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Rail Launch Missile Simulation using MSC.Nastran Software

Author: Peter Zeman Paper: 2001-34 COMPANY: MBDA Inc. 5701 Lindero Canyon Road, Suite 4-100 Westlake Village, CA 91362 USA Phone: (818) 991-0300 (x 248) Fax: (818) 991-4668 peter.zeman@mbda-us.com ABSTRACT: The purpose of this paper is to present a dynamic simulation of a rail launched missile as it is fired from its rail. Missile loading conditions during a launch change rapidly based on the missile’s position on that rail. The missile's time spent on the rail is a fraction of a second and the simulation must take into account the missile's dynamic characteristics. Rail stiffness is also position dependent and the gaps and friction between the missile hangers and rail require modeling. The nonlinear finite element transient analysis is capable of simulating the missile's dynamic conditions during its travel along the rail. The outcome of the analysis has multiple usage. The missile's movement on the rail, in real time, is observable and the missile's velocity, acceleration, roll angle and roll rate can be plotted. For structural purposes, the missile's component stresses can be plotted and also valuable missile shoe reaction forces can be determined at different locations on the rail. The sample problem described in this paper does not represent any specific missile design. However, the presented analysis technique was successfully utilized and verified in the Brimstone missile project at Alenia Marconi Systems.

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INTRODUCTION: Rail launched missiles can be divided into three basic categories: a) Ground launched missiles (no aerodynamic load during the launch) b) Helicopter launched missiles (aerodynamic load is low during the launch) c) Fast Jet launched missiles (aerodynamic and inertia load can be very high during the launch)

It is usually a high aerodynamic and inertia load acting in the lateral axis, which introduces high reaction forces between the missile shoes (hangers) and the launch rail. These high reaction forces can cause structural damage to the missile components or the rail. They can also prevent a successful missile launch by slowing or even stopping the missile on the rail and thus causing a missile “hang fire”.

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MISSILE/RAIL SKETCH: MISSILE SHOE REACTIONS:

Rail, Cross - section

Missile Shoe

Missile

Lateral Load F1

Reaction, -F1

Reaction, -R1

Reaction, +R1

A relatively small lateral load (F1) generates high shoe reaction forces (-R1 and +R1).

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PROBLEM DEFINITION: During a successful launch:

• The missile rapidly accelerates on the rail. • The missile usually does not remain on the rail longer than 150

milliseconds. • The missile shoe reaction forces change rapidly during the launch based

on the missile’s rail position. The main contributors to these changes are varying aerodynamic missile loads and rail stiffness for various positions along the rail.

Other considerations requiring modeling:

• The missiles shoes fit loosely in the rail (some free play exists). • Friction exists between the shoes and the rail.

The analysis simulates: a) Dynamic conditions on the rail (Nonlinear, transient analysis). b) Friction and gaps between shoes and rail (Slide lines with friction option). c) Calculation of missile load for each position on the rail (Function). d) Calculation of rocket motor thrust as a time function (Function). ANALYSIS OBJECTIVES: a) Determination of shoe reaction forces during the launch. b) Determination of missile acceleration, velocity and roll rate on the rail. c) Determination of missile tip – off roll rate d) Obtaining missile and rail stress plots for various positions on the rail. FINITE ELEMENT MODEL DESCRIPTION: Major Features: a) The model has to be dynamically representative. The missile/rail mass and

stiffness must be correctly simulated. b) Missile’s shoe/rail interface has to be representative. Slide line elements

must be placed in the shoe/rail contact areas. Friction between the missile shoes and rail has to be considered.

c) The model size should be moderate (sample problem includes approximately 8 000 dof). The nonlinear transient analysis is an iterative analysis, which requires numerous time steps. Large models require long run times!

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Modeling Hints: a) A convenient combination of element types was selected to obtain a highly

representative model, which was still of moderate size. b) Slide line elements have to be defined in X -Y plane of assigned coordination

system which is defined in the slide line element property. While the default coordinate system was proper for vertical slide line elements, a new coordinate system, which was rotated by 90 degrees, was assigned to horizontal slide line element property.

c) Slide line elements are gradually added to the model. The model is “run” and correct functions of the added slide line element are then verified.

d) Slide line master nodes are located on the rail. There is just one slave node for each slide line element, which is associated with the missile shoe.

e) Slide line elements do not have gap force measuring capability, hence the shoe load can not be determined from the slide line element. This deficiency is overcome by adding two extra elements for each slide line element. In the nonlinear transient analysis the output can be written for DOF Spring Element force, hence the shoe reaction force can be determined if this element is incorporated in the model. The extra 5 DOF are added by rigid element(s) as shown on the picture below.

f) The aerodynamic load acting on the missile changes with the missile position

on the rail. The load change is simulated by two independent MSC.Nastran functions. Function No 2 is time dependent, and function No 3 is associated with a Nonlinear Force load, which is position dependent. The nonlinear, position dependent force is superimposed on the time dependent force.

g) The analysis is gradually run with various coefficient of frictions, typically 0.0, 0.15 and 0.25. All these output sets are stored in the same database. This enables the plotting of shoe reaction forces, missile acceleration and velocity on the same plot for various coefficient of frictions.

SLIDE LINE SLAVE NODE RIGID ELEMENT MASTER NODE

DOF SPRING ELEMENT (1 DOF) and RIGID ELEMENT (REMAINING 5 DOF)

SHOE ELEMENTS (STIFF BEAMS)

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Missile Finite Element Model: Rail finite element model: Rail Finite Element Model

Front Shoe Detail

FWD Rail Top View

Front Shoe Intermediate Shoe Aft Shoe

Rail Bottom View

Constraints location

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Missile/Rail Finite Element Model:

Constraints

Shoe Detail

DOF SPRING ELEMENT AND RIGID ELEMENT (5 DOF)

DOF SPRING ELEMENT: The DOF Spring Element is inserted between the missile shoe beam element and the Slide Line Element. The purpose of this DOF Spring Element is to “measure” the reaction force between the missile shoe and the rail. The DOF Spring Element is relatively stiff and does not reduce the actual stiffness between the shoe and the rail.

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Slide Lines: There are nine slide line elements in this model. Each shoe contact with the rail is a separate slide line element. Slide Line Parameters (Specified in Slide Line Element Property): a) Stiffness Factor = 1.0 b) Width = 5.0 c) Coefficient of Friction = 0.0, 0.15 and 0.25 d) Non sliding Friction Stiffness = 1000 e) Unsymmetrical Penetration f) One slave node for each slide element g) Slide line coordinating system definition (X-Y plane, correct orientation). ANALYSIS: Software: MSC.Nastran for Windows, version 4.6. Nonlinear Transient Analysis Parameters: a) Convergence Tolerance: Displacement = 0.01, Load = 0.01, Work = 1e-5 b) Solution: Full Newton - Raphson c) Time increment: 0.0005 sec, 650 steps, Max. iterations = 25 d) Output: ALL, Every Step, e) Overall Damping: 0.08 (Critical Damping = 0.04) (F= 10 Hz) f) Analysis: Nonlinear Transient , Advanced options, Output requested for DOF Spring Force (9 elements), Displacement for all model, Acceleration and Velocity for Node 979.

Front and Intermediate Shoe Slide Line Elements LH Side, (Property 11)

Front and Intermediate Shoe Slide Line Elements RH Side, (Property 9)

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Load acting on the missile:

ROCKET MOTOR THRUST (associated with Function 1)

Aerodynamic and Inertia Load (associated with Function 2)

LOAD ACTING ON THE MISSILE

Non linear Force (associated with Function 3)

The missile load is gradually increased for the first 50 ms. Afterwards, this component of the missile load is steady, in this sample case.

The rocket motor thrust starts at 100 ms. At this time the missile is loaded and it can be considered “steady”. The thrust profile is simplified in this sample case, but reflects the general rocket motor thrust shape.

Function 2, Aero and Inertia Load Function 1, Rocket

Motor Thrust Function 3, Nonlinear Force

The nonlinear force is the missile load component, which changes with the missile position on the rail.

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ANALYSIS RESULTS: Missile movement on the rail, Coefficient of Friction = 0.15

Comments: During the first 100 ms, the load is gradually applied to the missile (load function 2). After 100 ms the rocket motor thrust starts to move the missile on the rail (load function 1). The missile starts to move on the rail as shown above. During successful launch the missile accelerates rapidly.

CAPTIVE CARRY POSITION

FRONT SHOE LEAVING THE RAIL

INTERMEDIATE and AFT SHOES LEAVING THE RAIL

MISSILE FREE FLIGHT

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Missile Acceleration on the rail, Coefficient of Friction = 0.0, 0.15 and 0.25 Missile Velocity on the Rail, Coefficient of Friction = 0.0, 0.15 and 0.25

Time [sec]

ROCKET MOTOR FIRES

Missile Acceleration [mm/sec^2]

µ =0.0

µ =0.15

µ =0.25

Time [sec]

µ = 0.25

µ = 0.15

µ = 0.0

Missile Velocity [mm/sec]

Missile velocity at the end of the rail

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Missile Roll Rate, Coefficient of Friction = 0.15 Missile/Rail Stress Plot – Cross-section:

Time [sec]

Roll Rate [Rad/sec]

Rocket Motor Fires

Missile Leaves The Rail

Missile Tip-off Roll Rate

Rail Stress - Detail

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Missile Shoe Reaction Forces: Deformed Shape, End of the Rail

DEFORMED SHAPE DEFORMED SCALE 1:1 In this image, the missile is leaving the rail. The intermediate and aft shoes are still engaged in the rail. The rail is noticeably deformed. The missile roll and yaw angles are also evident.

Rocket Motor Fires

Time [sec]

Shoe Reactions [N]

Front Shoe Reactions

Intermediate Shoe Reactions

Aft Shoe Reactions

µ =0.0

µ =0.15

Shoe reactions change rapidly with the missile position on the rail. Aft shoe reaction achieves its maximum magnitude just before the missile leaves the rail.

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DISCUSSION: Shoe reactions are the most valuable outcome of the analysis. With this rail design the aft shoe reactions achieve a very high magnitude at the end of the rail position. This is caused by relatively small torsional rail end stiffness in comparison with mid section rail stiffness. CONCLUSION: MSC.Nastran nonlinear transient analysis enables the simulation of dynamic phenomena like a missile launch from a rail under extreme load conditions and with high coefficients of friction. Valuable shoe reaction forces can also be determined with this simulation. Alternatively, measurement of reaction forces is difficult to obtain during a missile launch and conventional analysis provides only approximate results. Missile acceleration on the rail obtained through MSC.Nastran analysis has been verified by measured acceleration obtained during trials. The MSC.Nastran analysis methodology is also capable of determining frictional forces between the rail and the missile’s shoes. Frictional forces contribute to acceleration anomalies and “rocking” that occurs as the missile progresses along the rail. BENEFITS TO MSC.SOFTWARE USERS: a) Slide lines can be used even if there is some sliding in the plane

perpendicular to the slide line plane. The slide line has a “width”. b) Slide lines are very “stable” and analysis converges quickly. c) If friction is defined in slide line element property, the analysis converges

more slowly, but still converges. d) Functions used in MSC.Nastran software are very useful. While the rocket

motor thrust was described by the simple time function, the missile aerodynamic load was calculated for various positions on the rail. This is an extremely useful feature of the MSC.Nastran interface modeler. This feature can be utilized for aerodynamic load calculations, which changes with geometrical parameters during analysis, such as the missile position on the rail.

e) Contact forces cannot be obtained directly during the nonlinear transient analysis. Slide lines do not provide this option yet. However, a combination of DOF spring and rigid elements, properly added to the slide line element (as described in the body of this article) enables the user to obtain these forces, as was demonstrated in this paper.