1. Mini-Seminar Dr. James Throne, Instructor
Advanced Topics in Thermoforming
Mini-Seminar Dr. James Throne, Instructor
8:00-8:50 - Technology of Sheet Heating
9:00-9:50 - Constitutive Equations Applied to Sheet Stretching
10:00-10:50 - Trimming as Mechanical Fracture

2. Mini-Seminar Advanced Topics in Thermoforming
Part 3: 10:00-10:50
Trimming as Mechanical Fracture

3. Let’s begin!

4. Mini-Seminar Advanced Topics in Thermoforming
All materials contained herein are the intellectual property of Sherwood Technologies, Inc., copyright
No material may be copied or referred to in any manner without express written consent of the copyright holder
All materials, written or oral, are the opinions of Sherwood Technologies, Inc., and James L. Throne, PhD
Neither Sherwood Technologies, Inc. nor James L. Throne, PhD are compensated in any way by companies cited in materials presented herein
Neither Sherwood Technologies, Inc., nor James L. Throne, PhD are to be held responsible for any misuse of these materials that result in injury or damage to persons or property

5. Mini-Seminar Advanced Topics in Thermoforming
This mini-seminar requires you to have a working engineering knowledge of heat transfer and stress-strain mechanics
Don’t attend if you can’t handle theory and equations
Each mini-seminar will last 50 minutes, followed by a 10-minute “bio” break
Please turn off cell phones
PowerPoint presentations are available at the end of this seminar for downloading to your memory stick

6. Mini-Seminar Advanced Topics in Thermoforming
For those concerned about hearing the plenary speaker at 1100 hours, please be assured that this mini-seminar will end promptly at 1050 hours…
And, if for some strange reason, it doesn’t, please feel free to leave…
THERE WILL BE NO FINAL!
You can download all PPTs at the end of this section

7. Part 3: Trimming as Mechanical Fracture
Outline
Fundamentals
Fracture mechanics
The mechanics of trimming
Trimming accuracy
Thin-gauge trimming
Heavy-gauge trimming

8. Part 3: Trimming as Mechanical Fracture
What is Trimming?
Trimming is semi-controlled mechanical breaking
The objective is to separate the formed part from the web, skeleton, unformed plastic around it
The methods of trimming are strongly dependent on sheet thickness
Trimming can be manual or robotic, it can take place on the mold surface or in a remote fixture

9. Part 3: Trimming as Mechanical Fracture
Traditional trimming methods
Manual - knives, serrated for foam
Routers - hand-held, table-mounted fixed-position, multi-axis
Band saws
Circular saws - stationary, hand-held small-diameter, toothless saws for foam
Abrasive wheels

10. Part 3: Trimming as Mechanical Fracture
Traditional trimming methods, cont.
Sharp-edged compression blades or dies - steel-rule, ground forged, machined
Linear shear guillotines - one-sided, two-sided
Flames
Lasers
Water jets

11. Part 3: Trimming as Mechanical Fracture
Traditional Trimming Methods

12. Part 3: Trimming as Mechanical Fracture
Mechanics of Fracture
Three general fracture modes
Mode I - tensile mode, fracture surfaces spread apart by stress
Mode II - shear mode, fracture surfaces slide perpendicular to advancing crack
Mode III - tearing mode, fracture surfaces spread by stress parallel to crack

13. Part 3: Trimming as Mechanical Fracture
Mechanics of Fracture

14. Part 3: Trimming as Mechanical Fracture
Mechanics of Fracture
Mode III is a shearing action. Guillotine cutting of heavy gauge sheet and punch-and-die cutting of thin gauge sheet are Mode III
Mode I is a compressing action. In-place trimming of thin-gauge sheet is Mode I

15. Part 3: Trimming as Mechanical Fracture
Mechanics of Fracture
Force needed to initiate a crack is substantially less than theoretical cohesive strength of polymer
Cracks initiate at flaws or defects
Consider a polymer having a small crack a in length under plane stress (Griffith crack theory)
where E is Young’s modulus and...

16. Part 3: Trimming as Mechanical Fracture
Mechanics of Fracture
G* is the fracture energy, given as G* = 2(P+g)
where P is the plastic work done during yielding,
g is the surface energy of the polymer,
Kc is the fracture toughness or stress intensity factor

17. Part 3: Trimming as Mechanical Fracture
Mechanics of Fracture
Polymers with low P/g ratios are brittle (PMMA~5)
Polymers with very high P/g ratios are ductile (vulcanized rubber ~ 500)
It is nearly always the case that the energy to initiate a fracture is far greater than that needed to sustain crack propagation

18. Part 3: Trimming as Mechanical Fracture
Mechanics of Fracture
Kc is the fracture toughness or stress intensity factor. It is written as Kc = f(s,a) or
C depends on crack geometry and surface being fractured
Polymer Kc (1000 lb/in3/2) PS
HIPS PE
PMMA

19. Part 3: Trimming as Mechanical Fracture
Mechanics of Fracture
An aside
Nanoparticles have initial sizes substantially below the Griffith crack criterion
As a result, theoretically, fracture is unlikely to initiate on a nanoparticle
Meaning that, theoretically, nano-filled polymers should have impact strengths equal to those of the polymers themselves
The functional word here is “theoretically”

20. Part 3: Trimming as Mechanical Fracture
Mechanics of Trimming
Five general mechanisms
1. Mode I
In-plane
unaxial
compression
(die-cutting)

21. Part 3: Trimming as Mechanical Fracture
Mechanics of Trimming
Five general mechanisms
2. Mode III
antiplane pure shear
(nibbling, shear cutting,
punch and die)

22. Part 3: Trimming as Mechanical Fracture
Mechanics of Trimming
Five general mechanisms
3. Abrasion or abrasive cutting (grinding, filing,buffing, water jet cutting)

23. Part 3: Trimming as Mechanical Fracture
Mechanics of Trimming
Five general mechanisms
4. Brittle tensile
fracture (routing,
drilling, sawing)

24. Part 3: Trimming as Mechanical Fracture
Mechanics of Trimming
Five general mechanisms
5. Thermal
(hot knife, hot wire,
laser cutting)

25. Part 3: Trimming as Mechanical Fracture
Trim Tolerance Limitation
Local polymer shrinkage
Polymer morphology
Time-dependent part shrinkage after trimming
Ductility of polymer
Fixture/part rigidity
Part temperature variation at trim line
Registry accuracy

26. Part 3: Trimming as Mechanical Fracture
Trim Tolerance Limitation, cont.
Trim die temperature variation
Part thickness, thickness variation
Allowable wall thickness variation at trim line
Die gap setting temperature v. trim die temperature
Clamp frame stiffness
Die flexing during trimming

27. Part 3: Trimming as Mechanical Fracture
Factors in Selecting a Trimming Technique
Sheet gauge
Part size
Number of parts
Overall draw ratio
Nonplanar nature of trim line
Cut surface roughness tolerance
Dimensional tolerance

28. Part 3: Trimming as Mechanical Fracture
Factors in Selecting a Trimming Technique, continued
Required speed of trimming
Extent of fixturing
Number of secondary operations [drilling, machining]
Skill of operator/pressman
Availability of desired trim equipment
Availability of resharpening methods

29. Part 3: Trimming as Mechanical Fracture
The mechanics of trimming depends on the sheet gauge
Thin-gauge trimming
Heavy-gauge trimming

30. Part 3: Trimming as Mechanical Fracture
Thin Gauge
Steel rule die cutting
In place, on the mold, in-situ
In machine, separate station
In line, separate machine

31. Part 3: Trimming as Mechanical Fracture
1. In-place trimming with steel-rule die

32. Thermoforming – 1. Form and in-place trimming [GN]
Part 3: Trimming as Mechanical Fracture
Thermoforming – 1. Form and in-place trimming [GN]

33. Part 3: Trimming as Mechanical Fracture
2. In-machine, usually with stacker

34. Part 3: Trimming as Mechanical Fracture
3. In-line trimming with canopy punch and die

35. Part 3: Trimming as Mechanical Fracture
Thin-gauge trimming
Primary methods
1. In-plane uniaxial compression or die-cutting
Cutting stress, s = Ee, where E is elastic tensile modulus and e is extent of strain
Solid compressibility is reciprocal of bulk modulus, B which is related to the elastic tensile modulus:
E = 3B(1-2n) where n is Poisson’s ratio, 0.3 < n < 0.4

36. Part 3: Trimming as Mechanical Fracture
Thin-gauge trimming
Primary methods
2. Mode III antiplane pure shear or punch-and-die cutting
Shearing stress, ss = Ges, where G is the modulus of rigidity or shear modulus and es is strain under shear force
Shear modulus is related to tensile modulus:
G = E/2(1+n) where n is Poisson’s ratio, 0.3 < n < 0.4

37. Part 3: Trimming as Mechanical Fracture
Thin-gauge trimming
Primary methods – Compared
Values for Poisson’s ratio
PA n=0.33 PMMA n=0.33
HDPE n=0.35 LDPE n=0.38
Average n=0.35
For average, E/G = 2.7, E/B = 0.9
Shear cutting force about 40% of that of compression cutting force (on average)

38. Part 3: Trimming as Mechanical Fracture
Thin-gauge trimming
Polymer response to compression cutting

39. Part 3: Trimming as Mechanical Fracture
Thin-gauge trimming
Polymer response to compression cutting of brittle polymers

40. Part 3: Trimming as Mechanical Fracture
Thin-gauge trimming
Compression cutting required force is function of
Trim length
Polymer type
Polymer temperature
Trim die temperature
Sharpness of die
General equation:
F (force/unit length of trim) =
a + b (polymer thickness)

41. Part 3: Trimming as Mechanical Fracture
Thin-gauge trimming
Various steel rule die designs
Curve D is for dulled version of cutter B
RPVC PS

42. Part 3: Trimming as Mechanical Fracture
Thin-gauge trimming- 1
Steel rule die cutting force as function of cutter temperature, F = a + b(tk)

43. Part 3: Trimming as Mechanical Fracture
Thin-gauge trimming- 2
Steel rule die cutting force as function of cutter temperature, F = a + b(tk)

44. Part 3: Trimming as Mechanical Fracture
Thin-gauge trimming- 1
Steel rule die cutting force as function of sheet thickness, cutter temp = 20oC, F = a + b(tk)

45. Part 3: Trimming as Mechanical Fracture
Thin-gauge trimming- 2
Steel rule die cutting force as function of sheet thickness, cutter temp = 20oC, F = a + b(tk)
competitive packaging polymers

46. Part 3: Trimming as Mechanical Fracture

47. Part 3: Trimming as Mechanical Fracture
Thin-gauge trimming -Example
Calculate the force required to die-cut 10-in x 10-in trays, 9-up from 40 mil sheet of a) HIPS, b) PET
Trim length- 4 x 10 x 9 = 360 inches
a) HIPS lbf/in x 360 = 20,304 lbf = 10 tons
b) PET lbf/in x 360 = 30,924 lbf = 15.5 tons

48. Part 3: Trimming as Mechanical Fracture
Heavy-gauge trimming
Hand-trimming using saws, routers
Automated, programmable multiaxial routers that include saws, drills

49. Part 3: Trimming as Mechanical Fracture
Heavy-gauge trimming
Within the past decade, CNC-driven multi-axis routers, borrowed from the woodworking industry, have become standard fare for high quality part production in heavy-gauge forming.
5-axis router - Quintax

50. Part 3: Trimming as Mechanical Fracture
Heavy-gauge trimming
“Three-Dimensional Trimming & Machining - The Five Axis CNC Router”, K.J. Susnajara, Thermwood Corporation, 1999
Contents
Machine Basics
CNC Router Design
Holding the Part
Tooling
Programming
Accuracy
Economics

51. Part 3: Trimming as Mechanical Fracture Accuracy
Heavy-gauge trimming
First Layer
Single v. multiple axis repeatability
Absolute positioning accuracy - Single v. multiple axis
Loaded v. unloaded repeatability, accuracy
Machine considerations
Lead screw backlash
Rotary resolution of servomotor
Encoder resolution and stepping interval
Rail linearity
Machine alignment [square and perpendicular]

52. Part 3: Trimming as Mechanical Fracture Accuracy
Heavy-gauge trimming
First Layer
Machine Design
Lead screw backlash
Rotary resolution of servomotor
Encoder resolution and stepping interval
Rail linearity
Machine alignment [square and perpendicular]
Head alignment - effect of crashes
Head worm spur gear tooth accuracy, backlash

53. Part 3: Trimming as Mechanical Fracture Accuracy
Heavy-gauge trimming
Second Layer
Servo System Tracking
Inertia during acceleration, deceleration
Vibration, push-off, flexing
Speed
Tool length accuracy
Tool-to-collet tightening
CAD/CAM interpretation of curves [splines]
Trimming of part v. computer trim path

54. Part 3: Trimming as Mechanical Fracture Accuracy
Heavy-gauge trimming
Third Layer
Overall part size variability
Molding temperature
Raw material formulation
Cooling characteristics
Polymer flexing under trim load
Bridge flexing during carriage movement
Dynamic flexing and bending v. speed
Polymer reaction to push-off
Bending, flexing of tool under load

55. Part 3: Trimming as Mechanical Fracture Accuracy
Heavy-gauge trimming
Third Layer
Thermal exansion, contraction
Different materials in router
Polymers being trimmed
Tool dimensional change during trimming
Polymer warping, distortion during trimming
Trim direction v. “grain” in polymer

56. Part 3: Trimming as Mechanical Fracture Accuracy
Heavy-gauge trimming
Conclusion - Repeating an accurate position in space is far easier than achieving that accurate position in space.

57. Part 3: Trimming as Mechanical Fracture
Heavy-gauge trimming
The mechanics of chip-breaking
[Saws, drills,
routers, mills]
Chip
Cutter
Work

58. Part 3: Trimming as Mechanical Fracture
Heavy-gauge trimming
Factors Affecting Cutting Characteristics of Plastics

59. Part 3: Trimming as Mechanical Fracture
Heavy-gauge trimming
Multiple Edged Tool Cutting

60. Part 3: Trimming as Mechanical Fracture
Heavy-gauge trimming
Multiple Edged Tool Cutting
Tooth depth of cut, g is:
g = V p sin f/U
V is the feed rate, p is the tooth spacing, U is the peripheral blade speed, U=pDN, D is the diameter of the cutting blade, N is the blade speed (RPM).

61. Part 3: Trimming as Mechanical Fracture
Heavy-gauge trimming
Multiple Edged Tool Cutting
The angle f is given as
f = cos-1 [(h-b/2)/R]
where h is the cut-off height or distance between the saw centerline and the bottom of the plastic sheet, b is the sheet thickness, R is the saw radius, R = D/2

62. Part 3: Trimming as Mechanical Fracture
Heavy-gauge trimming
Multiple Edged Tool Cutting
Feed rate, V, proportional to blade speed, N, and diameter, D
Feed rate, V, inversely proportional to tooth spacing, p
[Arithmetic holds for multiple-edge routers as well]

63. Part 3: Trimming as Mechanical Fracture
Heavy-gauge trimming
Drilling

64. Part 3: Trimming as Mechanical Fracture
Heavy-gauge trimming
Drilling
Depth of cut per drill tooth, d:
d = (s/n) sin q/2 = (V/nN) sin q/2
n is number of teeth on drill (one or two), N is the drill speed, V is the axial feed rate, s is drill feed speed, s = V/N, and q is the point tooth angle

65. Part 3: Trimming as Mechanical Fracture
Heavy-gauge trimming
Effect of Drill Geometry on Drilling Conditions
Drill Parameter Drill Condition
Point angle Rotational drill speed
Rake angle Drill feeding speed
Relief angle Work temperature
Helix angle Cooling provisions
Shape of flutes Nature of the hole

66. Part 3: Trimming as Mechanical Fracture
End of
Part 3
Trimming as
Mechanical Fracture

67. Part 3: Trimming as Mechanical Fracture
End of
Mini-Seminar
Advanced Topics in Thermoforming

68. Advanced Topics in Thermoforming
Mini-Seminar
Advanced Topics in Thermoforming
THANK YOU FOR YOUR ATTENTION!