Surface hardness of a cricket bat after knock-in

Transcription

1 Technical Note Surface hardness of a cricket bat after knock-in A.T. Sayers, M. Koumbarakis, S. Sobey Department of Mechanical Engineering, University of Cape Town, South Africa. Abstract New cricket bats need to be knocked in prior to use, but just what this process does to the surface fibres of the bat is unknown and unquantified. One quantitative measurement of knockin is the resultant surface hardness of the bat, and this paper describes knock-in tests to determine the surface hardness following differing durations of knock-in. The design of a cricket bat knock-in machine is first described. This takes the form of a cradle in which a cricket bat can be secured horizontally and then traversed at constant speeds in two mutually perpendicular directions while at the same time being struck with constant force by a cricket ball. The traverses are driven by lead screws, the motors of which can be independently switched on or off. The traverse distance can be varied with adjustable limit switches and relays that reverse the direction of rotation of the lead screws when activated. The cricket ball is attached to a rod that is lifted cyclically by a cam against a coil spring extension, and then allowed to fall under that force to impact on the bat surface. The impact (knocking-in) force was measured by a previously calibrated strain gauge attached to the rod holding the cricket ball. By judicious setting of the limit switches, selected areas of the bat surface were continuously knocked in for periods varying from 1 to 4 hours. After knocking in, the surface hardness was measured in accordance with British Standard 373 using a penetrator designed in accordance with the same standard. Analysis of the load/penetration curves shows an increase in surface hardness with knock duration. Photographs of the cell structure of the surface wood, obtained using a scanning electron microscope, show that under knock-in conditions, the wood cells collapse to form a mesh-like hardened layer which increases in hardness with increase in knock-in duration. Keywords: cricket, bat, knock-in, hardness Introduction The willow tree (Salix babylonica) belongs to the broadleaved species of tree or hardwoods as they are usually Correspondence address: Prof. A.T. Sayers Department of Mechanical Engineering University of Cape Town Rondebosch, 7700 South Africa Tel: Fax: asayers@ebe.uct.ac.za called (Bulletin 48, 1977). The trunks of hardwoods are the principal source of woody material for the manufacture of many products and consist of millions of individual cells differing in size and shape. Various types of cells comprise the trunk of the tree as shown in Fig. 1, but those that contribute significantly to the mechanical strength of the wood are found in the latewood (Koehler, 1924), which is the growth ring formed during winter when the transport canal or lumen is small, and the cell wall thick. This principally marks the difference between a good or bad cricket bat, since the bat quality is dependent on the number of 2005 isea Sports Engineering (2005) 8,

2 Surface hardness of a cricket bat after knock-in Sayers et al. latewood rings present in the blade; most manufacturers recommend that ideal bats have between 6 to 12 latewood rings (Middlepeg, 2001). The wood from the willow tree is very resilient and has good shock resistant properties, making it the preferred choice for the manufacture of cricket bats. The bat blades are cut from radial portions of the trunk, as shown in Fig. 2, after which they undergo various drying procedures before being shaped and pressed into the final product. Because of the soft and fibrous nature of the wood, it is imperative that the bat be knocked in prior to use. The purpose of knocking in is to compress the wood fibres, particularly around the peripheral edges of the bat where most, if any, damage is likely to occur. The process is usually performed by hitting the bat surface with a wooden bat mallet or cricket Figure 1 Cell structure of willow tree (Silvester, 1967) ball for times varying between 2 to 6 hours, after which the bat should initially be used in the practice nets with old soft balls. Just how long it is necessary to knock in a bat depends upon to whom the question is addressed and the frequency of strike of the knockin mallet. Damage to new bats is reported despite their having been said to have been knocked in. Research by Grant & Nixon (1996a, b), Grant & Paisley (1997) and Grant & Davidson (1998) concentrated on the dynamic response of the bat to impact by the ball. This paper reports on controlled experiments that were carried out to quantify the surface hardening of cricket bats with time during the knock-in process and to see the effect of knock-in on the microstructure of the surface. Experimental apparatus Bat knock-in device design So that some measure of control could be exercised over the forces exerted on the bat face during knockin, a device previously designed for the automated knocking in of cricket bats was modified and utilised. The machine, shown schematically in Fig. 3, was designed to accept all sizes of cricket bat to relieve the human tedium of knocking in. The bat is clamped by its handle and supported horizontally along its length by two adjustable nylon straps that are secured in pillars so that any shape of bat back face curvature can be accommodated. The pillars (and bat) are fixed to a bed plate which moves longitudinally on two horizontal silver steel guide rods and is driven by a lead screw through a 12 V DC motor. During this movement, a ball mallet strikes the horizontal bat face cyclically. The striking ball mallet is also able to move transversely across the face of the Figure 2 Structural axes of wood (Silvester, 1967) 234 Sports Engineering (2005) 8, isea

3 Sayers et al. Surface hardness of a cricket bat after knock-in Figure 3 Schematic of cricket bat knock-in device bat, so that eventually the entire bat surface will be automatically knocked in. The knocker system operates in a manner similar to that of a bass drum pedal. The mallet is lifted against a coil spring by the pull of a twined stainless steel cable set in a groove in a hemispherical pulley. The pulley rotates a shaft to which the mallet is also fixed. Rotation of the hemispherical pulley and the concomitant lifting of the mallet is via a cam and cam follower. The cam rotates at a constant speed, being driven by a second 12 V DC motor. It makes periodic contact with a follower plate, at one end of which is crimped the twined wire, while the other end is hinged to a base plate. As the cam comes into contact with the follower plate, the plate is rotated downwards to pull the twined wire, and therefore raise the mallet. As the cam continues to rotate, it suddenly loses contact with the follower plate and thus permits the spring to pull the mallet down onto the face of the bat. The whole knocker assembly is able to move at right angles to the longitudinal direction on two other slide rails, and is again driven by a third 12 V DC motor and lead screw. Each of the three drive motors has a built in 28:1 reduction gearbox to produce high torque to the lead screws and cam. Two relays and two micro-switches are used to change the direction of rotation of each motor when the mallet and bat reach the limits of their traverses. The relays change the polarity of the motors, while the micro-switches, when pressed, allow for the switching of the relays to change the direction of rotation of the motors. The overall length, width and height of the knock-in machine are 900 mm, 360 mm and 520 mm, respectively, while the total mass is 23 kg. The maximum force exerted by the ball mallet is 2800 N. Modifications to knock-in device While the knock-in device described in the previous section could be used successfully to knock in a range of bats, several modifications were required to enable accurate surface hardness experiments to be performed. Under general knocking-in conditions, the bat tended to move slightly with each strike of the ball. Also, the original support cradle and bed plate 2005 isea Sports Engineering (2005) 8,

4 Surface hardness of a cricket bat after knock-in Sayers et al. were designed to withstand only the instantaneous impact load of the ball during one knock-in interval, as opposed to the much larger and continuous penetration load required during surface hardness testing. A new cradle was therefore designed which permitted the bat to be rigidly secured during knock-in, thus ensuring the same conditions on each point of the surface. The whole cradle could then be removed with the bat still clamped in position, for location in the hardness tester. This was accomplished by fitting additional nylon support straps under the bat, with a clamping plate at each end to hold the bat rigidly in position on the straps (Fig. 4). A second locating plate was designed for the hardness tester so that the cradle (and bat) could be held in the same horizontal position as in the knocking-in machine while the hardness tests were carried out. Surface hardness penetrator The surface hardness penetrator assembly consists of the penetrator itself and the linear voltage displacement transducer (LVDT) guide plate shown in Fig. 5. The penetrator was designed in accordance with British Standard 373 (1957) and consisted of an 11.3 mm highly polished stainless steel hemisphere brazed into a stainless steel housing which screwed into the end of a 17 mm diameter stainless steel rod. This 17 mm rod was, in turn, screwed into a 30 mm diameter housing, which located in the compression testing machine through an M30 male thread at its upper end. The housing had a 40 mm diameter collar, against which the LDVT guide plate was seated. The LVDT guide plate was of 6 mm thick steel with a central 11 mm hole. Two reamed holes drilled equidistant from the central hole were used to locate Figure 4 Modified bat cradle and secured bat Female joint LVDT Guide plate Penetrator Figure 5 Penetrator assembly 236 Sports Engineering (2005) 8, isea

5 Sayers et al. Surface hardness of a cricket bat after knock-in each of the LVDTs. The guide plate was held against the end of the upper housing by the hemispherical ball assembly, which was tightened using spanner flats machined onto its outer diameter. The LVDTs themselves were held in place in their reamed holes by small grub screws. Ball mallet The cricket ball used for knocking in was a Gunn & Moore 156 g Match Senior ball, which was glued into the end of a wooden support rod. So that the impact force exerted by the ball during the time of knock-in could be monitored to ensure that it was reasonably constant, two resistance strain gauges were bonded to the upper and lower sides of the support rod at the built in end, and their electrical output statically calibrated for load by suspending weights at the position of the ball. During knocking in, strain gauge voltages were fed via a strain gauge amplifier to a digital storage oscilloscope. Scanning electron microscope A scanning electron microscope (SEM) was used for microscopic examination of the bat surface at the desired magnification. This apparatus could hold eight specimens at a time in the evacuated observation chamber. Experimental method Penetration tests The bat face was divided into five zones, shown in Fig. 6. One zone was reserved as a reference nonknocked surface, while the others were knocked in for 1, 2, 3 and 4 hours, respectively, at a rate of 45 strikes per minute, which is typical of a human strike rate. Confinement of the impact to a particular zone was accomplished by suitable placement of the adjustable longitudinal and transverse movement limit switches. After knocking-in, the bat, complete with its cradle, was removed from the knocking-in machine, placed on the fixed cross-head under the penetrator and levelled off by adjusting appropriate supports. The penetrator assembly was located under the compression tester load cell. The LVDTs were secured in their guide plate holes, levelled and clamped in position. The penetrator was lowered until the LVDTs were in contact with the surface of the bat, when their output signal was zeroed on the displacement indicators of the compression tester. Once adjusted, the amplification was set to average the readings of the two LVDTs. The compressive load scale was zeroed by manually lowering the penetrator until it just contacted the surface of the bat. Vertical movement of the penetrator into the surface of the bat then commenced at a constant speed of 6 mm min 1 to a depth of 5.65 mm (British Standard ). For each test, graphs of compression load against depth of penetration were plotted. Three penetrations were performed on each knocked-in zone and the mean surface hardness calculated. A set of typical load curves is shown in Fig. 7. Electron microscope examination The specimens to be examined had to be removed from the surface of the bat prior to preparation. Figure 6 Knock-in zones and locations of the hardness test penetrations 2005 isea Sports Engineering (2005) 8,

6 Surface hardness of a cricket bat after knock-in Sayers et al. 3 kn 2 kn 1 kn Calibration OMID OR OL Small rectangular pieces of the bat approximately 8 mm 20 mm were cut from their respective zones with a small saw blade. The cut surfaces were further shaved with a Sledge Microtone blade using standard plant specimen preparation techniques. They were then ultrasonically treated to loosen and remove sawdust that may have become trapped in the wood vessels and lumen. Finally the specimens were coated with a metallic film of gold palladium to provide the conduction path necessary for observation, and placed on the viewing plate. Two photographs were taken of each specimen under two different magnifications to observe the compression of the lumen and vessels. Results and discussion Since the knock-in period was relatively short, it was assumed that the results obtained during the knock-in process were independent of changes in atmospheric conditions. The hardness of wood is approximately proportional to its density and moisture content, so any large scale environmental change during testing could influence the results. Hardness tests Figure 7 Load-penetration curves for 0 hours knock-in The data in Table 1 show the maximum loads reached at the prescribed penetration depth of 5.65 mm, and these are plotted in Fig. 8. The scatter in the right- and left-hand side values is attributed to the design of the cradle, which did not account for the transverse curvature of the bat face. This resulted in the penetrator not being truly perpendicular to the surface at the outer positions, causing the load to reach a maximum after about 2 hours, and then to decrease. The middle penetration, however, shows a 3.5 Maximum load (kn) Time (h) Figure 8 Maximum compression load variation with knock-in duration Table 1 Maximum penetration loads (kn) Left Middle Right Average trend towards a maximum value and then remained constant, implying no further hardening after about 3 hours. The depth of wood affected by knock-in is small, and once this depth is exceeded, only a small area of hardened wood is in contact with the hemispherical ball, the remainder of the ball being in contact with the unhardened wood below the hardened surface. It is therefore more appropriate to examine the rate of load increase or slope of the load/penetration curve. The slope of each curve was obtained by taking the tangent of a straight line lying along the curve and passing through the maximum load point. These results are tabulated in Table 2 and plotted in Fig. 9. This shows the hardness rate increasing with time of knock-in for all zones, while, for the first two hours, the hardness achieved is about the same for each position. A trend line curve fit to the average data curve is a third-order polynomial. The middle position tests are probably the most reliable once again, because of the curvature of the bat face Left Middle Right Average kn kn kn kn Knock zone h Knock zone h Knock zone h Knock zzone h Knock zone h 238 Sports Engineering (2005) 8, isea

7 Sayers et al. Surface hardness of a cricket bat after knock-in Table 2 Slope of load/penetration curve kn/mm. a) Left Middle Right Average kn kn kn kn Knock zone h Knock zone h Knock zone h Knock zone h Knock zone h b) Vessels Lumen Slope (kn/mm) Knock-in duration (h) Left Middle Right Average c) Vessels Lumen Figure 9 Slope of load/penetration curve versus knock-in duration. towards the edges. The data points for the middle show a rapidly increasing hardness, again with a trend line polynomial of order three. After four hours of knocking in along the centre section, the hardness of the surface had more than doubled and it is debatable as to just how long knock-in should continue for any discernible benefit in terms of bat performance. It is suggested that a knock-in time of about 2 to 3 hours is sufficient to adequately harden the surface fibres, and this broadly agrees with the anecdotal evidence of players and manufacturers (abcofcricket, 2004). Extending the knock-in time only increases the depth of increased hardness. Wood is not homogeneous, so it is not surprising that there was a range of scatter. Figs. 10a c show the microscopic state of the bat surface. In Fig. 10a, the wide open vessels and lumen of the unknocked reference area are clearly seen. As the knock-in period increases, the vessels and lumen become increasingly narrowed and collapsed. Figure 10 Scanning electron microscope studies of the bat face. a) 0 hour surface b) 2 hour surface c) 4 hour surface. Conclusions Vessels Lumen A machine has been designed to knock in automatically the surfaces of new cricket bats. This was used to knock in selected areas of a bat face for different lengths of time, and the hardness of these areas was determined using a penetrator designed to a standard recommended for wood testing. The maximum penetration load and rate of penetration were measured, and show that the hardness of the bat face can be 2005 isea Sports Engineering (2005) 8,

8 Surface hardness of a cricket bat after knock-in Sayers et al. doubled in a period of four hours. Scanning electron microscope photographs show that the surface wood fibres become increasingly enmeshed and compressed with knock-in duration. References British Standard (1957) BS 373: Methods of Testing Small Clear Specimens of Timber. Bulletin 48 (1977) The Mechanical Properties of Timber, Department of Forestry. Grant, C. & Nixon, S.A. (1996a) Parametric modeling of the dynamic performance of a cricket bat. In: The Engineering of Sport: Proceedings of the International Conference on the Engineering of Sport (ed S.J. Haake), , Balkema, Rotterdam. Grant, C. & Nixon, S.A. (1996b) The effect of microstructure on the impact dynamics of a cricket bat. In: The Engineering of Sport: Proceedings of the International Conference on the Engineering of Sport (ed S.J. Haake), , Balkema, Rotterdam. Grant, C. & Paisley, P. (1997) Raising the game through modeling. Proceedings of Fourth International Conference on Composite Engineering, Hawaii, USA. Grant, C. & Davidson, R.A. (1998) Design of a cricket bat test machine. In: The Engineering of Sport: Proceedings of the International Conference on the Engineering of Sport (ed S.J. Haake), 41 47, Blackwell, Oxford. Koehler, A. (1924) The Properties and Uses of Wood, McGraw-Hill, New York. Silvester, D.F. (1967) Mechanical Properties of Timber, Pergamon Press, Oxford. (2004). (2001). 240 Sports Engineering (2005) 8, isea