Silver formation

Appendix-I

Kinematics of Picking System

Power consumed in picking can be derived from considerations of loom rpm (n), average velocity of free flight (v m/s), angular displacement of crank during free flight (θ degrees), the reed space (R meters), the length of shuttle (L meters) and the shuttle mass (m kilograms). The steps involved are listed in the following.

No. of picks per second = n / 60 which is equivalent to 6n degrees of crank displacement in one second.
Time taken by crank to get displaced by θ degrees is therefore {θ / 6n} seconds
Distance covered by the shuttle in {θ / 6n} seconds is {R + L} m
Hence average velocity of shuttle in free flight v = [6 n (R + L)}/ θ] m/s
Assuming no loss in velocity subsequent to loss of contact with picker, the kinetic energy of shuttle at the instant of its escape from picker is [½ m v²]
This amount of energy has to be supplied by the picking system during each pick
Each picking cycle consumes [60/n] seconds
Hence power consumed by picking system in kW is [½ m v²] [n/60] 10^-3

On substitution of the expression of v in the equation, the resultant form is

Picking power P in kW = [{3 m (R + L)² n³} / θ² ] 10^-4

If a loom is operated manually by turning the fly wheel slowly and the displacement of shuttle noted as function of crank position then one finds that the shuttle slowly moves a short distance towards the centre of reed and then comes to a halt. This displacement when recorded graphically yields the nominal displacement curve, shown in Fig 40. The nature of this displacement is governed by the contour of picking tappet. However when the loom is operated by power the nature of displacement of shuttle as a function of the angular position of crank is quite different. Indeed there is a considerable lag initially followed by an exponential rise, as shown by the actual displacement profile.

Fig. 40

The lag between the nominal and the actual displacement of shuttle is caused by strain in the picking system arising out of impulsive nature of the input force and the inertia of picking system. This strain results in a buildup of elastic energy within the system which on its release accelerates the shuttle very fast to its final velocity. Indeed the shuttle loses contact with the picker around the crank position at which the curves of nominal displacement and actual displacement intersect. If M is the combined equivalent mass of the shuttle and the picker, λ is the stiffness of the system expressed in units of force/unit distance, s and x are the nominal and actual displacements of shuttle at any instant and “a” is the uniform value acceleration then

M. a = λ (s – x)

If the ratio (λ / M) is written as n² then the equation of motion of shuttle during the acceleration phase in shuttle box can be expressed as

a = n² (s – x)

The quantity ‘n’ is the natural frequency of the system; higher the value of ‘n’, closer is the profiles of the actual and normal displacement of shuttle.

If shuttle acceleration is to be maintained at a constant value ‘A’ then by integrating the aforesaid expression, the shuttle displacement curves are given by

x = (A t² / 2) + B t + C

and

s = (A t² / 2) + B t + C + (A / n²)

The constants B and C can be eliminated if the boundary condition is imposed that at t=0 both displacement and velocity are zero. This leads to expression of the nominal displacement profile

s = (A t² / 2) + (A / n²)

There is therefore a finite nominal displacement at the beginning of the picking motion, a condition satisfied by a pre-strained picking mechanism, if uniform acceleration is desired throughout the acceleration phase.

One can extend this exercise and impose other types of desirable nature of shuttle acceleration such as of constant nominal velocity, constant nominal acceleration or of a sinusoidal actual acceleration, and work out the corresponding profile of nominal displacement. After all the design of picking tappet – such as of the picking cone – would be governed by the desired profile of nominal displacement of shuttle. A detailed account of this study can be read from an article authored by M Catlow and J J Vincent, published in the November, 1951 issue of the Journal of the Textile Institute, pp T413 – T488.