Mechanics of Creping in Tissue Making

Kui Pan A. Srikantha Phani & Sheldon Green

Department of Mechanical EngineeringUniversity of British Columbia, Vancouver, BC

Outline

Background

Research Objectives

Methodology and Results

Conclusion

2

Background

Research Objectives

Methodology and Results

Conclusion

3

H.F. Jang, FPI, 2013SEM cross-sectional image of tissue

Schematic of tissue structure

𝜆2𝐴

Wavelength: 𝜆 ~ 0.3mmAmplitude: A ~ 0.1mm

Creping Influences Tissue Properties

Creping: a de-densification process

MD: machine direction; CD: cross direction.

Before

After

Dry-Creping Process

DoctorBlade

CleaningBlade

Adhesive Spray Nozzle

Felt

PressureRoll

Wet Web

DryerHoods

DryerHoods

Reel

Yankee DryerDiameter ~3m

Velocity~1500 m/minCrepedTissue

20℃, SC: ~20%

SC: ~40%

100℃, SC: ~94%

𝑉𝑖𝑛

𝑉𝑜𝑢𝑡

Crepe Ratio=𝑉𝑖𝑛−𝑉𝑜𝑢𝑡

𝑉𝑖𝑛

SC: solid content

4

5

Creping Regimes

W. McConnel, The science of creping. 2004.

√

Governing Parameters Typical Control Parameters: Yankee surface speed

𝑉𝑖𝑛(1000~2000𝑚/𝑚𝑖𝑛)

Creping angle 𝛿 (80°~100°)

Crepe ratio 𝑉𝑖𝑛−𝑉𝑜𝑢𝑡

𝑉𝑖𝑛(10%~30%)

Adhesion 𝐺𝑐 (50~400 𝑁/𝑚)

Blade Friction (0.25~0.35)

Current situation: trial and error.

Fundamental study is necessary.Guide the choice of adhesive chemicals,process parameters, blade type and so forth.

𝛿: Creping angle

𝑉𝑖𝑛

𝑉𝑜𝑢𝑡

𝛿

Crepe Ratio=𝑉𝑖𝑛−𝑉𝑜𝑢𝑡

𝑉𝑖𝑛

quality, runnability and productivity

6

Creping Mechanism

Micro-fold to Macro-fold Transition

High Speed Imaging Study

Limited surface speed: 140 m/minNo further validation about the mechanism.

H. Hollmark, STFI 1972

7

Creping ratio: 32%

Outline

Background

Research Objectives

Methodology and Results

Conclusion

8

Research Objectives

Experiments:

Observe the creping process under high speed to reveal relevant

phenomenon and understand the mechanism.

Modeling:

Develop mechanistic creping model to study the effects of process

parameters (adhesion, creping angle…) and dynamic effects (creping ratio,

surface velocity…) on tissue structure.

9

Outline

10

Background

Research Objectives

Methodology and Results

Conclusion

Methodology: High speed imaging

11Goal: reveal creping mechanism at high speed

Creping testing rig based on Lathe

Edge-on view of set-up

12

Laser informationPower: 500mW; Fan angle: 5°;Length: 20mm; Thickness: 0.1mm.

Disk informationRadius: 89mm; 𝜔𝑚𝑎𝑥: 1500 rpm;Maximum surface speed: 838 m/min.

Doctor bladeCreping angle 𝛿: adjustable;Blade thickness: 1.2 mm.

𝛿

Surface speed: 𝑉𝑖𝑛=217 m/min

Creping angle 𝛿 =45°

No creping ratio: 𝑉𝑜𝑢𝑡 ≈ 0

Micro-fold to macro-fold transition is observed.

Creping Video

13

1 mm

45°

1 mm

Increase Creping Angle

14

Surface speed: 𝑉𝑖𝑛=195 m/min

Creping angle 𝛿 = 90°

No creping ratio: 𝑉𝑜𝑢𝑡 ≈ 0

Transition mechanism still exists, when we increase creping angle.

90°

1 mm

Creping Ratio by Hand Pulling

15

Surface speed: 𝑉𝑖𝑛=217 m/min

Creping angle 𝛿 = 90°

Creping ratio: 𝑉𝑖𝑛−𝑉𝑜𝑢𝑡

𝑉𝑖𝑛≈ 25%

Micro-fold to macro-fold transition disappeared Indicating creping ratio is important.

1 mm

𝑉𝑖𝑛𝑉𝑜𝑢𝑡

16

Summary of Current Experiment

Lathe creping experiment

Relative high speed 800 m/min; System is stable;Creping process is clearly recorded;Verified micro-fold to macro-fold transition mechanism.

Limitations: Creping ratio not well-controlled; Non-uniform adhesion.

17

Yankee

web adhesive

CZM CZM CZM

web

adhesive

Methodology: Discrete Particle Model

Particle’s mass: 𝑀 = 𝜌𝑎0ℎ𝑤.

ℎ is thickness, w is width of paper, 𝑎0 is initial spacing, 휂𝑎 is damping coefficient,𝑘𝑎 is axial stiffness.

axial elastic force : 𝒇𝑎 = 𝑘𝑎 𝒓𝑖−1 − 𝒓𝑖 − 𝑎0 𝒆𝑖,𝑖−1 + 𝑘𝑎 𝒓𝑖+1 − 𝒓𝑖 − 𝑎0 𝒆𝑖,𝑖+1damping force: 𝒇𝑑 = −휂𝑎 𝒓𝑖 − 𝒓𝑖−1 ∙ 𝒆𝑖,𝑖−1 𝒆𝑖,𝑖−1 − 휂𝑎 𝒓𝑖 − 𝒓𝑖+1 ∙ 𝒆𝑖,𝑖+1 𝒆𝑖,𝑖+1

bending force and viscous bending force: 𝒇𝑏 , 𝒇𝑣

Spring damper coefficients are related to paper layer properties.

𝛿

𝑖

𝑖 𝑖+1

𝑖+1

𝒇𝑐

𝒇

18

traction vs. separation

Nonlinearsprings

Yankee

web

D. Xie, A.M. Wass, Engng. Fract. Mech., 2006

Normal tractionShear traction

Cohesive Zone Model

Cohesive force applied on particle: 𝒇𝑐 = −𝜎𝑎0𝑤𝒆 − 𝜏𝑎0𝑤𝒆

𝒆 and 𝒆 : normal and tangential unit vectors

𝜎𝑐: normal strength; 𝜏𝑐: shear strength;𝐺𝐼𝐶: mode I fracture toughness; 𝐺𝐼𝐼𝐶: mode II fracture toughness. (adhesion)

CZM parameters are related to adhesive layer properties.

Newton’s equations ∶ 𝒇𝑡𝑜𝑡 = 𝒇𝑎 + 𝒇𝑑 + 𝒇𝑏 + 𝒇𝑣 + 𝒇𝑐 = 𝑀𝒂

A

B

C

𝑑𝑡: threshold distance. 𝑑𝑡 = ℎ/100.

When 𝑑𝑠>= 𝑑𝑡, no contact force 𝐹𝑐1 = 0.

When 𝑑𝑠 < 𝑑𝑡,

New function: 𝐹𝑐1 = α[𝑒𝛽

𝑑𝑠 −1]. 𝛼, 𝛽 are constants

𝑑𝑡

𝑑𝑠𝐹𝑐1

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10

1000

2000

3000

4000

5000

6000

7000

8000

9000

ds/h

Fc

Self-Contact Model

Motivation:

19

8 8.5 9 9.5 10 10.5 11 11.5 120

1

2

3

4

5

6

7

8

x/h

Deflection

/h

8.5 9 9.5 10 10.5 11 11.50

1

2

3

4

5

6

7

8

x/h

Deflection

/h

No self-contact Include self-contact

𝐿

𝐿′

∆𝐿 = 𝐿 − 𝐿′ = 0.87𝐿

Self-Contact Model

20

휀∗ = 𝜋2ℎ2 12𝑎2

maximum deflection:

휁 = ℎ4

3

휀0휀∗− 1

The experimental data comes from: “Atomic force microscopy of in situ deformed nickelThin films”, C. Coupeau et. al., 1999, Thin Solid Films.

휁

Validation of Model

Buckle-delamination

21

Creping Simulation

Schematic of creping model

𝑉 is Yankee surface speed, 𝛿 is creping angle.

22

Radius of Yankee (~1.5𝑚) ≫ Paper thickness (~0.1𝑚𝑚)Surface can be considered as flat

Single Fold Simulation

23

𝑉 = 1200𝑚/𝑚𝑖𝑛, 𝛿 = 80°.

Single Fold Simulation

Three stages: delamination propagation (Mode I) buckle initiation; buckling-driven delamination. (Mixed-mode)

24

Mixed-mode fracture toughness

0 5 10 15 20 25

2.5

3

3.5

4

4.5

Mixed-mode GIIC

/GIC

Wavele

ngth

/h

0 5 10 15 20 252800

2850

2900

2950

3000

3050

Mixed-mode GIIC

/GIC

Cre

pin

g F

orc

e (

N/m

)

(a) (b)

𝐺𝐼𝐶 is varied to change the mixed-mode.

Creping wavelength is dependent on both

𝐺𝐼𝐶 and 𝐺𝐼𝐼𝐶;

Creping force is determined by 𝐺𝐼𝐼𝐶 .

𝜎

𝜎𝑐

𝛿𝑐 𝛿𝑚

𝛿

𝐺𝐼

𝐺𝐼𝑐

𝐺𝐼𝐼

𝐺𝐼𝐼𝑐

𝜏

𝜏𝑐

0 0 𝑐 𝑚

(a) (b)

25

Periodic Folding Simulation

FFT analysis:𝜆 = 0.35𝑚𝑚𝐴 = 0.052𝑚𝑚

26Schematic of tissue structure

𝜆2𝐴

Wavelength: 𝜆 ~ 0.3mmAmplitude: A ~ 0.1mm

Creping angle: 85°;V_in=20m/s;

V_out=0.7*V_in

Creping angle: 85°; V_in=20m/s; V_out=0

A few micro-folds evolve into a macro-fold.

Self-Contact Simulation

27

Parametric Study

28

Larger modulus results in larger creping wavelength; Larger adhesion results in smaller creping wavelength.

29

Limitation of Current Model

Currently one-dimensional model.

Plastic deformation of fiber is not included.

Outline

Background

Research Objectives

Methodology and Results

Conclusion

31

Conclusion

31

Lathe creping experimentRelative high speed 800 m/min; System is stable;Clear view of creping process;Micro-fold to macro-fold transition mechanism is verified and it is found to be affected by creping ratio.

Conclusion

32

Discrete particle model has been developed.One-dimensional dynamic, creping-ratio included.Process parameters included.

Simulation of creping process.Single fold formation shows three typical stages.The periodic creping process is successfully simulatedand simulation results are close to experimental values.

Parametric studies.Effects of modulus, adhesion, and creping angle. Need to be compared with experimental data.

Future Work

33

Extend current model to microscopic level to account forfiber properties and explosive bulk.

Pilot Tissue Machine, FPInnovations, Montreal.

Maximum Yankee surface speed: 1500 m/min;Able to process parameters and furnish. 34

Future WorkCompare simulations with experimental data from

commercial machine.

Thank you!

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