CAPÍTULO 1 MARCO TEÓRICO
1.2 REFUERZO SONORO Y MEGAFONÍA
A number of transducers operating on the basis of different principles for measuring vibration amplitude and frequency were evaluated. These include infrared interference and reflective detectors, Hall effect transducers as well as strain gauges. The strain gauge was the most sensitive, however, the direct contact with the reed caused instability and interference during vibration. The spring particle sizer employs a reflective traducer (RS Components, type 307-913) that can be remotely mounted and therefore the interference with the system is eliminated. This transducer is based on the principle of emission followed by detection of infrared light signal that is reflected from the vibrating part of the structure.
5.4 Spring Design
Design of an extension spring with linear characteristics in which the intercoil distance remains uniform in response to an applied tension is the most important criteria in minimising the error in size analysis. This is primarily governed by several factors including spring material of construction, wire uniformity, the residual tension and the uniformity of the applied tension during the winding process as well as the heat treatment applied during the manufacturing stage.
The material of construction dictates the elastic properties of the spring. High modulus of elasticity, low density, high resistance to wear and corrosion as well as low temperature coefficient of expansion are preferred. This makes a ceramic as the ideal material of construction. However this material is unsuitable due to manufacturing difficulties and its brittle nature.
Wire uniformity ensures complete coil contact when the spring is closed and a constant aperture diameter when it is extended. Experiments with various springs have indicated that the linearity in response increases with residual tension. The latter is defined as the minimum amount of force required ju st prior to causing the opening of the spring coil gaps. Residual tension can be applied to a spring during the winding process. Apart from ensuring uniform spring opening, the residual tension also reduces spring ‘sagging’ during extension with superimposed vibration.
According to Roberts [64] the spring index (ratio of coil to wire diameter) is also another factor influencing residual tension. In practice, the residual tension decreases with spring index.
During winding, the tension between the spool holding the wire and the spring winding coil should be kept constant to ensure minimum variation in tension between successive coils. For this, the spool of wire should be moved at the same rate as the winding coil to minimise any tension variation. The exposure time of the wound coil to heating and the subsequent cooling cycle should be equal along the spring length to ensure uniformity in the spring openings. One way to ensure this is to make units of ‘sm all’ spring lengths. Also the temperature rise and fall should be gradual rather than sudden.
Table 5.1 shows the main characteristics of springs commisioned in accordance with the above criteria. Two types of spring are used. Small spring is based on the spring used by Shaeri [12], whereas the large spring is designed to increase the spring capacity. This will help to deal with larger sample volume which would more representative of the bulk sample. The spring stiffness, k in the table is given by
[65]:
d^G
k = T (5.1)
SnD^
where,
G = M odulus of rigidity (N/m^) = 8.0 x 10^^ N/m^ for stainless steel [66] d = wire diameter (m)
D = Coil diameter (m) n = Number of active coils
The stepper m otor used for extending the spring has a holding torque of 500 mNm and with use o f a gearbox of (RS Components, type 718-852, ratio 5:1) provides a maximum coil gap of 1 mm.
Table 5.1: Characteristics of the main springs used.
Spring characteristics Spring (type A) Large spring (type B)
W ire diameter, d 1.63 X 10^ m 2.34 X 10 ^ m
Coil diameter, D 12 X 10 ^ m 25 X 10 ^ m
Spring length, 1 105 X 10'^ m 56 X 10'^ m
Number of active coils, n 63 24
Spring internal volume, V 6.3cc 18.6cc
Spring stiffness, k 648.43 N/m 799.53N/m Spring Index 7.36 10.68 Initial Residual Tension [67] 31% of the maximum spring load 21% of the maximum spring load
Maximum coil opening 1000 |L im 2329 |im
The performances of these springs were evaluated. This involved examination of spring coil openings uniformity in conjunction with spherical particles, the measurement of the amount of tension require to cause spring extension, and visual examination of the spring profile during vibration. Figure 5.14 shows a typical response for spring type A showing the variation of spring intercoil distance plotted against the angular rotation of the spring extension control screw (6) (see figure 5.7). The spring intercoil distance, dg is calculated as the ratio of the spring length and the number of active coils. As it may be seen, dg increases in a linear manner in response to the applied tension. The excellent reproducibility in response indicates the absence of hysterisis in the ranges tested.
Figures 5.15 and 5.16 show the variation of spring coil gap with particle size for spring types A and B respectively. The vibration amplitude is ca. 20 mV corresponding to a maximum displacement of ca. 2mm as measured at the spring end of the cantilever. These experiments were conducted by charging the spring with different sieve cut sizes of 3 g glass ballotini particles, in the range 58 - 600