polynomial equation, the computing device 44 determines the radial distances of the forming tool, 'rF , during each pass for each interval of rotation of the workpiece, , given by: rFi = MAX r(ei, zFi)) + a. ( F;)"

Where 'r{Q zF _t y is the radial distance to each target shape point located at the longitudinal distance, 'zF , corresponding to the relevant interval of rotation, , and located in the angular plane corresponding to the relevant interval of rotation , with angular coordinates 'θ ; and 'a is a coefficient of the polynomial equation defined by the deviation input for each pass and 'ri is an exponent of the polynomial equation defined by the deviation input for each pass.

For the sake of clarity, the deviation inputs that provide the coefficients and the exponents do not need to be integer numbers.

Thus, the first toolpath consists of a sequence of command positions of the forming tool 6 defined by the coordinates '(rFi. zFi)', during each pass, for each interval of rotation, . A spline fit between the command positions produces a continuous route for the forming tool 6 to follow during each pass. Between each pass the first toolpath returns the forming tool 6 to the first end 54 of the article 50. The position of the forming tool 6 is further offset to adjust for the nose radius of the forming tool 6.

In this embodiment, the method uses polynomial equations to determine the deviation. There are many possible ways of defining the deviation. However, a polynomial equation allows simple adjustments for maximum control and user flexibility.

The deviation effectively adds a deliberate error or offset to the command positions of the moulding passes compared to the finishing pass. The polynomial equation allows for the deviation to increase with longitudinal distance. Thus, referring back to Figure 19, the first 171 , second 172, third 173 and fourth 174 moulding passes have the same exponent, 'η', but reducing coefficients, ' ', with each successive pass. As a result, the forming tool 6 iteratively deforms the workpiece 2 towards the target shape with a reducing deviation between each subsequent pass. The final moulding pass 175 would have the coefficient, 'a , set to zero such that the forming tool 6 reproduces the outer surfaces of the target shape and deforms the workpiece 2 into the shape that substantially matches the target shape. Though not described in detail, the third toolpath for the second and third support tools 34, 36 substantially matches the first toolpath for the forming tool 6 but includes suitable offsets to engage the second and third support tools 34, 36 with the inner surface of the workpiece 2. Thus, in step 108 of the method, the computing device 44 comprises a first toolpath for moving the forming tool 6, a second toolpath for moving the first support tool 32 and a third toolpath for moving the second and third support tools 34, 36.

Advantageously, the same method can be repeated for a variety of target shapes without necessarily making any changes to the user inputs because the first and second toolpaths are based on the target shape. Instead the computing device 44 will determine new toolpaths based on the updates to the target shape.

In step 109, the computing device 44 converts the first, second and, optionally, third toolpaths into a form that the controller 42 can understand, for example, as computer readable code. The code may be suitable for a CNC controller 42 and the computing device 44 outputs the code to the controller 42.

The workpiece 2, for example in the form of a sheet metal blank, is then mounted on the lathe 4 of the mandrel-free spinning apparatus 20. The workpiece 2 may have been designed based on the shape of the desired article 50 and may have an approximately square initial shape. The initial shape may be designed by modelling a forming process using Finite element analysis and iteratively refining the initial shape or by using an analytical design method. The workpiece 2 is mounted such that the orientation of the workpiece 2 corresponds with the first angular plane of the target shape.

In step 1 10, the spin forming process is initiated and the controller 42 uses the computer readable code to determine corresponding control signals and operate the mandrel-free spinning apparatus 20. The control signals dictate the rotation of the workpiece 2 on the lathe 4 and the movement of the forming tool 6 and the first, second and third support tools 32, 34, 36 according to the relevant toolpaths. In step 1 1 1 , the first support tool 32 moves according to the second toolpath and the forming tool 6 moves according to the first toolpath. The motion of the first support tool 32 resists deformation of the workpiece 2 along the edges 78 of the base shape 80 to form the base portion 52 of the target shape as the forming tool 6 completes each successive passes to deform the workpiece 2 into the shape that substantially matches the target shape.

Optionally, the second and third support tools 34, 36 also move according to the third toolpath and mimic the motion of the forming tool 6 at the inner surface of the workpiece 2 to guide the deformation.

In step 1 12, the forming tool 6 finishes executing the first toolpath and the workpiece 2 is moulded into a shape that substantially matches the target shape. The article 50 can then be removed from the mandrel-free spinning apparatus 20.

If the results are unsatisfactory, the operator may choose to repeat the process, as shown by step 1 13, and apply different user inputs to refine the various toolpaths. For example, a first toolpath that features additional passes and/or larger deviations may be less prone to wrinkling or thinning of the workpiece 2 during the spin forming operation.

It is noted that the steps of the production process 100 are merely provided as an example of the invention and the steps are not intended to limit the method of controlling the spin forming machine. As such, it is understood that the processes involved may be altered, reordered, added and removed as will be appreciated by the person skilled in the art.

In an embodiment, the workpiece 2 may not be a sheet of metal and the workpiece 2 may instead have an initial shape that is part formed towards the shape of the article 50. However, the same method can be used to deform the workpiece 2 from its initial shape towards the target shape.

In an embodiment, the user input only includes a single pass. In this case, the forming tool 6 must deform the workpiece 2 from its initial shape into the shape of the article 50 in a single continuous movement from a start point, at the first end 54 of the article 50, to an end point, at the second end 60 of the article 50. Such a single pass toolpath was shown previously in Figure 14. Thus, when the first toolpath consists of a single pass, the radial distances of the forming tool, 'rFi , for each interval of rotation of the workpiece, , are given by: rFi = MAX{r{e _{il Z} Fd)

Where 'r{Q zF )' is the radial distance to each target shape point located at the longitudinal distance, 'zF , corresponding to the relevant interval of rotation, , and located within the angular plane corresponding to the relevant interval of rotation , with angular coordinates -

Therefore, in this case, the first toolpath consists of a sequence of command positions of the forming tool 6 defined by the coordinates '(rFi. zFi)' for each interval of rotation, . A spline fit between the command positions produces a continuous route for the forming tool 6 to follow and, in practice, the position of the forming tool 6 is further offset to adjust for the nose radius of the forming tool 6.

Deforming the workpiece 2 in a single pass may cause thinning of the workpiece 2 along its length. Accordingly, single pass spin forming in this manner can be considered equivalent to a shear spinning method.

In another embodiment of the invention, the spin forming machine may take the form of a traditional spin forming apparatus 1 as described in Figures 1 and 2. In this case, the method will only determine a first toolpath to direct the motion of the forming tool 6. However, the first toolpath will still be determined substantially as described in the example above.

For the sake of clarity, when a rotational velocity is known the toolpaths can similarly be defined in terms of time instead of intervals of rotation.

Many modifications may be made to the above examples without departing from the scope of the present invention as defined in the accompanying claims.