Component Testing Idea Book
Formulas to Approximate
Test Requirements
100-110-096
CES
3/03
1 of 2
Peak Oil Flow in GPM (Sinusoidal Motion) {Used for servovalve sizing}
Linear Actuators
Peak-Peak Displacement(in) x Piston Area(in2) x Freq.(Hz) x 0.816 = GPM
Peak-Peak Displacement(cm) x Piston Area(cm2) x Freq.(Hz) x 0.1885 = LPM
Rotary Actuators
Peak-Peak Rotation (Deg) x Oil Displacement (in3/RAD) x Freq.(Hz) x 0.0142 = GPM
Peak Rotation (Deg) x Oil Displacement (cm3/RAD) x Freq.(Hz) x 0.00328 = LPM
Average Oil Flow in GPM (Sinusoidal Motion)
{Used to approximate pump demand}
Multiply above Peak GPM flow by 0.6366 to find Average GPM flow.
F ormulas for
performance
are
estimates. A
ctual
results may va
ry.
Computing Other Criteria for Actuators
Linear
Maximum P-P Disp.(in) (Sinusoidal)
Maximum Freq.(Hz) (Sinusoidal)
Maximum no load Velocity(in/sec) (Linear)
Required GPM for Ramp Test
Required GPM for Ramp Test
Required GPM for Ramp Test
= Valve GPM (at test frequency below) / [Piston Area(in2) x Freq.(Hz) x 0.816]
= Valve GPM (at calculated max frequency) / [Piston Area(in2) x P-P Displacement x 0.816]
= [Valve GPM x 3.85]/Actuator Piston Area(in2)
= [Piston Area(in2) x Total Disp.(in) x 0.2597386] / Ramp Time(sec)
= [Piston Area(in2) x Displacement Rate(in/sec)] / 3.85
= [Piston Area(in2) x Displacement Rate(in/min)] / 231
Rotary
Maximum P-P Disp.(deg) (Sinusoidal)
Maximum Freq.(Hz) (Sinusoidal)
Maximum Velocity (deg/sec) (angular)
Required GPM for Ramp Test
Required GPM for Ramp Test
Required GPM for Ramp Test
= Valve GPM (at test frequency) / [Oil Displacement(in3/RAD) x Freq.(Hz) x 0.0142423]
= Valve GPM (at calculated max freq.) / [Oil Disp.(in3/RAD) x P-P Disp.(deg) x 0.0142423]
= [Valve GPM x 220.588]/Oil Displacement(in3/RAD)
= [Oil Displacement(in3/RAD) x Total Disp.(deg) x 0.0045333] / Ramp Time(sec)
= [Oil Displacement(in3/RAD) x Displacement Rate(deg/sec)] / 220.588
= [Oil Displacement(in3/RAD) x Displacement Rate(deg/min)] / 13235.324
Sinusoidal Motion
Peak Acceleration (g's)
Instantaneous Acceleration (g's)
Peak Velocity (in/sec)
Instantaneous Velocity (in/sec)
P-P Displacement (in)
= 0.0511 x P-P Displacement(in) x Freq.(Hz)2 or =0.0201181 x P-P Disp.(cm) x Freq.(Hz)2
= 0.0511 x P-P Displacement(in) x Freq.(Hz)2 x (-)sin θ, θ = Wave Phase Angle
= π x P-P Displacement(in) x Freq.(Hz) or (cm/s) = π x P-P Disp.(cm) x Freq.(Hz)
= π x P-P Displacement(in) x Freq.(Hz) x cos θ, θ = Wave Phase Angle
= 19.5695 x g's/Freq.(Hz)2 or (P-P cm) = 49.7065 x g's/Freq.(Hz)2
Accumulator Requirements
One Shot Test
1 gallon accumlator provides 12 in2 of oil at 300 psi drop with 1500 psi pre-charge
4 liter accumulator provides 210 cm3 of oil at 21 bar drop with 104 bar pre-charge
Cyclic Test
Accumulator (Gal)
Accumulator (Liters)
= 0.03 x Piston Area (in2) x P-P Displacement(in)
= 0.007 x Piston Area (cm2) x P-P Displacement(cm)
MTS Actuator Piston Area(in2) can be approximated by: Force Rating in LBS / 3000psi
NOTE: The exact piston area is available on the actuator name plate.
Component Testing Idea Book
Unit Conversions
100-110-096
CES
3/03
2 of 2
FORCE
ounces(ozf)
pounds(lbs)
pounds(lbs)
pounds(lbs)
kilograms(Kg)
x 0.2780138
x 4.4482216
x 0.00045359
x 0.4535924
x 9.807
= newtons(N)
= newtons(N)
= metric tons(t)
= kilograms(Kg)
= newtons(N)
x 3.596943
x 0.2248089
x 2204.634
x 2.2046
x 0.1019716
= ounces(ozf)
= pounds(lbs)
= pounds(lbs)
= pounds(lbs)
= kilograms(Kg)
LINEAR
inches
inches
inches
feet
yards
miles
nautical mile
x 25.4
x 2.54
x 0.0254
x 0.3048
x 0.9144
x 1.60934
x 1.852
= millimeters(mm)
= centimeters(cm)
= meters(m)
= meters(m)
= meters(m)
= kilometers(km)
= kilometers(km)
x 0.03937008
x 0.3937008
x 39.37008
x 3.28084
x 1.09361
x 0.621371
x 0.539957
= inches
= inches
= inches
= feet
= yards
= miles
= nau. Miles
PRESSURE
pounds/in2
(1 newton/sq meter = 1 pascal) pounds/ft2
pounds/in2
inches Hg(60°F)
inches H20(60°F)
Bars
kgf/cm2
x 6.89476
x 0.04788
x 2.03602
x 3.386388
x 0.2488
x 100
x 98.07
= kilopascals(kPa)
= kilopascals(kPa)
= inches Hg(60°F)
= kilopascals(kPa)
= kilopascals(kPa)
= kilopascals(kPa)
= kilopascals(kPa)
x 0.145038
x 20.855
x 0.491154
x 0.2953
x 4.0193
x 0.01
x 0.010197
= pounds/in2
= pounds/ft2
= pounds/in2
= inches Hg
= inches H20
= Bars
= kgf/cm2
VOLUME
inches3
inches3
inches3
quarts
gallons
feet3
gallons
fluid oz
x 16387
x 16.387
x 0.016387
x 0.946349
x 3.785397
x 28.317
x 231
x 29.57
= millimeters3(mm3)
= centimeters3(cm3)
= liters(L)
= liters(L)
= liters(L)
= liters(L)
= inches3(in3)
= milliliters(mL)
x 0.0000610237
x 0.0610237
x 61.0237
x 1.056692
x 0.264173
x 0.03531
x 0.004329
x 0.033818
= inches3
= inches3
= inches3
= quarts
= gallons
= feet3
= gallons
= fluid oz
TORQUE
pound-inches
pound-feet
kgf-cm
kgf-m
kgf-m
x 0.1129848
x 1.355818
x 0.09807
x 9.807
x 86.796
= newton-meters(Nm)
= newton-meters(Nm)
= newton-meters(Nm)
= newton-meters(Nm)
= pound-inches
x 8.850748
x 0.737562
x 10.196798
x 0.10196798
x 0.0115205
= lb-in
= lb-ft
= kgf-cm
= kgf-m
= kgf-m
ACCELERATION
feet/sec2
inches/sec2
x 0.3048
x 0.0254
= meters/sec2(m/s2)
= meters/sec2(m/s2)
x 3.28084
x 39.37008
= feet/sec2
= in/sec2
VELOCITY
inches/sec
feet/sec
miles/hour
miles/hour
miles/hour
kilometers/hr
x 0.0254
x 0.3048
x 1.46667
x 0.44704
x 1.6093
x 0.27778
= meters/sec(m/s)
= meters/sec(m/s)
= feet/sec(f/s)
= meters/sec(m/s)
= kilometers/hr(km/h)
= meters/sec(m/s)
x 39.37008
x 3.28084
x 0.681818
x 2.23694
x 0.62137
x 3.6
= in/sec
= feet/sec
= miles/hour
= miles/hour
= miles/hour
= kilometers/hr
AREA
inches2
inches2
feet2
feet2
yards2
miles2
miles2
x 0.0069445
x 6.452
x 0.0929
x 0.00002296
x 0.8361
x 640
x 2.59
= feet2
= centimeters2(cm2)
= meters2(m2)
= acres
= meters2(m2)
= acres
= kilometers2(km2)
x 144
x 0.15499
x 10.764
x 43560
x 1.196
x 0.0015625
x 0.3861
= inches2
= inches2
= feet2
= feet2
= yards2
= miles2
= miles2
FLOW
Gal/min
Gal/min
x 3.785397
x 0.00006309
= Liters/min(L/m)
= meters3/sec(m3/s)
x 0.264173
x 15850.37
= Gal/min
= Gal/min
TEMPERATURE,
THERMAL and POWER
C° = (F° - 32)x 5/9, F° = (C° x 9/5) + 32, K° = (C° + 273.15)
1 hp = 745.7 watts = 550 ft-lb/sec = 2546 btu/hour= 745.7 J
1 watt = .00134102 hp = .737562 ft-lb/sec = 3.41424 btu/hour
MTS Systems Corporation • 14000 Technology Drive • Eden Prairie, MN 55344 • Phone 952-937-4000 • Fax 952-937-4515 • www.mts.com • 100-110-096 03/03