Understanding the dynamic behaviour of a tennis racket under play conditions

The 'feel' of tennis rackets is of increasing importance to manufacturers seeking product differentiation in a context where further performance enhancements are prevented by a combination of mechanical limits and regulations imposed to protect the integrity of the sport. Vibrations excited during a shot contribute greatly to the perception of 'feel'. Previous studies have been reported but none has covered the full set of mode families or the frequency range in this study. In-plane vibrations associated with the routine use of topspin shots in modern tennis have not been documented so far in the literature. To consider modal behaviour, multiple measurements during play conditions are required but this is practically impossible. This paper proposes an alternative approach and successfully relates a comprehensive modal analysis on a freely suspended racket to vibration measurements under play conditions. This is achieved through an intermediate stage comprising a necessarily more limited modal analysis on a hand-gripped racket and use of the mass modification modal analysis tool. This stage confirmed the prevailing view that hand-gripping can be considered as a mass modification distributed along the handle of the freely suspended racket but the associated mass was much lower than that of an actual hand and the hand also increased the damping ratio of frame modes significantly. Furthermore, in frame vibration measurements during forehand groundstrokes, a greater reduction in bending mode frequencies was observed, consistent with a mass-loading of around 25 % of the actual hand as a consequence of the tighter grip. In these play tests, the first two bending modes, the first torsional mode, the first eight stringbed modes, the first three hoop modes and the third in-plane bending mode were identified, with the stringbed modes being particularly prominent. © 2013 Society for Experimental Mechanics

On the measurement and modelling of high pressure flows in poppet valves under steady-state and transient conditions

Flow coefficients of intake valves and port combinations were determined experimentally for a compressed nitrogen engine under steady-state and dynamic flow conditions for inlet pressures up to 3.2 MPa. Variable valve timing was combined with an indexed parked piston cylinder unit for testing valve flows at different cylinder volumes whilst maintaining realistic in-cylinder transient pressure profiles by simply using a fixed area outlet orifice. A one-dimensional modelling approach describing three-dimensional valve flow characteristics has been developed by the use of variable flow coefficients that take into account the propagation of flow jets and their boundaries as a function of downstream/upstream pressure ratios. The results obtained for the dynamic flow cases were compared with steadystate results for the cylinder to inlet port pressure ratios ranges from 0.18 to 0.83. The deviation of flow coefficients for both cases is discussed using pulsatile flow theory. The key findings include: 1. For a given valve lift, the steady-state flow coefficients fall by up to 21 percent with increasing cylinder/manifold pressure ratios within the measured range given above; 2. Transient flow coefficients deviated from those measured for the steady-state flow as the valve lift increases beyond a critical value of approximately 0.5 mm. The deviation can be due to the insufficient time of the development of steady state boundary layers, which can be quantified by the instantaneous Womersley number defined by using the transient hydraulic diameter. We show that it is possible to predict deviations of the transient valve flow from the steady-state measurements alone