XVI
XVI
Rule 1.Pulley Speed.—When the diameter of both pulleys and the speed of one is given, to find the speed of the other: Place the points of spacing dividers upon the two given diameters in inches upon the scale (Fig. 97); then raise the dividers, keeping the space obtained, and place one point on the given speed and the otheraboveit for speed ofS, orbelowit for speed ofL(SandLmeaning smaller and larger pulley, respectively). This point will fall upon the required speed.
[12]Contributed to Power by A. G. Holman, M. E.
[12]Contributed to Power by A. G. Holman, M. E.
Example: If the two pulley diameters are 10 and 25 inches and speed of larger pulley is 120 revolutions per minute, what is speed of small pulley?
Place the points of dividers on 10 and 25 on scaleA, then lift the dividers and place one point on 120 and the other above it upon the scale; the other point now rests on 300 as the speed ofS. If the speed ofShad been given, one point would have been placed at 300 and the otherbelowit, falling upon 120, the required speed ofL.
Note.—In applying this rule, if the speed comes beyond the range of scaleA, the result may be readby carrying the space to the revolution scale on scaleB, and proceeding in the same way.
Fig. 97.
Fig. 97.
Example: Diameter of pulleys 12 and 36 inches and speed ofL500, what is speed ofS? Place points of dividers on 12 and 36. Now, if dividers are raised and one point placed on 500 and the other above it on scaleA, it will come beyond the top of the scale. Hence go to scaleB, placing lower point on revolution scale at 500 and the other point above, which will fall upon 1500, the answer.
Rule 2.Pulley Diameters.—When the speed of both pulleys and the diameter of one is given, to find diameter of the other: Place points of dividers on the two speeds on scaleAor revolution scaleB. Then place one point of dividers on given diameter and the other above it to find diameter ofL, or below it for diameter ofS. The figure thus indicated is the required diameter.
Example: Speeds 180 and 450 and diameter of smaller pulley 20. What must be diameter ofL?
Place points of dividers on 180 and 450 on scaleA. Then place one point on 20 (the given diameter). The other point falls at 50, the required diameter ofL.
If the point falls between two graduations in any problem, the result can be closely judged by the relative position.
The other and more labor-saving use for this chart is its application to belting problems. It is generally conceded that there is no subject of more general interest in practical mechanics and none on which there is a greater difference of opinion than the proper allowanceto be made in the selection of belt sizes for given requirements. The general formula for the horse-power transmitted by belting is
HP=WS/Cin whichHP= horse-power,
W= width of belt in inches,S= speed of belt in feet per minute, andC= constant.
The proper values of this constant, or the feet per minute that each inch of width must run to transmit a horse-power, under certain conditions, is the point in question.
On the right-hand side of lineAon the chart is a series of lines representing different values for this constant. The lower one, marked 4, represents 400 feet belt speed per minute, the next above is for 500, and so on. Against some of these values are suggestions as to belts often recommended in connection with these constants. For instance, 2 to 6Ssuggests the constant 1100 to be used for 2- to 6-inch single leather belt, 1000 for 6½- to 10-inch single, 600 for 2- to 6-inch double, etc.
These suggestions practically agree with the advice of the Geo. V. Cresson Company's catalog and the deductions of Kent's Handbook.
More power may be transmitted than these suggestions will allow, by increasing the tension, but this is accompanied by the disadvantage of requiring extra attention and undue pressure upon bearings.
The use of the chart for horse-power and width of belting is explained by the following rules:
Rule 3.Horse-power of Belting.—To find the horse-power that can be transmitted when diameter and speed of pulley and width of belt are given: Place one point of dividers on scaleAat the width of belt in inches and the other point at the bottom of the line (at 1). Next add this space to the hight representing diameter of pulley by placing lower point of dividers upon the given diameter and allowing the other point to rest upon the scale above. Then holding the upper point stationary, open or close dividers until the other point falls upon the proper constant on the scale at right-hand side of lineA. Now transfer this space last obtained to the scaleBby raising the dividers, carrying them square across toBand placing the point that was on the constant upon the given speed on the revolution scale. Note the location of the other point of dividers upon the horse-power scale, which indicates the horse-power that can be transmitted under the given conditions.
Example: What horse-power can be transmitted by an 8-inch double belt running on a 40-inch pulley at 500 feet per minute? Place one point of dividers on lineAat 8 (width of belt) and the other point at bottom of line. Next raise dividers and place lower point on 40 (diameter of pulley) and let the other point fall above upon the scale. Then close dividers until lower point comes to the constant for 6½ to 10 double. Carry this space to scaleBwith lower point on 500 on revolution scale. Under point now falls upon 84 on horse-power scale, which is the required horse-power.
Rule 4.Width of Belting.—To find the necessarywidth of belting when size and speed of pulley and the horse-power are given: Place one point of dividers on scaleBupon the horse-power and the other point upon the revolutions. Next transfer this space to scaleAby raising the dividers, carrying them square across and placing the point that was on revolutions upon the constant. Then holding the other point stationary, raise the point that was on the constant and open dividers until this point falls upon the given diameter. Now lift the dividers and carry the lower point down to bottom of line (the point 1). The upper point will now indicate the required width of belt.
Note.—If, in finding width of belt, there is doubt about the proper constant to take, a medium value, say 6, may be assumed and a hasty "cut and try" will show in what classification the required belt will come.
Example: What width of belt for 100 horse-power with 40-inch pulley at 500 revolutions?
Place point of dividers on scaleBupon 100 on horse-power scale and the other upon 500 on the revolution scale. Then carry the space to scaleAwith lower point on constant 5. Then resting dividers upon upper point open them until lower point is at 40 (diameter). Finally, raise dividers and place lower point at bottom of line. Upper point is now at 9½, indicating the nearest even width 10 as the answer.
A little practice will make one familiar with these rules, and it will be seen that in the belting rules the four motions perform two multiplications and a division.