Useful Formulas and Calculations

Transcription

1 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) 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: (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) = 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 (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 = ( 60 (PD - pd) ) CD Where: PD = Large pitch diameter, in. pd = Small pitch diameter, in. CD = Drive center distance, in. 103

2 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 Teeth in Mesh Multiply by Teeth in Mesh Multiply by 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 lb/in Aluminum lb/in 3 Iron 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 mm mm mm MGT GT3 6mm mm mm mm MGT GT3 9mm mm mm mm 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 mm mm M HTD 9mm mm mm MXL 1/ / / XL 1/ /

3 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 ( 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 ) G 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 ( G) ( hp ) GV Where: Slack Side Tension (4:1) T S = 33,000 ( G) ( hp ) GV Where: TS = Slack side tension, lb. 105

4 Power Transmission Conversions Newton Meters x = Ounce Inches Newton Meters x = Pound Inches Newton Meters x = Pound Feet Kilowatt x = Horsepower Watt x = Horsepower Torque Conversion Constants Ounce Inches x = Newton Meters Pound Inches x = Newton Meters Pound Feet x = Newton Meters Power Conversion Constants Horsepower x = Watt Horsepower x = Kilowatt Metric to Metric Newton Meters x = Kilogram Centimeters Kilogram Centimeters x = Newton Meters Newton Meters x = Kilogram Meters Kilogram Meters x = Newton Meters Meters/Second x = Feet/Minute Velocity Conversion Constants Feet/Minute x = Meters/Second Metric to Metric Meters/Second x = Kilometers/Hour Other Conversions Newtons x = Ounces Newtons x = Pounds Kilograms x = Pounds Millimeters x = Inches Meters x = Inches Meters x = Feet Meters x = Yards Kilometers x = Feet Kilometers x = Statute Miles Kilometers x = Nautical Miles Square Millimeters x = Square Inches Square Centimeters x = Square Inches Square Meters x = Square Feet Square Meters x = Square Yards Hectares x = Acres Square Kilometers x = Acres Square Kilometers x = Square Miles Ounces x = Newtons Pounds x = Newtons Pounds x = Kilograms Inches x = Millimeters Inches x = Meters Feet x = Meters Yards x = Meters Feet x = Kilometers Statute Miles x = Kilometers Nautical Miles x = Kilometers Square Inches Square Inches Square Feet Square Yards Acres Acres Square Miles Force Conversion Constants Length Conversion Constants Area Conversion Constants x = Square Millimeters x = Square Centimeters x = Square Meters x = Square Meters x = Hectares x = Square Kilometers x = Square Kilometers Metric to Metric Kilograms x = Newtons Newtons x = Kilograms Grams x = Grains Grams x = Ounces (Avd.) Grams x = Fluid Ounces (water) Weight Conversion Constants Kilograms x = Ounces (Avd.) Kilograms x = Pounds (Avd.) Metric Tons (1000 Kg) x = Net Ton (2000 lb) Metric Tons (1000 Kg) x = Gross Ton (2240 lb) 106

5 Other Conversions Continued Grains Ounces (Avd.) = 144 pounds per square foot = atmosphere 1 pound per square inch = 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 = Grams x = Grams Fluid Ounces (water) x = Grams Ounces (Avd.) x = Kilograms = 30 inches of mercury at 62 F = 14.7 pounds per square inch = pounds per square foot = feet of water at 62 F Weight Conversion Constants continued Pounds (Avd.) Net Ton (2000 lb) x = Kilograms x = Metric Tons (1000 Kg) Gross Ton (2240 lb) x = Metric Tons (1000 Kg) Measures of Pressure 1 foot of water at 62 F = pounds per square foot = pounds per square inch = feet of water at 62 F 1 inch of mercury at 62 F = inches of water = pounds per square inch Column of water 12 inches high, 1 inch in diameter = lb. Inches Fractions Decimals Millimeters 1/ / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / Decimal and Millimeter Equivalents of Fractions Inches Fractions Decimals Millimeters 33/ / / / / / / / / / / / / / / / / / / / / / / / / / / / / / /

6 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

7 Gates Application Data Worksheet Company: Address: Contact: Title: Phone: Fax: 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

8 GATES CORPORATION For Power Transmission drive design assistance, contact Gates Product Application at or 2015 Gates Corporation /2015