Design Considerations Motor Sizing

Torque Requirements Torque Equations - (servo or step motor) The torque required to move a LINTECH positioning table for a specific application requires the calculation of several Horizontal Applications simple equations. These equations require you to evaluate T = T + T + T + T carriage speeds, acceleration rates, and load weights. Total-AccelAcc Breakaway Friction Gravity Careful torque calculations allow the proper selection of an electronic motor/drive system. T Total-Constant= T Breakaway + T Friction + TGravity

The maximum torque demand from any motor is usually T Total-Decel= TAcc - T Breakaway - T Friction - TGravity during the acceleration portion of a move profile and consists of several parts - Acceleration Torque, Friction Vertical Applications Torque, Breakaway Torque, and for vertical applications the Upward Move Torque to overcome Gravity. T Total-Accel= TAcc + T Breakaway + T Friction + TGravity The torque required from a motor varies as the move profile changes from acceleration to constant velocity to decelera- T Total-Constant= T Breakaway + T Friction + TGravity tion. Constant velocity torque and deceleration torque become important when sizing for a servo motor system. T = T - T - T - T Torque to overcome gravity becomes extremely important Total-DecelAcc Breakaway Friction Gravity in vertical applications. The upward move places the highest torque demand on the motor, while the downward Vertical Applications move sometimes requires the motor/drive system to act as a Downward Move brake. T Total-Accel= TAcc + T Breakaway + T Friction - TGravity

Step Motors T Total-Constant= T Breakaway + T Friction - TGravity When sizing for a step motor system, calculate the maximum torque demand for the application. This will usually T Total-Decel= TAcc - T Breakaway - T Friction - TGravity be the total torque required during the acceleration portion of a move profile. Select an electronic motor/drive system which will deliver more torque than is absolutely required. Servo motor RMS calculation This torque margin accommodates mechanical wear, extra loads, lubricant hardening, and other unexpected factors. Consult the individual motor manufacturer for details on their required torque margin and inertia matching. ta tc td toff Servo Motors When sizing for a servo motor system, two calculations 2 2 2 2 T = ( T ) t + ( T ) t + ( T ) t + ()T t must be performed - maximum (peak) torque and RMS RMS a a c c d d off off (continuous) torque. The maximum torque demand for the ta + tc + td + toff application will usually occur during the acceleration portion of a move profile. The RMS torque calculation will T = T = acceleration torque require values for acceleration torque, constant velocity Total-Accel a torque, deceleration torque, and the time between move T Total-Constant = Tc = constant velocity torque profiles. All servo motor systems have a peak and continuous torque rating. Select an electronic motor/drive system T Total-Decel = Td = deceleration torque which will deliver more peak torque than the calculated T = torque at standstill - usually a 0 value maximum torque value and more continuous torque than the off RMS calculated value. This torque margin accommodates T RMS = RMS (continuous) torque mechanical wear, extra loads, lubricant hardening, and other unexpected factors. Consult the individual motor manufac- ta = acceleration time in seconds turer for details on their torque margin and inertia match- t = constant velocity time in seconds ing. c td = deceleration time in seconds

toff = dwell time in seconds between moves

A-46 LINTECH ® Positioning Systems Design Considerations Motor Sizing

Torque Equations - Screw Driven (Linear Motion) Terms C = potential thrust force (lbs) T A d = lead of screw (in/rev)

O e = screw efficiency (90% =.9) = total frictional force (lbs) F T

J = load inertia (oz-in2 ) T Total = T Acc +++TTTBreakaway Friction Gravity SF (oz-in) Load = screw inertia (oz-in2 ) J Screw 1 J Load T = + J + J (oz-in) = motor inertia (oz-in2 ) Acc Screw Motor J Motor 386 e t a L = screw length (in) 2 WW+ d ( Load Other ) ( 16 oz ) 2 J = (oz-in ) O = angle of load from Load 2 ( 2 ) lb horizontal (degrees)

L R4 = density of steel screw J = (oz-in2 ) 3 Screw 2 (4.48 oz/in )

See Motor Data (not included in this catalog) = radius of screw (in) J Motor = (oz-in2 ) R SF = safety factor (see note #3) 2 V M = (rad/sec) d = acceleration time (sec) t a T = See values in individual screw technical sections (oz-in) Breakaway = required torque to accel T Acc the load (oz-in) d F Cos O ( 16 oz ) T T Friction = (oz-in) T = breakaway torque (oz-in) 2 e lb Breakaway T = required torque to overcome = WW+ Friction F T ( Load Other ) (lbs) system friction (oz-in)

= required torque to d ( WWLoad+ Other ) Sin O ( 16 oz ) T Gravity T = (oz-in) overcome gravity (oz-in) Gravity 2 e lb = motor output torque at T Motor Notes: calculated speed (oz-in) 1) TTotal is the maximum torque required from a motor during a move. This usually occurs during the acceleration portion of a move profile for horizontal applications and an upward = required torque to move T Total move for vertical applications. During the deceleration portion of a move profile, TFriction and the load (oz-in) TBreakaway are subtractions from TTotal. For horizontal applications TGravity has a zero value. = coefficient of friction for 2) The factor 386 in the denominator for the TAcc equation represents acceleration due to linear bearing system (.01) gravity (386 in/sec2 or 32.2 ft/sec2 ) and converts inertia from units of oz-in2 to oz-in-sec2. = max linear velocity (in/sec) V M 3) The safety factor (SF) should be between 1.4 to 1.6 for step motor systems and between 1.1 to 1.2 for servo motor systems. = angular velocity (rad/sec)

W = weight of load (lbs) Thrust Force Equation Load = weight of carriage or weight WOther 2 e ( T Motor - T Total ) lb of mounting hardware (lbs) C T = (lbs) d (16 oz) = 3.1416

LINTECH ® Positioning Systems A-47 Design Considerations Motor Sizing

Torque Equations - Belt Driven (Linear Motion) Terms

= potential thrust force (lbs) CT

e = gearhead efficiency (90% = .9)

O g = gearhead ratio (5:1 = 5) = belt inertia (oz-in2 ) J Belt

J = load inertia (oz-in2 ) T Total = T Acc +++TTTBreakaway Friction Gravity SF (oz-in) Load = motor inertia (oz-in2 ) J Motor 1 J Load J Pulley J Belt T = + + + J (oz-in) = pulley inertia (oz-in2 ) Acc Motor J Pulley 386 e e e t a O = angle of load from 2 horizontal (degrees) ( WWLoad+ Other ) r ( 16 oz ) J = (oz-in2 ) Load 2 lb g r = radius of drive pulley (in) 2 ( W ) r 2 ( for 2 pulleys ) Pulley 2 SF = safety factor (see note #3) J Pulley = (oz-in ) 2 g 2 = acceleration time (sec) 2 t a ( WBelt ) r J = (oz-in2 ) Belt 2 = required torque to accel g T Acc the load (oz-in) J = See Motor Data (not included in this catalog) (oz-in2 ) Motor = breakaway torque (oz-in) T Breakaway V M = required torque to overcome = (rad/sec) T Friction r system friction (oz-in)

See values in individual belt technical sections = required torque to T = (oz-in) T Gravity Breakaway g e overcome gravity (oz-in)

T = motor output torque at ( WWLoad+ Other ) r Cos O ( 16 oz ) Motor T = (oz-in) calculated speed (oz-in) Friction g e lb = required torque to move T Total the load (oz-in) ( WWLoad+ Other ) r Sin O ( 16 oz ) T Gravity = (oz-in) g e lb = coefficient of friction for linear bearing system (.01) Notes: 1) T is the maximum torque required from a motor during a move. This usually occurs Total V = max linear velocity (in/sec) during the acceleration portion of a move profile for horizontal applications and an upward M move for vertical applications. During the deceleration portion of a move profile, T and Friction = angular velocity (rad/sec) TBreakaway are subtractions from TTotal. For horizontal applications TGravity has a zero value. = weight of belt (oz) WBelt 2) The factor 386 in the denominator for the TAcc equation represents acceleration due to 2 2 2 2 gravity (386 in/sec or 32.2 ft/sec ) and converts inertia from units of oz-in to oz-in-sec . = weight of load (lbs) WLoad

3) The safety factor (SF) should be between 1.4 to 1.6 for step motor systems and between = weight of carriage or weight WOther 1.1 to 1.2 for servo motor systems. of mounting hardware (lbs)

W = weight of pulley (oz) Thrust Force Equation Pulley

( T Motor - T Total ) g e lb C T = (lbs) r (16 oz)

A-48 LINTECH ® Positioning Systems Design Considerations Motor Sizing

Torque Equations - Worm Gear Driven (Rotary Motion) Terms e = worm gear assembly efficiency (90% =.9) A

= load inertia (oz-in2 ) J Load

= motor inertia (oz-in2 ) J Motor

= worm gear assembly J Worm inertia (oz-in2 ) T Total = T Acc + T Breakaway SF (oz-in) N = worm gear reduction (45:1 = 45) 1 J Load T Acc = + J Worm + J Motor (oz-in) 386 e t a R = radius of table top (in)

2 = safety factor (see note #3) ( WWLoad+ Table Top ) R ( 16 oz ) SF J = (oz-in2 ) Load 2 2 N lb = acceleration time (sec) t a T = required torque to accel See values in individual rotary table technical sections 2 Acc J Worm = (oz-in ) the load (oz-in)

= breakaway torque (oz-in) 2 T Breakaway J Motor = See Motor Data (not included in this catalog) (oz-in ) = required torque to move T Total the load (oz-in) = 2 N V M (rad/sec) = max table top velocity V M (revs/sec) T Breakaway = See values in individual rotary table technical sections (oz-in) = angular velocity (rad/sec)

Notes: = weight of load (lbs) WLoad 1) TTotal is the maximum torque required from a motor during a move. This usually occurs during the acceleration portion of a move profile for horizontal applications and an upward = weight of table top or weight WTable Top move for vertical applications. During the deceleration portion of a move profile, TFriction and of mounting hardware (lbs) TBreakaway are subtractions from TTotal. For horizontal applications TGravity has a zero value. = 3.1416

2) The factor 386 in the denominator for the TAcc equation represents acceleration due to gravity (386 in/sec2 or 32.2 ft/sec2 ) and converts inertia from units of oz-in2 to oz-in-sec2.

3) The safety factor (SF) should be between 1.4 to 1.6 for step motor systems and between 1.1 to 1.2 for servo motor systems.

4) The frictional torque value is so small, it can be ignored for rotary table torque equations.

LINTECH ® Positioning Systems A-49