# Presentation: 139918

## A Multi-Disciplinary Approach to Calculate Displacement Due to Random Vibration For A Space Based Focal Plane

Anthony J. Davenport
Senior Mechanical Engineer
Northrop Grumman, ESSS

**Anthony J. Davenport**
**Senior Mechanical Engineer**
**Northrop Grumman, ESSS**

**FEMCI Conference**

## Focal Plane Geometry

**Housing**

**Filter (x6)**

**Cover**

**Flex Cable Strain Relief**

## So What Is The Problem?

**Focal Plane Cross-Section**

**Cover**

**Filter**

**Housing**

**Gap of Concern**

**Sensors**

**1. Out of Plane Bowing from Cryogenic Loading**
**2. Random Vibration Displacement of the Cover**
**3. Lack of Material Properties (Adhesives)**

## Design & Analysis Path for the Focal Plane

**Housing**

**Deflection**

**Housing**

**Deflection**

**Bolt**

**Analysis**

**Bolt**

**Analysis**

**Simplified**

**Model**

**Simplified**

**Model**

**Simplified**

**Testing**

**Simplified**

**Testing**

**Model**

**Refinement**

**Model**

**Refinement**

**Apply To**

**Detailed Model**

**Apply To**

**Detailed Model**

- Phase I: Thermal Testing & Correlation

- Phase II: Detailed Thermal Analysis & Results

- Phase III: Random Vibration Testing & Correlation

- Phase IV: Detailed Flight Hardware Analysis & Results

**Displacement**

**Analysis**

**Displacement**

**Analysis**

**Stress**

**Analysis**

**Stress**

**Analysis**

**Bolt**

**Analysis**

**Bolt**

**Analysis**

**Pre-Qual**

**Testing**

**Pre-Qual**

**Testing**

**Testing**

**Results**

**Testing**

**Results**

**Model**

**Refinement**

**Model**

**Refinement**

**Goals For**

**Random **

**Vib**

**.**

**Goals For**

**Random **

**Vib**

**.**

**Proven**

**Design**

**Proven**

**Design**

**Define**

**Problem**

**Define**

**Problem**

## Thermal Expansion Analysis Method

**Create a simplified model in PTC’s Mechanica using mechanical properties determined by the NG materials group.**
**Run model between 295 oK to 110 oK (********T = 185 oK)**
**Examine relative displacement in the out-of-plane direction (Z)**
**Compare results to testing completed in laboratory and correlate model.**
**Apply what is learned to detailed model.**

## Simplified Test Model

**Dial Gages (x3)**

**Molybdenum**

**Adhesive**

**Substrate**

**Temperature**
**Sensors**

**Cold Finger With**
**Heater Element**

## Laboratory Test Setup

**Focal Plane**

**Cold Finger & Heater**

**Measuring Dials (x3)**

**Three Dial Gages Touch**
**The Focal Plane in**
**3 Locations to Measure**
**Bowing in Focal Plane**

**Temperature Range 295 oK - 110 oK**

## 1/4 Simplified Analysis Model

**Molybdenum**

**Adhesive**

**Substrate**

**Symmetry Constraint, Y**

**Constraint, Z on Bottom Curve**

**Substrate**

**Substrate Removed**

**Symmetry**
**Constraint, X**

## Relative Displacement Results From Testing & Analysis

**Analysis Model**

**Testing**

**Comparison**

## Detailed Analysis Model

**Uniform Temperature Load:  Cure to Cryogenic (295 ****o****K to 110 ****o****K)**

**Molybdenum**

**Ceramic Substrate**

**Mounting Surface Z Constraint**

**Mounting Surface**
**Z Constraint**

**X,Y Constraint**

**Focal Plane Bows 5.3 ********m, or +/- 2.6 ********m Across a Mid-Plane**

## Random Vibration Derived Requirements

**From Cryogenic Analysis**

## Random Vibration Test Setup

**Random Vibration Test Setup**

## Test Setup

**Focal Plane**

**Accelerometers**

## Test Results: Housing

**Mode 2: 1717 Hz**

**Mode 1: 1513 Hz**

**39.3 G****rms**

## Testing Results: Cover

**Mode 2: 1717 Hz**

**Mode 1: 1513 Hz**

**118.9 G****rms**

## What Can Be Derived From Test?

**3******** Absolute Displacement**

**Damping Factors**

**Relative Displacement (500 Hz - 2000 Hz):  2.379 +/- mil Using Method Discussed in Appendix B (3% Diff.)**

## Method of Correlation

**Match the Frequency of the Test Model**
**Boundary Conditions**
**Mass of Components**
**Stiffness**
**Geometry**
**Material Properties**
**Match the Displacement**
**Acceleration PSD Input**
**Damping Value:  ******** = 1/(2Q)**

## Matching Frequency

**Iso - View**

**Aniso - View**

**Geometry:  Built from Unigraphics Model**
**Boundary Conditions:  Bolt Stiffness Applied**
**Mass from Tested Components**
**Materials:  Varied Young’s Modulus for Molybdenum within range found in multiple sources.**

## Matching Frequency Results

**Mode 1:  1477 Hz (2.4% Diff)**

**Mode 1:  1717 Hz (0.0% Diff)**

## Matching Displacement

**Adjust PSD Input to Match Testing.**
**Tolerance allowed for a +1 dB overall variance.**
**For a small response, this makes a large difference.**
**It was found that the PSD input was +0.4 dB higher than Specification.**
**Adjust Damping to fine tune the model              (******** = 0.00351)**
**2.380 mil Deflection (0.042 % diff. from testing) for 500 - 2000 Hz.**

## Conclusions

**Bowing due to Thermal Expansion is determined by defining material properties via testing, modeling, and correlation.**
**Cryogenic deflections help drive the random vibration allowable.**
**Random vibration correlation helps in examining future changes to the focal plane design and it’s inputs.**