In the frame — tennis racket development
The evolution of tennis, after it was introduced as lawn tennis in the 1870s, can be characterised by the technological advances of materials used in racket frames. When lawn tennis began, wood and animal glues were the only available materials for shaping strong and lightweight frames.
Wood lamination benefited constructions from the 1940s, as different woods in different parts of the frame could be combined to strengthen and stiffen the racket according to the specific requirements of performance and the player’s needs. A decade or so later, metal-tube frames became the player’s choice, as these offered significantly greater shape stability over wooden frames, which tended to warp.
The 1960s and 70s saw many changes in the size, shape, materials and manufacture of tennis rackets, instigated by the availability of stronger, lighter and more versatile aluminium alloys. This allowed the size of the racket head to grow without significant weight penalties. While these advances favoured recreational players, the new applications had more complex consequences for professional tennis, as games could be won on the basis of superior equipment and the fastest serve. In 1974, the previously unspecified tennis racket was finally regulated for racket head size by the International Tennis Federation.
The use of carbon fibre-reinforced composites in tennis rackets, from the early 1970s, offered even greater prospects for development than aluminium, due to their higher specific stiffness. Currently, the majority of rackets are composite constructions, but has the single-minded quest for high stiffness composite rackets gone too far?
The stiffness-related vibration of the frame and shock transmission to the player are common complaints that manufacturers are addressing through applications such as piezo materials. The significant change in the essence of the professional game is another contentious issue which seems to implicate the composite racket. Should manufacturers initiate change to the feel and performance of the composite racket to widen the appeal of tennis?
Fibre-reinforced polymer matrix composites fit into two broad categories of composite materials which can be distinguished by the aspect ratio (length/diameter) of the fibre – long-fibre reinforced composites and short-fibre composites. Composites exploit the beneficial aspects of the individual components. Reinforcing fibres exhibit high strength and modulus while the polymer provides the protective medium in which the fibre is able to impart strength, stiffness, toughness and creep resistance characteristics. In reality, there are a range of industrial polymer composite materials that have been tailored for specific property and application requirements.
The current carbon fibre tennis racket frames are manufactured by arranging ready-to-mould, pre-impregnated sheets of aligned, continuous fibre lengths and 0/90º weaves of fibre in a thermoset resin in different orientations and proportions so that the optimum balance in racket properties can be achieved for a given frame shape and weight. However, this is labour intensive.
To reduce the handwork, in the 1980s Dunlop produced rackets based on short carbon fibre-reinforced nylon which was injection moulded into the final frame shape, with moulded-in holes, in the same process. Injection moulded rackets were produced for about 10 years and successfully used to win the Wimbledon championships in the UK. However, this approach could not be adapted to make large headed, lighter long frame carbon fibre composite rackets, largely due to the lower mechanical properties exhibited by short-fibre reinforced composites.
Injection moulding of fibre-reinforced composites uses short chopped fibre suspensions in a molten plastic which are injected into the mould cavity of the final part shape. The lower mechanical properties of these materials are linked to the discontinuous state of short fibre and the associated reinforcement inefficiencies that are not obviously present in long-fibre composites. Also, the complex fibre orientation patterns in the solidified part can have a negative impact on reinforcement performance, as fibres are difficult to orientate in preferred directions and for optimum design use.
Many recent advances in injection moulding and materials offer greater opportunities to mould larger and stronger components than were previously possible with short fibre composites. The benefits have arisen mainly from the development of discontinuous long-fibre reinforced moulding materials, containing fibre, 10-15mm in length rather than the one to two millimetre length found in traditional short-fibre materials. Also, the reinforcement efficiency improves with increasing fibre length.
QinetiQ, in collaboration with a major tennis racket manufacturer, explored the possibility of using these types of materials for tennis racket frames, with the aim of developing a competitive, low cost frame of comparable performance to existing composite versions.
Analysis and modelling
The initial stage of the project was to structurally analyse an existing frame so that the key properties could be benchmarked and realistically featured. Beam sections, representing the frame, were then produced in a discontinuous long-fibre reinforced thermoplastic material and empirically validated against the existing racket frame benchmark.
Finite element (FE) structural modelling of the existing frame was used to characterise structural behaviour when bending is applied to the racket, as when striking a ball. The model was validated for the materials and the different composite lay-up configurations used in the racket construction. It helped identify the highly stressed areas so that their behaviour could be replicated in new designs based on the characteristics of discontinuous fibre composite materials.
The FE model validation required data for the elastic moduli and strain properties of the composite frame under an applied bending moment. The elastic moduli of the various sections were determined using the composite laminate theory, calculating elastic properties or stiffness from the properties, orientation and distribution of the individual layers. The loading strains in the different areas of the composite frame were determined experimentally as the racket was deflected under a bending moment, using miniature electronic strain gauges mounted on the surface of the frame.
A basic analytical solution for featuring the properties of the long-fibre composite frame in an injection mouldable material hypothesised that the space and volume of the racket frame profile, plus the volume of material, provided the frame’s specific properties. These parameters were explored using modified beam theory to generate the new injection mouldable profiles.
Initial proof-of-concept demonstrators of racket frame cross-sections have been produced by extruding hollow profiles in a discontinuous carbon fibre thermoplastic material rather than by injection moulding. This simplified profile manufacture and the ensuing fibre orientation patterns, so that the data could be effectively translated into injection mouldable frame designs.
The structural performance of the extruded profiles has been determined by comparative assessment of their strength and stiffness in bending against the pre-selected section of the long-fibre composite racket.
Representative load-deflection responses indicate that while the extruded profiles exhibit similar stiffness to the long-fibre racket section, the failure strength is lower. This situation is somewhat improved when the hollow core of the profile is filled with a lightweight polyurethane foam, mainly by altering the response of the profile sidewalls to the loads.
A more informative performance comparison between the extrusions and the long-fibre composite frame section is made in the graph above, which shows comparable specific strength and stiffness properties (dividing the measured properties by the density of the material) of the extruded profiles, especially with foam in-fill, to those of the long-fibre composite frame section.
This demonstrates the potential of discontinuous long-fibre thermoplastic composite materials to produce wide-headed tennis racket frames. These frames may offer a different perspective on existing composite rackets on the basis of alternative manufacturing technologies, materials and racket behaviour attributes.
The significant developments in injection moulding and associated technologies over the last two decades widen the options available to racket manufacturers for exploring different composite matrices, racket structures and manufacturing/ assembly practices.
Thermoplastics are probably more suited to injection moulded racket frames and, as such, could provide a different feel to the racket, possibly through the intrinsic characteristics of these materials. Designs of the frame with structural features built into the hollow cross-sections offer opportunities for low cost moulding and assembly. Further substantive performance and cost benefits may arise if multiple injection practices are implemented, such as to mould handle cushions, impact protectors and string grommets all in the same tool.
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