Drive Design Speed Ratio = rpm (faster) = PD = N rpm (slower) pd n Where: rpm = Revolutions per minute PD = Larger pitch diameter pd = Smaller pitch diameter N = Larger sprocket grooves n = Smaller sprocket grooves (Q) (rpm) 63025 Where: Q = Torque, lb-in rpm = Revolutions per minute Be sure to use torque and rpm values at the same shaft; do not mix torque and rpm values from different shafts. (Te)(V) 33,000 Where: Te = Effective tension, lb. Design hp x SF Where: SF = Service Factor Torque (lb-in) = Where: 63025 (hp) rpm rpm = Revolutions per minute Belt Speed (V) = (PD) (rpm) 3.82 Where: PD = Pitch diameter, in. rpm = Revolutions per minute of same pulley The exact belt pitch length, in inches, can be found as follows: Pitch Length = 2(CD)(Cos ) + (PD + pd) + (PD - pd) 2 180 = Sin -1 ( PD pd ) 2CD Where: CD = Drive center distance, in. PD = Large pitch diameter, in. pd = Small pitch diameter, in. The approximate center distance in inches can be found as follows: Center Distance = K + K 2-32(PD - pd) 2 16 K = 4PL - 6.28 (PD + pd) Where: PD = Large pitch diameter, in. pd = Small pitch diameter, in. PL = Belt pitch length, in. The exact center distance can be calculated using an iterative process between the center distance and belt length equations above. The exact center distance has been found when the two equations converge. Span Length = CD 2 - (PD - pd)2 4 Where: PD = Large pitch diameter, in. pd = Small pitch diameter, in. CD = Drive center distance, in. Design Torque = Q x SF Where: T = Torque load SF = Service factor Service Factor = Rated T a (T e + T c) Where: T a = Rated belt working tension, lb. T c = Centrifugal tension, lb. The arc of contact on the smaller pulley in degrees can be found as follows: Arc of Contact = 180 - ( 60 (PD - pd) ) CD Where: PD = Large pitch diameter, in. pd = Small pitch diameter, in. CD = Drive center distance, in. 103
Drive Design Continued The number of teeth in mesh on the smaller sprocket can be found as follows: Teeth in Mesh = (Arc) (n) 360 Where: Arc = Arc of contact; small sprocket, degrees n = number of grooves, small sprocket Drop any fractional part and use only the whole number as any tooth not fully engaged cannot be considered a working tooth. If the teeth in mesh is less than 6, correct the belt torque rating with the following multiplication factors: 5 Teeth in Mesh Multiply by 0.8 4 Teeth in Mesh Multiply by 0.6 3 Teeth in Mesh Multiply by 0.4 2 Teeth in Mesh Suggest Redesign 1 Tooth in Mesh Suggest Redesign Torque loading due to flywheel effect (acceleration or deceleration) can be calculated as follows: Torque (lb-in) = 0.039(RPM - rpm) (WR 2 ) t Where: RPM = Final revolutions per minute rpm = Initial revolutions per minute WR2 = Flywheel effect, pound-feet 2 (lb-ft 2 ) (1 ft-lb-sec 2 is equivalent to 32.2 lb-ft 2 ) t = time, seconds The flywheel effect of a sprocket can be estimated as follows: WR 2 (lb-ft 2 ) = (F) (Z) (D4 - d 4 ) 1467 Where: F = Face width of rim, in. Z = Material density, lb/in 3 D = Outside rim diameter, in. d = Inside rim diameter, in. Typical Values: 2024 Aluminum - 0.100 lb/in 3 6061 Aluminum - 0.098 lb/in 3 Iron - 0.284 lb/in 3 Synchronous Belt Tension Effective Pull T e = T T - T S = 2(Q) pd Q = Torque Load, lb-in pd = Pitch diameter, in. Total Tension (8:1) T T + T S = 2.571(Q) pd Q = Torque load, lb-in pd = Pitch diameter, in Tight Side Tension (8:1) T T = 2.286(Q) pd Q = Torque load, lb-in pd = Pitch diameter, in. Slack Side Tension (8:1) T S = 0.285(Q) pd Where: Q = Torque load, lb-in pd = Pitch diameter, in. Working Tension T w = (T e + T c) (SF) Where: T w = Working tension, lb. T c = Centrifugal tension, lb. SF = Service Factor Centrifugal Belt Tension T c = (M) (PD) 2 (rpm) 2 Where: Belt Section Belt Width M 2MGT GT3 4mm 0.026 6mm 0.039 9mm 0.059 12mm 0.078 3MGT GT3 6mm 0.078 9mm 0.117 12mm 0.156 15mm 0.195 5MGT GT3 9mm 0.172 12mm 0.229 15mm 0.286 25mm 0.476 16.2 x 10 6 T c = Centrifugal tension, lb. M = Belt mass constant Belt Section Belt Width PD = Smaller pitch diameter, in. rpm = Smaller sprocket revolutions per minute M 3M HTD 6mm 0.067 9mm 0.100 15mm 0.167 5M HTD 9mm 0.163 15mm 0.272 25mm 0.453 MXL 1/8 0.019 3/16 0.029 1/4 0.038 XL 1/4 0.071 3/8 0.106 104
Polyflex JB Belt Tension Effective Pull T T - T S = 33,000 ( hp ) = Te V Micro-V Belt Tension Effective Pull T T - T S = 33,000 ( hp ) = Te V Total Tension (5:1) T T + T S = 33,000 (2.5 - G) ( hp ) GV Total Tension (4:1) T T + T S = 33,000 (2.67 - G) ( hp ) GV Tension Ratio T T / T S = 1 (Also, T T / T S = e K ) 1-0.8G e = Base of natural logarithms K =.51230, a constant for V-belt drive design = Arc of contact in radians Tension Ratio T T / T S = 1 (Also, T T / T S = e K ) 1-0.75G e = Base of natural logarithms K =.44127, a constant for Micro-V drive design = Arc of contact in radians Tight Side Tension (5:1) T T = 41,250 ( hp ) GV Tight Side Tension (4:1) T T = 44,000 ( hp ) GV Where: TT = Tight side tension, lb. Slack Side Tension (5:1) T S = 33,000 (1.25 - G) ( hp ) GV Where: Slack Side Tension (4:1) T S = 33,000 (1.33 - G) ( hp ) GV Where: TS = Slack side tension, lb. 105
Power Transmission Conversions Newton Meters x 141.6119 = Ounce Inches Newton Meters x 8.8508 = Pound Inches Newton Meters x 0.7376 = Pound Feet Kilowatt x 1.3410 = Horsepower Watt x 0.0013 = Horsepower Torque Conversion Constants Ounce Inches x 0.0071 = Newton Meters Pound Inches x 0.1130 = Newton Meters Pound Feet x 1.3558 = Newton Meters Power Conversion Constants Horsepower x 745.6999 = Watt Horsepower x 0.7457 = Kilowatt Metric to Metric Newton Meters x 10.1972 = Kilogram Centimeters Kilogram Centimeters x 0.0981 = Newton Meters Newton Meters x 0.1020 = Kilogram Meters Kilogram Meters x 9.8067 = Newton Meters Meters/Second x 196.8504 = Feet/Minute Velocity Conversion Constants Feet/Minute x 0.0051 = Meters/Second Metric to Metric Meters/Second x 3.6000 = Kilometers/Hour Other Conversions Newtons x 3.5969 = Ounces Newtons x 0.2248 = Pounds Kilograms x 2.2046 = Pounds Millimeters x 0.0394 = Inches Meters x 39.3701 = Inches Meters x 3.2808 = Feet Meters x 1.0936 = Yards Kilometers x 3280.84 = Feet Kilometers x 0.6214 = Statute Miles Kilometers x 0.5396 = Nautical Miles Square Millimeters x 0.0016 = Square Inches Square Centimeters x 0.1550 = Square Inches Square Meters x 10.7639 = Square Feet Square Meters x 1.1960 = Square Yards Hectares x 2.4711 = Acres Square Kilometers x 247.105 = Acres Square Kilometers x 0.3861 = Square Miles Ounces x 0.2780 = Newtons Pounds x 4.4482 = Newtons Pounds x 0.4536 = Kilograms Inches x 25.4000 = Millimeters Inches x 0.0254 = Meters Feet x 0.3048 = Meters Yards x 0.9144 = Meters Feet x 0.0003048 = Kilometers Statute Miles x 1.6093 = Kilometers Nautical Miles x 1.8532 = Kilometers Square Inches Square Inches Square Feet Square Yards Acres Acres Square Miles Force Conversion Constants Length Conversion Constants Area Conversion Constants x 645.160 = Square Millimeters x 6.4516 = Square Centimeters x 0.0929 = Square Meters x 0.8361 = Square Meters x 0.4047 = Hectares x 0.004047 = Square Kilometers x 2.5900 = Square Kilometers Metric to Metric Kilograms x 9.8067 = Newtons Newtons x 0.1020 = Kilograms Grams x 15.4324 = Grains Grams x 0.0353 = Ounces (Avd.) Grams x 0.0338 = Fluid Ounces (water) Weight Conversion Constants Kilograms x 35.2740 = Ounces (Avd.) Kilograms x 2.2046 = Pounds (Avd.) Metric Tons (1000 Kg) x 1.1023 = Net Ton (2000 lb) Metric Tons (1000 Kg) x 0.9842 = Gross Ton (2240 lb) 106
Other Conversions Continued Grains Ounces (Avd.) = 144 pounds per square foot = 0.068 atmosphere 1 pound per square inch = 2.042 inches of mercury at 62 F = 27.7 inches of water at 62 F = 2.31 feet of water at 62 F 1 atmosphere x 0.0648 = Grams x 28.3495 = Grams Fluid Ounces (water) x 29.5735 = Grams Ounces (Avd.) x 0.0283 = Kilograms = 30 inches of mercury at 62 F = 14.7 pounds per square inch = 2116.3 pounds per square foot = 33.95 feet of water at 62 F Weight Conversion Constants continued Pounds (Avd.) Net Ton (2000 lb) x 0.4536 = Kilograms x 0.9072 = Metric Tons (1000 Kg) Gross Ton (2240 lb) x 1.0160 = Metric Tons (1000 Kg) Measures of Pressure 1 foot of water at 62 F = 62.35 pounds per square foot = 0.433 pounds per square inch = 1.132 feet of water at 62 F 1 inch of mercury at 62 F = 13.58 inches of water = 0.491 pounds per square inch Column of water 12 inches high, 1 inch in diameter = 0.341 lb. Inches Fractions Decimals Millimeters 1/64.015625.397 1/32.03125.794 3/64.046875 1.191 1/16.0625 1.588 5/64.078125 1.984 3/32.09375 2.381 7/64.109375 2.778 1/8.125 3.175 9/64.140625 3.572 5/32.15625 3.969 11/64.171875 4.366 3/16.1875 4.763 13/64.203125 5.159 7/32.21875 5.556 15/64.234375 5.953 1/4.250 6.350 17/64.265625 6.747 9/32.28125 7.144 19/64.296875 7.541 5/16.3125 7.938 21/64.328125 8.334 11/32.34375 8.731 23/64.359375 9.128 3/8.375 9.525 25/64.390625 9.922 13/32.40625 10.319 27/64.421875 10.716 7/16.4375 11.113 29/64.453125 11.509 15/32.46875 11.906 31/64.484375 12.303 1/2.500 12.700 Decimal and Millimeter Equivalents of Fractions Inches Fractions Decimals Millimeters 33/64.515625 13.097 17/32.53125 13.494 35/64.546875 13.891 9/16.5625 14.288 37/64.578125 14.684 19/32.59375 15.081 39/64.609375 15.478 5/8.625 15.875 41/64.640625 16.272 21/32.65625 16.669 43/64.671875 17.066 11/16.6875 17.463 45/64.703125 17.859 23/32.71875 18.256 47/64.734375 18.653 3/4.750 19.050 49/64.765625 19.447 25/32.78125 19.844 51/64.796875 20.241 13/16.8125 20.638 53/64.828125 21.034 27/32.84375 21.431 55/64.859375 21.828 7/8.875 22.225 57/64.890625 22.622 29/32.90625 23.019 59/64.921875 23.416 15/16.9375 23.813 61/64.953125 24.209 31/32.96875 24.606 63/64.984375 25.003 1 1.000 25.400 107
Power To or From Machinery In the absence of accurate data on horsepower requirements for a drive, it is sometimes possible to calculate the power output from a driver machine or the required power input to a driven machine. In each formula below, efficiency must be known or estimated. For checking a drive which is providing power to a pump or generator, it is more conservative to estimate a low efficiency for the driven machine. For power input to a drive from a motor or turbine, is more conservative to estimate high efficiency for the driver machine. Efficiency is used as a decimal in the formulas. For example, if a pump is 70% efficient, use.70 in the formula. Hydraulic Machinery Power required by pumps Kilowatts = (volts) (amps) (p.f.) Y Where: p.f. = Power factor Y = 1000 (Single phase) Y = 577 (Three phase) Power required for generator (alternator) (volts) (amps) (p.f.) (Z) (eff) Where: eff = Overall mechanical and hydraulic p.f. = Power factor A.C. Machinery Z = 746 (Single phase) Z = 431 (Three phase) Kilowatts = (volts) (amps) 1000 Power required for generator (volts) (amps) (746)(eff) Where: eff = Overall mechanical and hydraulic Power from motor D.C. Machinery (volts) (amps) (eff) 746 Where: eff = Overall mechanical and hydraulic (F) (p) (1714) (eff) Power from motor Where: F = Flow rate, gallons per minute P = Discharge pressure for pumps, inlet pressure for turbines, pounds/square inch eff = Overall mechanical and hydraulic Power from water wheel or turbine (volts) (amps) (p.f.) (EFF) (Z) Where: eff = Overall mechanical and hydraulic p.f. = Power factor Z = 746 (Single phase) Z = 431 (Three phase) (F) (p) (eff) (1714) Where: F = Flow rate, gallons per minute P = Discharge pressure for pumps, inlet pressure for turbines, pounds/square inch eff = Overall mechanical and hydraulic 108
Gates Application Data Worksheet Company: Address: Contact: Title: Phone: Fax: Email: Application Summary General Description: Product Type: Estimated Production Volume: Prototype Time Schedule: Production Time Schedule: Function: Motion Transfer Reversing Light Loads Moderate Loads Heavy Loads On/Off Cycle Continuous Operation Cycle Description: Design Parameters DriveR Motor Type & Description (Servo, Stepper, D.C., A.C., etc.): Nominal Motor Torque/Power Output: RPM: Max/Peak Motor Torque/Power Output: RPM: Motor Stall Torque (If Applicable): DriveN Description of DriveN Component:: Required Operating RPM: Speed Ratio: Speed Up/Down: Additional Details: Geometry Two Point Drive Multi-Point Drive If Multi-Point: Are Layout Prints Available? Yes No Center Distance Range: To Fixed Design Adjustable Design Type of Adjustment: Tensioner Idler: None Inside Outside Slack Side Tight Side Diameter: DriveR: Max O.D. Max Width DriveN: Max O.D. Max Width Special Requirements Product Design Life: Belt Design Life: Usage: Hours/Day: Hours/Year: Shafts: DriveR DriveN Pulley Materials: Prototype Production Environmental Conditions: Temperature Moisture Oil Abrasives Static Conductivity Special Requirements (Registration, Motion Control, Speed Control, Etc.) 109
GATES CORPORATION 800.777.6363 For Power Transmission drive design assistance, contact Gates Product Application at 303-744-5080 or 2015 Gates Corporation 17183 1/2015