9.3 Tube Expanding Mechanics, Rolling Torque Calculations, Wall Reduction & Flaring/Beading

8.3 Tube Expanding Mechanics, Rolling Torque Calculations, Wall Reduction & Flaring/Beading

Core Trade Concept: Tube expanding (rolling) is a mechanical process that creates a high-pressure, leak-tight seal and structural joint between a boiler tube and a drum or tubesheet hole without structural welding. The integrity of the joint depends entirely on the elastic-plastic interaction between the tube and the tubesheet hole. Boilermakers must master percentage wall reduction calculations, torque-controlled rolling drives, flaring geometries, and firetube beading techniques.

1. Fundamentals of Tube Expanding Mechanics

To achieve a permanent, leak-proof mechanical joint capable of withstanding operating pressures up to $3{,}000\text{ psig}$ and high thermal cycling, boilermakers rely on the fundamental difference in elastic limits between the tube and the tubesheet.

                  MECHANICS OF TUBE EXPANSION

   STAGE 1: CLEARANCE UPTAKE       STAGE 2: PLASTIC FLOW & ELASTIC SPRINGBACK

     Tubesheet Hole (Elastic)        Tubesheet Hole Expanded Within Elastic Limit
     +---------------------+         +-------------------------------------+
     |  Clearance Gap      |         |  Compressive Elastic Springback (==>)|
     |    [=== Tube ===]   |         |    [====== PLASTICALLY =======]     |
     |    [   Wall     ]   |  ====>  |    [     DEFORMED TUBE        ]     |
     |                     |         |    [      (WALL THINNED)      ]     |
     +---------------------+         |  Compressive Elastic Springback (==>)|
                                     +-------------------------------------+
     Tube Expands Free               Tubesheet Compresses Over Tube to Create
     to Contact Hole Wall            Permanent High-Pressure Friction Seal

The Elastic-Plastic Joint Principle

1. Phase 1 — Clearance Uptake: The rotating roller expander forces the tube wall radially outward until its outer diameter makes solid contact with the internal bore of the tubesheet hole.
2. Phase 2 — Plastic Deformation of the Tube: As rolling torque increases, the tube metal is stressed well beyond its yield point, undergoing permanent plastic deformation (the tube wall is rolled thinner, increasing its inside and outside diameters).
3. Phase 3 — Elastic Deflection of the Tubesheet Hole: The expanding tube pushes outward against the heavier, rigid tubesheet ligament, forcing the tubesheet hole to expand within its elastic limit (below its yield point).
4. Phase 4 — Elastic Recovery (Springback): When the expander tool is extracted, the plasticized tube has no tendency to return to its original shape. However, the surrounding tubesheet ligament attempts to snap back to its original dimension via elastic springback. This exerts a permanent, massive compressive hoop force (interfacial gripping pressure) around the outer surface of the tube, creating an airtight, watertight, high-strength friction joint.

Parallel-Roll vs. Flare-Roll Expanding

• Parallel-Roll Expanding: Utilizes rolls arranged to produce a uniform cylindrical expanded diameter along the entire thickness of the tubesheet seat. Used where tubes are cut flush or inside thick drum walls.
• Flare-Roll Expanding (Combination Roll & Flare): Utilizes combination expanders equipped with straight cylindrical rolls and angled flaring rolls. The tool expands the tube inside the hole while simultaneously forming a smooth $15^\circ\text{ to }30^\circ$ bellmouth flare on the projecting tube end in a single operation.

2. Tube Expander Tool Construction, Components & Maintenance

A mechanical tube expander is a precision tool designed to convert rotational torque into controlled radial outward expansion while automatically feeding itself into the tube.

                  TUBE EXPANDER TOOL ANATOMY

   Square Drive               Cage (Houses Rolls       Combination Flaring Roll
   for Air/Electric Motor     at Forward Lead Angle)   (15° - 30° Angle)
         |                            |                     |
      +--v--+   +=====================+=====================v==+
      |     |===| [===]               [===]               //   |
      |     |   |   |                   |                //    | <=== Thrust Collar
      +-----+===| [===]               [===]               \\   |      (Sets Depth)
         ^      +==============================================+
         |                            ^
   Tapered Mandrel                    |
   (Driven Inward)             Hardened Steel Rolls
                               (Reverse-Tapered to Mandrel)

Core Components of a Tube Expander

1. Mandrel (Drive Pin): A hardened, precision-ground tool steel pin with a continuous forward taper (typically $1/4\text{ to }3/8\text{ in.}$ taper per foot). As the drive motor rotates the mandrel clockwise, the tapered profile forces the expanding rolls radially outward.
2. Cage: The cylindrical steel housing that retains the rolls. The slots in the cage are machined at a slight angle to the mandrel centerline (called the lead angle or roll tilt). This lead angle causes the rotating mandrel to automatically pull itself forward into the tube without manual pushing force.
3. Rolls (Rollers): Hardened alloy tool steel rollers mounted in the cage slots.
   • Reverse-Taper Geometry: The rolls are tapered in the exact reverse direction of the mandrel taper. Because the reverse tapers cancel each other out, the working outer face of the rolls remains perfectly parallel to the tube axis, creating a uniform cylindrical expansion rather than an unwanted conical bore.
4. Thrust Collar & Stop Assembly: An adjustable threaded collar equipped with heavy-duty thrust ball bearings that rests against the face of the tubesheet. It sets the precise depth of expansion and prevents the expander from feeding too deep into the drum.

Lubrication Standards

Mandatory Code Practice: Tube expanding generates severe frictional heat and sliding contact pressure between the mandrel and rolls. Boilermakers must continuously lubricate expanders using approved water-soluble lubricants (or specialized synthetic non-sulfurized paste).

• Why Water-Soluble? Petroleum oils, animal fats, or heavy sulfurized greases must never be used. Traditional oils leave hydrocarbon residues that are extremely difficult to remove, preventing subsequent seal welding or vaporizing during boiler startup to leave carbon deposits that promote under-deposit corrosion. Water-soluble lubricants wash out cleanly with hot water or solvent flushes.

3. Percentage Wall Reduction (% WR) Calculations & Target Ranges

The quality and holding power of a rolled tube joint are governed by the Percentage Wall Reduction (% WR) (also termed tube thinning). Rolling too little causes leakage; rolling too much destroys the tubesheet.

               TUBE EXPANSION DIAMETRAL STAGES

       1. Original State:   Tube OD < Hole ID  (Initial Clearance Gap)
       2. Contact State:    Tube OD = Hole ID  (Metal-to-Metal Contact)
       3. Final Rolled:     Tube Wall Thinned  (Plastic Wall Reduction)

       Total ID Increase = [ Clearance Uptake ] + [ 2 x Wall Thinning ]

The Wall Reduction Formula

When a tube expands to fill the hole clearance, the initial increase in tube inside diameter equals the initial diametral clearance ($Hole_{ID} - Tube_{OD}$). Any subsequent increase in tube ID directly thins the two opposing tube walls ($2 \cdot \Delta t$).

The Percentage Wall Reduction (% WR) is calculated as:

$\%\text{ WR} = \left[ \frac{(ID_{rolled} - ID_{orig}) - (Hole_{ID} - OD_{orig})}{2 \cdot t_{orig}} \right] \times 100\%$

Where:

• $ID_{rolled} =$ Final inside diameter of the tube after rolling (inches)
• $ID_{orig} =$ Initial inside diameter of the tube before rolling (inches)
• $Hole_{ID} =$ Measured inside diameter of the tubesheet hole (inches)
• $OD_{orig} =$ Initial outside diameter of the tube before rolling (inches)
• $t_{orig} =$ Original measured tube wall thickness ($\frac{OD_{orig} - ID_{orig}}{2}$, inches)

Target Wall Reduction Ranges

Step-by-Step Worked Rolling Calculation

$\text{Field Problem:}$ A boilermaker is preparing to roll a batch of carbon steel generating tubes (SA-178 Grade A) into a steam drum. The field measurements are:

• Tubesheet Hole Diameter ($Hole_{ID}$) $= 2.015\text{ inches}$
• Original Tube OD ($OD_{orig}$) $= 2.000\text{ inches}$
• Original Tube ID ($ID_{orig}$) $= 1.760\text{ inches}$
• Original Wall Thickness ($t_{orig}$) $= \frac{2.000 - 1.760}{2} = 0.120\text{ inches}$
• Target Wall Reduction $= 8.0%$

$\text{Step 1: Calculate Total Clearance to be Taken Up}$ $\text{Clearance} = Hole_{ID} - OD_{orig} = 2.015 - 2.000 = 0.015\text{ inches}$

$\text{Step 2: Calculate Required Total Wall Thinning }(2 \cdot \Delta t)$ $\text{Wall Thinning Amount} = \%\text{ WR} \cdot (2 \cdot t_{orig}) = 0.08 \cdot (2 \cdot 0.120) = 0.08 \cdot 0.240 = 0.0192\text{ inches}$

$\text{Step 3: Calculate Target Rolled Inside Diameter }(ID_{rolled})$ $ID_{rolled} = ID_{orig} + \text{Clearance} + \text{Wall Thinning Amount}$ $ID_{rolled} = 1.760 + 0.015 + 0.0192 = 1.7942\text{ inches (approx. } 1.794\text{ in.)}$

Trade Practice: The boilermaker sets the torque limiter on the rolling drive motor and test-rolls a mockup block until an internal 3-point micrometer confirms an expanded ID of $1.794\text{ inches}$.

4. Over-Rolling vs. Under-Rolling Hazards & Torque Control

Achieving the precise percentage wall reduction is one of the most critical quality control operations in the boilermaker trade.

                  CONSEQUENCES OF INCORRECT ROLLING

   UNDER-ROLLING (< 5% WR)               OVER-ROLLING (> 12% WR)
   - Interfacial pressure too low        - Tubesheet ligament yield & distortion
   - Hydrostatic test leaks              - Tubesheet bowing / warping
   - Low pull-out strength               - Severe work hardening & micro-cracks
   - Crevice corrosion behind seat       - Axial tube extrusion & buckling

The Dangers of Over-Rolling

1. Tubesheet Ligament Distortion: Over-rolling exerts excessive radial pressure that exceeds the yield point of the tubesheet metal itself. This permanently distorts the narrow web of metal (ligament) between adjacent tube holes, relaxing the compressive grip on neighboring tubes and causing surrounding tight joints to leak.
2. Tubesheet Bowing (Warping): When hundreds of tubes in a tubesheet are over-rolled, the cumulative radial expansion causes the entire tubesheet plate to dish or bow outward, inducing severe bending stresses on drum heads and shell seams.
3. Severe Work Hardening & Micro-Cracking: Excessive cold working hardens the tube metal, making it brittle and creating microscopic longitudinal stress-corrosion cracks in the rolled transition zone.
4. Axial Extrusion & Tube Buckling: Over-rolling thins the wall excessively, forcing displaced metal to flow axially (longitudinally). This extrudes the tube lengthwise, causing adjacent tube circuits to bow, buckle, or lift off their support saddles.

The Dangers of Under-Rolling

• Hydrostatic Test Weeping: Insufficient wall reduction leaves microscopic void channels between the tube OD and hole bore, resulting in immediate leakage during the post-maintenance ASME hydrostatic test ($1.5\times$ MAWP).
• Loss of Pull-Out Strength: Under-expanded tubes lack sufficient friction resistance to withstand high internal pressure thrust loads, creating a catastrophic blowout hazard.

Torque-Controlled Rolling Drives

To prevent operator error, modern boilermakers use electric or pneumatic torque-controlled rolling motors.

• Operation: The motor incorporates an automatic electronic or mechanical torque sensor. The operator presets the calculated torque shut-off value. As the expander rolls the tube, torque resistance climbs exponentially as plastic wall thinning begins. When the preset torque threshold is reached, the motor automatically stops and reverses the mandrel, extracting the tool without over-rolling.

5. Tube Projection, Flaring, Beading & Seal Welding Rules

Once tubes are expanded into tubesheets or drums, the projecting tube ends must be finished according to ASME Section I, ASME Section IV, and NBIC construction codes.

               TUBE TERMINATION & FINISHING DETAILS

   WATERTUBE DRUM: FLARED BELLMOUTH       FIRETUBE BOILER: ROLLED & BEADED
   (Reduces Turbulence / High Pull-Out)   (Prevents Overheating / Burning Lip)

     Projection (3/16" - 3/8")                Curled Flush Against Sheet
         |                                           |
      +--v--+   15° - 30° Flare                   +--v--+
      |     /                                     (     ) <=== Bead Formed with
   ===+    /   <=== Flared Lip                 ===+=====+      Pneumatic Tool
   Tubesheet                                   Tubesheet
   Plate                                       Plate
   ===+    \                                   ===+=====+
      |     \                                     (     )
      +-----+                                     +-----+

   SEAL-WELDED TUBE JOINT (ASME SECTION I / NBIC)
   
   Tubesheet Face
       |   Small GTAW Seal Weld (3/16" Throat)
       |    |
     +-v-+--v-+
     |   | ///| <=== Fully Degreased Prior to Welding
   ==+===+----+=======================================
   Tubesheet Hole   [ Expanded Contact Zone ]
   ==+===+----+=======================================

Tube Projection & Flaring Standards (Watertube Boilers)

• Tube Projection: Under ASME Section I (PWT-11), tubes in watertube boilers projecting into drums or headers must extend beyond the tubesheet face by a minimum of $3/16\text{ inch}$ ($5\text{ mm}$) to a maximum of $3/8\text{ inch}$ ($10\text{ mm}$).
  • Projection $< 3/16\text{ in.}$: Insufficient metal to form a proper code flare.
  • Projection $> 3/8\text{ in.}$: Excessive projection impedes water circulation, creates stagnant flow eddies, and overheats the uncooled protruding lip.
• Flaring (Bellmouthing): Tubes must be flared to an included angle of $15^\circ\text{ to }30^\circ$ using combination flare rolls.
  • Purpose: Flaring provides a smooth hydrodynamic entrance profile that reduces pressure drop and prevents inlet eddy erosion. Mechanically, the flared bellmouth acts as a positive retaining flange, doubling the joint's resistance to axial pull-out forces under high pressure.

Tube Beading (Firetube Boilers)

• The Beading Requirement: In firetube boilers, hot combustion gases pass inside the tubes while water surrounds the outside. If tube ends project out into the radiant furnace gas stream, the uncooled protruding metal will quickly overheat, oxidize, and crack.
• Execution: After parallel rolling and initial flaring, the boilermaker uses a pneumatic beading tool (beading shoe) fitted in a chipping hammer. The tool is guided around the circumference to curl the flared lip tightly back against the tubesheet face, forming a continuous, smooth, rounded bead.
• Inspection: The bead must make $100%$ solid metal-to-metal contact with the tubesheet around its entire periphery without gaps, sharp gouges, or rolled-over burrs.

Seal Welding Rolled Tubes (ASME Section I / NBIC Rules)

In severe cyclic service or high-pressure boilers, rolled joints are frequently reinforced with a cosmetic or pressure-tight seal weld.

Mandatory Code Sequence: Degreasing & Roll-Weld-Roll Protocol

1. Initial Light Roll (Contact Expansion): The tube is lightly expanded ($2%\text{--}3%\text{ WR}$) simply to center the tube in the hole and ensure intimate contact.
2. 100% Solvent Degreasing: Before striking an arc, the tube end and hole interface must be thoroughly flushed with non-chlorinated solvent (such as acetone) and dried with heated air. Any residual rolling lubricant trapped in the crevice will vaporize under the welding arc ($> 5{,}000^\circ\text{F}$), causing severe weld porosity, wormholes, and hydrogen cracking.
3. Application of Seal Weld: A single-pass GTAW (TIG) or SMAW seal weld (typically with a $\frac{3}{16}\text{-inch}$ throat) is deposited around the tube circumference to fuse the tube projection to the tubesheet face.
4. Final Re-Rolling (Behind the Weld): After the weld has cooled, the boilermaker performs a final light roll $1/2\text{ to }3/4\text{ inch}$ behind the weld.
   • Why Re-Roll? The intense heat of welding causes the tube metal to shrink, loosening the mechanical expansion grip behind the weld. Final re-rolling closes the crevice between the tube OD and hole bore, preventing crevice corrosion without overstressing the weld bead.