# Presentation: 014215

## Fastened Joint Analysis and Test Correlation of the MLA Beam Expander

- Craig L. Stevens
- Craig.Stevens@nasa.gov
- Mechanical Systems Analysis & Simulation Branch
- NASA Goddard Space Flight Center
- Greenbelt, Maryland

- FEMCI Workshop Presentation
- May 6, 2004

## Overview

- Introduction
- Problem Description
- Pre-Test Analysis
- Test Results
- Model Correlation
- Conclusions

## Mercury Laser Altimeter (MLA) on Mercury Surface, Space Environment, Geochemistry, and Ranging (MESSENGER) spacecraft
MLA produces accurate measurements of topography and measures Mercury's wobble (due to the planet's libration)
MESSENGER Objectives:
Determine the structure of Mercury’s mantle and crust
Investigate Mercury's polar caps 
Determine the state of Mercury’s core (fluid or solid?)
MESSENGER developed by Johns Hopkins University Applied Physics Laboratory (APL)
MLA developed by NASA Goddard Space Flight Center (Delivered to APL June 2003)
Launch
August 2004
Delta II 2925H-9-5

- MLA produces accurate measurements of topography and measures Mercury's wobble (due to the planet's libration)
- MESSENGER Objectives:
- Determine the structure of Mercury’s mantle and crust
- Investigate Mercury's polar caps
- Determine the state of Mercury’s core (fluid or solid?)
- MESSENGER developed by Johns Hopkins University Applied Physics Laboratory (APL)
- MLA developed by NASA Goddard Space Flight Center (Delivered to APL June 2003)
- Launch
- August 2004
- Delta II 2925H-9-5

**Introduction**

## MESSENGER Configuration

**Plasma Spectrometer**

**Neutron Spectrometer**

**Gamma-Ray Spectrometer**

**X-Ray Spectrometer **

**Dual Imager on Pivot Platform **

**Atmospheric and Surface Spectrometer  **

**Energetic Particles Spectrometer**

**MLA**

**Introduction**

## Introduction

- Receiver tubes [4] (Be)
- Laser beam expander (Be)
- Laser bench (Be)
- Main housing (Be)
- Mounting flexures [3] (Ti)
- Aft optics (Be)
- Power Converter Assy. Housing (Mg)

- MLA Configuration

## Problem Description

**Problem Description**

- 80001

- 80002

- Flight laser bench with attached beam expander
- Three point mount: #2-56 fasteners
- Beam expander: mass ~0.4 lbm, height ~6.5”
- MLA laser workmanship level vibration test/analysis
- Low level: 0.04 G2/Hz, 6.8 GRMS
- Task:
- Pre Test Analysis:  **Predict natural frequencies** and loads
- Correlate FEM with test data
- Investigate test anomalies and determine cause
- FEM:
- CQUAD4 model
- Fixed Base

- 80003

## Pre-Test Analysis

- Initial joint stiffness estimated using tension joint theory
- Bolt:
- Fitting:
- where,
*E**b* = Bolt Young’s modulus
*A**eff* = Bolt effective area
*L**b* = Grip
*E**f* = Fitting Young’s modulus
*D* = Bolt diameter
*L* = Clamped fitting thickness
*d**w* = Washer diameter
** = Apex angle (assume 30o)
- Bolt carries 10% of applied load

*K**f**=1.1E+7#/in*

*K**b**= 1.2E+6 #/in*

- Preload = 250#

- 0.1” thick flange

- 0.5” thick bench

- #2-56 Fastener

## Pre-Test Analysis

- Use Springs (CELAS) to model joint stiffness:
- 	Fitting stiffness = Kf/4 (9)
- 	Bolt stiffness = Kb (3)
- 	Normal constraints (center flange) = KNC (3)
- 	Normal constraints (near bolt) = KNCb (6)
- Normal constraint locations chosen based on aluminum engineering model test data
- Value of KNC and KNCb chosen based on aluminum engineering model test data and fitting stiffness
- Same order of magnitude as fitting stiffness
- 1E+7 #/in
- X and Y shear forces reacted through bolts using RBE2

- 1

**Pre-Test Analysis**

## Pre-Test Analysis

- Normal modes analysis:

## Test Results

- Z-axis:
- Test performed with no issues (no major modes)
- Y-Axis:
- Sine Signature Y

## Test Results

**Test Results**

- Y-axis (cont’):
- Frequency shift as random vibration levels increased:
- Harmonics observed in random beam expander responses
- Integer multiples of resonant frequency
- Indicates nonlinear response
- Not present in sine runs

## Test Results

- Why do harmonics of resonant frequency exist?:
- Asymmetrical distortion of sine wave
- Several reasons:
- Contact
- Boundary Condition

## Test Results

- Y-Axis Sine FRF

- Frequency, Hz

- H12(f)

- 10-1

- 10-2

- 101

- 100

- 102

- 10-3

- 10-4

- Frequency shifts observed in pre and post sine sweeps
- Modal frequencies drop over 10%
- X and Y modes switch order

## Model Correlation

- Use MSC NASTRAN Solution 200 to correlate model and investigate frequency shift
- Assume linear modes and mode shapes
- Vary CELAS stiffnesses to investigate preload loss
- Key cards:
- MODTRAK:  Performs cross orthagonality check to ensure proper modes meet constraints
- DEQATN:  Create Least squares objective function formulation
- For Post Sine Y correlation:
*W**1* = 1.0
*W**2* = 1.0
*f**n2act* = 451 Hz (Y Mode)
*f**n1act* = 482 Hz (X Mode)

## Model Correlation

- $
**DESVAR *               1NCS               7.72887313E+05  1.00000000E+04+D    1V**
***D    1V  1.00000000E+10**
- DESVAR *               2KB1               1.19993400E+06  1.00000000E+04+D    2V
- *D    2V  1.00000000E+10
**DESVAR *               3KF1               9.05991600E+05  1.00000000E+04+D    3V**
***D    3V  1.00000000E+10**
- DESVAR *               4KB2               1.19993800E+06  1.00000000E+04+D    4V
- *D    4V  1.00000000E+10
**DESVAR *               5KF2               3.37498700E+06  1.00000000E+04+D    5V**
***D    5V  1.00000000E+10**
- DESVAR *               6KB3               1.19594200E+06  1.00000000E+04+D    6V
- *D    6V  1.00000000E+10
**DESVAR *               7KF3               1.45899362E+05  1.00000000E+04+D    7V**
***D    7V  1.00000000E+10**
- DESVAR *               8NCB1              8.14678800E+06  1.00000000E+04+D    8V
- *D    8V  1.00000000E+10
- DESVAR *               9NCB2              4.54948100E+06  1.00000000E+04+D    9V
- *D    9V  1.00000000E+10
**DESVAR *              10NCB3              1.00000000E+04  1.00000000E+04+D   10V**
***D   10V  1.00000000E+10**
**$ MODE TRACKING HAS BEEN PERFORMED SUCCESSFULLY WITH SOME CHANGE IN THE MODE ORDER.**
**$ ALL THE DRESP1 ENTRIES ASSOCIATED WITH MODE TRACKING ARE WRITTEN HERE FOR CONVENIENCE.**
**$**
**DRESP1       101FN1         FREQ                       2**
**DRESP1       102FN2         FREQ                       1**

- Results:

**Model Correlation**

## Model Correlation

- Results (Cont’):
- Over 90 % stiffness loss in fastener 3 (or 2)
- Preload ~0
- Results from post test investigation verified no structural failure and no other significant source for frequency shift

**Model Correlation**

## Conclusions

- Presence of harmonics in broadband responses indicative of nonlinearities in test data
- Optimizer is quick and efficient method to correlate modes and mode shapes of models
- Over 90% stiffness loss in fastener 2 or 3
- Results indicate preload loss is the probable cause of frequency shift
- References
- Joseph Shigley. *Mechanical Engineering Design*. Fifth Edition. McGraw-Hill, Inc. New York. 1989
- Thomas Sarafin. *Design and Analysis of Fastened Joints for Aerospace Engineers.* Course Notes. Instar Engineering and Consulting, Inc.  2001.* *
- John H. Bickford. *Handbook of Bolts and Bolted Joints. *Marcel Dekker, Inc. New York
- Ryan Simmons. *MLA Laser Subassembly Workmanship Vibration Post-Test Report*. NASA GSFC, Greenbelt, Maryland, 2003. MLA-RPT-000127
- Steven W. Smith. *The Scientist and Engineer’s Guide to Digital Signal Processing, 2**nd** Edition.* California Technical Publishing, San Diego, California, 1999.
- Scott Gordon. *Private Correspondence*. NASA GSFC, Greenbelt, Maryland.
- Daniel Kaufman. *Private Correspondence*. NASA GSFC, Greenbelt, Maryland.