Modern Machine-Shop Practice Part 190

From the average of these quant.i.ties we find the moment of resistance to be expressed by the following formulae for straight open belts between 2"

journals:

At 160 r. p. m.:

_M_ = .053_S_ + 14.7, (5.)

At 18 r. p. m.:

_M_ = .11_S_ + 9, (6.)

in which

_M_ = moment of resistance in inch lbs.

_S_ = sum of tensions.

When a crossed belt does not rub upon itself, the resistance is the same as for an open belt.

The resistance offered by the introduction of carrying pulleys and tighteners is appreciable, and depends upon the pressure brought to bear against their journals. If the belt rubs against the f.l.a.n.g.es of the carrying pulleys, the resistance is very much increased, and this is often liable to occur in horizontal belts from a change of load. The friction on journals of carrying pulleys may be estimated by the formulae already given if we subst.i.tute for _S_ the pressure against their journals. In the experiments which were made upon internal resistances, the greatest resistance was offered by a quarter-twist belt 6 feet between journals on 20-inch pulleys.

The equation for this belt may be written:

_M_ = .35_S_ + 58, (7.)

but the introduction of a carrying pulley reduced the resistance to no more than what might be expected from the same number of journals with a straight belt.

With quarter-twist belts the resistance lies chiefly in slip, which occurs as the belt leaves the pulleys, and this naturally depends upon the distance between journals in terms of the diameters of the pulleys.

The effect of time upon the tension of the belt used in Table VIII. is plainly shown by experiments 588 to 613 inclusive, between which the pulleys remained at a fixed distance apart, and the belt slowly stretched from a tension of 380 to 280 lbs.

To estimate the efficiency of belt transmission for an average case, we may a.s.sume 40 in. lbs. as the moment of internal resistance for a belt whose tension is 500 lbs. and 40 in. lbs. statical moment = about 20 ft.

lbs. per revolution. If the belt is transmitting 400 lbs. with two per cent. of slip on 20 in. pulleys, then .02 400 5 = 40 ft lbs. are lost per revolution in slip, making a total loss of 60 ft. lbs. per revolution.

TABLE VIII.

SHOWING THE INCREASE IN THE SUM OF THE TENSIONS ON A VERTICAL BELT 4"

WIDE BY 1/4" THICK, AND 24 FT. LONG, ON 20" CAST-IRON PULLEYS, AT 120 R.

P. M.

------+---------+-----------+-----+-----+--------+---------+---------- No. of| Scales | Tension | | | Incre- |Percen'e | exper-+----+----+-----+-----+ | | m'nt |of Incre-| Date.

im'nt.| A. | B. |_T_ +|_T_ -| _T_ | _t_ |of _T_ +| ment. | |[44]|[44]| _t_ | _t_ | | | _t_ | | ------+----+----+-----+-----+-----+-----+--------+---------+---------- 578 | 93 | 101| 194 | 16 |105 | 89 | 0 | |5-15-1885.

579 | 70 | 142| 212 | 144 |178 | 34 | 18 | | 580 | 67 | 170| 237 | 206 |221.5| 15.5| 43 | | 581 | 66 | 180| 246 | 228 |237 | 9 | 52 | | 582 | 66 | 188| 254 | 244 |249 | 5 | 60 | .323 | 583 | 91 | 101| 192 | 20 |106 | 86 | -2 | | ------+----+----+-----+-----+-----+-----+--------+---------+---------- 584 |202 | 210| 412 | 16 |214 |214 | 0 | |5-15-1885.

585 |167 | 250| 417 | 166 |292.5|292.5| 5 | | 586 |145 | 300| 445 | 310 |376.5|376.5| 33 | .171 | 587 |185 | 195| 380 | 20 |200 |200 | -32 | | ------+----+----+-----+-----+-----+-----+--------+---------+---------- 588 |190 | 199| 380 | 0 |190 |190 | 0 | |5-18-1885.

589 |133 | 250| 393 | 214 |303.5| 89.5| 13 | .033 | ------+----+----+-----+-----+-----+-----+--------+---------+---------- 590 |177 | 177| 354 | 0 |177 |177 | 0 | |5-19-1885.

591 |156 | 203| 359 | 94 |226.5|132.5| 5 | | 592 |138 | 235| 373 | 194 |283.5| 89.5| 19 | | 593 |135 | 250| 385 | 230 |307.5| 77.5| 31 | | 594 |128 | 275| 403 | 294 |348.5| 34.5| 49 | | 595 |125 | 300| 425 | 350 |387.5| 37.5| 71 | | 596 |123 | 325| 448 | 404 |426 | 22 | 94 | .333 | 597 |168 | 168| 336 | 0 |168 |168 | -18 | | ------+----+----+-----+-----+-----+-----+--------+---------+---------- 598 |143 | 143| 286 | 0 |143 |143 | 0 | |5-25-1885.

599 |140 | 148| 288 | 16 |152 |136 | 2 | | 600 |130 | 160| 290 | 60 |175 |115 | 4 | | 601 |122 | 170| 292 | 196 |194 | 98 | 6 | | 602 |116 | 180| 296 | 28 |212 | 84 | 10 | | 603 |112 | 190| 302 | 156 |229 | 73 | 16 | | 604 |108 | 200| 308 | 184 |246 | 62 | 22 | | 605 |105 | 210| 315 | 210 |262.5| 52.5| 29 | | 606 |102 | 220| 322 | 236 |279 | 43 | 36 | | 607 |100 | 230| 330 | 260 |295 | 35 | 44 | | 608 | 99 | 240| 339 | 282 |310.5| 28.5| 53 | | 609 | 98 | 250| 348 | 304 |326 | 22 | 62 | | 610 | 98 | 260| 358 | 316 |337 | 21 | 72 | | 611 | 99 | 270| 369 | 342 |355.5| 13.5| 83 | | 612 |100 | 280| 380 | 360 |370 | 10 | 94 | .357 | 613 |140 | 140| 280 | 0 |140 |140 | -6 | | ------+----+----+-----+-----+-----+-----+--------+---------+----------

[44] Scales A recorded the reduction of the load on the testing device for _vertical_ belts by the tension of the loose part of the belt (_t_). Scales B, by that of the tight side of the belt (_T_).

The total power expended per revolution is about 2,000 ft. lbs., therefore .03 is lost.

Under light loads, the internal resistance, which is nearly constant in amount, may be a large percentage of the power transmitted, while under heavy loads the percentage of slip may become the princ.i.p.al loss.

It would be difficult to work out, or even to use, a general expression for the efficiency of belt transmission, but, from the foregoing, it would seem safe to a.s.sume that 97 per cent. can be obtained under good working conditions.

When a belt is too tight, there is a constant waste in journal friction, and when too loose, there may be a much greater loss in efficiency from slip. The allowance recommended of 2 per cent. for slip is rather more than experiment would indicate for any possible crawl or creep due to the elasticity of the belt, but in connection with this, there is probably always more or less actual slip, and we are inclined to think that in most cases this allowance may be divided into equal parts representing creep and slip proper. Under good working conditions, a belt is probably stretched about 1 per cent. on the tight side, which naturally gives 1 per cent. of creep, and to this we have added another per cent. for actual slip in fixing the limit proposed.

The indications and conclusions to be drawn from these experiments are:

1. That the coefficient of friction may vary under practical working conditions from 25 per cent. to 100 per cent.

2. That its value depends upon the nature and condition of the leather, the velocity of sliding, temperature, and pressure.

3. That an excessive amount of slip has a tendency to become greater and greater, until the belt finally leaves the pulley.

4. That a belt will seldom remain upon a pulley when the slip exceeds 20 per cent.

5. That excessive slipping dries out the leather and leads toward the condition of minimum adhesion.

6. That rawhide has much greater adhesion than tanned leather, giving a coefficient of 100 per cent. at the moderate slip of 5 ft. per minute.

7. That a velocity of sliding equal to .01 of the belt speed is not excessive.

8. That the coefficients in general use are rather below the average results obtained.

9. That when suddenly forced to slip, the coefficient of friction becomes momentarily very high, but that it gradually decreases as the slip continues.

10. That the sum of the tensions is not constant, but increases with the load to the maximum extent of about 33 per cent. with vertical belts.

11. That, with horizontal belts, the sum of the tensions may increase indefinitely as far as the breaking strength of the belt.

12. That the economy of belt transmission depends princ.i.p.ally upon journal friction and slip.

13. That it is important on this account to make the belt speed as high as possible within the limits of 5,000 or 6,000 ft. per minute.

14. That quarter-twist belts should be avoided.

15. That it is preferable in all cases, from considerations of economy in wear on belt and power consumed, to use an intermediate guide pulley, so placed that the belt may be run in either direction.

16. That the introduction of guide and carrying pulleys adds to the internal resistances an amount proportional to the friction of their journals.

17. That there is still need of more light on the subject.

CHAPTER x.x.xIII.--FORGING.