Pneumatic Rotary Actuator Sizing-Selecting Tools

Shaft Loads

Design Torque

Design torque represents the maximum torque than an actuator must supply in an application. This maximum is the greater of the Demand Torque or the Cushion Torque. If the demand torque exceeds what the actuator can supply, the actuator will either move too slowly or stall. If the cushion torque is too high, the actuator may be damaged by excessive pressure. Demand torque and cushion torque are defined below in terms of load, friction and acceleration torque, along with equations for calculating demand torque and cushion torque for some general applications.

T - Torque
The amount of turning effort exerted by a rotary actuator.

TD - Demand Torque
The torque required from the actuator to do the job - the sum of the load torque, friction torque and acceleration torque, multiplied by an appropriate design factor. Design factors vary with the applications and the designers' knowledge.

TD = Tα  + Tf + TL

TL - Load Torque
The torque required to equal the weight or force of the load. The load torque term is intended to encompass all torque components that aren't included in the friction or acceleration terms.

Tf - Friction Torque
The torque required to overcome friction between any moving parts, especially bearing surfaces.

Tf = μWr

Tα - Acceleration Torque
The torque required to overcome the inertia of the load in order to provide a required acceleration or deceleration. See the Rotary Actuators Basic Equations page for more information regarding mass moments of inertia and equations for determining acceleration (α).

Tα = Iα

TC - Cushion Torque
The torque that the actuator must apply to provide a required deceleration. This torque is generated by restricting the flow out of the actuator (meter-out) to create a back pressure which decelerates the load. This back pressure/deceleration often must overcome both the inertia of the load and the driving pressure (system pressure) from the pump.

TC = Tα + PrV/θ - Tf ± TL

The friction torque Tf reduces the torque the actuator must apply to stop the load. The load torque TL may add to, or subtract from the torque required from the actuator, depending upon the orientation of the load torque. For example, a weight being swung upward would result in a load torque that is subtracted.

WARNING: Rapid deceleration can cause high pressure intensification at the outlet of the actuator. Always insure that cushion pressure does not exceed the manufacturer's pressure rating for the actuator.

KE - Kinetic Energy (1/2 Jmω2)
The amount of energy that a rotating load has. The rotator must be able to stop the load. All products have kinetic energy rating tables. Choose the appropriate deceleration option (i.e., bumper, cushions, shock absorbers, etc.) that meets or exceeds the kinetic energy of the load.

Mass Moments of Inertia Equations Table

Rectangular Prism Ix = 1/12m(b2 + c2) Iy = 1/12m(c2 + a2) Iz = 1/12m(a2 + b2 )		Circular Cylinder Ix = 1/2ma2 Iy = Iz = 1/2m(3a2 + L2)
Thin Rectangular Plate Ix = 1/12m(b2 + c2) Iy = 1/12mc2 Iz = 1/12mb2		Circular Cone Ix = 3/10ma2 Iy = Iz = 3/5m(1/4a2 + h2)
Sphere Ix = Iy = Iz = 2/5ma2		Thin Disk Ix = 1/2mr2 Iy = Iz = 1/4mr2
Parallel Axis Theorem Ip = ⌈ + md2		Ip = Mass moment of inertia about an axis parallel to a centroidal axis ⌈ = Mass moment of inertia about a centroidal axis m = Mass d = Distance between axes

Where:

t = time

θ = angular position

ω_t = angular velocity at time = t

ω₀ = angular velocity at time = 0

α = angular acceleration

When Acceleration Is Constant:

θ = ω₀t + 1/2αt² ;   α = 2θ/t²

θ = ω₀t + 1/2ω_tt ;  α = (ω_t - ω₀)²/2θ

ω = (ω₀² + 2αθ)^1/2 ; α = (ω_t - ω₀)/t

When Velocity Is Constant:

 θ = ωt

Basic Velocity, Acceleration, Kinetic Energy and Torque Equations

(The equations below are based on triangular velocity profile.)

Where:

Θ = Angle of rotation (degrees)

t = Time to rotate through Θ (sec)

ω = Angular velocity, radians/sec

α = Angular accelerations (radians/sec²)

WL = Weight of load (lbf)

T_a = Torque to accelerate load (lb-in)

U_s = Coefficient of static friction

J_m* = Rotational mass moment of inertia (lb-in-sec²)

T_f = Torque to overcome friction (lb-in)

TL = Torque to overcome effects of gravity

* Use "I" values from the Mass Moments of Inertia table

Equations:

ωmax = 0.35 x Θ/t

α = ωmax²/ (Θ/57.3)

α = ωmax/(t/2)

K.E. = 1/2 J_mω²

T_a = α x J_m

T_f = W x U_s x (Distance from pivot point to center of external bearings)

TL = (Torque arm length to C.G. of load) x WL x cos (Φ)

(Where Φ = Angle between torque arm and horizontal plane)

Coefficients of Friction

*Dry contact unless noted

Parker rotary actuators provide output torque up to 10,000 lb-in. The chart below shows the nominal torque output range of various actuator models at 100 psi.

Caution: This chart is intended as a guide only. Refer to actual product data pages before specifying an actuator. Factors such as pressure rating, rotation and actual torque output may be affected by specific product details and options.

Nominal Torque at 100 PSI

Force Conversion Factors

Multiply value A by conversion factor in table to calculate value B.

Torque Conversion Factors

Multiply value A by conversion factor in table to calculate value B.

Rotational Inertia Conversion Factors

Multiply value A by conversion factor in table to calculate value B.

Length/Distance Conversion Factors

Multiply value A by conversion factor in table to calculate value B.