Modern Machine-Shop Practice Part 188

216| |345|122|320|332.5| 12.5|25.8 | 9.4|18.8 |164 |1.13 | |[B]

---+---+---+---+---+-----+-----+-----+----+-----+----+-----+------+--- 217|200|200| | 48|124 | 76 | 1.63| .4| .8 |179 | .156| | 219| |240| |160|200 | 40 | 5 | 1 | 2 |176 | .524| | 220| |360| |320|340 | 20 |17 | 2.7| 5.4 |170 | .954| | 221| |430| |400|415 | 5 |27.7 |15 |30 |167 |1.13 | | ---+---+---+---+---+-----+-----+-----+----+-----+----+-----+------+--- 222|300|318| |160|239 | 79 | 3.03| .8| 1.6 |179 | .354| | 223| |350| |240|295 | 55 | 5.36| 1.2| 2.4 |177 | .543| | 224| |400| |320|360 | 40 | 9 | 2 | 4 |175 | .719| | 225| |470| |440|455 | 15 |30.3 | 8 | 1.6 |167 |1.17 | |[C]

226| |450| |400|425 | 25 |17 | 4 | 8 |172 | .943| 1 m.| 227| |450| |400|425 | 25 |17 | 8 |16 |172 | .943| 5 m.| 228| |450| |400|425 | 25 |17 |17.3|34.6 |172 | .943| 10 m.|[D]

229| |418| |360|389 | 29 |13.4 | 3 | 6 |173 | .859| 15 m.|[E]

---+---+---+---+---+-----+-----+-----+----+-----+----+-----+------+--- 230|400|405| |160|282.5|122.5| 2.30| .8| 1.6 |179 | .267| | 232| |455| |320|387.5| 67.5| 5.74| 1.4| 2.8 |177 | .566| | 233| |495| |400|447.5| 47.5| 9.42| 1.9| 3.8 |176 | .730| 1 m.| 234| |495|370|400|447.5| 47.5| 9.42| 2.1| 4.2 |176 | .730| 5 m.| 235| |560| |480|520 | 40 |13 | 2.7| 5.4 |175 | .859|Start.| 236| |560| |480|520 | 40 |13 | 4.5| 9 |175 | .859| 5 m.| 237| |560| |480|520 | 40 |13 | 7.5|15 |175 | .859| 10 m.| 238| |550|380|480|465 | 85 | 5.47|20 |40 |178 | .547| 15 m.| ---+---+---+---+---+-----+-----+-----+----+-----+----+-----+------+--- 239|400|560| |480|520 | 40 |13 | 3.4| 6.8 |175 | .859| 1 m.|[F]

---+---+---+---+---+-----+-----+-----+----+-----+----+-----+------+--- 240|500|610| |480|545 | 65 | 8.38| 2.1| 4.2 |177 | .688| 1 m.| 241| |610| |480|545 | 65 | 8.38| 2.5| 5 |177 | .688| 5 m.| 242| |660| |560|610 | 50 |12.2 | 3.2| 6.4 |176 | .814| 1 m.| 243| |655| |560|607.5| 47.5|12.8 | 8.4|16.8 |176 | .830| 5 m.|[G]

---+---+---+---+---+-----+-----+-----+----+-----+----+-----+------+--- 244|600|700| |560|630 | 70 | 9 | 1.9| 3.8 |177 | .711| 1 m.| 245| |700| |560|630 | 70 | 9 | 2.1| 4.2 |177 | .711| 5 m.| 246| |690|550|560|625 | 65 | 9.69| 2.3| 4.6 |177 | .735| 10 m.| ---+---+---+---+---+-----+-----+-----+----+-----+----+-----+------+--- 247|600|750| |600|675 | 75 | 9 | 2.2| 4.4 |177 | .771| 1 m.| 248| |740|585|600|670 | 70 | 9.57| 2.4| 4.8 |177 | .731| 5 m.| ---+---+---+---+---+-----+-----+-----+----+-----+----+-----+------+--- 249|600|770| |640|705 | 65 |10.8 | 2.5| 5 |177 | .770| 1 m.| 250| |765| |640|702.5| 62.5|11.2 | 3.5| 7 |177 | .782| 5 m.| 251| |770|600|640|685 | 85 | 8.06| 4.2| 8.4 |178 | .672| 10 m.| ---+---+---+---+---+-----+-----+-----+----+-----+----+-----+------+--- 252|600|790| |680|735 | 55 |13.4 | 4.3| 8.6 |176 | .845| 1 m.| 253| |790| |680|735 | 55 |13.4 | 6.3|12.6 |176 | .845| 5 m.|[H]

---+---+---+---+---+-----+-----+-----+-----+-----+----+-----+------+--- 254|100|100| | 44| 72 | 28 | 2.57| .6| 1.2 |176 | .307| |[I]

256| |160| |120|140 | 20 | 7 | 2.1| 4.2 |172 | .648| | 257| |200| |160|180 | 20 | 9 | 4 | 8 |171 | .736| | 258| |230| |200|215 | 15 |14.3 | 6.6|13.2 |168 | .907| 1 m.| 259| |230|100|200|215 | 15 |14.3 | 7.2|14.4 |168 | .907| 5 m.| ---+---+---+---+---+-----+-----+-----+----+-----+----+-----+------+--- 261|100|100| | 44| 72 | 28 | 2.57| .6| 1.2 |176 | .307| |[J]

263| |160| |120|140 | 20 | 7 | 2.8| 5.6 |172 | .648| | 264| |200| |160|180 | 20 | 9 | 5.1|10.2 |171 | .736| | 265| |230| |200|215 | 15 |14.3 | 7.3|14.6 |168 | .907| 1 m.| 266| |230| |200|215 | 15 |14.3 | 7.9|15.8 |168 | .907| 5 m.| 267| |270| |240|255 | 15 |17 |10.7|21.4 |168 | .966| 1 m.|[K]

---+---+---+---+---+-----+-----+-----+----+-----+----+-----+------+--- 268|300|350| |240|295 | 55 | 5.36| 1.4| 2.8 |177 | .544| | 269| |400| |320|360 | 40 | 9 | 3 | 6 |175 | .719| | 270| |450| |400|425 | 25 | 17 | 6.8|13.6 |172 | .943| 1 m.|[K]

271| |418| |360|389 | 29 |13.4 | 8.8|17.6 |173 | .859| 1 m.| 272| |418| |360|389 | 29 |13.4 |15.6|31.2 |173 | .859| 5 m.|[G]

---+---+---+---+---+-----+-----+-----+----+-----+----+-----+------+--- 273|600|700| |560|630 | 70 | 9 | 6.3|12.6 |177 | .711| | 274| |650| |480|565 | 85 | 6.65| 3.1| 6.2 |178 | .610| 1 m.| 275| |650| |480|565 | 85 | 6.65| 3.9| 7.8 |178 | .610| 5 m.| 276| |650| |480|565 | 85 | 6.65| 4.4| 8.8 |178 | .610| 10 m.| ---+---+---+---+---+-----+-----+-----+----+-----+----+-----+------+--- 277|600|652| |400|526 |126 | 4.17| 1.4| 2.8 |178 | .460| |[L]

279| |715| |560|637.5| 77.5| 8.23| 2.4| 4.8 |177 | .682| | 280| |705| |560|632.5| 72.5| 8.72| 2.8| 5.6 |177 | .701| | 281| |700|560|560|630 | 70 | 9 | 3 | 6 |177 | .711| | ---+---+---+---+---+-----+-----+-----+----+-----+----+-----+------+--- 282|560|750| |640|695 | 55 |12.6 | 4.1| 8.2 |176 | .824| 1 m.| 283| |735|535|640|682.5| 47.5|14.3 |22 |44 |176 | .866| 5 m.|[M]

284| |770| |640|705 | 65 |10.7 | 5.4|10.8 |177 | .767| 1 m.|[N]

---+---+---+---+---+-----+-----+-----+----+-----+----+-----+------+--- 285|300|350| |240|295 | 55 | 5.36| 1.2| 2.4 |177 | .543| |[O]

286| |400| |320|360 | 40 | 9 | 1.8| 3.6 |175 | .719| | 287| |430| |360|395 | 35 |11.3 | 2.7| 5.4 |174 | .798| | 289| |465| |400|432.5| 32.5|13.3 | 5.3|10.6 |174 | .852| | 290| |455| |400|427.5| 27.5|15.5 | 7.3|14.6 |173 | .907| | 291| |460| |400|430 | 30 |14.3 |11.6|23.2 |173 | .881| | ---+---+---+---+---+-----+-----+-----+----+-----+----+-----+------+--- 292|100|100| | 44| 72 | 28 | 2.57| .5| 1 |176 | .307| | 293| |125| | 80|102.5| 22.5| 4.55| .8| 1.6 |173 | .502| | 294| |165| |120|142.5| 22.5| 6.33| 1.2| 2.4 |173 | .611| | 295| |200| |160|180 | 20 | 9 | 2.1| 4.2 |171 | .736| | 296| |230| |200|215 | 15 |14.3 | 3.4| 6.8 |168 | .907| | 297| |230| |200|215 | 15 |14.3 | 3.9| 7.8 |168 | .907| | ---+---+---+---+---+-----+-----+-----+----+-----+----+-----+------+--- 298|100|270| |240|225 | 15 |17 | 5.7|11.4 |168 | .966| 1 m.| 299| |270| |240|255 | 15 |17 | 7.6|15.2 |168 | .966| 5 m.| 300| |270| |240|255 | 15 |17 | 9.3|18.6 |168 | .966| 10 m.|[P]

---+---+---+---+---+-----+-----+-----+----+-----+----+-----+------+--- 303|100|110| | 40| 75 | 35 | 2.14| .1| .4 |177 | .246| |[Q]

304| |132| | 80|106 | 26 | 4.08| .4| 1.6 |174 | .463| | 305| |160| |120|140 | 20 | 7 | 1 | 4 |172 | .648| | 306| |195| |160|177.5| 17.5|10.1 | 1.9| 7.6 |169 | .814| | 307| |230| |200|215 | 15 |14.3 | 3 |12 |168 | .907| 1 m.| 308| |230| 90|200|215 | 15 |14.3 | 3.5|14 |168 | .907| 5 m.| 309| |270| |240|255 | 15 |17 | 4.5|18 |168 | .966| 1 m.| 310| |270| |240|255 | 15 |17 | 5.8|23.2 |168 | .966| 5 m.| 311| |270| |240|255 | 15 |17 | 6.2|24.8 |168 | .966| 10 m.| 312| |270| |240|255 | 15 |17 | 6.2|24.8 |168 | .966| 15 m.|[R]

313| |270| |240|255 | 15 |17 | 2 | 8 |168 | .966| 1 m.| 314| |270| |240|255 | 15 |17 | 2.1| 8.4 |168 | .966| 5 m.|[S]

315| |305| |280|292.5| 12.5|23.4 | 3.4|13.6 |165 |1.09 | 1 m.| 316| |305|100|280|292.5| 12.5|23.4 | 3.5|14 |165 |1.09 | 5 m.| ---+---+---+---+---+-----+-----+-----+----+-----+----+-----+------+--- 317|100|335| |320|327.5| 7.5|43.7 | 5.2|20.8 |152 |1.42 | 1 m.| 318| |335| |320|327.5| 7.5|43.7 | 6.5|26 |152 |1.42 | 5 m.| ---+---+---+---+---+-----+-----+-----+----+-----+----+-----+------+--- 319|300|380| |320|350 | 30 |11.7 | 1.3| 5.2 |173 | .814| 1 m.| 320| |380| |320|350 | 30 |11.7 | 1.4| 5.6 |173 | .814| 5 m.| 321| |440| |400|420 | 20 |21 | 2.1| 8.4 |170 |1.03 | 1 m.| 322| |440|260|400|420 | 20 |21 | 2.4| 9.6 |170 |1.03 | 5 m.| ---+---+---+---+---+-----+-----+-----+----+-----+----+-----+------+--- 323|300|480| |440|460 | 20 |23 | 2.8|11.2 |170 |1.06 | 1 m.|[T]

324| |480|285|440|460 | 20 |23 | 3 |12 |170 |1.06 | 5 m.| 325| |510| |480|495 | 15 |33 | 3.2|12.8 |167 |1.20 | 1 m.| 326| |510| |480|495 | 15 |33 | 5 |20 |167 |1.20 | 5 m.|[U]

Legend Remarks: [A] = Sag 10" at middle of belt.

[B] = Finally slipped off.

[C] = Belt finally slipped off.

[D] = Belt slip'd off.

[E] = Continuing.

[F] = After running 5 m. without load.

[G] = Belt slipped off 2 m. later.

[H] = Belt sl. off 2 m. lat. Pul. warm.

[I] = Belt sc.r.a.ped.

[J] = Belt dres'd with preparation recommend'd by maker.

[K] = Belt slipped off 3 m. later.

[L] = One day later.

[M] = Belt slipp'd off.

[N] = After 3 min. intermission.

[O] = Temp. 52.

[P] = Belt slipped off 4 m. later.

[Q] = 20 in. pulleys.

[R] = Temp. 56.

[S] = Temp. 42.

[T] = Temp. 46.

[U] = Belt sl. off 5 m. lat. Pul. warm.

A peculiar and important feature of Tables III. and IV. is the effect of time upon the percentage of slip. In previous experiments the percentage of slip was measured at once after the load was applied, but it was accidentally discovered that repeated measurements seldom agreed, and investigation showed that these discrepancies were princ.i.p.ally due to the duration of the experiment. The continual slipping of the belt was found to cause a deposit of a thick black substance upon the surface of the pulley, which, acting as a lubricant, continued to increase the slip still further.

Upon removing the load on brake-wheel, this deposit would be again absorbed by the belt, and the original adhesion would be restored. The temperature was also found to affect the slipping, and, in general, the colder the weather the slower would this deposit take place.

Experiments 353 to 360 inclusive were made to determine the limit at which the belt would run continuously without increasing its percentage of slip. After the pulleys had become well coated and the slip had reached a high per cent., the load on the brake-wheel was gradually removed until a marked improvement was reached, as shown by experiments 359 and 360. The highest allowable coefficient of friction for this belt is therefore estimated to be somewhere between 1.13 and .995, or we may safely say 1. The highest coefficient obtained was 1.67, but, of course, this was temporary. The diameter of the pulley also appears to affect the coefficient of friction to some extent. This is especially to be noticed at the very slow speed of 18 revolutions per minute on 10 in.

and 20 in. pulleys, where the adhesion on the 20 in. pulleys is decidedly greater; but, on the other hand, at 160 revolutions per minute the adhesion on the 10 in. pulleys is often as good, and sometimes better, than appears for the 20 in. at the same velocity of sliding.

It might be possible to determine the effect of pulley diameter upon adhesion for a perfectly dry belt, where the condition of its surface remains uniform, but for belts as ordinarily used it would be very difficult, on account of the ever-changing condition of surface produced by slip and temperature. It is generally admitted that the larger the diameter the greater the adhesion for any given tension, but no definite relation has ever been established, nor, indeed, does it seem possible to do so except by the most elaborate and extensive experiments.

It should be observed, however, that such a variation, if true, implies a corresponding variation in the coefficients of friction for different intensities of pressure upon the same pulleys, and that, consequently, our experiments should show higher coefficients under the lighter loads for the same velocity of sliding. Referring to Table II., where the condition of the belt is dry and uniform for a large range of tensions, we find that this inference is generally sustained, although there are some few exceptions.

Experiment 106 may be compared with 116, and 112 with 133, also 108, 113, and 135, all showing great reductions in the coefficients of friction for increments in tension. The exceptions are all to be found under the smallest velocities of sliding, and appear only in the third decimal place, so that the weight of their record against the probability of such a law is light. By a similar inference it should also follow that a wide belt would drive a little more at a given tension than a narrow one, on account of the reduction in pressure per square inch against the pulley. The mean intensity of pressure of a belt against its pulley may be considered as proportional to the sum of the tensions divided by the product of pulley diameter and width of belt, and an a.n.a.lysis of the experiments referred to will show the relation there existing between intensity of pressure and coefficient of friction.

If we let [Iota] = intensity of pressure, and [phi] = coefficient of friction, we shall find that [phi] is approximately proportional to [Iota]^{-.15}, or, in other words that doubling the width of belt or diameter of pulley would apparently increase the coefficient of friction about 10 per cent. of its original value. This relation is not proved, of course, and it is given only as a suggestion toward the solution of the question. If the coefficient of friction does vary with the intensity of pressure, the problem of determining the driving power of a belt on strictly mathematical principles will indeed be complicated.

The coefficient of friction in the tables has been calculated by a well-known formula, developed upon the a.s.sumption of a uniform coefficient around the arc of contact, but this could no longer be considered as correct if the coefficient is known to vary with the pressure. Referring from Table II. to Table III., we shall find at once the proof and contradiction of the inferences drawn from Table II., and we are left as much in the dark as ever respecting the value of pressure intensity.

Practical millwrights all know, or think they know, that an increase of pulley diameter increases the drive, and it is a matter of common observation that when large and small pulleys are connected by a crossed belt, the smaller pulley will invariably slip first.

On one side a great deal of testimony can be adduced to show that pressure intensity should be an important factor in the theory of belt transmission, and, on the other hand, we have strong evidence to the contrary. I may refer, in this connection, to the experiments of Mr.

Holman in _Journal of Franklin Inst.i.tute_ for September, 1885, in which there is no indication that the coefficient of friction varies at all with the pressure. The coefficients obtained by Mr. Holman follow the variations in slip like our own, and it gives us pleasure to observe that our general results and conclusions are so strongly corroborative of each other. There is at the same time a great difference in the methods pursued in arriving at the same results. In his experiments, the velocity of sliding was the fixed condition upon which the coefficient of friction was determined, while, in ours, the conditions were those of actual practice in which the percentage of slip was measured. Our least amount of slip, with a dry belt running at the extremely slow speed of 90 feet per minute, was 1.08 inches, and ten times this would be perfectly proper and allowable. A great many of Mr. Holman's experiments are taken at rates below 1" per minute, and the coefficients obtained are very much below the average practice, as himself seems to believe.

The velocity of sliding which may be a.s.sumed in selecting a proper coefficient is directly proportional to the belt speed, and may safely be estimated at .01 of that speed. For a pair of pulleys we should have .01 on each pulley, and therefore .02 for slip. Few belts run slower than 200 or 300 ft. per minute, and consequently a slip of less than 2 or 3 ft. per minute need seldom be considered. Another point of difference which may possibly affect the coefficients obtained, is that, in Mr. Holman's case the same portion of belt surface was subject to continuous friction, while in ours, the friction was spread over the belt at successive portions as in actual work. This we consider a new and important feature of our experiments. As a matter of practical importance, care was taken to observe, as nearly as possible, the maximum slip which might safely take place before a belt would be thrown from its pulley. A number of observations taken throughout the experiments led to the final conclusion that 20 per cent. of slip was as much as could safely be admitted. This information has been found of value in cases where work is done intermittently by a fly-wheel and the belt has to restore the speed of the wheel. It cannot be said in regard to a maximum value of [phi] that any was determined or even indicated, although it is certain that the increase at high rates of slip becomes less rapid.

We have now seen that the driving power of a leather belt depends upon such a variety of conditions, that it would be manifestly impracticable if not impossible to correlate them all, and it is thought better to admit the difficulties at once than to involve the subject in a labyrinth of formulae which life is too short to solve.

The relative value of pulley diameters may vary with different belts, and all that can be expected or desired is some general expression covering roughly the greatest number of cases. Our apparatus did not admit of extensive variations in this respect, and our attention was given princ.i.p.ally to the question of slip.

The coefficients given in Table III. are remarkably high, and show a great superiority for the rawhide over tanned leather in point of adhesion. The belt in question was very soft and pliable, but a little twisted from use on a cone pulley where it had rubbed against one side.

It is not desirable, on account of its soft and adhesive nature, to use this kind of belt where frequent shifting is required, and when used on cone pulleys it is liable to climb and stretch against the side of the cone; but for a plain straight connection, there seems to be little room for improvement. Table IV. contains the results of similar experiments upon an oak-tanned leather belt made by Chas. A. Shieren & Co. Here the coefficients are much smaller than those given in Table III., and there is quite a marked difference between the coefficients for 10 in. and 20 in. pulleys.

As before noticed, the outside temperature has its effect, and it is probable that much lower results would have been obtained had the experiments been made in the heat of midsummer. The high coefficients obtained, together with the rapid increase of tension, show that the pulling power of a long horizontal belt must, in many cases, be limited by its strength rather than by its adhesion.

Table V. gives the results of experiments upon a light planer belt at very slow and very high speeds. As would naturally be expected, much higher coefficients were found at the high speed on account of the greater velocity of sliding.

TABLE V.

OAK-TANNED LEATHER BELT 2" WIDE BY 3-16" THICK AND 30' 4" LONG, WEIGHING 4 LBS., ON 20" CAST-IRON PULLEYS. DRY AND SMOOTH, TAKEN FROM SERVICE ON PLANER.

Legend column headings: [A] = No. of Experi'nt.

[B] = Sum of Tensions. _T_ + _t_ Initial.

[C] = Sum of Tensions. _T_ + _t_ Working.

[D] = Sum of Tensions. _T_ + _t_ Final.

[E] = _T_ - _t_ Working.

[F] = _T_ [G] = _t_ [H] = _T_/_t_ [I] = Percentage of Slip.

[J] = Velocity of Slip in ft. per min.

[K] = Arc of contact.

[L] = Coefficient of Friction.

[M] = Duration of run at time of experiment.

[N] = Remarks.

---+---+---+---+---+-----+----+----+----+------+----+----+------+--- [A]|[B]|[C]|[D]|[E]| [F] | [G]|[H] | [I]| [J] | [K]| [L]| [M] |[N]

---+---+---+---+---+-----+----+----+----+------+----+----+------+--- 429|100|110| | 40| 75 |35 |2.14| 1.2| .54|179|.243| |18 430| |115| | 60| 87.5|27.5|3.18| 6.1| 2.75|178 |.372| |r.

431| |118| | 70| 94 |24 |3.92|16.5| 7.42|178 |.440| |p.