**Applications** A fixture designer must be able to design a test fixture that will transmit the intended input forces directly to the Device Under Test. To accomplish this, a designer must have specific skills as well as an understanding of vibration and shock, structures, dynamic theory, materials, fabrication and welding.

**For Whom Intended ** This seminar is intended for dynamics test and evaluation personnel desiring an understanding of practical approaches to the design and fabrication of test fixtures used in vibration and shock testing. Tooling Engineers responsible for fixture design need this training.

Quality Assurance and Reliability specialists will find the course useful. So will test and instrumentation specialists. The writers of specifications for environmental tests and for manufacture of fixtures will benefit from knowing of practical limitations that exist. Weapon and product designers who are seeking solutions to vibration and shock problems will also find the course helpful.

**Brief Course Description ** This course reviews structural design fundamentals and dynamic theory. The importance of stiffness of structures and bolted connections are emphasized. Useful data on structures, bolted connections etc., is included in the course workbook, which will be an invaluable reference tool back at the workbench.

Practical simplified designs and fabrication techniques are discussed and class projects are undertaken to design some typical fixtures.

An important area covered is that of evaluating a fixture once it is built. Only by physical measurements on a completed fixture does a designer know how well the test requirements are met, whether changes are needed and whether these changes are successful. Fixture designers who evaluate their own fixtures gain valuable insights.

**Diploma Programs** This course is an optional course for TTi's Specialist Diploma Programs. It is most applicable to the Dynamic Test Specialist (DTS) diploma program.

**Related Courses ** The design portion of this course is available separately as TTi’s Course 310, Mechanical Design for Product Reliability, which goes into greater detail on design issues such as modal analysis, fatigue, accelerated testing and electronics chassis design. TTi's open Course 157 combines the complete contents of course 310 with full coverage of fixture design in a 5-day format.

**Prerequisites ** Prior participation in TTi’s Introduction to Mechanical and Structural Theory (or equivalent) is required. A TTi Fundamentals of Vibration course would be helpful. Participants will need first-year college mathematics (or equivalent experience) and some facility with fundamental engineering computations. Some familiarity with electrical and mechanical measurements and vibration will be helpful, as will an understanding of and familiarity with tooling and manufacturing.

**Text** Each student will receive access to the on-line electronic course workbook, including most of the slides used in the course presentation. An initial subscription is included in the price of the course and renewals are available for an additional fee.

**Course Hours, Certificate and CEUs** Open courses meet seven hours per day. Upcoming presentation dates can be found on our current open course schedule. Class hours/days for on-site courses can vary from 14-35 hours over 2-5 days as requested by our clients. Upon successful course completion, each participant receives a certificate of completion and one Continuing Education Unit (CEU) for every ten class hours.

Click for a printable course outline (pdf).

- Introduction to Vibration
- Design and Testing for Vibration and Shock
- Rotational Unbalance Example-Automobile engine
- Vibration and Shock Examples
- Natural Frequency (Resonance)
- Forcing Frequency
- Prolonged Excitation of Natural Frequency
- Tacoma Narrows Bridge
- Dynamic Inputs
- Fragility
- Effect of Failures

- Dynamic Theory
- Laws of Motion
- Weight, Mass and Gravity
- Specific Weight
- Relative Density or Specific Gravity
- Principles of Analysis
- Stiffness
- Mass
- Degrees of Freedom
- Single-Degree-of-Freedom (SDoF)
- Undamped Vibrations—Single Degree of Freedom Systems
- Basic Math Review/Radians
- Sinusoidal Waveform
- Relationship between Displacement, Velocity and Acceleration
- Sinusoidal Relationships
- Natural Frequency
- Calculating Natural Frequency
- Decaying Sinusoidal Vibration
- Ringing
- Undamped MDoF System Vibration
- Dimensionless Ratio Graph for 2DoF Systems
- Complex Systems
- Parallel Spring Stiffness
- Multi-Degree-of-Freedom (MDoF) Modeling
- Rayleigh’s Method
- Dunkerley’s Method
- Forced Vibration for SDoF System
- Transmissibility
- Isolation
- Damping
- Determining Damping Ratio Experimentally
- Effect of Damping
- Transient Peak Ratio vs. Damping Ratio
- Example-Damped Resonant System
- Types of Damping Mechanisms
- Resonances and Natural Frequency
- Response Factors for a Viscous-Damped SDoF System
- SDoF Forced Response—Magnification Factor

- Structural Theory
- Definitions of Common Mechanical Terms
- Friction and Wear
- Work, Power; Energy/Mechanical Advantage
- Engineering Materials: Metals
- Stress and Strain
- Definition of Stress
- Shear Stress and Tensile Stress
- Examples of Stress: 1) Simple Tension or Compression, 2) Pure Shear
- Strain
- Shear Strain
- Elasticity-Definitions and Laws
- Stress-Strain Relationship
- Tensile Strength
- Non-linear Elastic and Anelastic Solid Material
- Non-Elastic (or Plastic) Load-Extension Curves

- Torque / Tangential Acceleration
- Mass Moment of Inertia
- Radius of Gyration
- Area Moment of Inertia
- Relative Stiffness (k) of Structural Members/Shearing Torques/Twisting Torques
- Torsional Stiffness of an Open Cross-Section
- Torsional Shape Factor (J) Comparisons
- Moments of Inertia and Torsional Shape Factors for Some Typical Cross Sections
- Torsional Shape Factors for Rectangular Sections
- Example: Finding Torsional Shape Factor (J)

- Moment of Inertia-Transfer Formula, Parallel Axis Method, Angular Transfer Method
- Properties of Materials
- Dynamic Response
- Simple Beam/Bending Moment
- Sandwich Structures
- Elastic Deflection of a Simply Supported Beam (with load concentrated at center of beam)
- Bending Strengths
- Structural Beams
- Bending Stiffness of a Beam
- Simple Uniformly Loaded Beam
- Finding Stiffness of a Composite Beam
- Beam Instability-Twisting

- Compression Member Instability
- Instability of Flanges
- Flange Buckling
- Structure Buckling
- Resonant Frequency of Flanges

- Frequency and Stiffness Considerations
- Frequency Oscillation of a Rod
- Natural Frequency of a Simply Supported Beam
- Natural Frequency of a Cantilever
- Effective Mass
- Beam Formulas
- Effective Mass of a Beam: Example
- Natural Frequency of Simply Supported Plate
- Beam Formulas
- Stiffness of Gussets-with End load
- Effective Stiffness of Gusset
- Plate Frequency Equation
- Plate Frequency Parameters
- Column Resonance
- Axial Resonance
- Example: Determining Stress in a Loaded Beam

- Bolted Connections
- Bolted Connections
- Bolted Joint Connections
- Pre-load
- Bolted Joint Stiffness
- Designing Bolted Connections
- Bolt Data
- Bolted Joint-Washer Design
- Bolt Joint Design—an Example
- Fastener Parameters (Socket Head Steel Bolts)
- Correction for Short Grip Length
- Recommended Hardware Dimensions for Bolting
- Bolt Configurations
- Calculating the Required Flange Material Area
- Thickness of the Fixture Material
- Stiffness of the Fixture Material
- Bolted Joint Stiffness-Example
- Effective Stiffness of Slip Plate
- Transverse Loads/Shear connections

- Effect of Stiffness on Resonant Frequency
- Total Stiffness of a Bolted Joint-Example

- Material Selection in Engineering Design
- Overall Material Properties
- Design-Limiting Material Properties
- Deriving Application-Specific Material Properties
- Numerical Comparison
- Bar-Chart Comparison
- 2-D Plot Comparison
- Optimization of Shaker Table

- Design Suggestions (optional chapter)
- Overcoming Problems
- Design Guidelines
- Structural Rules of Thumb
- Stresses in Printed Circuit Boards

- Introduction to Fixture Design for Vibration and Shock Testing
- Dynamic Test Philosophy
- Fixture Performance
- Evaluating Fixtures
- Considerations in Fixture Design

- Vibration Test Fixtures - General Remarks
- The "black art" of designing fixtures
- Function of the test fixture
- Difficulty in achieving identical motion at all attach points
- Required information about the test item and the test program
- Required information about shaker
- Bolting to the shaker table
- An example of successful redesign
- Fixture weight relative to test item weight
- Temperature and altitude affect fixture design for combined environments

- Interface Items
- Table expanders
- Horizontal accessory tables: oil-film slip tables
- Slip Plate Overturning Moment
- Connecting horizontal accessory tables to shakers
- Hydrostatic bearings
- Misuse of horizontal accessory tables
- Avoid using bolts in shear
- A note of warning on wide plates

- Measurement, Readout and Recording of Vibration
- Accelerometers
- Amplifiers
- Frequency response
- Mounting affects frequency response
- Cable routing affects frequency response
- Cross-axis sensitivity
- Readout of Vibration Intensity and Frequency: Conversion to numbers
- Oscilloscopes and oscillographs
- Decibel scaling
- Need for tracking filter in evaluating fixtures
- Calibration checks on the entire measuring system
- MEMS Devices

- Basic Fixture Types
- Adapter plates
- Cube fixtures
- Hemispheres
- Conical fixtures
- Enclosed box fixtures
- Drum fixtures
- L-type fixtures
- T-type fixtures
- Open box fixtures
- Bolted Clamp Fixture Example
- Hose Clamps as Fasterners

- Fixture Fabrication Methods
- Introduction
- Materials for fixtures
- Machining fixtures from solid stock
- Bolted fixtures
- Cast fixtures
- Welded fixtures
- Bonded fixtures
- Laminated fixtures
- Epoxy formed fixtures
- Potted fixtures
- Foamed plastics for damping
- Inserts
- Shop Capabilities

- Analysis of an L-Fixture
- Design of a Cubical Test Fixture
- Final Review
- Conclusion
- Award of Certificates for successful completion