Training Path Module 5: Difference between revisions

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__NOTOC__
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<div style="font-size:170%; font-weight:bold; margin-bottom:4px;">Self-Guided Learning Path: automet® FAB</div>
<div style="margin-bottom:8px;">'''Module 5: Analysis''' &nbsp;·&nbsp; Interpreting survey results, visual reports, least-squares fit optimization, manual transforms, and report generation.</div>
<div style="font-size:90%;">''Estimated Time: 30 minutes''</div>
</div>
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<div style="display: flex; flex-wrap: wrap; justify-content: center; gap: 15px; background-color: #f8f9fa; padding: 25px; border: 1px solid #dee2e6; border-radius: 10px; margin-bottom: 30px;">


[[Training_Path_Module_1 | <span style="background-color: #0053a3; color: white; padding: 18px 28px; border-radius: 6px; text-decoration: none; font-weight: bold; font-size: 1.1em; display: inline-block; min-width: 160px; text-align: center; box-shadow: 0 2px 4px rgba(0,0,0,0.1);">1. Getting Started</span>]]
[[Training_Path_Module_1 | <span style="background-color: #767a7d; color: white; padding: 18px 28px; border-radius: 6px; text-decoration: none; font-weight: bold; font-size: 1.1em; display: inline-block; min-width: 160px; text-align: center; box-shadow: 0 2px 4px rgba(0,0,0,0.1);">1. Getting Started</span>]]


[[Training_Path_Module_2 | <span style="background-color: #767a7d; color: white; padding: 18px 28px; border-radius: 6px; text-decoration: none; font-weight: bold; font-size: 1.1em; display: inline-block; min-width: 160px; text-align: center; box-shadow: 0 2px 4px rgba(0,0,0,0.1);">2. Design Input</span>]]
[[Training_Path_Module_2 | <span style="background-color: #767a7d; color: white; padding: 18px 28px; border-radius: 6px; text-decoration: none; font-weight: bold; font-size: 1.1em; display: inline-block; min-width: 160px; text-align: center; box-shadow: 0 2px 4px rgba(0,0,0,0.1);">2. Design Input</span>]]


[[Training_Path_Module_3 | <span style="background-color: #0053a3; color: white; padding: 18px 28px; border-radius: 6px; text-decoration: none; font-weight: bold; font-size: 1.1em; display: inline-block; min-width: 160px; text-align: center; box-shadow: 0 2px 4px rgba(0,0,0,0.1);">3. Survey Setup</span>]]
[[Training_Path_Module_3 | <span style="background-color: #767a7d; color: white; padding: 18px 28px; border-radius: 6px; text-decoration: none; font-weight: bold; font-size: 1.1em; display: inline-block; min-width: 160px; text-align: center; box-shadow: 0 2px 4px rgba(0,0,0,0.1);">3. Survey Setup</span>]]


[[Training_Path_Module_4 | <span style="background-color: #767a7d; color: white; padding: 18px 28px; border-radius: 6px; text-decoration: none; font-weight: bold; font-size: 1.1em; display: inline-block; min-width: 160px; text-align: center; box-shadow: 0 2px 4px rgba(0,0,0,0.1);">4. Execution</span>]]
[[Training_Path_Module_4 | <span style="background-color: #767a7d; color: white; padding: 18px 28px; border-radius: 6px; text-decoration: none; font-weight: bold; font-size: 1.1em; display: inline-block; min-width: 160px; text-align: center; box-shadow: 0 2px 4px rgba(0,0,0,0.1);">4. Execution</span>]]


[[Training_Path_Module_5 | <span style="background-color: #0053a3; color: white; padding: 18px 28px; border-radius: 6px; text-decoration: none; font-weight: bold; font-size: 1.1em; display: inline-block; min-width: 160px; text-align: center; box-shadow: 0 2px 4px rgba(0,0,0,0.1);">5. Analysis</span>]]
<span style="background-color: #3366cc; color: white; padding: 18px 28px; border-radius: 6px; text-decoration: none; font-weight: bold; font-size: 1.1em; display: inline-block; min-width: 160px; text-align: center; box-shadow: 0 2px 4px rgba(0,0,0,0.15);">5. Analysis</span>


</div>
</div>


=Overview=
== Overview ==
The analysis section has been designed to allow the user to review and compare captured survey data against the design data.


==Files==
Selecting '''Visual Report''' from the main application menu following a survey compares captured field observations against design specifications (`.DES`).
To view a survey within analysis, you will always need two files: survey (.SUR) and design (.DES).  


If you want to open a previous survey file, load the SUR file by pressing the button [Survey File:__________Open for Analysis]; the design should be loaded automatically.
The visual analysis suite enables surveyors to rotate and translate models, include or exclude specific flanges from least-squares fit calculations, zero individual tie-ins, adjust fit weighting preferences, and isolate gross fabrication errors.


==Fit Tools==
<gallery mode="packed" heights="350px">
[[File:Fit Tools.png|thumb|200 px|Fit Tools]]
File:Analysis123.png|Graphical visual analysis display comparing survey to design
The default fit of the survey data is defined as the best match between all observational data and the design data. The default fit is always given first, using all available data.
</gallery>


The user can quickly review other orientations of the survey data by using the tools on the right.
== File Dependencies and Opening Surveys ==


These tools enable the user to manipulate and present data; they are discussed in greater depth later in the analysis section.
Analyzing survey data requires two corresponding files:
* '''Survey File (`.SUR`):''' Contains observed field coordinate data.
* '''Design File (`.DES`):''' Contains baseline CAD model geometry.


* ''There is a link to that section here.'' [[Analysis Tools |[Analysis Tools]]]
To analyze a previously completed survey, select '''Open for Analysis''' adjacent to **Survey File:** on the main interface—the corresponding design file loads automatically. If a survey was just completed, click '''Visual Report''' directly.


==Transform==
<gallery mode="packed" heights="280px">
File:Analysis_main_menu_details_labelled.png|Main menu analysis launch controls
</gallery>


The transform button allows the user to alter survey data with six degrees of freedom.
== Visual Report Controls ==
This means that the survey results can be translated and rotated around the XYZ axis.


* ''Have a look at this video:'' [[https://youtu.be/htBRhwdpzY8| Analysis Transform]]
=== Navigation and Interface Controls ===


==What is shown on the Visual Report==
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<div style="font-weight:bold; font-size:110%; margin-bottom:8px; color:#3366cc;">Main Visual Report Interface Overview</div>
[[File:Analysis_iso_view_labelled.png|center|1200px]]
</div>


<div style="font-size:130%; font-weight:bold; margin:24px 0 12px 0; color:#333;">Isometric View Controls</div>


The first and most crucial thing to know is that all values presented are deviations from the design requirement, and if the pipe spool was manufactured exactly as designed, all values would be zero.
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'''Vector error''' is the positional difference between a measured work point and the design.
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<div style="font-weight:bold; margin-bottom:8px; color:#3366cc;">Reset Camera View</div>
<div style="margin-bottom:10px;">Sets the image's North (+Y) to the top left corner.</div>
[[File:North Button.png|center|280px]]
</div>


'''Touch point/high point/flange alignment error/mitre error'''. The point on the flange face that will come into contact with the adjoining flange. The value displayed represents the gap in millimeters opposite the touch point.
<div style="flex:1 1 30%; min-width:280px; padding:16px 20px; border:1px solid rgba(128,128,128,0.35); border-top:4px solid #3366cc; border-radius:6px; background:#ffffff; text-align:center;">
<div style="font-weight:bold; margin-bottom:8px; color:#3366cc;">Toggle Back Vectors</div>
<div style="margin-bottom:10px;">Displays the flange's weld face vector errors.</div>
[[File:B button.png|center|280px]]
</div>


'''Rotational error''' is where a flange bolt-holes are not oriented as intended.
<div style="flex:1 1 30%; min-width:280px; padding:16px 20px; border:1px solid rgba(128,128,128,0.35); border-top:4px solid #3366cc; border-radius:6px; background:#ffffff; text-align:center;">
<div style="font-weight:bold; margin-bottom:8px; color:#3366cc;">Toggle Point Spheres</div>
<div style="margin-bottom:10px;">Shows the surveyed location of the prism ball.</div>
[[File:P button.png|center|280px]]
</div>


==Reports==
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Three reports can be generated: '''Visual''', '''Text''' and '''QA'''.  
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<div style="font-weight:bold; margin-bottom:8px; color:#3366cc;">Toggle Model Full Shrink</div>
<div style="margin-bottom:10px;">Toggle full shrink and return to full size.</div>
[[File:Toggle Shrink 2.png|center|280px]]
</div>


* [[Automet® FAB - Vector Error Graphical Report|Vector Error Graphical Report Help]]
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* [[Text Report Help|Text Report Help]]
<div style="font-weight:bold; margin-bottom:8px; color:#3366cc;">Toggle Model Full Size</div>
* [[QA Report Help|QA Report Help]]
<div style="margin-bottom:10px;">Toggle full shrink and return to full size.</div>
[[File:Toggle Shrink 1.png|center|280px]]
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<div style="font-weight:bold; margin-bottom:8px; color:#3366cc;">Rotation Mode</div>
<div style="margin-bottom:10px;">Toggle between 'Turntable' and 'Free' rotation.</div>
[[File:Free Rotate.png|center|280px]]
</div>
 
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<div style="font-weight:bold; font-size:110%; margin-bottom:8px; color:#3366cc;">Expanded Viewer Controls and Display Scaling Sliders</div>
[[File:KB 250b.png|center|700px]]
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<div style="font-weight:bold; font-size:105%; margin-bottom:6px; color:#333;">Iso view navigation controls</div>
<b>Video guide:</b> [https://youtu.be/uRAoadBmtv0 Controls for Iso View in Analysis] (2:41)
<br><br>
<i>Summary:</i> Demonstrates camera rotation, wheel zoom, mouse pan, camera resets, showing observed point spheres, scaling vector arrows, and adjusting model shrink parameters.
</div>
 
== Manual Transforms and Model Adjustments ==
 
The **Transform** module allows surveyors to alter survey data with six degrees of freedom by translating and rotating models around the X, Y, and Z axes.
 
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<div style="font-weight:bold; font-size:110%; margin-bottom:8px; color:#3366cc;">Transform Control Panel Interface</div>
[[File:Transform Interface.png|center|750px]]
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<div style="font-weight:bold; font-size:105%; margin-bottom:6px; color:#333;">Transform video guides</div>
* [https://youtu.be/htBRhwdpzY8 Aligning Spool Geometry to Grid Reference Axes] (3:34)
* [https://youtu.be/csy13yclGL0 Manual 3-Axis Spool Rotation] (2:10)
* [https://www.youtube.com/watch?v=jhPrYXEIBpk Manual 3-Axis Spool Translation (Nudging)] (2:10)
</div>
 
== Open Tie-In Surveys ==
 
When analyzing open tie-in site surveys, enable the **Open Tie-In** function to prevent coordinate fit distortions.
 
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<div style="font-weight:bold; font-size:110%; margin-bottom:8px; color:#3366cc;">Open Tie-In Configuration Options</div>
[[File:Open Tie-In Button.png|center|750px]]
</div>
 
== Report Generation ==
 
automet® FAB generates three specialized documentation reports following analysis setup:
 
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'''Visual Error Report'''<br>3D graphical view displaying vector arrows, rotational offsets, and face touch-point gap dimensions.
</div>
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'''Text Report'''<br>Tabular coordinate listing showing actual vs. design coordinates, D-point locations, and alignment angles.
</div>
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'''QA Integrity Report'''<br>Quality audit verifying face planarity, PCD errors, device types, and multi-setup instrument move precision.
</div>
</div>
 
== Visual Error Graphical Report ==
 
All displayed values represent deviations from design; a perfectly manufactured spool yields all '''zero values'''.
 
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<div style="font-weight:bold; font-size:110%; margin-bottom:8px; color:#3366cc;">Full 3D Graphical Visual Error Report</div>
[[File:PDF Link VEGR 04.png|center|700px]]
</div>
 
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<div style="font-weight:bold; margin-bottom:8px; color:#3366cc;">Vector Errors (Black Arrows)</div>
<div style="margin-bottom:10px; text-align:left;">Indicate displacement magnitude and direction (+1.4 mm Z, +0.6 mm Y North, +0.8 mm X East). Correct by adjusting physical flange in the opposite direction (-1.4 mm Z, -0.6 mm South, -0.8 mm West).</div>
[[File:PDF Link VEGR 01.png|center|300px]]
</div>
 
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<div style="font-weight:bold; margin-bottom:8px; color:#3366cc;">Bolt-Hole Rotation (Blue Curved Arrow)</div>
<div style="margin-bottom:10px; text-align:left;">Shows rotational error magnitude (in mm) and direction.</div>
[[File:PDF Link VEGR 03.png|center|300px]]
</div>
 
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<div style="font-weight:bold; margin-bottom:8px; color:#3366cc;">Touch Point (Gold Value)</div>
<div style="margin-bottom:10px; text-align:left;">Identifies the raised-face high point contacting the mating flange first. The value represents the gap opening on the opposite side.</div>
[[File:PDF Link VEGR 02.png|center|300px]]
</div>
 
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<div style="font-weight:bold; margin-bottom:8px; color:#3366cc;">Open Pipe End Long Point</div>
<div style="margin-bottom:10px; text-align:left;">Identifies the longest point on un-flanged pipe ends to guide field bevel grinding.</div>
[[File:PDF Link VEGR 06.png|center|300px]]
</div>
 
</div>
 
== Text Report ==
 
Contains tabular alignment, orientation, and global coordinate comparisons essential for field site surveys.
 
<!-- ===================== MAIN SUMMARY CARD ===================== -->
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<div style="font-weight:bold; font-size:110%; margin-bottom:8px; color:#3366cc;">Text Report Coordinate Summary Page</div>
[[File:PDF Link Text Report 01.png|center|800px]]
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<div style="font-weight:bold; font-size:110%; margin-bottom:8px; color:#3366cc;">Flange Specification & Gasket Summary</div>
<div style="margin-bottom:12px; text-align:left;">Displays design vs. actual flange angles, bolt-hole rotation, OD/PCD dimensions, and gasket gaps.</div>
[[File:Text Report Flange Info.png|center|480px]]
</div>
 
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<div style="font-weight:bold; font-size:110%; margin-bottom:8px; color:#3366cc;">Calculated Work Point Centerlines</div>
<div style="margin-bottom:12px; text-align:left;">Shows actual, design, and positional mismatch error coordinates for each flange center point.</div>
[[File:Text Report Centre Locations.png|center|480px]]
</div>
 
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<div style="font-weight:bold; font-size:110%; margin-bottom:8px; color:#3366cc;">Plane Point Coordinate Locations</div>
<div style="margin-bottom:12px; text-align:left;">Lists 3D coordinates ($X, Y, Z$) for points taken across the flange face using laser or prism.</div>
[[File:Text Report Plane Points.png|center|480px]]
</div>
 
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<div style="font-weight:bold; font-size:110%; margin-bottom:8px; color:#3366cc;">Individual Observed Point Coordinates</div>
<div style="margin-bottom:12px; text-align:left;">Displays measurement type (laser or prism) and exact raw coordinate readings.</div>
[[File:Text Report Points.png|center|480px]]
</div>
 
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<div style="font-weight:bold; font-size:110%; margin-bottom:8px; color:#3366cc;">Flange Midpoint Coordinate Summary</div>
<div style="margin-bottom:12px; text-align:left;">Calculates midpoints and average separation distances across crossover locations between flanges.</div>
[[File:Text Report Mid-Points.png|center|480px]]
</div>
 
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<div style="font-weight:bold; font-size:110%; margin-bottom:8px; color:#3366cc;">D-Point Location Reference States</div>
<div style="margin-bottom:12px; text-align:left;">Visual key showing the 6 possible diameter point placement states (bolted vs. open, front vs. back).</div>
[[File:Text Report 6 States Bolted Design, Bolted Tie-In, Design Front, Design Back, Open Tie-In Front, Open Tie-In Back.png|center|480px]]
</div>
 
</div>
 
== QA Integrity Report ==
 
Validates observation quality, face flatness (plane error), target seating (Max OD error), and instrument setup resection accuracy across multiple station moves.
 
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<div style="font-weight:bold; font-size:110%; margin-bottom:8px; color:#3366cc;">QA Integrity Summary Page 1</div>
[[File:PDF Link QA Report 01.png|center|450px]]
</div>
 
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<div style="font-weight:bold; font-size:110%; margin-bottom:8px; color:#3366cc;">QA Integrity Summary Page 2</div>
<div style="margin-bottom:8px; text-align:left;">Includes support base plate dimension verification and instrument station relocation residuals.</div>
[[File:PDF Link QA Report 02.png|center|450px]]
</div>
 
</div>
 
=== Key QA Validation Parameters ===
 
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<div style="font-weight:bold; margin-bottom:8px; color:#3366cc;">Plane Error (Face Flatness)</div>
<div style="margin-bottom:10px; text-align:left;">Maximum deviation from a flat plane across the flange face. Values exceeding 2.0 mm trigger automatic warnings.</div>
[[File:Plane Error1.png|center|300px]]
</div>
 
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<div style="font-weight:bold; margin-bottom:8px; color:#3366cc;">Circle / Max OD Error</div>
<div style="margin-bottom:10px; text-align:left;">Maximum radial deviation from a true circle, highlighting unseated target devices or ovality.</div>
[[File:Circle Error1.png|center|300px]]
</div>
 
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<div style="font-weight:bold; margin-bottom:8px; color:#3366cc;">PCD Deviation Error</div>
<div style="margin-bottom:10px; text-align:left;">Difference between actual Pitch Circle Diameter and database standards.</div>
[[File:PCD Error image.png|center|300px]]
</div>
 
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<div style="font-weight:bold; margin-bottom:8px; color:#3366cc;">Max Pitch (Angle) Error</div>
<div style="margin-bottom:10px; text-align:left;">Maximum angular pitch error between adjacent bolt holes.</div>
[[File:Max Pitch image.png|center|300px]]
</div>
 
</div>
 
=== Live QA Reports During Data Capture ===
 
QA integrity metrics can be evaluated live during data capture via the **Objects Tab**, allowing surveyors to identify and re-shoot misplaced points prior to moving the total station.
 
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<div style="font-weight:bold; margin-bottom:8px; color:#3366cc;">Live Capture QA Report (Flanges)</div>
[[File:objects tab QA report after capture.png.png|center|450px]]
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<div style="font-weight:bold; margin-bottom:8px; color:#3366cc;">Live Capture QA Report (Detailed)</div>
[[File:objects tab QA report after capture2.png.png|center|450px]]
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</div>


Text and QA reports are available after setting up the survey data in the visual report interface.
== Training Path Completion & Next Steps ==


The visual report transforms the survey data and compares it to the design.  
Congratulations on completing the **automet® FAB Self-Guided Learning Path**.


The visual report displays '''vector errors''' in position, flange '''alignment (touchpoint)''' and '''rotational errors'''.
To continue expanding your technical expertise, explore the following specialized workflows:


This report is the most effective way to observe deviations from the design for pipe spools with multiple configurations.
- [[Automet® FAB - Site Survey]] – Detailed field site survey procedures.
- [[Automet® FAB - Control Capture Methods]] – Advanced resection networks and control station management.
- [[Pressure Vessels]] – Modelling and surveying pressure vessel nozzles and shell alignments.


The spool can be viewed in any orientation, while the text remains flat.
For technical assistance or training inquiries, contact MLTech support at **info@mltech.co.uk**.

Latest revision as of 10:24, 27 October 2026

Self-Guided Learning Path: automet® FAB
Module 5: Analysis  ·  Interpreting survey results, visual reports, least-squares fit optimization, manual transforms, and report generation.
Estimated Time: 30 minutes

1. Getting Started

2. Design Input

3. Survey Setup

4. Execution

5. Analysis

Overview

Selecting Visual Report from the main application menu following a survey compares captured field observations against design specifications (`.DES`).

The visual analysis suite enables surveyors to rotate and translate models, include or exclude specific flanges from least-squares fit calculations, zero individual tie-ins, adjust fit weighting preferences, and isolate gross fabrication errors.

File Dependencies and Opening Surveys

Analyzing survey data requires two corresponding files:

  • Survey File (`.SUR`): Contains observed field coordinate data.
  • Design File (`.DES`): Contains baseline CAD model geometry.

To analyze a previously completed survey, select Open for Analysis adjacent to **Survey File:** on the main interface—the corresponding design file loads automatically. If a survey was just completed, click Visual Report directly.

Visual Report Controls

Main Visual Report Interface Overview
Isometric View Controls
Reset Camera View
Sets the image's North (+Y) to the top left corner.
Toggle Back Vectors
Displays the flange's weld face vector errors.
Toggle Point Spheres
Shows the surveyed location of the prism ball.
Toggle Model Full Shrink
Toggle full shrink and return to full size.
Toggle Model Full Size
Toggle full shrink and return to full size.
Rotation Mode
Toggle between 'Turntable' and 'Free' rotation.
Expanded Viewer Controls and Display Scaling Sliders
Iso view navigation controls

Video guide: Controls for Iso View in Analysis (2:41)

Summary: Demonstrates camera rotation, wheel zoom, mouse pan, camera resets, showing observed point spheres, scaling vector arrows, and adjusting model shrink parameters.

Manual Transforms and Model Adjustments

The **Transform** module allows surveyors to alter survey data with six degrees of freedom by translating and rotating models around the X, Y, and Z axes.

Transform Control Panel Interface
Transform video guides

Open Tie-In Surveys

When analyzing open tie-in site surveys, enable the **Open Tie-In** function to prevent coordinate fit distortions.

Open Tie-In Configuration Options

Report Generation

automet® FAB generates three specialized documentation reports following analysis setup:

Visual Error Report
3D graphical view displaying vector arrows, rotational offsets, and face touch-point gap dimensions.

Text Report
Tabular coordinate listing showing actual vs. design coordinates, D-point locations, and alignment angles.

QA Integrity Report
Quality audit verifying face planarity, PCD errors, device types, and multi-setup instrument move precision.

Visual Error Graphical Report

All displayed values represent deviations from design; a perfectly manufactured spool yields all zero values.

Full 3D Graphical Visual Error Report
Vector Errors (Black Arrows)
Indicate displacement magnitude and direction (+1.4 mm Z, +0.6 mm Y North, +0.8 mm X East). Correct by adjusting physical flange in the opposite direction (-1.4 mm Z, -0.6 mm South, -0.8 mm West).
Bolt-Hole Rotation (Blue Curved Arrow)
Shows rotational error magnitude (in mm) and direction.
Touch Point (Gold Value)
Identifies the raised-face high point contacting the mating flange first. The value represents the gap opening on the opposite side.
Open Pipe End Long Point
Identifies the longest point on un-flanged pipe ends to guide field bevel grinding.

Text Report

Contains tabular alignment, orientation, and global coordinate comparisons essential for field site surveys.

Text Report Coordinate Summary Page
Flange Specification & Gasket Summary
Displays design vs. actual flange angles, bolt-hole rotation, OD/PCD dimensions, and gasket gaps.
Calculated Work Point Centerlines
Shows actual, design, and positional mismatch error coordinates for each flange center point.
Plane Point Coordinate Locations
Lists 3D coordinates ($X, Y, Z$) for points taken across the flange face using laser or prism.
Individual Observed Point Coordinates
Displays measurement type (laser or prism) and exact raw coordinate readings.
Flange Midpoint Coordinate Summary
Calculates midpoints and average separation distances across crossover locations between flanges.
D-Point Location Reference States
Visual key showing the 6 possible diameter point placement states (bolted vs. open, front vs. back).

QA Integrity Report

Validates observation quality, face flatness (plane error), target seating (Max OD error), and instrument setup resection accuracy across multiple station moves.

QA Integrity Summary Page 1
QA Integrity Summary Page 2
Includes support base plate dimension verification and instrument station relocation residuals.

Key QA Validation Parameters

Plane Error (Face Flatness)
Maximum deviation from a flat plane across the flange face. Values exceeding 2.0 mm trigger automatic warnings.
Circle / Max OD Error
Maximum radial deviation from a true circle, highlighting unseated target devices or ovality.
PCD Deviation Error
Difference between actual Pitch Circle Diameter and database standards.
Max Pitch (Angle) Error
Maximum angular pitch error between adjacent bolt holes.

Live QA Reports During Data Capture

QA integrity metrics can be evaluated live during data capture via the **Objects Tab**, allowing surveyors to identify and re-shoot misplaced points prior to moving the total station.

Live Capture QA Report (Flanges)
Live Capture QA Report (Detailed)

Training Path Completion & Next Steps

Congratulations on completing the **automet® FAB Self-Guided Learning Path**.

To continue expanding your technical expertise, explore the following specialized workflows:

- Automet® FAB - Site Survey – Detailed field site survey procedures. - Automet® FAB - Control Capture Methods – Advanced resection networks and control station management. - Pressure Vessels – Modelling and surveying pressure vessel nozzles and shell alignments.

For technical assistance or training inquiries, contact MLTech support at **info@mltech.co.uk**.