Life Extending Control for Rocket Engines - NASA Technical Reports ...

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NASA

Technical

Memorandum

Life Extending

C.F. Lorenzo Lewis

and J.R.

Research

Cleveland,

"

I

.

/

.-_,

105789

Control

for Rocket

Engines

Saus

Center

Ohio

and A. Ray, M. Carpino, Penn

State

University

August

and M.-K.

Wu

University Park,

Pennsylvania

1992

L_.F_

F XT_Nu

,,:s [',!r i

')

S

,._,

I _-,.

31203

{_,;A?A)

"%

tJnc

o,_/3t

i aS

li

Life Extending

Control

C. F. Lorenzo NASA Mail

77-I,

Engines

& J. R. Sans

Lewis

Stop

for Rocket

Research 21000

Cleveland,

Center

Brookpark

Ohio

Rd.

44135

A. Ray, M. Carpino, M.-K. Penn State University

Wu

ABSTRACT Tile given

concept

of Life

and the need

Two approaches a basis

damage

is presented. engine

Control

design.

is defined.

life prediction

to life extending

for control

continuous

Extending

for an alternative

control

A second

non-linear

called

Progress

programming

discussion

The tile

Implicit

ilfitial

life prediction

uses

relationship

cyclic

Life Prediction

formulation

to develop

fatigue

functional

Approach

Continuous

oll an initial

is used

of current

based on a continuous

are considered:

approach

law is also discussed.

Finally,

A brief

model

fatigue

results

which

(in time)

for life extension

is

life prediction

Approach

of a continuous

methods is established.

as

requires

fatigue

for a simplified

a

model rocket

(model). INTRODUCTION

Systems with high performance requirements, such as Space Shuttle Main Engine (SSME) Systems, often have a small number

of criticalcomponents

define the effectivelifetime of the system,

hl particular these components

transientsand itisduring the transientsthat large decrements in component transient loading on SSME

or Hypersonic Propulsion

that operate close to mechanical

turbine blades isa typical example.

design limits azld that

are often maximally

stressed through

lifeare experienced. The effectof thermal

It isagainst the backdrop

of the durability problems

of the SSME that the concept of Life Extending Control (LEC) has evolved. However, itclearlyhas applicabilityto a broad range of mechanical/thermodynamic systems. The fundamental concept of lifeextending control isto control rates of change and levelsof some performance variables to minimize damage while simultaneously maximizing

dynamic

(or damage

rates) of criticalcomponents

performance of the plant.

BACKGROUND

The

fundamental

concept

of life extending

control

Two basic approaches have been considered 1.) damage laws and 2) Direct Life Extending Control The continuous

damage

a much

implementation.

simpler

form will allow

has been

a more straightforward

In the paper that follows, the Life Extending The potentialdurabilityimprovement

forwarded

in references

development

of the Life Extending

A continuous

Finally, are those damage

damage

to be expressed preliminary

which

will

model in terms results

being

possiblewith these concepts has been demonstrated

for controls extrema

for life extension

lead to a Direct

start-upshut-down

developed

of the cyclic

Life Extending

and

use will

Control

be discussed.

the stress

for a Simplified

Lorenzo

Control

& Merrill. cycle based damage law. concept

and

Reusable

method

and

on simplifiedapplications

Control. This

model

allows

the intra-cycle

level. Rocket

Engine

may have

near

will be presented.

The results

term

application

for a minimal

and

the

of a proposed

sequence. LIFE

Both extension

by

Control concept will be reiterated briefly.

[Ref I]. This paper will show current work applying the Implicit Life Extending

damage

(I-3)

Implicit Life Extending Control, which uses current which assumes the development of a continuous form

PREDICTION

the basics of a current theory (cyclic) for life prediction (or damage (to a non-cyclic continuous model) of this theory are presented.

model)

results

CURRENT

LIFE

PREDICTION

APPROACH

Tile cyclic life prediction process is highly nonlinear The material that follows is based on the local strain Usually estimate

the life estimates

that

result

will be calculated

and used

operation. estimated

It is assumed to occur locally

to simplify at critical

procedure

for life prediction

the

version

local

c, is calculated

where

cl,

c2, and

and

depends

the subscript

procedure cycles,

r indicating

and involves

tile

that

load

depend

Fig (2),

a reference

a careful

are described

on many

for life calculation

from

F, by

upon

the material

ordering

point.

e-e, = _; 2

The

undergoes

component transient

can be based upon used in life prediction

design.

loading

loading.

Here

during

that

system

the stresses and strains analysis. The detailed

factors. For cyclic

(stress-strain)

loading,

Fig (1), first

and

8F

=

F-F r

determination

of the hysteresis-like

of metal fatigue due to cyclic follows reference [,I].

life for a particular

is as follows.

history,

8¢

with

service

life as tile component

the analysis that the life calculations points. This is a typical assumption

of the procedure

d are constants

to forecast

to manage

is complicated

A simplified strain,

are used

directly

and comes from tile study approach and substantially

(:z)

2

of the reference

stress-strain

cycles

point

is critical

by magnitude

to the calculation

and direction.

These

by

where a isthe stress,6¢=(a-ar)/2, and E, A, and s are material constants. Once the stress-stralncycles are calculated, the lifeusage associated with a single cycle of the given load history cazlbe estimated from

(4)

Here #r',b, _t',and c are material constants, D, is the lifelostdue to cycle i,hereafter called damage, and aav s isan average tensilestresswhich isused to correct for nonzero mean tensilestressesin predominately elasticcycles. Once the cyclic analysis has been completed, total damage

may

be estimated by

D = _ Dl i

using damage

the

Palmgren-Miner

given

the

cyclic

approach analysis

(Ref

are possible

4).

Other, (Ref

5).

more

accurate

(5)

and

complex

approaches

to deternfining

total

The has

been

closure

procedure

of equations

completed, for updating

procedure

the

ttowever,

the

therefore

the ultimate life estimation

effect

LIFE

can

of loading

control

direct

be solved

All

PREDICTION

life makes

a direct

application

of a life estimation

procedure

to control

would

require

This

new

control.

formulation

bookkeeping

To accomplish

would

the number

consist

of cycles,

efforts

in this regard

have

U, fig 3. (eg. stress

derived

by a small

This requires or strain).

the following

incremental

a functional

damage

strain

dD

d6

dt

dt

law.

(or stress),

--=w--÷(1-w)

where &e and 6p represent damages

life estimation

be described

be more this goal,

of a continuous

in a later

beneficial

and

is

a new formulation form

their respective

on cycle

of the

amplitudes,

damage and their

APPROACH

effect, D, for any chosen control action of damage with measurable variables, Initial

will

cycle

dependence

of the current and

for life extending

a stress-strain

This

is possible

In the concepts that follow, the need for a continuous (non-cyclic) form Specifically, in order to control damage accumulation it is necessary to know

stress-strain cycles that differ be found in reference [61.

i.e. whenever

network.

application

modelling

which

of time,

or by a neural

indirect

is required.

forms

instances

approach

oil component

application

procedure

at discrete

computing

impossible.

goal of damage

laws instead of the current order of occurrence. CONTINUOUS

(1)-(5)

by a traditional

to life extending

section, of the

either

d_

for the damage relations will be apparent. for tile next increment of time the damage relationship

This

form

see figure

(in terms

has been 4.

The

of differential

derived

details

_

by comparing

of the derivation

rates)

two may

(6a)

dt

due to tile"elastic _ and nplastic" effectsrespectively,and

w: I_,-,,,I ,,_ I_-,, I

l-w=

I_,-%1 l e-_, I

(6b)

and

d8

05, =-do + --08 "

do

,to

(ec)

ao,

a_. dSp=--_.-°

do

+ aSr

do r

The da r terms bring in the effectof the change of referencepoints (ur which between extrema.

are tilestress extrema), these are zero

Finally the total derivatives d6Jdt

and d6p/dt in Eq. (6c) are evaluated from the respective partialderivatives:

++.2 a_ b x

+ (}{+++

--

=

c

ao

2Kin Ic

1

× tT)

LIFE

Tile fundamental

J

___ , (lo--,l/--

I

\1

I

j

×

These equations can then be used to obtain the damage

(Od)

12o/-o-o

)_

z!

variables to minimize

, -7--'

, x (2o/-o-%)

1

tTzj

I

(

j

rate at any instant.

EXTENDING

CONTROL

concept of life extending control is to control rates of change and levels of some damage

(or damase

/

rates) of criticalcomponents

performance

while simultaneously maximizing

dynamic

performance of the plant. It is emphasized that a fundamental tradeoff exists between the level of achievable performance a_id the abilityto extend the llfeof system components generating that performance. Since the lifeprediction procedure isgrosslynonlinear sad isintimately connected with the determination ofstressstraiJzhysteresiscycles,any control strategy will depend upou the total time history of the force applied to the critical component.

However,

as long as some flexibility in obtaining system transientperformance

exists,the opportunity to

ms,rage lifeusage exists.A study of the lifeprediction procedure indicates two factors which will be important when devising a control strategy, strain cycle maguitude From

and average (mean) tensilestress.

figure 5, which isa solution of equation (4),it isclear that lifeusage isdirectlyrelated Lo strain magnitude.

Strain magnitude

isdirectlyrelated to force. Thus, a control which minimizes forces applied to the critical component

will extend life. This is hardly remarkable. based upon

However,

LEC

allows a comparison

work, the time to achieve control performance can be varied to manage component.

of two differentcontrol objectives

a quantitative analysis of the forces required to accomplish the differentobjectives. As assumed In thisway

total system performance over the lifeof the component

Also, from figure 5,itcan be seen that nonzero mean

in this

the forces and therefore the lifeof the critical

tensilestress(MTS)

can be maximized.

applied during predorninately elasticload

cycles can substmitiallydegrade Life.For example ifa particular commanded

trajectory has leftthe component

a nonzero average tensilestress,small force perturbations willbe more damaging

with

than ifthey occur aftera commanded

trajectory that resultsin an average compressive stress. This shows clearlythe need to manage

the operating domain

(level)as well as cyclic amplitude. A third tractor, not explicitlyshown

by the equations, iscomponent

temperature.

Higher component

temperatures

can have a marked effecton lifeusage. Higher temperatures change the material property constants in equations (I)-(4) and increase the lifeusage for comparable values of strain. These effects,although important, willnot be considered in this paper. The basic ideas of lifeextending control can be more of tlds additional factor.

effectivelyillustratedwithout the consideration

Two general approaches to LEC are presented. The firstisbased on the cyclic lifeprediction approach and iscalled the Implicit Approach. Assuming the existence of the continuous lifeprediction approach, an additional concept for Life Extending I_[PLICIT

Control ispresented. This iscalled Direct Life Extending Control.

LEC

The implicitapproach to Life Extending Control recognizes that current fracture/fatiguesciencecannot predict the differential damage conunand

on lessthan a fullcycle of strain. The implicitapproach (see figure 6) selectsa sequence of typical

transients (tolddisturbances) that are representative of those the system would experience in service. Two

performance measures are defined: Jp, an objective function that maximizes

dynamic

performance

(possibly by

minimizing

quadratic

fatigue/fracture overall

state

theory

performance

and

control

available

measure

excursions)

to calculate

can

also

and,

the daInage

be defined

JD,

a damage

accumulated

measure

over

tile

which

sequence

uses

the

best

of command

(current)

transients.

An

as

j =j

where

a represents

a "best" and

tile relative

control

damage

algorithnt

algorithm

accumulation The

damage

control

and

(i.e.

J).

control

Intuitive temperature Also,

LEC

algorithms and the

An example component above LEC CYCLIC

The time

study

life (about approach.

DAMAGE

calculation

element

such

to that

the

selected

approach

The measures)

the loss in dynamic

then

dynamic

selects

performance

against

the

performance

control

is small

(i.e.

mechanics

separately)

JD

approach

is calculated.

performance/life

are

readily

rninilnizing

number

of the implicit

are

detailed

are considered: 1) the performance variables of the performance variables representative

as follows.

During

normally used of the damage

tile

to manage variables

design

dynamic (stresses,

Superior

LEC

algorithms

can then

be identified

as

the

formulated. cyclic

of cycles

of stress

at very

and

strain

cost

been

established.

minimizing

of stress,

control

small

have

Clearly

amplitude

(ref 1) of a load positioning two times)

tradeoff

the

strain,

should

contribute

(actuator)

indicated

in dynamic

mean

and

response.

tensile

stress,

mean

strain,

temperature

should

minimize

to extending

critical

component

the ability

to substantially

This

indicated

study

and

damage. life.

extend

critical

the potential

of the

ESTIMATOR

of cyclic

of the

damage

is required

Life Management

A neural damage developed (Fig. 8). relationships tensile stress,

(relative

Tire implicit

transients.

JD separately). A family of algorithms can be developed which are parameterized a. The final control carl be selected from this set of algorithms with confidence that

a desirable

levels

minintizing

optimized

life extension.

of command

rates). Various control algorithms are then exavtfined within this feedback structure. performance and disturbance transients are applied to a simulated system with a trial

J (or Jp arrd

and

are

and

sequence

is to find an algorithm

The

those that minimize J (or Jp and by the relative tradeoff parameter an effective

sequence

variables functions

and various of selected

performance

performance

for tile full

7), for a significant reduction in accumulated damage over tile sequence of transients (i.e., and life is extended), ttere the subscript o refers to optimizing for dynamic performance gain set (point q in figure 7) is then chosen which satisfies the desired weiglfing between

process, two types of feedback performance and 2)nonlinear strains, temperature That is, the sequence

the

expectation

Jp,z,min " Jl_,o,min in figure JD,o,mln " aD,_,mln is large only. An actual operating and

between

is applied

over

parameters.

performance

importance

which

(7)

estimator, For ttfis

to generate etc. These

in the Implicit

Life Extending

LEC

Control

approach

Concept

for off-line

(Ref

capable of assessing tempertaure-influenced, estimation, temperature from a monitored

temperature properties

geometry-specific stress concentration strain in accordance with Neuber's

dependent values are then used with factor, Rule.

for material tile nominal

kt, in a neural

net

optimization.

cyclic damage, at a critical point has been location is used with known functional

properties such as stress of the critical

(trained)

It is also a real-

1).

to map

Young's Modulus, ultimate component and an a priori

nominal

stress

into

local

stress

and

The extrema detector monitors nominal stressto determine cycle extrema and "tags_ the local strain values at the extrema for use in a subsequent

damage

calculation. Also the cycle local mean

stress isdetermined.

These values

together with temperature sensitivematerial properties are then used as inputs to a neural net trained to map values into cycle damage. The mapping isconsistent with Dowllng's Local Strain Approach damage is then determined by post-processing tilecycle damage by a damage accumulation Miner, Double Linear Damage Rule, etc..

DIRECT

The

LIFE

EXTEDING

Implicit

components.

Life

Direct

CONTROL

Extending

control

the

Ref [4]. Accumulated law such as Palmgren-

requires

Control

approach

does

a continuous

form

unreferenced continuous damage model is still progress toward direct life extending control.

needed,

not

directly

of the damage tile

damage

control laws model

(or limit)

instead

the

of the cyclic

forwarded

in the

damage forms. previous

rates

of critical

While section

a simple, allows

MEASURED

DAMAGE

In this

approach

forces, etc.) the control.

VARIABLES

(figure

9) both

related variables Here the control

approaches.

LIFE the plant

associated attempts

It is presumed

that

on the behavior

with

variable

damage

in damages

DI,

modelled critical

(7) can

while

be used

One

implementation

modifying

the control The

of the existing

approach.

ESTIAIA

TED

Unlike estimate models models

life variables

of local

stress,

maximizing

damage

issue

DAA_IAGE

damage variables

damage

variables damage

variables

could

LIFE

Variables

described

variables

as for the

and/or

previously

damage

The

example

that

gas for a fuel (LH2} combustion chamber. behavior, (presumed

follows

(monopropellent)

figure

12.

variables

would

directly

approach,

temperatures,

exists

that

A, the damage

would

function then

The

associated

u3 are considered of time,

is to minimize

performance

achieve

control

at a "setpoint"

in a feedback desired

and

result

will likely damage

objective

be

of the

approach

tlds concept,

result

in real

output.

The

rate over time

a linear

operation

shown

in figure

components.

by available

model

by

rate,

law or to modify

system

the

adaptively

gains

by an active,

damage

time

models

measures.

damage

controller

10 uses a real

The

influence coefficients to detailed, The damage estimator would

would

performance

or even feedback

an approach.

of critical

augmented

can

Conceptually

time be

model driven

to by

the structural

non-linear, real time structural be a direct consequence of the

rate design

estimates would

based

follow

on measured

in much

the same

approach. ENGINE

the preliminaries dynamic

the feed system

to be a criticalcomponent}.

LEC

CONTROL

LIFE

EXTENSION

for Direct

model

Presently, oxidant lumped parameter

Additionally,

u2, and

problem

of the plant.

EXTENDING

and

engine

turbopump. Standard

control

to such

dynamic

establishes rocket

above)

3, at time

ul,

as a continuous

is fundamental

ROCKET

simplified

(described

in figure

to accumulate

be used

accumulation)

variables

a structural

measured

shown

The

model

actions

here is on obtailffng

LEC

damage

or performance

life model

performance

etc.)

Thus,

performance

The emphasis

(and

strains,

D1, D2, ...) as a continuous function of measured in the performance variables (presumed to be

(here

while

to permit

of controllability

Damage

action

strain,

(dynamic)

VARIABLES

rates

stresses,

tiffs optillfization.

structure

control.

(measured

(or life)

is known.

damage

can vary from simple, precomputed, linear, which may require considerable computation.

contimmus manner

The

the Measured the

performance

measured

the damage

damage

for ally control

of a measured

the structure

predictive

(Note,

to aclffeve

feedback

for example. control

of the critical

function

and

damage (or local Damage rates Also, the influence of changes

D 2, and D a, respectively).

life components

of equation

performance

a "real-time"

D 1 can be predicted

as a continuous

CONTROL

witil critical components are measured and used as feedback information for to directly regulate life as a resource'rather than indirectly as in the previous

allow the prediction of the incremental stressses, strains and temperatures. controllable)

EXTENDING

is shown

Life Extending

for Rocket

A

is separately supplied to both the gas generator and modelling methods are used to represent the system

the main dynalrfic

by a structural

a gas generator

Engines.

the drive

is augmented

11. Here

Control

provides

model

in figure

model

of a typical

turbine

blade

The blade isrepresented as a three lump mass, with sixdegrees of freedom at

each lump, (i.e., an 18 D.O.F. model). The load on the blade consistsof two parts, the firstis (I/n th of) the drive torque as inferred by the performance equations, where n is the number of turbine blades, and the second part isa dynalulc term which represents the oscillatoryload of the blade passing each stator. Fatigue at the blade root isused as blade damage

indicator. The

damage

model of equation 6 is used in the resultsthat follow.

The general approach for thisstudy isto use non-linear programming

to determine optimum

position sequences to vary the thrust (throttle)of the rocket engine. Then

(life extending) valve

a control could be designed to emulate these

responses. A future option isto selectan appropriate control structureand to use non-linear programming the best gain selectionwith both dynamic performmlce

measure

used

in this

study

J = E

response and component

is quadratic

and

(ZrQr Z, + UrRkUk

is given

to determine

lifein a quadratic performaJlce measure J. The by:

÷ W(0_/H2 )z

where

Z k = [x['Vr]

,

(8)

Jt,._

here X is the plant state vector, U tilecontrol input vector and v the damage the state variables are: Turbine shaft speed, Pump combustor

gas pressure, combustor

state vector. For the following results

mass flow rate, Preburner gas pressure, Preburner gas density,

gas density. The

oxygen

to hydrogen

mass

flow ratio was brought into the

optimization

to directly

position

O 2 Valve

aud

Ill the case

that

maintain #2

tlleO2/tl

position.

follows

the

Chamber All other

:

The

rocket

engine

standard tile

is

=

O2/H

2ratio. case

Two

cases

in which

then

D
.

OF O2

VALVE 21

pl P NOZZLE

Torque Angular

SOURCE

Speed Figure 12. A Simplified Rocket Engine Dynamic Model Block Diagram

13

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