216 Rotary Actuators
Heavy duty, torque generating devices designed
for precise servo-control applications

T H E 216 RO TA RY A C TU ATO RS ARE HE AVY-DUT Y T ORQUE GE NE RAT ION
D E V I C ES TH AT OPERATE U N DE R P RE CISION SE RVOVALVE CONT ROL.
W H E N MATCH ED WI TH M TS S E RVOVALVE S, T RANSDUCE RS, AND
C LO S E D -LO O P CO N TRO L ELEC T RONICS, T HE Y ARE IDE ALLY SUIT E D FOR
T E S T I N G M ATERI A LS, STRUCT URE S, AND COMP ONE NT S.

2

Description

The double-vane rotor design accommodates full force application through 100° ofrotation. Matched reaction brackets, diaphragm flexures, and reaction bases allow
you to create versatile test configurations that you can easily reconfigure. Available
instrumentation options include angular displacement transducers (ADT), torquecells, and differential pressure cells (∆P).

Features»

Actuators are available in force ratings from 200,000 to
730,000 lbf-in. (22 597 to 82 479 N-m)»

Servovalve ports are compatible with standard MTS
servovalve manifolds»

Heavy-duty bearings accommodate significant radial andaxial loads»

Balanced double vane rotor design reduces friction andprovides continuous torque output through 100° of rotation»

Precision chamber and rotor design ensures zero actuator
backlash during torque reversals»

Separate actuator mounting and fixture attachment equipment
accommodate diverse test articles and configurations»

Available with a complete line of fixturing and angulardisplacement transducer options»

Diaphragm flexures are available to reduce excessive thrustand side loads exerted on the test specimen

Components» Chamber Seals – Cap seals between theactuator cylinder and end caps prevent hydraulicfluid from flowing around the rotor vane seals.
» Radial Bearing – Precision bearing designed
to tolerate the high radial and axial forces thatcan be encountered during testing.
» Front End Cap – Provides a modular carrier
for the actuator seals, bearings, and drainback
ports.
» Actuator Rotor Shaft – Machined steel alloy
shaft with replaceable rotor vanes.
» High Pressure Seal – Low friction seal design
prevents high pressure hydraulic fluid fromflowing out of the cylinder.
» Rotor Vane – Bolt on vane design equippedwith non-metallic seals.
» Rotor Vane Seals – Replaceable seals ensure aminimum of leakage between chambers.
» Low Pressure Seal – U-shaped seal/wiper
ring prevents external leakage and protects
against internal contamination.
» Drainback Port – Collection port for fluid
allowed to flow through the high pressure seals
and bearing. Fluid is returned to the hydraulicpower supply.

Drainbck
Port
Drainbck
Port
Rotor Vane
Seals

High Pressure
Sealing Surface

Rotor
Vane
Low Pressure
Seal

Actuator
Rotor Shaft

Front
End Cap
RadialBearing

ChamberSeals

216 Rotary Actuator Cut-Away View3

4

Fixturing Options

There are a variety of options for the Series 216 Rotary Actuators. The following
photograph shows a typical test system containing a rotary actuator and the available
optional components. Each of the options is described below.

Reaction Base

Reaction Bracket

A reaction base is used with the rotaryactuator for two purposes: (1) themachined flat surface and edge ensure
accurate alignment at any actuator
position; (2) it provides a rigid structure
which can react the high torques
generated by the rotary actuator.

Reaction brackets attach securely to thereaction base or T-slot table and provide
a mounting surface for the torque cell.
Each reaction bracket is designed torestrain a specific model torque cell.

Flange Adapter
The flange adapter (located behind thediaphragm flexure in the photograph) is
secured to the actuator rotor shaft by twoconcentric lock ring assemblies. It provides
a coupling surface between the actuatorand the specimen or diaphragm flexure.
Diaphragm Flexures
Diaphragm flexures are used at both endsof the specimen if large axial and angulardeflections are generated during testing.
If reaction forces exceed stated actuator
operating limits, diaphragm flexures help
reduce the thrust and side loads reacted
by the actuator and test specimen.

Torque Cell

A torque cell provides a precise electrical
feedback signal that is proportional to thetorque applied to the specimen. For more
information on MTS torque cells, refer tothe appropriate MTS product specification.
ADT

An angular displacement transducer(ADT) connected to the rear shaft of theactuator produces a DC electrical signalthat is proportional to the angular

Reaction Bracket

Diaphragm
Fixturesposition of the actuator. Rotation of theactuator will generate a feedback signal
from the ADT to a transducer conditioner.
Rotation is continuous with no reactive
torque induced. The ADT is a precisiondifferential capacitor coupled to a solidstate oscillator, demodulator, and amplifier
to yield DC input/DC output performance.
Differential Pressure Cell

The differential pressure (∆P) cell is asingle-unit, dual port, bonded strain gagepressure sensor. Depending on the specificapplication, the ∆P cell is used to stabilize
or control actuator force output. The ∆P cell(located beneath the servovalve) provides
a feedback signal to monitor fluid pressure
within the actuator housing. For more
information on MTS ∆P cells refer to theappropriate MTS product specification.

FlangeAdapter∆P Cell

Torque Cell

ADT
Typical Rotary Actuator
Test System with
Optional Equipment

Reaction Base Plateor T-Slot Table

5

Specifications

figure. Subsequent tables list the
specifications for the actuator options.
The letters in parenthesis indicate values
used in calculations performed in the
Testing Considerations section (page 11)of this specification.

The 216 Rotary Actuators are available inthree models. Table 1 lists the actuator
performance characteristics by model
number. Table 2 (following page) lists
the specifications for the basic actuator
assembly shown in the accompanying

Table 1. Actuator Specifications
Model

Dynamic* Torque Rating

Displacement

lbf-in.

N-min.3/radcm3/rad200,000

22,60070

1,147216.20397,000

44,900137

2,245216.30730,000

82,500252

4,130216.10Model

Maximum Thrust Load*

Maximum Load on Front Bearing (W)Maximum Side Load† (P)

kip

kN

kip

kN

kip

kN

216.10

3.8

16.9

12.7

56.5

5.7

25.4

216.20

7.2

32.0

17.6

78.3

7.7

34.3

15.0

66.7

28.8

128.1

13.1

58.3

216.30Model

Maximum Velocity Into Vane Stops††

Rotational Inertia of Actuator

Dynamic Seal Friction‡‡

U.S. Customary
rad/sec

Metricrad/sec

lbm-in.2

kg-m2

lbf-in.

N-m216.10w = 867√J

w = 1486
√J

725

0.212

2,500

282.5

216.20w = 1166√J

w = 19.95
√J

2,180

0.637

4,500

508.4

216.30w = 1580√J

w = 27.02
√J

6,350

1.858

8,500

960.4

* Structural fatigue rating. Rated at differential pressure of 2900 psi (203 kg/cm2).
† Applied at end of output shaft and (M) equal to 0.0 lbf-in.
†† If values are excessive, additional internal or external cushions are required. Contact MTS Systems Corporation.
‡ Where w = rotational velocity in rad/sec and J or I = rotational inertia in lbm-in.2 or kg-m2 including inertia from rotary actuator, flange, flexure, and 1/2 of test specimen.
‡‡ Average test data at 1500 psi (10.3 MPa) strut pressure.
Specifications subject to change. Contact MTS for specifications critical to your needs.

6

Table 2. Actuator Dimensions
Model

Weight

216.10

A

B

C

lb

kg

in.

mm

in.

mm

in.

mm

750

340

5.118

130.0

14.00

356

16.00

406

216.20

1300

590

6.299

160.0

17.75

451

20.00

508

216.30

2700

1230

7.874

200.0

22.00

559

27.00

686

Model

D

E

F

G

in.

mm

in.

mm

in.

mm

in.

mm

216.10

6.86

174

2.62

76

6.50

165

12.00

304.8

216.20

7.55

186

2.87

82

8.00

203

16.00

406.4

216.30

8.26

210

4.14

105

8.50

216

23.00

584.2

Model

H

216.10

I

J

s

u*

in.

mm

in.-Thd

in.

mm

in.

mm

in.

mm

4.50

114.3

3/4 - 10

2.00

50.8

7.35

186.7

9.12

231.6

216.20

5.00

127.0

1-8

2.25

57.2

8.30

210.8

10.75

273.0

216.30

6.00

152.4

1-8

2.25

57.2

10.00

254.0

12.00

304.8

*Not including specimen adapter.
Specifications subject to change. Contact MTS for specifications critical to your needs.

P

u

B

s

A dia.

M
C
0.12 in.
3 mm

C/2
0.12 in.
3 mm

F

C

W
E

D

E

H
I threadJ depthG
7

Table 3. Diaphragm Flexure Dimensions and Ratings
Model

A

B

C

D

lb

kg

in.

mm

in.

mm

in.

mm

216.10

13.00

330.2

14.25

361.9

15.75

400.0

4.05

102.9

216.20

15.00

381.0

17.25

438.1

19.75

501.6

5.22

132.6

17.00

431.8

21.25

539.7

23.75

603.2

5.46

138.7

216.30Model
216.10E

F

G

Max Thrust Load*

in.

mm

in.-Thd

in.

mm

lbf

N

0.80

20.3

1-8

11.00

279.4

1,700

7,500

216.201.01

25.6

1 1/2 - 6

12.00

304.8

2,000

8,900

216.301.01

25.6

1 1/2 - 6

14.00

355.6

1,800

8,000

Model

Maximum Deflection

Maximum Bending Moment* (MF1)

Maximum Angular Deflection. (θF1)

in.

mm

lbf-in.

Nm

Radians216.10

0.05

1.3

5,000

560

216.20

0.13

3.3

6,600

750

216.30

0.39

9.9

8,000

900

Rotational Inertia
lbm-in2

kg-m2

0.002

3,338

0.98

0.005

10,296

3.01

0.017

21,112

6.18* Thrust load and bending moment are interdependent. If bending moment = 75% of rating, bending moment must not exceed 25% of rating, etc.
Specifications subject to change. Contact MTS for specifications critical to your needs.

A

F thread equally
spaced on
G diameter

E
8

D

B

C

Table 4. Flange Adapter Dimensions and Ratings
Model

A

B

C

D

E

in.

mm

in.

mm

in.

mm

in.-Thdin.

mm

216.10

5.118

130.0

14.00

355.6

6.25

158.7

1-8

3.25

82.5

216.20

6.299

158.2

15.00

381.0

7.62

193.5

1 1/2 - 6

4.00

101.6

7.874

200.0

17.00

431.8

8.25

209.5

1 1/2 - 6

4.00

101.6

216.30Model

F

216.10G

H

Rotational Inertia

in.

mm

in.

mm

in.

mm

lbm-in.2

kg-m2

1.031

26.2

1.00

25

11.00

279.4

6,550

1.92

216.20

1.531

38.9

1.00

25

12.00

304.8

10,4003.04

216.30

1.531

38.9

1.00

25

14.00

355.6

18,3005.35

Specifications subject to change. Contact MTS for specifications critical to your needs.

Table 5. Reaction Base Dimensions and Ratings
Model

LengthWidth

HeightMax Space*

Torsional Stiffness† (K1)

Weight

in.

mm

in.

mm

in.

mm

in.

mm

lb

kg

lbf-in./rad

N-m/rad216.10

120

3048

24

610

26

660

75.3

1913

2000

1200

0.66 x 109

0.075 x 109

216.20

120

3048

27

686

29

737

67.5

1714

3600

1600

1.40 x 109

0.160 x 109

216.30

120

3048

32

813

34

864

60.5

1537

5700

2600

2.80 x 109

0.320 x 109* Maximum space between mounting surfaces of actuator output flange and torque cell (with the MTS reaction bracket upporting the torque cell). (excludes diaphragm flexures.)† Torsional stiffness over entire length. Stiffness increases proportionately as the actuator and reaction bracket are moved toward each other.
Specifications subject to change. Contact MTS for specifications critical to your needs.

A

Thread: D, E depth

B

C

Counterbore: F diameter, G depth
Bolt Circle: Equally spaced on H diameter9

Table 6. Reaction Bracket Dimensions
Model

A

B

C

D

lb

kg

in.

mm

in.

mm

in.

mm

216.10

7.00

177.8

8.00

203.2

16.00

406.4

29.25

742.9

216.20

8.00

203.2

10.00

254.0

20.00

508.0

32.25

819.1

216.30

9.00

228.6

13.50

342.9

27.00

685.8

37.25

946.1

Model

E

F

G

H

lb

kg

in.

mm

in.

mm

in.

mm

216.10

26.00

660.4

1.50

38.1

2.00

50.8

1.50

38.1

216.20

29.00

736.6

2.00

50.8

2.00

50.8

2.00

50.8

216.30

34.00

863.6

2.50

63.5

2.00

50.8

2.00

50.8

Model

I

J

K

L

M

lb

kg

in.

mm

in.

mm

in.

mm

in.

mm

216.10

1.031

26.2

1.062

27.0

11.00

279.4

16.00

406.4

14.50

368.3

216.20

1.031

26.2

1.562

39.7

12.00

304.8

18.00

457.2

16.00

406.4

216.30

1.031

26.2

1.516

38.5

14.00

355.6

26.00

660.4

18.50

469.9

Specifications subject to change. Contact MTS for specifications critical to your needs.

M

1.625 typical

I diameter

F
G
G
E

H

L
J diameter
K diameterbolt circle

C
H

B

D

10

A

Testing Considerations

This section describes factors that must
be considered when using the Series 216
Rotary Actuators in a test system. It
includes sample calculations that should
help you determine the constraints on
your planned testing scenario.
The thrust and side loads that may be
encountered during testing are generally
the result of the following factors:» Specimen shortening or lengthening
due to torsional force» Specimen shortening or lengthening
due to temperature» Misalignment of the test specimen
when initially mounted» Reaction base or T-slot table twisting» Permanent deformation of thespecimen due to torsional force
Thrust loads

Table 1 lists the maximum allowable thrustload that can be applied to the actuatorrotor shaft. Because thrust loads can be
induced by a wide variety of experimental
conditions, this specification will not

attempt to define or predict the forces thatcan result from specific testing situations.
If there is a possibility that the maximum
thrust load rating of the actuator will be
exceeded during testing, steps should betaken to minimize the load. One way of
reducing the effect of thrust loads on theactuator bearings is to install diaphragm
flexures.
As an example of thrust loads (which area function of specimen geometry andmaterial), increase the temperature of asteel shaft 1 in. (25.4 mm) in diameter and
50 in. (1,270 mm) in length by 40°F (22°C).
The increase in specimen temperaturecauses the shaft to expand by approximately
0.012 in. (0.305 mm). If the shaft is mounted
in a force train using a 216 Rotary Actuator,
the shaft expansion would exert a resultant
force of 6,000 lbs. on the actuator bearings.
To confine the resultant force to an
acceptable maximum requires the additionof flexure diaphragms to the force train.
Use the values from Table 3 to complete
the following formula:
Maximum thrust load
= Flexure stiffness
Maximum deflection(of flexure)

Multiply the flexure stiffness by the amountof specimen expansion to determine thethrust load imposed on the actuator
bearings. Ensure that the resultant trust
load does not exceed the maximum
allowable thrust load listed in Table 1.
Side loads

Side loads, which are normally inducedby specimen misalignment and/or reaction
base or T-slot table compliance, may be
active at the same time thrust loads areactive. If the specimen is soft, such as alength of rubber hose, side loads are
relatively small. This is because thespecimen bends easily and exerts little
resistance to the deflection caused byreaction base twisting.
However, if the specimen is stiffer, thenthe increased resistance of the specimen
to bending exerts substantial side loads
on the specimen, actuator bearings andtorque cell due to the restraining
characteristics of the test setup. As in
the test setup for thrust loads, diaphragm
flexures can be used to reduce the sideloads to a practical limit.

11

Definition of Mathematical Terms

This section lists and defines the mathematical terms that are required to complete thesample calculations. The terms are listed in alphabetical order and defined in both
U.S. Customary and SI Metric units of measure.
Table 7. Mathematical Terms
Term

12

Definitiona=Distance from actuator’s center line to center of reaction base’s solid height (in.) (mm).

b=Width of reaction base (in.) (mm).

d=Thickness of reaction base (in.) (mm). Measurement of solid metal only. Do not include T-slot depth.

ES=

Modulus of elasticity of the reaction base or T-slot table, shear (lb/in.2) (N/m2).

E=

Modulus of elasticity of the specimen, tension (lb/in.2) (N/m2).

I=

Moment of inertia (πr 4/4) for a round solid (in.4) (mm4).

K1=

Torsional stiffness of a thin flat plate (lbf-in./rad) (N-m/rad).

K2=

Lateral stiffness of a solid cylindrical specimen (lbf/in.) (kN/mm).

K F1

=

Angular horizontal stiffness of actuator and reaction bracket (lbf-in./rad) (N-m/rad).

K F2

=

Lateral stiffness of diaphragm flexures (lbf-in./rad) (N-m/rad).

L1=

Length of reaction base or T-slot table subjected to twisting (in.) (mm).

L2=Length of test specimen (in.) (mm).
Do not include specimen adapter plates unless their compliance is equal to or greater than that of the specimen.

M=

Bending moment on test specimen (lbf-in.) (N-m).

M1=

Bending moment on test specimen fitted with flexure diaphragms (lbf-in.) (N-m).

MF 1

=

Maximum horizontal bending capacity of flexures (lbf-in.) (N-m).

P=

Side load imposed on test specimen and actuator (lbf-in.) (N-m).

r=

Radius of test specimen (in.) (mm).

s=Distance between front and rear bearings (in.) (mm).

SB=

Bending stress on test specimen due to reaction base twisting (psi) (N/m2).

T=

Applied torque (lbf-in.) (N-m).

u=

Distance from front bearing to specimen (in.) (mm). Include specimen adapter plates if they are less compliant than the specimen.

W=

Load on front actuator bearing (lbf) (kN).

∆=Centerline offset between actuator and reaction bracket mountings due to twisting of reaction base or T-slot table (in.) (mm).

θ=Angle of flex imposed on actuator and reaction bracket flexure (radians).

θF 1

=

Maximum horizontal angular deflection of flexures (radians).

Side Load Calculations when Excluding Flexures

If diaphragm flexures will not be used in the rotary actuator test system, special attention
should be paid to the side loads that will be imposed on the specimen and actuatorby twisting of the reaction base or T-slot table. The following side load calculation
procedure is used to determine side loads due to the reaction base or T-slot tabletorsional compliance. When side loads are unacceptable as determined from theprocedure, optional components are required in the force train to reduce the load
imposed on the actuator and torque sensor.

L1

P

W

∆

T

M

b
M

T

P

s

u

L2
d

2r

a
d/2

Loads on an Actuator and Specimen due to Reaction Base Twist (Excluding Thrust Loads)

13

Sample Calculation

The preceding figure illustrates the forces and measurements pertinent to the calculations.
Refer to Tables 1 and 2 for dimensions and ratings of the Model 216.10 Rotary Actuator
used in the example.
The following procedure uses sample values. When performing
the calculations to determine the anticipated test forces, the values
appropriate to your specific test should be substituted for the
sample values. In addition, the example uses U.S. Customary
units of measure. The equivalent SI metric units of measure aredefined in Table 7.
The following values are supplied for the sample calculations:a = 11 in. (distance from actuator center line to reaction
base center)b = 20 in. (width of reaction base)d = 6 in. (thickness of reaction base)
L1 = 51 in. (length of reaction base subjected to twisting)
L2 = 10 in. (length of test specimen and specimen adapter plates)r = 1.75 in. (radius of test specimen)

B. Calculate the value of K2, the lateral stiffness of a solid
cylindrical specimen, by using the formula:
K2 = 12 EI
L23
where: E = 29 x 106 lb/in.2
4
I = πr		4
r = 1.75 in.
L2 = 10 in.

π(1.75)4
12 (29 x 10 lb/in. ) 4
then: K2 =(10)36
		 = 2.563 x 10 lbf/in.
6

C. Substitute the calculated values for K1, K2, and the example
values into the original equation to compute the side load (P).
K2
aT
K1
P =
K
1 + 2 a2
K1

s = 7.35 in. (distance between front and rear actuator bearings)
T = 150,000 lbf-in. (applied torque)u = 9.12 in. (distance from front actuator bearing to specimen)
ES = 12 x 106 lb/in.2 (modulus of elasticity of the reaction baseor T-slot table)
1. Calculate the side load (P) imposed on the test specimen andactuator bearing as a result of reaction base twist using thefollowing formula:

K2

P =

aT

K1
K
1 + 2 a2
K1

The values of K1 and K2 can be found using the following equations:
A. If you are using an MTS reaction base, select the appropriate
value for K1 from Table 5. Otherwise, calculate the value ofK1, the torsional stiffness of a thin flat plate, by using thefollowing formula*:dES [(0.333 - (0.21 x b )] bd3
K1 =
L1
6
12 x 106 lb/in.2 [(0.333 - (0.21 x 20 )] (20 in.) (6 in.)3
then: K1 =51 in.
lbf-in.
= 274.4 x 106 radd* In the formula, [0.333 - (0.21 x )] is used in place of J (polar momentarybinertia) due to warpage that occurs in thin flat plates under torque.

142

where: a = 11 in.
T = 150,000 lbf-in.

then:

2.563 x 106 lbf-in.
		(11 in.) (150,000 lbf-in.)274.4 x 106 lbf-in./radP=
2.563 x 106 lbf-in.
1+(11 in.)2
274.4 x 106 lbf-in./rad= 15411.625 = 7,234.873 lbf
2.1301859

The value of 7,234.873 lbf is the side load (P) imposed on the test specimen
and actuator by reaction base twist.

2. Calculate the bending moment (M) on the test specimen byusing the following formula:

PL
M= 2
		 2

where:(7,234.873 lbf) (10 in.)M=2			
= 36,174.365 lbf-in.
The value of 36,174.365 lbf-in. is the bending moment exerted on the actuator
shaft and specimen.

3. Calculate the load on the front actuator bearing (W) by using thefollowing formula:

5. Calculate the stress (SB) induced in the specimen due toreaction base twist by using the following formula:

SB = MrIMu
W = P {1+ s } + s
Substitute the calculated value for P, M, and the example constants
into the equation and compute the load on the front actuator
bearing (W) given:

where: I = πr44

= π(1.75) = 7.366 in.4
44

s = 7.35 in.
u = 9.12 in.
then:

W = 7,234.873 lbf (1+ 9.12 in.) + 36,174.365 in.
7.35 in.
7.35 in.

SB = 36,174.365 lbf-in.4 (1.75 in.)
7.366 in.
= 8,594.24 psi

s = 21,133 lbf

The value, 8,594.24 psi represents the amount of stress experienced
by the specimen due to reaction base twist. In a torsion test, stresscaused by reaction base or T-slot table twist should typically be
zero or as close to zero as possible. In the sample calculation, theexcessive stress imposed on the test specimen can invalidate thetest results or cause premature failure of the specimen. To reducethese loads requires the use of diaphragm flexures or a stiffer
mounting surface.

4. Compare the result of step 3 with the specific model actuator
bearing capacity in Table 1.

In the sample problem, the actuator bearing capacity of a Model
216.10 Rotary Actuator is 12,700 lbf. The calculated force on theactuator bearing is 21,133 lbf. This force is significantly greaterthan the actuator bearing capacity. Operating the actuator withsuch a large force applied to the bearing causes additional wearof the actuator, reduces its service life, and can cause premature
failure of the test specimen due to the additional stress.

Side Load Calculations when Using Flexures
L1

If the values derived from the calculationsin the previous example indicate that
diaphragm flexures must be used toreduce side loads to acceptable levels,then the following calculations should
be completed to ensure that the selected
diaphragm flexures are adequate. In
addition, this subsection contains theequations necessary for calculating thestress experienced by the specimen when
diaphragm flexures are installed in thetest system.

P

W

∆

θ
M

T

T

b

M
P
s

u

L2

d

2r

a

d/2

Force Train with Diaphragm Flexures Mounted at Both Ends of Test Specimen

15Sample Calculation

The following procedure uses the values derived from the previous sample calculations.
The preceding figure illustrates the forces and measurements pertinent to the calculations.
Refer to Tables 1 and 2 for dimensions and ratings of the Model 216.10 Rotary Actuator
used in the example.
The following sample values will be used in the equations:a = 11 in. (distance from actuator center line to reaction
base center)
K1 = 274.4 x 106 lbf-in./rad (torsional stiffness of thin flat plate)
L1 = 51 in. (length of reaction base subjected to twisting)
L2 = 18.1 in. (length of specimen, adapter plates, and flexures)
MF1 =15,000 lbf-in. (maximum horizontal flexure bending capacity)

θF1 = 0.002 rad (maximum horizontal flexure angular deflection)

4. Calculate the lateral stiffness (KF1) of the diaphragm flexures byusing the following formula:

KF1 = MF1
θ F1
where: MF2 = 5,000 lbf-in.
θF1 = 0.002 rad

KF = 5,000 lbf-in.
then:
			 1
0.002 rad= 2.5 rad x 106 lbf-in./rads = 7.35 in. (distance between front and rear actuator bearings)
T = 150,000 lbf-in. (applied torque)u = 9.12 in. (distance from front actuator bearing to specimen)

5. Calculate the bending moment (M1) that is applied to the test
specimen when equipped with flexures.
M1 = (KF1) (θ)

1. Calculate the center line offset (∆) between actuator and reaction
bracket due to reaction base twist by using the following formula:

M1 = (2.5 x 106 in.-lb/rad) (0.000332 rad)= 830 lbf-in.

∆ = TaK1

a = 11 in.
K1 = 274.4 x 106 lbf-in.
rad			
T = 150,000 lbf-in.
where:(150,000) (11 in.)
∆ = 274.4 x 106
then:
			
= 0.00601 in.

6. Calculate the load (W) on the front actuator bearing when
diaphragm flexures installed by using the following formula:Mu
W = P (1+ s ) + s 1
2M1 2 (830 lbf-in.)where:
P === 46 lbf
18.1 in.
			L1

u = 9.12 in.
s = 7.35 in.

2. Calculate the angle of flex (θ) imposed on each diaphragm
flexure by using the following formula:

θ= ∆

L2

where: L2 = 18.1 in.
0.00601 in.
θ=then:			 18.1 in.
= 0.000332 rad
3. Compare the maximum horizontal angular deflection of thediaphragm flexures (θF1 = 0.002 rad) with the calculated angle offlex imposed on one diaphragm flexure (θ = 0.000601 rad) todetermine if the flexures are adequate.

		 θ < θF1
In the case of the sample calculation, the flexures are adequate.
If the flexures are not adequate, additional flexural capability isrequired or reaction base stiffness must be increased. Consult
MTS Systems for assistance.
16

L2 = 18.1 in.
M1 = 1502.5 lbf-in.
912 in. ) 830 lbf-in.
then:
W = 46 lbf (1 ++			
7.35 in.
7.35 in.
= 216.0 lbf

7. Calculate the stress (SB) induced in the specimen due toreaction base twist by using the following formula:

SB = M1r
I
where:

M2 = 830 lbf-in.
r = 1.75 in.
I = 7.366 in.4

SB =
then:
		

830 lbf-in. (1.75 in.)
7.366 in.4
= 197.2 psi

Rotational Inertia

This section describes how to calculate the total rotational inertia of the 216 Rotary
Actuator, specimen, and optional equipment. If the total rotational inertia exceeds
recommended levels and the actuator is allowed to rotate until the rotor vane makes
contact with the rotor vane stops, then the flange adapter may rotate on the actuator
shaft or the actuator may be damaged.

To determine if the internal actuator rotor vane stops are adequate,
the total rotational inertia (JT) must be determined for therotating mass. JT equals the sum of the calculated J for the
specimen, plus known J for the actuator, flange, and flexures.

2. To determine JS refer to Substeps A, B, and C and select theformula appropriate to the specimen configuration.
Refer to the figure on page 18 and note that m is equal to the mass ofthe specimen.

A. If the specimen is a regular solid mass, use the following
formula to calculate JS:

Table 8 provides the rotational inertia values for the actuatorand optional components. Table 9 lists the maximum allowablerotational inertia values in both U.S. Customary and SI metricunits for each available actuator/servovalve combination. The
following procedure describes how to calculate the totalrotational inertia.

JS =where:

12 mr2

m = πr2Lρ

L = lengthρ = density

Rotational Inertia Equations

B. If the specimen is a regular hollow mass, use the following
formula to calculate JS:
JS = 12 m (r02 + r12)

1. Calculate the total rotational inertia by using thefollowing formula:
JT = JR + JF + JD + JS
where:

where:

JR = rotational inertia for actuatorm = π(r02 + r12)Lρ
L = length

JF = rotational inertia for flange adapter options

ρ = density

JD = rotational inertia for diaphragm flexure
JS = rotational inertia value for specimen 					 configurations (step 2)

C. If the specimen is an offset mass, use the following formula
to calculate JS:
JS = mr2

Table 8. Rotational Inertia for Actuator Components
Model
216.10Rotary Actuator (JR)Flange Adapter (JF)

Diaphragm Flexure (JD)

lbm-in.2

kg-m2

lbm-in.2

kg-m2

lbm-in.2

kg-m2

725

2.12

6,500

1.92

2,700

0.79

216.20

2,180

6.37

10,400

3.04

7,900

2.30

216.30

6,350

18.43

18,3005.35

14,300

4.20

17

3. After calculating the total rotational inertia (JT), compare the value to the maximum
allowable JT for the specific actuator and servovalve combination indicated in Table 9. If
the maximum allowable JT exceeds the maximum levels specified in Table 9, then steps
must be taken to control actuator motion and limit servovalve pressure. Contact MTS
Systems Corporation for information on available actuator cushions and cross portrelief valves.

m 1 Massr
m 1 Massam 1 Massr0(a)Solid Mass

m

r1

(b)
Hollow Mass(c)
Offset Mass

Rotational Mass Measuring Points

Table 9. Maximum Allowable Rotational Inertia (J) When Using Only Internal Actuator Rotor Vane Stops
U.S.Customary
Model

Max JT for Actuator Model (lbm-in.2)

Servovalve Flow
Rated (gpm)

Peak* (gpm)216.10216.20216.30252.2515

26367,592

2,546,602

15,821,000

252.3125

43

134,392

931,0455,784,381

252.3240

70

50,712

351,327

2,182,718

252.3360

103

23,422

162,268

1,008,136

256.0550

87

32,830227,441

1,413,042

256.0990

156

10,21070,738439,458

180

311

2,569

17,798110,579

256.18SI Metric
Model
252.25Max JT for Actuator Model (lbm-in.2)

Servovalve Flow
Rated (l/m)

Peak (l/m)

216.10216.20216.3070.11

443.951854.42

56.77

98.40

252.31

94.62

162.7525.63

162.31

677.98252.32151.39264.94

9.67

61.25

255.83

252.33227.09389.83

4.47

28.29

118.16256.05189.24329.28

6.26

39.65

165.62

256.09340.63590.43

1.95

12.33

51.51

256.18681.261177.07

0.49

3.10

12.96

*Flow through the valve at 3,000 psi (∆P). Using reduced system pressures (∆P) will decrease peak flow Q peak = Q rated
Decreasing peak flow will allow an increase in acceptable inertia (J). Refer to Table 1 for the maximum velocity into vane3
stops where W = Q peak x 3.85 in. /sec .
Displacement in. 3/rad

18√1000 .
∆P

Ordering Information

The standard Series 216 Rotary Actuator
assembly includes the actuator, ADT,
servovalve manifold (standard MTS
Model 256 type), flange adapter, and one
diaphragm flexure. The following
optional equipment is also available:» Diaphragm flexure» Torque cell

216 Rotary
Actuator/
Supports» Reaction bracket» Reaction base
When ordering, please indicate the desired actuator
force rating and specify the desired options.

Related Products

Refer to the following MTS ProductSpecifications for information on
products that are commonly used inconjunction with the Series 216 Rotary
Actuator:» Series 252 Servovalves» Series 256 Servovalves» Models 660.22 and 660.23 Differential
Pressure Cells» Series 633 Reaction Torque Sensors

19Regional Business Centers

T HE AM E R IC AS

EU R O PE

A S I A / PA C I FI CMTS Systems Corporation
14000 Technology Drive
Eden Prairie, MN 55344-2290
USA
Telephone: 952-937-4000
Toll Free: 800-328-2255
E-mail: info@mts.com
Internet: www.mts.com

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BAT EXA 16
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94046 Créteil Cedex
FranceTelephone: +33-(0)1-58 43 90 00
E-mail: contact.france@mts.com

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Raiden Bldg. 3F 3-22-6,
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Tokyo 130- 0026
Japan
Telephone: +81 3 5638 0850
E-mail: mtsj-info@mts.com

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Telephone: +49-(0)30 81002-0
E-mail: euroinfo@mts.com

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Telephone: +39-(0)11 45175 11 sel. pass.
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Datavägen 37b
SE-436 32 Askim
SwedenTelephone: +46-(0)31-68 69 99
E-mail: norden@mts.com
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98 Church Street,
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Leeds
LS102AZ
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Telephone: +44 (0) 113 270 8011
E-mail: mtsuksales@mts.com

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ISO 9001 Certified QMS
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New Caohejing International
Business Center,
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Xuhui District
Shanghai 200233
P.R.China
Telephone: +021-24151000
Market: +021-24151111
Sales: +021-24151188
Service: +021-24151198
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India
Telephone: + 91 80 46254100
Email: mts.india@mts.com

Specifications subject to change without notice.
MTS is a registered trademark of MTS Systems Corporation in the UnitedStates. This trademark may be protected in other countries. RTM No. 211177.
©2023 MTS Systems Corporation
100-032-134c 216RotaryActuator • Printed in U.S.A. • 08/23