pneumatic stiffness paper

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Linear Piston Actuators

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

By Sekhar Samy, CCI, and Dave Stemler, CCI

21st AOV Users’ Group Conference •Winter 2002, January 9-11Clearwater Beach, FL, USA

2 Linear Piston Actuators | 521 ©2002 CCI. All rights reserved.

Linear Piston Actuatorsn Sekhar Samy, Control Components Incorporated, Rancho

Santa Margarita, California, USA; and Dave Stemler, Control Components Incorporated, Rancho Santa Margarita, California, USA.

21st AOV Users’ Group Conference, Winter 2002, January 9-11,

Clearwater Beach, FL, USA

Introduction

High Reliability of actuation is of paramount importance in the nuclear power industry. Pneumatic actuators form the largest

installed base with many in safety significant applications. This paper addresses the issues related to actuation, such as available Thrust, Stiffness, Sensitivity, Hysteresis, Dead band, Dynamic Stability and a sizing example.

This paper will also present comparisons between various types of linear actuators and their relative advantages and disadvantages. Also presented will be evaluation techniques for troubleshooting actuator problems and improving plant performance.

Actuation Requirements

In a nuclear power plant typically 90% of the control valve actuators are pneumatic. Hence, it is not surprising that the AUG and its participants expend considerable time in studying pneumatic actuators. The reason pneumatic actuator are widely used is primarily due to the fact that compressed air readily provides a large source of available power for valve actuators. Most valves do not move at once so the total power requirements at any given time in a plant can be easily met. Most importantly, this ready source of stored energy is also available during short-term outages.

In critical service valve applications, in addition to reliable operability there are other important considerations:

n Repeatable Tight Shutoff

n Optimal controllability during normal operating conditions (Resolution)

n Good controllability during transients

n Environmental Qualification

n Compact with a low center of gravity, and a high weight to thrust ratio for seismic considerations

n Stroke Speeds

Operability of an actuator in a general sense just means that it can be actuated when required to do so. It does not ensure that any of the important criteria listed above has been carefully considered before selecting an operator.

Repeatable tight shutoff

There are no consistent guidelines for achieving the required level of tightness within the valve industry, so it is imperative that the user spell out quantitative criteria in ensuring that the actuator has sufficient thrust. In an ideal situation with perfectly machined seating surfaces even a small positive force is adequate for tight shutoff. This is not the case in real world applications, where there are manufacturing tolerances. Over time a sealing surface goes through normal wear and tear and would quickly deteriorate to allowing more leakage then desired. So while a valve may leak test to the specified class in the shop in mint condition, it may not provide the specified shutoff after some use. The important quantitative criterion is Pounds of thrust per Lineal Inch (PLI) of seating circumference. In the valve industry this value for an ANSI/FCI 70.2 Class IV shutoff varies from 40 to 400 PLI.

Just such a wide variation suggests that sufficient conservatism is necessary based on empirical study of contact stresses between sealing members and field observations. The Instrument Society of America (ISA) Guide (Ref 1) recommends a value of 300 PLI for Class IV shutoff.

Optimal Controllability

It is often overlooked that control valves are final control elements in process control. The best control systems cannot make up for limitations of a control valve. Small hysteresis and dead band, quick response to small changes in input signal are all key to good performance. The quantifiable measure for fine controllability is Resolution.

Resolution is defined as the smallest possible change in position of the control valve. When a valve is asked to change position from a steady state of zero stem velocity, what is the smallest incremental travel possible? To answer this question the valve actuator system is modeled as an elastic spring mass system and analyzed. The smallest change in force is due to change from the static to dynamic friction as the valve makes a change in position. The friction under consideration is due to valve plug piston seals, valve packing and actuator seals. Dynamic friction is smaller than static friction (Ref 2).

©2002 CCI. All rights reserved. 521 | Linear Piston Actuators 3

( )

The elastic system is simply as spring mass system that can be modeled using the equation of motion for a Single Degree Of Freedom (SDOF) system. The “spring” has a pneumatic component (trapped air in actuator) and a mechanical component (compression spring). So the smallest change in a control valve position is:

(1)

where,

Fstatic = Summation of static friction forces, such as, packing, seals and piston rings

Fdynamic = Summation of dynamic friction forces, such as, packing, seals and piston rings

Ksystem = Summation of pneumatic and mechanical stiffness at the valve travel of interest

For a valve stroke with total stroke “H”, in terms of percentage resolution equation may be rewritten as follows:

(2)

It is clear from equation that larger the “stiffness” of the actuator, smaller its resolution. With smaller resolution better process control is possible. Similarly, longer the stroke smaller the resolution.

Appendix A, derives the expression for the stiffness of a pneumatic spring diaphragm actuator and a piston actuator.

For a spring diaphragm actuator it is

(14)

And the lowest stiffness at a given supply pressure occurs when LL = H. For a double acting piston actuator the stiffness is

(15)

The lowest stiffness generally occurs when LU = LL. Refer, to the Appendix A for the nomenclature and figures. The piston actuator is definitely stiffer when compared to a equivalent spring diaphragm actuator.

How does the “resolution” translate into better controllability? The step change in the flow capacity corresponding to the smallest change in position that the actuator can accomplish can be determined by determining the slope of the Valve Capacity “Cv” versus Lift curve at the point of interest (i.e., Lift).

(3)

By substituting the resolution of the actuator from equation into equation , the fractional change in valve capacity ∆Cv is determined. Next, by using the ISA sizing equations one can calculate the actual flow change possible with a given actuator.

In Appendix B, we have presented a calculation showing how to perform resolution calculations in a typical feedwater regulator application. Poor control, high vibration and pressure swings are endemic of this application. In this application, high rangeability and fine resolution are required to maximize control. Long stroke lengths and a stiff actuator is the key to performance enhancements. The authors use such calculations to diagnose control problems in actual plant applications.

The pneumatic stiffness of a typical double-acting piston actuator easily allows positioning accuracy’s of 0.5% where required; in comparison, positioning accuracy’s of a diaphragm actuator ranges from 2% to 5%.

Controllability under Transient Conditions

Operability under transient conditions, whether they are fluid flow related buffeting forces or a system related pressure transient phenomenon - a piston actuator would be better able to resist such forces due to its inherent high stiffness. If one could estimate the magnitude and waveform of the transient pressures, it is possible to study its effect on the controllability of the valve.

Environmental Qualification

Environmentally qualified actuators must withstand high ambient temperatures, radiation, high mechanical stresses due to vibration or fast actuation, seismic loads and finally any Design Basis Events.

Piston actuators feature a high thrust to weight ratio because they can operate at higher supply pressures. This also helps to keep the design compact without much overhanging mass, which will reduce the natural frequency of the actuator-yoke system. Higher natural frequency system is desired when the valve is designed to withstand seismic loads.

The only elastomers in a piston actuator are o-rings, which are robust because the stresses on the o-rings are quite low. Diaphragm actuators with fabric reinforced diaphragms are under higher stresses and typically fail at the bolt holes due to high stress concentrations.

∆X =Fstatic - Fdynamic

Ksystem

∆X =Fstatic - Fdynamic

Ksystem

1H

100%

PL

LL

+Kspring

Kd = γ A

Kp = γ APU PL

LU LL+ + Kspring

∆Cv = Cvoo x

∆X


ENHANCING SYSTEM PERFORMANCE

A pneumatic actuator’s performance can improve by the simple addition of a positioner. But in valves with high seal friction a positioner would only exacerbate control problems. An important element for improved control stability is actuator stiffness. Actuators with insufficient stiffness can be adversely affected by process dynamics, which will tend to contribute to control instability, especially in fast response systems such as pressure control. This is best understood by looking at the natural frequency of a SDOF system.

(4)

Where,

fn = Natural frequency of the system, Hz

g = Acceleration due to gravity, 386 in/sec2

F = External Load moved by the actuator, lbf

Ksystem = Stiffness of the actuator pneumatic + spring system, lbf/in

If an actuator with a low natural frequency, is trying to respond fast it will become unstable as its velocity ramp rate gets closer to its Time Period. In other words, if an actuator tries to reach its final velocity from rest within its Time Period, it will become unstable. The Time Period of a system is defined as Ts = 1/fn seconds.

transmission of the force to the load and instead tend to excite the “spring-mass” system.

The advantage of a piston actuator with its higher Stiffness, consequently larger natural frequency or smaller time constant becomes evident.

Even slow processes such as level control will benefit from better stability, shortened settling time and better control stability when positioners are used. If a diaphragm actuator is used without a positioner, it must use a specific range spring and bench-set for the application. Any change in the application parameters will require re-calibration of the bench set. Due to bench set an actuator without a positioner may not use all of its signal range of 3-15 signal or 6-30 psig, hence reducing its effectiveness in controlling the process.

Diaphragm actuators are widely used in nuclear power plants. While they provide good performance in many applications, there are some critical applications where they have shortcomings. One of the major concerns is the non-linear change in effective area of a simple flat diaphragm. This has in some cases resulted in over estimation of the available actuator thrust, which can be a serious problem in safety significant applications. The simple flat diaphragms are not capable of providing long strokes, but this is somewhat remedied by using a “rolling” or molded diaphragm with a large fold. Still they do not come close to what a piston actuator can offer in large stroke lengths. The wall thickness of the stamped housings and the strength of the diaphragm itself limit the supply pressure to the diaphragm actuators. The upper bound for diaphragm actuators is around 60-80 psig on the average, while the piston actuators are routinely designed to operate at 150 psig.

Misapplications of linear actuators to Gate valves are significant because quantifying the required force accurately, problems due to pressure locking thermal binding are significant as is evidenced by NRC Generic Letter 89-10 and Information Notice 96-08 respectively. The large seating and un-seating forces require special dampening devices to prevent damage to the backseats.

These gate valves retrofitted with the system media operated actuators now offer the most reliable solution. They use piston actuators except the power source is the system media itself. They provide such a large thrust margin that all concerns for accurately estimating wedging and un-wedging forces under a variety of scenarios become unnecessary.

REFERENCES

1) Borden G., Friedmann P. Editors, 1998, “Control Valves – Practical Guide of Measurement and Control”, Instrument Society of America, Research Triangle Park, North Carolina, USA

2) Ludema K., 1996, “Friction, Wear, Lubrication – A Textbook in Tribology” CRC Press, Boca Raton, FL, USA

Figure 1: Ramp Velocity Profile

The velocity profile of a actuator is shown in figure 1. The system ramps up to a final velocity then travel at the constant final velocity and ramps down as the actuator reaches its final position. A first order system reaches 99.8% of its final value in six Time Periods. So the ideal time required to reach the final velocity desired should about 6 times the Time Period of system, i.e., Tr > 6Ts

Actuators with lower stiffness and equipped with volume boosters for fast stroke speeds are prone to oscillatory problems. Any attempts to speed up a system makes the system Time Period impede the

fn = 1

Ksystem g

F2


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( )

APPENDIX A

PNEUMATIC ACTUATOR STIFFNESS

To compute the pneumatic stiffness of an actuator, assume that the changes in stem position occur so rapidly that there is no air supplied or exhausted from the actuator. Such a process is adiabatic in nature. Let the initial volume of the actuator chamber under consideration be “V1” and the initial pressure be “P1” in absolute units. Now let the volume of the actuator chamber suddenly change to a lower volume “V2” and the pressure increase to “P2”in absolute units. The relationship that defines the change is given by the following equation.

(5)

Where,

γ = Ratio of the specific Heats

Let the infinitesimal change in the piston stroke be “x”, and the surface area of the piston “A”. Then the new pressure and volume can be re-written as follows:

(6)

Where, “k” is the pneumatic stiffness (or Spring Rate) that is to calculated. The change in volume can be re-written as follows:

(7)

Substituting (6) and (7) into (8) and re-arranging:

(8)

Using the Taylor Series expansion and keeping just the first two terms in the series gives,

(9)

Expanding the above equation

(10)

And dropping out the term containing x2 , since x2 << 0 and simplifying gives the expression for pneumatic “spring rate”.

(11)

ACTUATOR STIFFNESS

This section derives the expression for the spring constant of a double acting actuator with a return spring (Figure A1) and a diaphragm with a return spring (Figure A2).

In a double acting actuator both sides of the piston are filled with air. In a diaphragm actuator one side is filled with air and the spring side is connected to the atmosphere. Notice the large volume of air that would be trapped in the bottom of the spring diaphragm actuator even when the valve is closed. In a piston actuator this volume is minimized to a small value. When this fact is applied to equation it is clear that smaller the volume, higher the stiffness. This makes the spring diaphragm operator to have a lower stiffness when compared to a piston actuator. Further, this has one other important consequence when throttling at low plug lifts. Commonly, known as the “Bath Stopper Effect”, spring diaphragm operators with flow over the plug and throttling at low lifts can slam into the seat causing severe water hammer. So most of the time they are specified as flow under the plug. This problem does not occur with well designed piston actuators which can have stiffness approaching very large values and can be used in flow over the plug applications.

Depending on the bias of the positioner, the maximum pressure in the cylinder is 2/3 to 3/4 of the supply pressure. The maximum pressure is set by the positioner manufacturer and is usually controlled by the clearances in spool machining. Hence it is fixed for a given model of positioner. Some smart positioners have a value as low as 1/2 of the supply pressure.

( )

P1V1 γ= P2V2

γ

(V1 - Ax)γ

P2 = P1 + kxA

V2 = V1 - Ax

P1V1 γ = P1+ kx

A

( ) V1γ 1 − P1V1

γ = P1+ kxA

( )AxV1

γ

1 − P1V1 γ = P1V1

γ + V1

γkxA ( )γAx

V1

P1V1 γ = P1V1

γ − γAxV1

V1 γkx

AP1V1

γ + V1

γkxA

γAxV1

-

k = P1γA2

V1


The systems all behave as though they are springs connected in parallel. Hence, their stiffness can be simply summed to come up with equivalent spring stiffness for the actuator.

For convenience it is possible to define air “equivalent air-volume lengths” as follows,

(12)

(13)

for the upper and lower chambers respectively

For a diaphragm actuator the equivalent spring is

(14)

Since, the upper chamber is connected to the atmosphere it does not act as a spring and is not included in the above equation.

Figure A1: Fail extend spring diaphragm actuator

For a piston actuator the equivalent spring is

(15)

Comparing equations and it can be seen a piston actuator that operates at a higher supply pressure would be much stiffer when compared to a diaphragm actuator.

Figure A2: Fail extend piston actuator

LU =

VU

A

LL =

VL

A

Kd= γA PL

LL

+ Kspring

Kp = γA

PU

LU

+ PL

LL

+ Kspring


uses

1003

pneumatic stiffness paper

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