Guided Wave Mode Selection for Paperboard Crease Shear Quality Assessment

Acoustics

Mechanical evaluation of creased folding carton stock has historically relied on bending resistance gauges that clamp a folded tab at ninety degrees. That quasi-static test records the peak restoring moment according to ISO 2493-1, yet it aggregates sheet bending stiffness with localized hinge delamination into a single unseparated value. High-frequency ultrasonic plate waves isolate the internal shear compliance of the scored zone by transmitting mechanical stress through the fibrous network.

Multi-ply cartonboard behaves as an orthotropic, layered viscoelastic plate exhibiting strong mechanical anisotropy. Elastic constants along the machine direction exceed cross-machine direction values by factors between two and four, while the through-thickness elastic modulus sits two orders of magnitude lower than in-plane parameters.

Ultrasonic energy introduced into paperboard propagates as guided modes bounded by the upper and lower surfaces of the sheet. At plate thicknesses below 0.8 millimeters and excitation frequencies between 50 kHz and 1 MHz, the acoustic field resolves into fundamental plate modes: symmetric Lamb mode S0, antisymmetric flexural Lamb mode A0, and fundamental shear-horizontal mode SH0. Each mode distributes mechanical displacement differently through the plies.

Guided Wave Mechanics in Multi-Ply Packaging

Stress wave propagation inside orthotropic fiber matrices follows the Christoffel equation modified for thin plates bounded by traction-free surfaces. The symmetric mode S0 exhibits predominantly in-plane particle displacements distributed symmetrically across the central mid-plane of the caliper. At low frequency-caliper products, typically under 0.2 MHz-mm, S0 phase velocity links directly to the in-plane Young modulus and density of the sheet:

c_S0 = sqrt( E_inplane / ( rho ( 1 – nu_xy nu_yx ) ) )

The flexural mode A0 exhibits dominant out-of-plane particle motion. At low frequency-caliper products, A0 phase velocity depends on frequency, caliper, in-plane stiffness, and out-of-plane shear stiffness:

c_A0 = ( ( D / ( rho h ) )^(1/4) ) sqrt( 2 pi f )

Here D represents the plate bending stiffness, rho denotes apparent density, h identifies board thickness, and f marks wave frequency. Because the A0 mode forces out-of-plane displacement, transverse shear stresses reach their maximum amplitude along the neutral axis of the sheet. The plies separate along shear planes.

That distribution makes the flexural mode sensitive to internal delamination cracks generated by creasing rules.

The shear-horizontal mode SH0 features in-plane particle motion oriented perpendicular to the direction of propagation. Unlike Lamb modes, SH0 is non-dispersive across isotropic media, maintaining constant phase and group velocities across the lower frequency spectrum. In orthotropic cartonboard, SH0 phase velocity tracks the in-plane shear modulus G12.

Energy remains trapped inside the solid without acoustic radiation into surrounding ambient air.

A 350-micron folding boxboard conditioned at 23 degrees Celsius and 50 percent relative humidity exhibits an S0 phase velocity of 2,850 meters per second along the machine direction and 1,620 meters per second across the cross direction.

Energy leakage into ambient air differs sharply between wave types. Flexural A0 waves propagate with phase velocities below the speed of sound in air (343 meters per second) at very low frequency-caliper products, creating evanescent near-fields that do not radiate. As frequency rises, A0 phase velocity surpasses the acoustic velocity of air, creating leaky Lamb waves that radiate pressure fronts into space at the Rayleigh angle.

The symmetric S0 mode travels faster than sound in air across almost all practical frequencies, leaking acoustic energy continuously along its path. Phase velocity drops immediately. Transducers positioned off-axis capture these radiated waves without touching the moving board surface.

What Signal Attenuation Resolves Delamination Depth?

Transmitted acoustic amplitude tracks the volume of uncoupled internal fiber bonds across the creased indentation. An intact paperboard sheet transmits high-amplitude coherent wave packets across both S0 and A0 branches. When a creasing rule forces the board down into a counter-die matrix, the induced shear forces exceed the internal z-directional bond strength (Scott bond value, TAPPI T 569).

Multiple delamination cracks open within the middle plies, decoupling the top linerboard from the bottom linerboard. The crease channel opens.

When the S0 mode enters this delaminated region, the incident wave splits into two independent symmetric modes propagating through the separated upper and lower sub-plates. Because each sub-plate possesses less than half the original caliper, the frequency-caliper product shifts leftward on the dispersion curve. The phase velocity of S0 in thin sheets remains relatively flat at low frequencies, so total time of flight across the score experiences minimal shift.

Amplitude drops by 3 to 8 decibels because of acoustic impedance mismatching at the entrance boundary of the shear zone.

The flexural A0 mode exhibits a distinct response. Delamination divides plate bending stiffness D, which scales with the cube of the thickness, into the sum of the individual bending stiffnesses of the detached plies. For a symmetrical delamination splitting a board of thickness h into two identical sheets of thickness h/2, total bending resistance drops from proportional to h^3 down to 2 (h/2)^3, which equals h^3 / 4.

Flexural stiffness decreases by seventy-five percent. This massive structural softening causes severe scattering of the A0 mode. Amplitude attenuation across a properly fractured crease reaches 18 to 28 decibels, accompanied by substantial phase delay.

Inadequately sheared creases, where internal plies remain unbroken, permit high A0 transmission with attenuation values below 9 decibels. Fiber bonds fail.

Track

Transducer placement dictates which acoustic wave modes register cleanly during online or benchtop scanning. Pitch-catch configurations utilize one transmitter and one receiver aligned across the path of the creased score. Pulse-echo arrangements position a single transducer over the target to detect backscattered reflections from the boundary of the delamination zone.

In high-speed carton production, pitch-catch transmission yields direct measurements of attenuation and transit delay, bypassing the complex boundary reverberations that degrade pulse-echo signals in porous cellulose substrates.

Transducers operate either via direct mechanical contact or through non-contact air coupling. Contact transducers require consistent normal force and coupling media to transfer acoustic energy across the board interface. The web advances quickly.

Dry-coupling elastomeric wheels circumvent liquid couplants, which swell cellulosic fibers and alter local elastic properties, yet their compliance limits inspection speeds to less than two meters per second. Air-coupled ultrasound (ACU) operates completely dry, decoupling acoustic verification from web speed limitations.

Air-Coupled Transducer Alignment and Pitch-Catch Geometries

Piezocomposite transducers fitted with quarter-wave acoustic impedance matching layers overcome the vast impedance mismatch between active piezoceramics (30 MRayl) and air (415 Rayl). To selectively generate either the S0 or A0 Lamb mode in paperboard, the transmitting transducer tilts relative to the surface normal according to Snell’s law of acoustic refraction:

sin( theta_air ) = c_air / c_mode

Here theta_air defines the incident angle in air, c_air is the acoustic velocity in air (343 meters per second at 20 degrees Celsius), and c_mode specifies the target phase velocity of the guided mode inside the paperboard. Because the S0 mode in cartonboard exhibits phase velocities between 1,500 and 3,500 meters per second, the matching incident angle theta_air sits between 5.6 and 13.2 degrees. The flexural A0 mode at 100 kHz travels much slower, often between 450 and 800 meters per second, demanding incident angles between 25.4 and 49.7 degrees.

The table below summarizes critical acoustic parameters across operating modes for standard paperboard substrates.

Angled transmitter and receiver pairs isolate the A0 wave packet from background acoustic noise. Aligning both transducer heads at 35 degrees relative to the sheet normal maximizes energy conversion into flexural motion while filtering out the faster S0 packet, which passes before the receiver window opens. The receiver records the packet.

Contact Wheel Probes on Calendered Surfaces

Surface roughness and barrier coatings complicate dry contact ultrasound. Heavy calendering compresses surface fibers, producing smooth top liners that transmit ultrasound efficiently, while uncalendered backsides scatter high-frequency contact signals. Synthetic rubber wheel probes require controlled pneumatic preloads between 15 and 35 Newtons to establish steady acoustic contact without mechanically crushing the board caliper.

The caliper remains uniform.

Wheel probes achieve spatial resolution dictated by the contact footprint width, typically 1.5 to 3.0 millimeters. When testing a crease line running across the machine direction, the beam must align precisely perpendicular to the crease axis. Angular misalignment exceeding three degrees disperses the wave front across the crease edges, generating spurious reflections that mimic internal delamination.

Transducer alignment parallel to the crease line causes immediate phase cancellation between the waves travelling through sheared fibers and waves bypassing through solid board.

A transducer misaligned by more than five degrees from the score normal produces phase cancellation that masks incomplete internal delamination.

Tighter probe alignment yields cleaner separation between the primary transmission pulse and secondary boundary echoes. The clean separation disappears whenever probe wear alters the contact footprint.

Rupture

Creasing forces paperboard through a controlled sequence of local shear ruptures. The male creasing rule pushes the sheet into the female matrix channel, generating three distinct stress zones: compressive indentation under the rule tip, localized bending over the matrix shoulders, and intense interlaminar shear within the sheet core. Without delamination across the neutral axis, the outer liners experience unmitigated tensile and compressive strains.

The score cracks open.

When the board bends ninety degrees on a packaging line, outer liner tensile strain must remain below the ultimate tensile elongation limit of the bleached chemical pulp (typically 2.5 to 4.0 percent). Shear failure between plies allows the layered structure to slide internally like a deck of playing cards, redistributing strain and shifting the neutral bending plane inward. A crease lacking internal rupture forces the exterior liner to carry all tensile loads, splitting the printed face, cracking varnishes, and fracturing barrier films.

Inter-Ply Cleavage under Rule Penetration

The progression of fiber network breakdown follows definite mechanical thresholds during die penetration. The rule descends through the board thickness, initiating specific damage modes:

1. Surface indentation crushes the coated top liner under high localized compressive stresses, densifying the top five to fifteen percent of the sheet thickness without initiating through-thickness cleavage.
2. Elastic-plastic bending draws the board over the edges of the female channel, generating peak out-of-plane shear stress along the middle plies containing mechanical pulp or recycled fibers.
3. Interlaminar shear cleavage begins when shear stresses exceed the internal bond threshold, propagating multiple horizontal delamination cracks parallel to the sheet surfaces.
4. Permanent hinge deformation occurs as the plies slip past each other, breaking secondary hydrogen bonds and creating permanent internal void spaces within the creased zone.

The mechanical integrity of these internal shear surfaces defines crease quality. Excessive rule penetration causes through-thickness shear cutting, severing the outer linerboards and destroying panel stiffness. Insufficient rule penetration leaves the middle plies bonded, preserving high flexural rigidity that resists automated folding.

Dry fiber bonds fail.

Mode Sensitivity across S0 and A0 Branches

Different acoustic wave branches display diverging sensitivity profiles when crossing these internal fracture networks. The fundamental symmetric mode S0 travels primarily through the high-modulus outer liners. Because the outer liners remain intact during proper creasing, the S0 mode finds a continuous acoustic pathway across the score.

S0 transmission drops only slightly due to the geometrical thinning and compressive densification directly under the rule tip. Tracking S0 transmission alone yields poor correlation with internal shear quality, registering false passes on uncreased, stiff boards.

The fundamental antisymmetric mode A0 relies entirely on the transverse shear stiffness of the core to support its out-of-plane flexural displacement. When interlaminar shear cleavage breaks the connection between plies, transverse shear stress transfer collapses. The A0 wave cannot propagate across an uncoupled multi-layer interface without dramatic energy loss.

The phase velocity drops, transit time extends, and signal attenuation surges by up to 25 decibels compared to solid board.

The fundamental shear-horizontal mode SH0 introduces distinct diagnostic capability. Polarized in the plane of the sheet, SH0 stresses the fiber network in pure in-plane shear. In a fully delaminated crease, the discontinuous interfaces generate friction and slip during high-amplitude SH0 wave passage, attenuating high-frequency spectral components while transmitting lower frequencies.

Measuring the transmission loss ratio between A0 and S0 modes provides a normalized, self-calibrating index of crease depth that cancels out absolute caliper variations and ambient humidity fluctuations.

Can multi-frequency ultrasonic wave packets distinguish between clean horizontal delamination and localized vertical micro-cracking across brittle top coatings without supplemental optical verification?

Board

Substrate morphology dictates how acoustic waves interact with creased fiber structures. Solid Bleached Sulfate (SBS), manufactured from pure virgin chemical pulp, exhibits high internal bond strength, uniform density across all plies, and exceptional fiber flexibility. Folding Boxboard (FBB) utilizes bleached chemical pulp liners over a thick, bulky middle core composed of stone groundwood or thermo-mechanical pulp (TMP).

White Lined Chipboard (WLC) incorporates multiple layers of recycled fiber slurry containing residual mineral fillers, starches, and fragmented fibers. Each board architecture responds differently to scoring rules and guided acoustic waves.

FBB boards generate sharp, well-defined interlaminar shear planes because the weak, bulky mechanical pulp core shears easily under rule penetration. The high stiffness difference between the chemical pulp liners and the mechanical core funnels shear stresses directly into the core interfaces. WLC boards exhibit scattered, unpredictable fracture patterns because inconsistent recycled fibers and localized filler concentrations disperse shear stresses randomly through the caliper.

The carton folds true.

Solid Bleached Sulfate and Folding Boxboard

Testing crease quality across these board grades requires calibrated acoustic thresholds. An SBS board of 300 grams per square meter requires higher creasing rule pressure to overcome its robust internal bond strength (Scott bond exceeding 250 Joules per square meter). Once delaminated, the long chemical fibers create fibrous bridges across the fracture planes, maintaining moderate acoustic continuity.

FBB of identical grammage features a lower Scott bond in the core (often 110 to 160 Joules per square meter), yielding complete mechanical separation of the plies under lower die loads. Gluers run at line capacity.

The structural divergence between board grades directly alters acoustic response metrics across scored lines, as detailed in the comparative assessment below.

The Shear Delamination Index represents the normalized ratio of A0 attenuation to S0 attenuation across the score line. An index above 0.85 indicates full, clean internal delamination across the middle plies with intact surface liners. An index below 0.65 reveals inadequate ply separation, warning of elevated bending resistance and high risk of carton burst during high-speed folding.

A shear delamination index dropping below 0.70 across 400-micron board correlates with a forty percent increase in carton erector feed jams.

Surface treatments modify wave transmission paths. Extrusion polyethylene coatings, metallized polyester laminations, and UV-cured gloss varnishes increase the mass per unit area without adding proportional shear stiffness. Polymer films damp high-frequency acoustic signals, shifting the optimal testing frequency downward to avoid excessive material attenuation.

Moisture drives this drift.

Will High Line Speed Degrade Mode Separation?

Evolving converting machinery operates at web speeds exceeding 300 meters per minute on roll-fed die-cutters, while folder-gluers process over 50,000 cartons per hour. At these feed rates, non-contact air-coupled transducers must capture wave packets within microsecond time windows. A cartonboard blank moving at five meters per second traverses a five-millimeter ultrasonic inspection zone in exactly one millisecond.

The web advances quickly.

High web speed introduces Doppler shifts and spatial signal smearing. For air-coupled Lamb wave systems operating at 200 kHz, moving board generates phase shifts that misalign the receiver angle. At five meters per second, the Doppler frequency shift in air remains below 0.5 kHz, which falls well within the transducer bandwidth.

Spatial smearing presents the greater hurdle: during the twenty-microsecond duration of a five-cycle tone burst, the moving board travels 0.1 millimeters. That minor displacement preserves spatial resolution across a crease channel that measures 1.2 to 1.8 millimeters wide.

Signal-to-noise ratio degrades as air turbulence from the moving web disrupts the acoustic path between transducer faces. Aeroacoustic noise generated by boundary layer air shear concentrates energy below 50 kHz. Operating guided wave inspection systems between 120 kHz and 300 kHz places the measurement signal safely above aerodynamic noise floors.

Multiple signal averages cannot be captured on a moving web; inline assessment must rely on single-shot wave packet acquisitions supported by high-gain, low-noise preamplifiers. Board suppliers often claim that variations in surface gloss and moisture explain poor crease formation, asserting that natural cellulose variations make uniform acoustic scores impossible across multi-origin board lots.

Contract

Specification dockets for premium printed packaging must establish objective mechanical criteria for crease quality rather than relying on visual inspection or operator touch. Bending force ratios recorded on static bench instruments define an acceptance window, yet they fail to capture internal damage distribution. Incorporating non-destructive ultrasonic guided wave metrics into quality contracts provides unambiguous verification of die performance, sheet make-ready precision, and carton folding reliability.

When scores fail to delaminate cleanly, packing lines encounter carton bulging, out-of-square folding, and high-speed gluer jams. In beverage multi-pack cartoning and pharmaceutical packaging lines running at 600 cartons per minute, a single defective crease that resists ninety-degree folding causes carton jamming, immediate line stops, and extensive waste clearance downtime.

Acoustic Shear Tolerances in Quality Dockets

Procurement agreements governing high-volume carton conversion specify acoustic attenuation limits to ensure machinability. A robust technical specification incorporates three verifiable acoustic parameters:

• Antisymmetric transmission attenuation across every primary score line must equal or exceed 18 decibels relative to adjacent uncreased board when excited by a 150 kHz tone burst.
• Symmetric mode continuity must remain within 6 decibels of solid board values, proving that outer linerboard fibers maintain structural continuity without through-thickness rule rupture.
• Cross-directional delamination uniformity requires that measurements taken across five points along any single score line show an attenuation variance of less than 2.5 decibels.

Applying these criteria prevents converters from delivering cartons with incomplete internal ply separation. This gap stops the line.

Under DIN 55437-1 testing conditions, carton lots showing crease shear indices below the contracted tolerance limit face immediate dockside rejection without sorting allowances.

Implementing these acoustic quality gates directly impacts plant economics by eliminating downstream processing waste. The financial dynamics of die make-ready verification illustrate the ledger benefits.

Converting Downtime and Die Wear Allowances

Steel counter-die matrix channels and steel creasing rules experience progressive wear across long production runs. As matrix edges round and rule shoulders erode, the effective penetration depth and induced shear stresses decline. Crease delamination quality decays steadily across hundreds of thousands of die impressions.

Consider a representative high-speed conversion scenario running a 400-micron FBB pharmaceutical carton. Assume a production job of two million blanks processed across an eight-station platen die-cutter. Traditional quality monitoring pulls five sheets every ten thousand impressions for manual bending resistance testing using an L&W Crease Tester (ISO 2493-2).

Manual verification requires twelve minutes per check, during which the press either idles or produces unverified stock.

If creasing matrix wear reduces shear delamination below acceptable thresholds at impression 650,000, manual testing detects the drift only after thirty thousand cartons have entered the delivery stack. Those 30,000 cartons represent scrap material valued at 0.045 dollars per unit in raw board, plus 0.030 dollars per unit in pre-press printing and lamination passes, generating a direct spoilage loss of 2,250 dollars. Inline guided wave acoustic sensors eliminate that blind spot by monitoring A0 attenuation continuously across every sheet.

Die wear triggers an automated press alert the moment attenuation drops below the 18-decibel threshold.

When converters ignore guided wave acoustic verification, they incur severe commercial consequences: unseparated plies force outer liner tensile rupture during carton erection, resulting in complete truckload rejections, cancelled distribution runs, and unrecoverable downtime chargebacks from automated packaging facilities.