Info

Source: Data adapted

in part from Chapter 4A by Evans and Chapter 7 by Scippa of Ref. 11-1.

spherical geometries (see Figs. 1-5, 11-1 to 11-4, and 11-17). The spherical shape gives the lowest case mass per unit of enclosed volume. The case is often a key structural element of the vehicle and it sometimes has to provide for mounting of other components, such as fins, skirts, electric conduits, or thrust vector control actuators. The propellant mass fractions of the motor are usually strongly influenced by the case mass and typically range from 0.70 to 0.94. The higher values apply to upper stage motors. For small-diameter motors the mass fraction is lower, because of practical wall thicknesses and the fact that the wall surface area (which varies roughly as the square of the diameter) to chamber volume (which varies roughly as the cube of diameter) is less favorable in small sizes. The minimum thickness is higher than would be determined from simple stress analysis; for a a fiber composite case it is two layers of filament strands and the minimum metal thickness is dictated by manufacturing and handling considerations.

Simple membrane theory can be used to predict the approximate stress in solid propellant rocket chamber cases; this assumes no bending in the case walls and that all the loads are taken in tension. For a simple cylinder of radius R and thickness d, with a chamber pressure p, the longitudinal stress a¡ is one-half of the tangential or hoop stress ae\

For a cylindrical case with hemispherical ends, the cylinder wall has to be twice as thick as the walls of the end closures.

The combined stress should not exceed the working stress of the wall material. As the rocket engine begins to operate, the internal pressure p causes a growth of the chamber in the longitudinal as well as in the circumferential direction, and these deformations must be considered in designing the support of the motor or propellant grain. Let E be Young's modulus of elasticity, v be Poisson's ratio (0.3 for steel), and d be the wall thickness; then the growth in length L and in diameter D due to pressure can be expressed as

Details can be found in a text on thin shells or membranes. For a hemispherical chamber end, the stress in each of two directions at right angles to each other is equal to the longitudinal stress of a cylinder of identical radius. For ellipsoidal end-chamber closures, the local stress varies with the position along the surface, and the maximum stress is larger than that of a hemisphere. The radial displacement of a cylinder end is not the same as that of a hemispherical or ellipsoidal closure if computed by thin-shell theory. Thus a discontinuity exists which causes some shearing and bending stresses. Similarly, a boss for the attachment of an igniter, a pressure gauge, or a nozzle can make it necessary for bending and shear stresses to be superimposed on the simple tension stresses of the case. In these locations it is necessary to reinforce or thicken the chamber wall locally.

Finite element computerized stress analysis programs exist and are used in motor design companies today to determine the case design configuration with reasonable stress values. This analysis must be done simultaneously with the ae = 2 a¡ = pR/d

stress analysis on the grain (since it imposes loads on the case), and with a finite element thermal analysis to determine thermal stresses and deformations, since these analyses are interdependent on each other.

The fast heating of the inner wall surface produces a temperature gradient and therefore thermal stresses across the wall. The theory of transient heat transfer has been treated by a number of authors, and, by means of a relaxation method, a reasonable approximation of the temperature—time history at any location may be obtained. The inner wall of the case, which is exposed to hot gas, is usually protected by thermal insulation, as described in Section 12.6. Therefore the heat transfer to the case is very low. In fact, for a single operation (not two thrust periods) it is the designer's aim to keep the case temperatures near ambient or at the most 100°C above ambient.

The case design has to provide means for attaching a nozzle (rarely more than one nozzle), for attaching it to the vehicle, igniters, and provisions for loading the grain. Sometimes there are also attached aerodynamic surfaces (fins), sensing instruments, a raceway (external conduit for electrical wires), handling hooks, and thrust vector control actuators with their power supply. For upper stages of ballistic missiles the case can also include blow-out ports or thrust termination devices, as described in Chapter 13. Typical methods for attaching these items include tapered or straight multiple pins, snap rings, or bolts. Gaskets and/or O-ring seals prevent gas leaks.

Metal Cases

Metal cases have several advantages compared to filament-reinforced plastic cases: they are rugged and will take considerable rough handling (required in many tactical missile applications), are usually reasonably ductile and can yield before failure, can be heated to a relatively high temperature (700 to 1000°C or 1292 to 1832°F and higher with some special materials), and thus require less insulation. They will not deteriorate significantly with time or weather exposure and are easily adapted to take concentrated loads, if made thicker at a flange or boss. Since the metal case has much higher density and less insulation, it occupies less volume than does a fiber-reinforced plastic case; therefore, for the same external envelope it can contain somewhat more propellant.

Figure 14-1 shows the various sections of a typical large solid rocket case made of welded steel. The shape of the case, particularly the length-to-diameter ratio for cylindrical cases, influences not only the stresses to be withstood by the case but the amount of case material required to encase a given amount of propellant. For very large and long motors both the propellant grain and the motor case are made in sections; the case segments are mechanically attached and sealed to each other at the launch site. The segmented solid rocket booster for the Space Shuttle is shown in Fig. 14-2 and discussed in Ref. 14-1. For the critical seal between the segments a multiple-O-ring joint is often used, as shown in Fig. 14-3 and discussed in Ref. 14-2. Segments are used when an unsegmented motor would be too large and too heavy to be transported over

Igniter assembly

Igniter assembly

.Igniter flange pressure seal

^.Attachment boll centerline

.Igniter flange pressure seal

^.Attachment boll centerline

Explosive /charge

Thrust termination port

Girth weld (typical)-

Forward equator

Longitudinal ec*uator weld (typical)

Forward equator

Longitudinal ec*uator weld (typical)

Explosive /charge

Aft closure

Nozzle flange /pressure seal

Nozzle assembly

Y-ring skirt attachment

Aft closure

Nozzle flange /pressure seal

Nozzle assembly

Attachment bolt J centerline

Attachment bolt J centerline

FIGURE 14-1. Typical large solid rocket motor case made of welded alloy steel.

Propellant: 70% AP 16% Al

14% PBAN & curative Burn rate 0.434 in./sec

Total propellant weight Total RSRM weight Maximum thrust (in vacuum) Burning action time at 70°F Assembled motor length Diameter of case Propellant mass fraction (motor) Temperature limits Chamber pressure max/av. Specific impulse, altitude

FIGURE 14-2. Simplified diagram of the four segments of the Space Shuttle solid rocket motor. Details of the thrust vector actuating mechanism or the ignition system are not shown. (Courtesy of NASA and Thiokol Propulsion, a Division of Cordant Technologies, Inc.)

1,106,280 Ibf 1,255,592 Ibf 3,060,000 Ibf 123.7 sec 1513 inch 146 Inch 88.2% 40 to 120°F 910/662 psla 268.2 sec

FIGURE 14-2. Simplified diagram of the four segments of the Space Shuttle solid rocket motor. Details of the thrust vector actuating mechanism or the ignition system are not shown. (Courtesy of NASA and Thiokol Propulsion, a Division of Cordant Technologies, Inc.)

Design

Redesign

FIGURE 14-3. The joints between segments of the Shuttle solid rocket booster (SRB) were redesigned after a dramatic failure. The improvements were not only in a third O-ring, the mechanical joint, and its locking mechanism, but also featured a redesign of the insulation between propellant segments. (Courtesy of NASA.)

Zinc Chromate putty

Design

Redesign

FIGURE 14-3. The joints between segments of the Shuttle solid rocket booster (SRB) were redesigned after a dramatic failure. The improvements were not only in a third O-ring, the mechanical joint, and its locking mechanism, but also featured a redesign of the insulation between propellant segments. (Courtesy of NASA.)

ordinary roads (cannot make turns) or railways (will not go through some tunnels or under some bridges) and are often too difficult to fabricate.

Small metal cases for tactical missile motors can be extruded or forged (and subsequently machined), or made in three pieces as shown in Fig. 11-4. This case is designed for loading a free-standing grain and the case, nozzle, and blast tube are sealed by O-rings (see Chapter 6 of Ref. 14-3 and Chapter 7 of Ref. 14-4). Since the mission velocities for most tactical missiles are relatively low (100 to 1500 m/sec), their propellant mass fractions are also relatively low (0.5 to 0.8) and the percentage of inert motor mass is high. Safety factors for tactical missile cases are often higher to allow for rough handling and cumulative damage. The emphasis in selecting motor cases (and other hardware components) for tactical missiles is therefore not on highest performance (lowest inert motor mass), but on reliability, long life, low cost, ruggedness, or survivability.

High-strength alloy steels have been the most common case metals, but others, like aluminum, titanium, and nickel alloys, have also been used. Table 14-2 gives a comparison of motor case material properties. Extensive knowledge exists for designing and fabricating motor cases with low-alloy steels with strength levels to 240,000 psi.

The maraging steels have strengths up to approximately 300,000 psi in combination with high fracture toughness. The term maraging is derived from the fact that these alloys exist as relative soft low-carbon martensites in the annealed condition and gain high strength from aging at relatively low temperatures.

Outer cylindrical 2-0 layer

Forward skirt

Inner layer is pressure vessel Aft skirt

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