Motor Case Loads 1
The case-loading profile shall include all individual design loads or the worst combination of design loads. The loading profile shall be determined by evaluation of any and all of the following loads.
All axisymmetric and local design loads (for definition of design load, see sec. 2.3.1.1), including dynamic loads (sec. 3.3.7), should be resolved into membrane loads to determine the critical design loading condition. The critical case loading condition, or worst critical combination loading, should be defined by summation of a load-temperature-time history profile of the case. This profile should be prepared by plotting all design loads and temperature exposure encountered (during handling, storage, assembly, and service use) versus time and motor case station. Then, the critical-loading condition for every structural element of the case determined from the loading profile should be used in the case structural analysis (sec. 3.3.6) to determine that not less than zero margins of safety exist at any area of the case while it is subjected to the maximum thermal exposure.
3.3.5.1 Attachment Loads
Motor Igniter
The motor igniter attached to the case structure produces an axial thrust load that is transmitted to the case at the local point of igniter attachment reinforcement. The igniter thrust should be treated as a local load on the case shell of revolution; it results in increased case tensile, shear, and bending stresses in the igniter attachment flange and adjacent case membrane. These stresses should be added to the basic membrane stresses adjacent to the igniter opening to define the maximum stress distribution in the igniter flange and adjacent case membrane.
Single or Multiple Nozzles
To minimize concentrated loading on the closure, the nozzle opening should be located in the closure at areas free of geometric discontinuities or other reinforcement discontinuities. For the same reason, the location of nozzle ports in the knuckle section of a torispherical closure (sec. 3.3.3) should be avoided where possible.
The nozzle produces an axial load (parallel with the nozzle axial centerline) on the case end closure; this load results from the summation of the internal pressure acting on the upstream vertical projected area of the nozzle from the nozzle throat to the nozzle-to-case-attachment pressure seal minus the pressure within the nozzle acting on the downstream vertical projected area of the nozzle from the nozzle throat to the exit plane. Bending loads that result from the pressure differential between the backside and topside of the submerged section may occur in submerged-nozzle designs. Also, bending loads are produced in nozzle designs with unsymmetrical entrance sections. These bending loads result from the internal pressure acting on the unsymmetrical projected area of the nozzle.
The nozzle axial and bending loads produce increased tensile, shear, and bending stresses in the end-closure nozzle attachment flange and closure membrane. These stresses should be added to the existing closure stresses to determine the maximum attachment-flange and membrane stress distribution.
Thrust-Vector-Control System
The TVC system produces a side load at some angle to the motor centerline. The magnitude of the side load and its location within the nozzle assembly depend upon the type of TVC system used. The TVC side load produces body shear and bending loads in the motor case. The magnitude of the loads at any case location should be determined by preparing a moment-and-shear diagram of the case. TVC systems that extend hardware into the thrust stream (i.e., jet tabs or jet vanes) also produce an axial tension load on the motor case because of the gas pressure acting on the projected area of the TVC hardware in the stream. The tensile, bending, and shear stresses produced by the TVC system should be added to the existing case membrane stresses to determine the membrane stress distribution.
Base overpressure, resulting from exhaust-gas recirculation in the area of the motor aft closure, is not normally of sufficient magnitude to be of concern in motor case design for typical space-vehicle application. However, the effect of base pressure in the area of the motor aft closure should be included in the case loads analysis when the combination of thrust deflection resulting from TVC and the arrangement of motor structure is such that a pressure buildup will occur. This condition would result in slight overpressure buildup on the aft closure and motor skirt, which should be added to existing loads to determine the critical stress distribution in the aft closure membrane as well as the critical aft motor-skirt buckling condition.
TVC system actuators produce axial, bending, and shear loads locally on the motor case at the point of actuator attachment. Also, the inertia load from TVC system fluid slosh, auxiliary equipment, and equipment-support structure can produce axial, bending, and shear stresses locally in the motor case, depending upon the auxiliary equipment required, and the method of its attachment to the motor case. In addition, axial compressive drag loads on external structure with a large frontal area (e.g., liquid-injection fluid tanks) are transferred through the structure to the case at the point of attachment. These axial (tension or compression), bending, and shear stresses should be added to the existing case membrane stresses to determine the stress distribution at the area of case attachment.
Motor Thrust Skirt
Skirt attachment to the pressure vessel causes two additional loads that must be included in the case design: (1) a discontinuity at the point of attachment can result from the restraint imposed by the skirt on the deflection of the pressure vessel under pressure and (2) the axial thrust can cause considerable additional discontinuity bending loads at the juncture between the skirt and case, depending on the load-line offset between the skirt and the case structural element. The Y-ring design similar to that shown in figure 13 is recommended for skirt attachment and cylinder-to-closure transition. This design provides gradual changes in section thickness without stress concentrations and can be modified to minimize or eliminate large discontinuity loads associated with offset load lines. The cutout (relief) section of the Y-ring shown in figure 13 minimizes discontinuity loads in the cylinder and closure membrane by balancing deflections with appropriate mass distribution. This approach should be used when required to reduce discontinuities.
The discontinuity loads discussed above produce bending and shear stresses in the case at the local area of skirt attachment. These stresses should be added to the existing case membrane stresses.
Clustering Structure
Vehicle clustering results in local loads on the motor case, and the clustering structure should be designed to minimize the concentration of loads at the point where the clustering structure is attached to the motor case. The magnitude and type of clustering loads obviously depend on the vehicle size and the design of the clustering system (refs. 72 and 73). In most circumstances, the clustering structure produces axial tension or compression, transverse shear, and body-bending-moment loads on the motor case. These loads produce additional tension, compression, shear, and bending stresses in the motor case that must be added to the existing case membrane stresses.
- --Motor £--
Figure 13—Y-ring skirt attachment.
Figure 13—Y-ring skirt attachment.
Where possible, the clustering structure should be located in the motor skirt or skirt support extensions where sufficient structure can be efficiently incorporated to provide an effective and uniform load distribution to the pressure vessel.
Motor Staging
Staging rockets located in the vehicle interstage structure produce bending and shear loads that are transmitted to the motor case skirt through the interstage structure. These bending and shear loads influence the skirt buckling stability (sec. 3.3.6.4) in combination with overall vehicle axial, bending, and shear loads that may exist instantaneously in the skirt prior to stage separation.
Buckling of the case forward closure should be evaluated when upper stage pressure is used to accomplish staging. An example of the analysis that should be made to determine the pressure load within the interstage is shown in reference 146.
Thrust-Termination or Thrust-Reversal Hardware
The transient pressure load in the case immediately after actuation of thrust termination or thrust reversal is the determining load that influences the design of the thrust-termination or thrust-reversal attachment reinforcement and adjacent case membrane. If the pressure drop is rapid enough, the system may not require a reinforcement around the opening. In any event, the transient-load condition in the area of a port must be analyzed to determine the maximum-loading condition to establish the maximum stress distribution in the reinforcement (if used) and the adjacent case membrane.
With either thrust termination or thrust reversal, a thrust spike occurs that imposes a load on the entire case structure. The magnitude and transient condition of the spike must be analyzed in combination with other existing case loads to determine the maximum case loading. If the thrust-reversal system has stacks through the interstage, discontinuity bending loads in the local area of the thrust-reversal port may result from differential expansion between the interstage structure, stack, and case. When these bending loads occur, they produce bending stresses that should be added to the existing membrane stresses.
Aerodynamic Control Surfaces
Where possible, the aerodynamic control surfaces should be attached to the case skirt, motor-support skirt, or interstage structure where an efficient load-transfer structure can be incorporated in the component design for more uniform load distribution to the motor case.
The aerodynamic control surfaces result in loads arising from both local and overall body tension; from compression; from shear; from bending; and from torsion; depending on the control-surface design and function,- and whether the control surfaces are attached remotely or directly to the pressure vessel. These loads produce corresponding stresses in the motor case, which should be added to the existing case stresses as required by the particular control-surface design and location.
Instrumentation, Electrical, and Destruct-System Hardware
In current motor designs, instrumentation, electrical, and destruct-system hardware result in negligible motor case loads. However, should hardware of appreciable mass be attached to the motor case, the stresses resulting from inertia and discontinuity bending loads should be added as required to existing case stresses in the area of attachment.
3.3.5.2 Internal Loads
Internal Pressure
The internal design pressure (i.e., the maximum expected operating pressure (MEOP) multiplied by the design safety factor) should be treated as a uniform pressure acting on the internal case structure. The maximum expected operating pressure should be determined by statistical methods (3 standard deviations) including the evaluation of internal combustion pressure and the influence of propellant composition and grain variations, erosive burning, ignition transient, and propellant temperature. Also, an aft-end igniter (ref. 147) located in the nozzle area can obstruct gas flow and thereby increase the case internal pressure (depending on igniter design). If an aft-end igniter is used, the maximum internal case pressure should be determined by analysis or by appropriate subscale or full-scale tests, and the maximum pressure obtained should be used to establish the case-design internal-pressure load.
The internal pressure produces hoop (circumferential) and meridional (axial) biaxial loads in the motor case structural membrane. The biaxial load should be calculated on the assumption that the aft-end closure has an opening equal in area to the unrestricted gas passage of the installed nozzle assembly. In some instances, the case is hydrostatically proof tested with fully closed (plugged) end closures. When proof test of the fully closed pressure vessel is a program requirement, the internal-pressure-limit load (sec. 2.3.5) should be established as the critical (maximum) case load resulting either from MEOP in conjunction with external flight loads or from the MEOP with a fully plugged case.
Axial Thrust
The motor thrust produces an axial load on the motor case that should be calculated by summation of the aerodynamic drag load, the inertial force, and the vehicle weight above the case station of interest (ref. 65, p. 5). The method of computing the thrust load distribution on a motor case during motor firing is shown in figure 14. In figure 14, the local axial load is computed by summing the local pressure loads on the vertical projected areas of the case to the right or left of a station, reduced by the inertial loads of the segment to the right or left of the station (ref. 65, pp. 3-5).
Thrust Misalinement
The thrust misalinements that should be analyzed are the radial displacement between the motor centerline (thrust line) and the nozzle centerline and the angular displacement between the motor centerline and the nozzle centerline. Additional thrust misalinement that should be included in the analysis exists in clustered motors, where three classes of quasi-steady misalinement can occur (ref. 72): angular misalinement of a motor in a cluster with respect to the total vehicle geometry, displacement of the motor thrust vector in a cluster with respect to the vehicle center of gravity, and deviation of a motor thrust level within the cluster.
In all cases of thrust misalinement, the motor case experiences a static body bending and shear load resulting from the thrust deviation from the vehicle center of gravity and from any shift in the vehicle center of gravity. The bending moment is reacted by the inertia of the vehicle mass and by the TVC system.
a = Vehicle acceleration mf = Forward mass m = Local unit mass N = Local axial load
P = Forward load reaction = mfa Pf = Local interna! pressure
Figure 14—Thrust load on a rocket motor (ref. 65, p. 4).
Thermal Stresses
Thermal stresses (sec. 2.2.6.1) are produced by thermal gradients within the case structure and by differential expansion of materials that have different coefficients of thermal expansion. The thermal stresses produce biaxial loads, discontinuity bending, and shear loads that should be included in the case membrane stress analysis where thermal stresses are encountered (ref. 65, pp. 91-114).
3.3.5.3 External Loads
Ground Handling
Tension, compression, shear, torsion, and bending loads, both axisymmetric and local, occur during ground handling, shipping, and assembly of the motor case, depending on the handling and support-equipment design. The handling operations and the type of equipment used during handling should be analyzed to determine the magnitude and type of handling loads that will be experienced by the motor case. No handling loads should exceed flight loads.
Launch-Pad Loads
In most applications, the motor case must have free standing capability on the launch pad after assembly of the entire vehicle, with the given stage unpressurized and the given stage and all upper stages fully loaded, or with external wind loads acting on the vehicle as well. Steady wind, wind gusts, and the turbulent wake from nearby structures produce body-bending and shear loads on the motor case while the vehicle is on the launch pad. Recommended practices for determining the prelaunch ground wind loads are contained in reference 148.
These weight and wind loads produce an interaction of axial compression, body-bending, and body-shear loads on the case that influence the buckling stability of the case (sec. 3.3.6.4).
Flight Loads
Atmospheric lift and drag produce case body-bending and shear loads during yaw and pitch flight control of the vehicle. The magnitude of the case body-bending and shear loads should be determined by preparing a vehicle shear-and-moment diagram using the maximum loads encountered. The roll mode of flight control and spin stabilization during flight produce body-torsion loads on the motor case that should be evaluated in the stress analysis.
Dynamic pressure acting on the vehicle frontal area produces axial compressive loads on the case during flight. The compressive loads influence the buckling stability of the case (sec. 3.3.6.4), particularly in unpressurized upper stage motor cases.
Wind gusts and steady-wind shear produce motor case body-bending and shear loads on the motor case during flight through the atmosphere. The magnitude of the case body-bending and shear loads is determined by preparing a bending-moment-and-shear diagram using the maximum wind loads determined from the specified atmospheric wind profile.
3.3.6 Structural Analysis 3.3.6.1 Thin-Shell Structure
The case design stress shall not exceed the allowable stress, whether yield or ultimate;
and the maximum deflections shall not exceed allowed deflections.
The motor case should be analyzed using general linear elastic theory based on Love's first approximation for thin shells (refs.|74 to 78), in which the following assumptions are made.
(1) The shell thickness is negligibly small compared to the principal radii of curvature of the shell middle surface.
(2) Linear elements normal to the unstrained middle surface remain straight during deformation, and their normal strain is negligible.
(3) Transverse shear strains are 0 throughout the thickness.
(4) Stresses normal to the shell surface are negligible.
The following factors should be included in the requirements for the structural analysis.
(1) Loads used should be design loads (sec. 3.3.5).
(2) Combined loading should be analyzed to determine the resultant stresses using the interaction equations available in reference 55 (and in most texts on stress analysis).
(3) When internal loads or other loads are compensating or are otherwise beneficial to the structural capability of the motor case, the minimum 3-standard-deviation values of the compensating load should be used for the particular stabilizing design condition being evaluated.
(4) The maximum permissible permanent strain anywhere in the motor case should be limited to 0.2 percent, except where plastic deformation in local regions of stress concentration may be unavoidable in the case design. (For example, see sec. 3.3.6.4.)
(5) Loads and load distributions used should be established on the basis of the worst (or most critical) buildup of case-design dimensional-control tolerances.
(6) The case thickness used should be the minimum thickness considering the maximum limit of material-procurement tolerance and any change that will occur during fabrication and processing (e.g., thinning of the material during forming).
(7) The material allowable strength used should be the minimum uniaxial strength guaranteed by the material procurement specification using the specified heat treatment, and should include any additional strength reduction resulting from fabrication and processing (e.g., welding). The minimum strength-value determination should also include additional factors applicable to the specific design (e.g., elevated-temperature strength, fatigue strength, creep strength, and any further reduction required by fracture-mechanics considerations). The 0.2-percent offset yield-strength value should be used with materials that have no sharply defined yield point.
(8) Biaxial strength should be used only when sufficient data have been obtained and when sufficient structural analysis has been accomplished to verify the actual condition of biaxial gain in the case. When biaxial gain is used, particular care should be exercised to determine the actual properties (sec. 3.2.2) that exist for the particular case design. The biaxial stress state, particularly in areas of discontinuity (e.g., cylinder-to-closure transition) should be determined by tests of a strain-gage-instrumented pressure vessel or by detailed analysis. The actual stress state is influenced by the change in radius of curvature and the meridional tension effect. In areas of bending, both the inner and outer fiber membrane stresses should be evaluated in the applications of biaxial gain.
(9) The structural analysis of every element of the case should be done using the critical-loading condition determined from a summation of the motor case load-time-temperature history profile.
(10) To obtain the most efficient design in geometric-discontinuity areas, the stabilizing effect of the longitudinal-membrane loads on the discontinuity shears and moments, as evaluated by meriodional tension effect analysis (refs. 84 and 149), should be incorporated into the overall analysis.
The structural analysis should also be used to identify areas of high stress concentration and compound discontinuity loads, if not previously apparent; if necessary, the case should be redesigned to eliminate or minimize the area of concentration or compound loading.
3.3.6.2 Local Attachments and Openings
The design stress at case local attachments and openings shall not exceed the allowable stress, whether yield or ultimate.
A finite-element computer program similar to that shown in reference 88 should be used in the analysis of the reinforced openings, reinforcing pads, nonaxisymmetric openings, and shell-supported rings when the reinforced thickness does not exceed four times the shell thickness. This computer program will handle a shell structure of arbitrary geometry and loading, and will also handle the intersection of two shells. The program was formulated by approximately representing the shell structure as a series of flat plate elements, expressing the membrane and bending characteristics of a plate element by combining a plate bending element and a plane-stress element, and insuring the compatible response of adjacent elements.
The NACA TN 929 ring analysis method (ref. 87) as modified for particular needs should be used for an approximate analysis of attachment fittings. Where critical loads or marginal safety factors are indicated, a more precise analysis should be performed using the plane-strain, finite-element technique (refs. 91 and 92).
3.3.6.3 Local Weld Discontinuities
The stress level at a weld shall not exceed the maximum value that can be tolerated by the specific material within established reliability requirements.
In a complex welded structure, there are residual stresses of a finite magnitude prior to any service loading. These stresses are primarily the result of forming and welding operations. Also, local bending stresses that occur during pressurization because of radial mismatch and angular mismatch (angular discontinuity at a weld resulting from weld sink) and discontinuity stresses from any adjacent source (e.g., Y-ring reinforcement) are possible and are superimposed on the residual stresses. With these additive stresses, the yield strength of the material can be reached at a relatively low level of internal pressure.
The importance of the local stresses depends largely on the toughness and ductility of the material used. In very tough and ductile materials, the local areas that exceed the yield stress will bridge the load by stress redistribution to adjacent membrane without failure, perhaps even in the presence of a defect. However, if the material has insufficient ductility, the local discontinuity stresses may not have a chance to redistribute before failure occurs.
Therefore, welds in brittle material should be designed for the full elastic stress resulting from the direct membrane stress and all discontinuity stresses. As an example, the elastic bending stress caused by mismatch across the longitudinal weld can be simply expressed as
_ 3pRd where p = Pressure
R = Radius of cylinder 6 = Amount of mismatch t = Chamber thickness
Because the basic membrane stress is pR/t, it can be shown that the elastic stress from mismatch is equivalent to 3k times the membrane stress, where k is the mismatch in terms of percent of thickness. Thus, for a 5-percent mismatch, the bending stress would be 15 percent of the membrane stress.
If the residual stress is assumed to be 10 percent of the yield strength Fty, the angular mismatch is assumed to be 20 percent of the yield stress, the design stress is the material yield strength, and the longitudinal-weld mismatch is 5 percent of the thickness, then the maximum elastic outer fiber stress across the weld at design pressure is ah (max) = residual + angular mismatch + radial mismatch + direct membrane
The values used in the above example are representative of those that might occur in practical motor case design, but specific values vary depending on the individual design (e.g., both angular and radial mismatch can be minimized or eliminated in components that are machined following welding, and angular mismatch can be minimized or eliminated by rerounding after welding).
Welds using ductile materials can be designed to allow a certain degree of yielding; however, a recommendation for a specific amount cannot be made. Whenever this design approach is used, it should be qualified by knowledge developed from specimen or burst tests representing the material and the discontinuities to be encountered. Whether the weld is designed for the full elastic stress or is designed to allow local yielding, the effect of the maximum elastic stress on the critical defect size should be evaluated. The residual stress and the angular and radial mismatch discontinuity stresses for both longitudinal and girth welds for large motor cases (156-in. and 260-in. diameters) using GTA-welded 200-grade 18 percent nickel steel, and GTA and submerged arc-welded 250-grade 18 percent nickel steel (ref. 95) have been evaluated. Correction factors for allowable flaw sizes are developed for these discontinuity conditions, including a girth weld adjacent to a Y-ring reinforcement. Although this study is directed toward large motor cases, it is representative of the factors that should be considered in any case-weld design.
3.3.6.4 Buckling of Thin-Wall Shells
The case buckling load, or worst combination of buckling loads, shall not exceed the allowable buckling load.
The motor case structural analysis must include the buckling analysis (ref. 65, pp. 84-89) for any of the loads defined in section 2.3.6.4 to insure that the buckling load in the case or in the case forward or aft skirt does not exceed the load that causes the onset of buckling. When the motor case may be subjected to a combination of buckling loads acting simultaneously, the buckling analysis should account for the interaction of these loads in accordance with the interaction equations provided in reference 65, pp. 195-197.
The beneficial effect of Hie propellant grain stiffness on buckling can be included in the case analysis when use of this analysis technique is necessary to determine the maximum buckling capability of the motor case. This approach is applicable only when the critical buckling loads, determined from the motor case load-time-history profile, occur at a time when the propellant grain is available to provide the beneficial effect. The following analysis techniques should be considered for use:
(1) An analysis of finite cylinder stability with an elastic core, as made by Seide (ref. 103)
(2) An evaluation as made by Brush and Almroth (ref. 104) of the elastic core as subjected to generally axially symmetric lateral pressure combined with a central
-axial force, with numerical results given for three lateral pressure distributions (uniform pressure, linearly varying pressure, and a circumferential band of pressure)
(3) An analysis of the stability under torsion of circular cylindrical shells with an elastic core, as shown in reference 105.
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