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Mechanism |
Equations |
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Motion |
Inertia
& Torque |
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GEARING |
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REDUCER |
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Jr = Inertia of reducer reflected to input.
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TIMING BELT |
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RACK-PINION |
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CONVEYOR |
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LEADSCREW |
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SYMBOLS & DEFINITIONS
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Symbol |
Definition |
Metric Unit |
EE Unit |
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CG CP1,2…n |
Circumference
of Gear Circumference
of Pulleys 1, 2…n |
m or cm “ |
in or ft “ |
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D DG DPL DPM DP1,2…n |
Diameter Diameter
of Gear Diameter
of Load Side Pulleys Diameter
of Motor Side Pulleys Diameter
of Pulleys 1, 2…n |
m or com “ “ “ “ |
in or ft “ “ “ “ |
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e |
Efficiency
of Mechanism |
% |
% |
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F Ffr Fg FP |
Forces Forces
due to Friction Forces
due to Gravity Push
or Pull Forces |
N “ “ “ |
lb “ “ “ |
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a or d α g |
Linear
Accel/Decel Rate Angular
Acceleration Rate Gravity
Accel Constant |
m-sec2 rad-sec2 9.81 m-sec2 |
in-sec2 rad-sec2 386 in-sec2 |
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J JB→M JC JG JL JL→M JM JPL JPM JPL→M JP:1,2,n Jr JTotal JS |
Mass
Moment of Inertia for… …Belt
Reflected to Motor …Coupling …Gear …Load …Load
Reflected to Motor …Motor …Load
Side Pulley …Motor
Side Pulley …Load
Side Pulley Reflected to Motor …Pulley
or Sprocket 1, 2,…n …Reducer
or Gearbox …Total
of all Inertias …Leadscrew |
kg-m2 or g-cm2 etc. “ “ “ “ “ “ “ “ “ “ |
lb-in2 or oz-in2 or lb-in-sec2 or oz-in-sec2 etc. “ “ “ “ “ “ |
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Nr Nt |
Number
Ratio of Reducer Number
of Teeth on Gear, Pulley, etc. |
none none |
none none |
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PG PS |
Pitch
of Gear, Sprocket or Pulley Pitch
of Leadscrew |
teeth/m rev/m |
teeth/in rev/in |
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t ta,c or d tm tTotal th |
Time… …for
Accel, Constant Speed, or Decel …for
Move …for
Total Cycle …for
Hold Time |
sec sec sec sec sec |
sec sec sec sec sec |
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T Ta,c or d TCL TC→M TH TL TP TRMS TTotal |
Torque… …During
Accel, Constant, or Decel …Constant
at Load …Constant
Reflected to Motor …Holding
(while motor stopped) …at
Load (not yet reflected to motor) …due
to Preload on Screw, Nut, etc. …RMS
(Average) Over Entire Cycle …Total
From All Forces |
Nm “ “ “ “ “ “ “ “ |
in-lb or in-oz “ “ “ “ “ “ |
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VL ω0 ωM ωmax |
Linear
Velocity of Load Initial
Angular/Rotational Velocity Angular/Rotational
Velocity of Motor Maximum
Angular/Rotational Velocity |
m/sec rad/sec “ “ |
in/sec rps or rpm |
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WL WB WT |
Weight
of Load Weight
of Belt (or chain or cable) Weight
of Table (or rack & moving parts) |
N or kg |
lb ” “ |
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XL |
Distance
X Traveled by Load |
m or cm |
in or ft |
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Θ Θa,c, or d θL θM θTotal |
Rotation… …During
Accel, Constant or Decel …of
Load …of
Motor Total
Rotation of Motor During Move |
rad “ “ “ “ |
rev “ “ “ “ |
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П 2П |
“PI”
= 3.141592654 Rotational
Unit Conversion (rad/rev) |
none rad/rev |
none rad/rev |
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µ |
Coefficient
of Friction |
none |
none |
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γ |
Load
Angle from Horizontal |
degrees |
degrees |
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Excerpt from: by Wilfred Voss Source: http://www.visualsizer.com |
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