Design Analysis
Bourdon Tube Pressure Gauge
|
Created By
ALGOR, Inc. Checked By
Engineering Manager |
The purpose of this design analysis was to validate and optimize the design of the pressure gauge prior to release to production. Since the gauge required a combination of FEA stress and kinematic motion analysis, ALGOR's Mechanical Event Simulation (MES) software was used to simulate the actual operation of the gauge as it was pressurized. The results of this design analysis verified acceptable stress levels in the bourdon tube and proper operation of the gauge mechanism.
Analysis Type -
MES with Nonlinear Material Models
Units -
English (in) - (lbf, in, s, deg F, deg R, V, ohm, A, in*lbf)
Model location -
D:\Simulation\pressure_gauge\BOURDON
The analysis results have been checked and verified. This model is approved for release to manufacturing.
| Default Nodal Temperature | 0 °F |
| Event Duration | 1 s |
| Capture Rate | 200 /s |
| Analysis Type | Mechanical Event Simulation (MES) |
| Acceleration Due To Body Force | 0 in/s² |
| X Mutiplier | 0 |
| Y Mutiplier | 0 |
| Z Mutiplier | 0 |
| Load Curve Number for Gravity Load | 2 |
| Type of Shell Pressure Loading | Follows Body |
| Load Curve Number for Shell Pressure Loads | 1 |
| Smooth Shell Pressure | Yes |
| Hydrostatic Pressure Control for Shell Elements | None |
| Z Coordinate Datum for Hydrostatic Pressure | 0 in |
| Weight Density of Fluid Causing Shell Hydrostatic Pressure | 0 lbf/in³ |
| Nodal Temperature Time-Variation Load Curve Index | 1 |
| Where On Disk Is Nodal Temperature Data Stored | No thermal Data |
| Temperature Data File | None |
| Output Results of All Time Steps | No |
| Output Results of All Time Steps With Wall Interaction | No |
| Calculate and Output Strains | No |
| Output Reaction Forces | Not Calculated |
| Number of time steps | 200 |
| Initial Time Step Size | 0.005 s |
| Nonlinear Iterative Solution Method | Combined Newton with Line Search |
| Maximum Number of Iterations | 15 |
| Convergence Criteria | Displacement |
| Displacement Tolerance | 1e-6 |
| Force Tolerance | 1e-15 |
| Line Search Convergence Tolerance | 0.5 |
| Number of Time Steps Between Iterations | 1 |
| Number of Time Steps Between Reforming Stiffness Matrix | 1 |
| Time Integration Methods Suggested for Type of Analysis | General: MES, NLS |
| Parameter for MES Integration Method | 1 |
| First Parameter for LS Integration Method | 0.50 |
| Second Parameter for LS Integration Method | 0.25 |
| Number of time steps | 0 |
| Initial Time Step Size | 0 s |
| Output interval | 1 |
| Starting Time for Event | 0 s |
| Resume/Extend Run | No |
| Time Step Number Extension | 0 |
| Use A Constant Time Step Size | No |
| Decrease Trigger: Rate of convergence | Automatically Set |
| Decrease Trigger: Allow for Non-monotonic convergence | Yes |
| Decrease Trigger: Compressed Elements | No |
| Decrease Trigger: High Solution Tolerance | Yes |
| Time Step Change Factor | 2 |
| Increase Trigger: Number of Convergent Time Steps | 4 |
| Increase Trigger: Increment to Number of Convergent Time Steps | 4 |
| Apply Rayleigh Damping | No |
| Mass-related Rayleigh Damping Coeeficient | 20 |
| Stiffness-related Rayleigh Damping Coefficient | 5 |
| Direction of Centrifugal Load Axis | Between Two Points |
| Centrifugal Load Curve Multiplier | 1 in/s² |
| Centrifugal Rotation | 0 RPM |
| Load Curve Number for Centrifugal Load | 1 |
| X Coordinate of First Point of Axis | 0 in |
| Y Coordinate of First Point of Axis | 0 in |
| Z Coordinate of First Point of Axis | 0 in |
| X Coordinate of Second Point on Axis | 0 in |
| Y Coordinate of Second Point on Axis | 0 in |
| Z Coordinate of Second Point on Axis | 0 in |
| Time Step Data In Output File | No |
| Equation Numbers Data in Output File | No |
| Element Stiffness In Output File | No |
| Global Stiffness In Output File | No |
| Displacement of Nodes In Output File | No |
| Velocity of Nodes In Output File | No |
| Acceleration of Nodes In Output File | No |
| Element Input Data in Output File | No |
| Nodal Input Data in Output File | No |
| Initial Condition Input Data In Output File | No |
| Printout Blocks Output To File | No |
| Mass Representation | Lumped |
| Matrix Reform Interval Within Each Time Step | 1 |
| Maximum Stiffness Reformations Per Interval | 1 |
| Number of Time Steps Between Reforming Stiffness Matrix | 1 |
| Ratio of Allocated Memory Space for Data Storage | 0.2 |
| Avoid Bandwidth Optimization | No |
| Bandwidth Optimization Method | Single Body |
| Run Static Analysis | No |
| Type of Solver | Sparse Symmetric |
| Tolerance for stiffness matrix entries | 0 |
| Load Curve 1 Index 1 Time | 0 |
| Load Curve 1 Index 1 Multiplier | 0 |
| Load Curve 1 Index 2 Time | 1 |
| Load Curve 1 Index 2 Multiplier | 1 |
| Load Curve 2 Index 1 Time | 0 |
| Load Curve 2 Index 1 Multiplier | 1 |
| Load Curve 2 Index 2 Time | 1 |
| Load Curve 2 Index 2 Multiplier | 1 |
| Part ID | Part Name | Element Type | Material Name |
|---|---|---|---|
| 1 | BASE | 3-D Kinematic | Red Brass |
| 2 | TUBE | Brick | [Customer Defined] |
| 3 | BRACKET | Brick | Red Brass |
| 4 | PIN | 3-D Kinematic | Red Brass |
| 5 | PIN | 3-D Kinematic | Red Brass |
| 6 | BRACKET2 | Brick | Red Brass |
| 7 | TAB | Brick | Red Brass |
| 8 | PIN2 | Brick | Steel (ASTM-A36) |
| 9 | SECTOR | Brick | Red Brass |
| 10 | GEAR | Brick | Red Brass |
| 11 | LINK | Brick | Red Brass |
| 12 | NEEDLE | 3-D Kinematic | Steel (ASTM-A36) |
| 14 | PIN3 | Brick | Steel (ASTM-A36) |
| 15 | PIN4 | Brick | Steel (ASTM-A36) |
| 16 | PIN5 | Brick | Steel (ASTM-A36) |
| 17 | PIN6 | Brick | Steel (ASTM-A36) |
| Element Type | 3-D Kinematic |
| Include Specified Initial Conditions | No |
| Initial X Translational Velocity | 0 in/s |
| Initial Y Translational Velocity | 0 in/s |
| Initial Z Translational Velocity | 0 in/s |
| Initial X Rotational Velocity | 0 RPM |
| Initial Y Rotational Velocity | 0 RPM |
| Initial Z Rotational Velocity | 0 RPM |
| Initial X Rotation Point | 0 in |
| Initial Y Rotation Point | 0 in |
| Initial Z Rotation Point | 0 in |
| 1st Integration Order | 2nd Order |
| 2nd Integration Order | 2nd Order |
| Midside Nodes | Not Included |
| Allow for overlapping elements | No |
| Use Solid Mesher Connectivity Data | No |
| Element Type | Brick |
| Material Model | Isotropic |
| Midside Nodes | Not Included |
| Orthotropic Material Principle Axis | X-direction |
| Material Axis Rotation Angle | 0 ° |
| Include Specified Initial Conditions | No |
| Initial X Translational Velocity | 0 in/s |
| Initial Y Translational Velocity | 0 in/s |
| Initial Z Translational Velocity | 0 in/s |
| Initial X Rotational Velocity | 0 RPM |
| Initial Y Rotational Velocity | 0 RPM |
| Initial Z Rotational Velocity | 0 RPM |
| Initial X Rotation Point | 0 in |
| Initial Y Rotation Point | 0 in |
| Initial Z Rotation Point | 0 in |
| Stress Free Reference Temperature | 0 °F |
| Creep Law | No Creep |
| Creep - Time Integration Method | Flexible Substeps |
| Creep - Stress Free Reference Temperature | 0 °F |
| Creep - Maximum Number of Substeps | 100 |
| Creep - Maximum Iterations in a Substep | 50 |
| Creep - Strain Definition | Effective |
| Creep - Strain Calculation Tolerance | 0.1 |
| Creep - Stress Calculation Tolerance | 0.01 |
| Creep - Time Integration Parameter | 0.5 |
| Analysis Formulation | Total Lagrangian |
| Compatibility | Automatic |
| 1st Integration Order | 3rd Order |
| 2nd Integration Order | 3rd Order |
| Allow for overlapping elements | No |
| Use Solid Mesher Connectivity Data | No |
| Material Model | Standard |
| Material Source | Algor Material Library |
| Material Source File | C:\Algor12\MatLibs\algormat.mlb |
| Date Last Updated | 1999/06/01-17:40:45 |
| Material Description | Cold-rolled 85% Cu, 15% Zn Mechanics of Materials, 2nd Edition, F.P.Beer and E.R. Johnston, Jr. (mechanical) "Material Selector Issue", Machine Design, December 12, 1994 (thermal & electrical) |
| Mass Density | 8.18E-4 lbf*s^2/in/in³ |
| Material Model | Standard |
| Material Source | Not Applicable |
| Material Source File | |
| Date Last Updated | 2001/07/31-08:35:04 |
| Material Description | From Library "Algor Material Library" Material "Copper" Oxygen-free copper (99.9% Cu) Annealed Mechanics of Materials, 2nd Edition, F.P. Beer and E.R. Johnston, Jr. "Materials Selector Issue", Machine Design, December 12, 1994 |
| Mass Density | 8.33e-4 lbf*s^2/in/in³ |
| Modulus of Elasticity | 2.45E6 lbf/in² |
| Poisson's Ratio | 0.33 |
| Shear Modulus of Elasticity | 6.4e6 lbf/in² |
| Damping | 0 s/in |
| Material Model | Standard |
| Material Source | Algor Material Library |
| Material Source File | C:\FEMPRO\MatLibs\algormat.mlb |
| Date Last Updated | 1999/06/01-17:40:45 |
| Material Description | Cold-rolled 85% Cu, 15% Zn Mechanics of Materials, 2nd Edition, F.P.Beer and E.R. Johnston, Jr. (mechanical) "Material Selector Issue", Machine Design, December 12, 1994 (thermal & electrical) |
| Mass Density | 8.18E-4 lbf*s^2/in/in³ |
| Modulus of Elasticity | 17e6 lbf/in² |
| Poisson's Ratio | 0.33 |
| Shear Modulus of Elasticity | 6.4E6 lbf/in² |
| Damping | 0 s/in |
| Material Model | Standard |
| Material Source | Algor Material Library |
| Material Source File | C:\Algor12\MatLibs\algormat.mlb |
| Date Last Updated | 1999/06/02-11:03:56 |
| Material Description | Structural Steel Mechanics of Materials, 2nd Edition, F.P. Beer and E.R. Johnston, Jr. (mechanical) |
| Mass Density | 7.35e-4 lbf*s^2/in/in³ |
| Modulus of Elasticity | 29e6 lbf/in² |
| Poisson's Ratio | 0.29 |
| Shear Modulus of Elasticity | 11.2e6 lbf/in² |
| Damping | 0 s/in |
| Part ID | Surface ID | Element Type | Type | Parameters |
|---|---|---|---|---|
| 2 | 2 | Brick | Normal (Pressure) | 50 lbf/in² (Follows moving surface) Load Curve: 1 Load Curve Multiplier: 1 |
| ID | Description | Node ID | Tx | Ty | Tz | Rx | Ry | Rz |
|---|---|---|---|---|---|---|---|---|
| 1 | Unnamed | 5569 | No | No | Yes | No | No | No |
| 2 | Unnamed | 5570 | No | No | Yes | No | No | No |
| 3 | Unnamed | 5583 | No | No | Yes | No | No | No |
| 4 | Unnamed | 5596 | No | No | Yes | No | No | No |
| 5 | Unnamed | 1011 | Yes | Yes | Yes | Yes | Yes | Yes |
| 6 | Unnamed | 1020 | Yes | Yes | Yes | Yes | Yes | Yes |
| 7 | Unnamed | 1015 | Yes | Yes | Yes | Yes | Yes | Yes |
| 8 | Unnamed | 1007 | Yes | Yes | Yes | Yes | Yes | Yes |
This is a rendering of the Pro/ENGINEER solid model which was created by the Design Department. The solid model was captured through the direct CAD/CAE data exchange provided by ALGOR's InCAD technology.
This is a Pro/ENGINEER bill of material drawing of the bourdon tube pressure gauge assembly. Note that since the dial was not a critical engineering component for the gauge mechanism, it was removed for analysis purposes.
This Virtual Reality Model Language (VRML) file of the pressure gauge mechanism was exported directly from ALGOR. Note that some stationary parts, such as the base, have been suppressed. In order to interactively zoom in or spin the model, your browser program will need to have a VRML plug-in installed. A free VRML plug-in may be obtained at www.cosmosoftware.com. If you are reviewing a printed hard copy of this report, no image for the VRML model will appear above.
This hidden-line display provides a close-up of the detail for the sector gear mechanism. To drive the motion of the gear mechanism during the analysis, surface-to-surface contact was defined between the teeth of the gears in the ALGOR Mechanical Event Simulation software package.
This plot of displacement versus time, obtained from the ALGOR Monitor utility, shows the horizontal and vertical movement of the needle tip, in inches, as the gauge is pressurized from 0 to 50 psi in a period of one second.
This animation shows the displacement, in inches, of the bourdon tube as the internal pressure is increased from 0 to 50 psi in a period of 1 second. As the tube is pressurized, the end of the tube displaces radially outward. This linear displacement is then converted to a rotation through a sector gear mechanism in order to turn the needle.
This animation shows the von Mises stress levels, in units of psi, as the internal pressure is increased from 0 to 50 psi in a period of 1 second. Elastic elements were used in the bourdon tube where stresses and deformation were expected to be the highest. Kinematic elements, which are rigid and do not calculate stresses, were used for the remaining components of the model where stress levels, by comparison, were expected to be insignificant.