A new analytical model to predict bone sawing forces is presented. Development of the model was based on the concept of a single tooth sawing at a depth of cut less than the cutting edge radius. A variable friction model was incorporated as well as elastic Hertzian contact stress to determine a lower bound for the integration limits. A new high speed linear apparatus was developed to simulate cutting edge speeds encountered with sagittal and reciprocating bone saws. Orthogonal cutting experiments in bovine cortical bone were conducted for comparison to the model. A design of the experiment’s approach was utilized with linear cutting speeds between 2600 and 6200 mm/s for depths of cut between 2.5 and 10 μm. Resultant forces from the design of experiments were in the range of 8 to 11 N, with higher forces at greater depths of cut. Model predictions for resultant force magnitude were generally within one standard deviation of the measured force. However, the model consistently predicted a thrust to cutting force ratio that was greater than measured. Consequently, resultant force angles predicted by the model were generally 20 deg higher than calculated from experimental thrust and cutting force measurements.

References

References
1.
Vankipuram
,
M.
,
Kahol
,
K.
,
McLaren
,
A.
, and
Panchanathan
,
S.
, 2010, “
A Virtual Reality Simulator for Orthopedic Basic Skills: A Design and Validation
,”
J. Bio. Informat.
,
43
(
5
), pp.
661
668
.
2.
Tsai
,
M. D.
,
Hsieh
,
M. S.
, and
Tsai
,
C. H.
, 2007, “
Bone Drilling Haptic Interaction for Orthopaedic Simulator
,”
Comput. Biol. Med.
,
37
, pp.
1709
1718
.
3.
Hsieh
,
M. S.
,
Tsai
,
M. D.
, and
Yeh
,
Y. D.
, 2006, “
An Amputation Simulator With Bone Sawing Haptic Interaction
,”
Biomed. Eng. Appl. Basis Commun.
,
18
(
5
), pp.
229
236
.
4.
Ko
,
T. J.
, and
Kim
,
H. S.
, 1999, “
Mechanistic Cutting Force Model in Band Sawing
,”
Int. J. Mach. Tool Manuf.
,
39
(
8
), pp.
1185
1197
.
5.
Lannin
,
T. B.
, 2011, “
Reciprocating Bone Saw with Orbital Blade Action
,” Thesis, Dept. of Mech. Eng., Tufts University, Medford, MA.
6.
Kelly
,
M. P.
, 2011, “
Sagittal Bone Saw with Orbital Blade Action
,” Thesis, Dept. of Mech. Eng., Tufts University, Medford, MA.
7.
Pearlman
,
J. J.
, 2011, “
Cutting Velocity Effects in Bone Sawing
,” Thesis, Dept. of Mech. Eng., Tufts University, Medford, MA.
8.
Grimshaw
,
R.
, 1880, “
Saws
,”
J. Franklin Institute
,
109
(
1
), pp.
25
36
.
9.
McKenzie
,
W. M.
, 1960, “
Fundamental Aspects of the Wood Cutting Process
,”
Forest Prod. J.
,
10
(
9
), pp.
447
456
.
10.
McKenzie
,
W. M.
, 1960, “
Fundamental Analysis of the Wood Cutting Process
,” Thesis, Dept. of Wood Science and Technology, University of Michigan, Ann Arbor, MI.
11.
Merchant
,
M. E.
, 1945, “
Mechanics of the Metal Cutting Process—I. Orthogonal Cutting and a Type 2 Chip
,”
J. Appl. Phys.
,
16
(
5
), pp.
267
275
.
12.
Le-Ngoc
,
L.
, and
McCallion
,
H.
, 2000, “
A Cellular Finite Element Model for the Cutting of Softwood Across the Grain
,”
Int. J Mech. Sci.
,
42
, pp.
2283
2301
.
13.
Costes
,
J. P.
,
Ko
,
P. L.
,
Ji
,
T.
,
Deces-Petit
,
C.
, and
Altintas
,
Y.
, 2004, “
Orthogonal Cutting Mechanics of Maple: Modeling a Solid Wood-Cutting Process
,”
J. Wood Sci.
,
50
, pp.
28
34
.
14.
Thompson
,
P. J.
, 1974, “
Factors Influencing the Sawing Rate of Hard Ductile Metals During Power Hacksaw and Bandsaw Operations
,”
Metals Tech.
,
1
, pp.
437
443
.
15.
Sarwar
,
M.
, and
Thompson
,
P. J.
, 1974, “
Simulation of the Cutting Action of a Single Hacksaw Blade Tooth
,
Prod. Eng.
,
53
(
6
), pp.
195
198
.
16.
Sarwar
,
M.
,
Persson
,
M.
,
Hellbergh
,
H.
, and
Haider
,
J.
, 2009, “
Measurement of Specific Cutting Energy for Evaluating the Efficiency of Bandsawing Different Workpiece Materials
,”
Int. J. Mach. Tool Manuf.
,
49
, pp.
958
965
.
17.
Soderberg
,
S.
, and
Ahman
,
L.
, 1983, “
A Metallurgical Study of the Wear of Bandsaw Blades
,”
Wear
,
85
, pp.
11
27
.
18.
Andersson
,
C.
,
Andersson
,
M. T.
, and
Stahl
,
J.-E.
, 2001, “
Bandsawing. Part 1: Cutting Force Model Including Effects of Positional Errors, Tool Dynamics, and Wear
,”
Int. J. Mach. Tool Manuf.
,
41
, pp.
227
236
.
19.
Sarwar
,
M.
,
Persson
,
M.
,
Hellbergh
,
H.
, and
Haider
,
J.
, 2010, “
Forces, Wear Modes, and Mechanisms in Bandsawing Steel Workpieces
,”
Proc. IMechE, J. Eng. Manuf. Part B
,
224
, pp.
1655
1662
.
20.
Domblesky
,
J. P.
,
James
,
T. P.
, and
Widera
,
G. E. O.
, 2008, “
A Cutting Rate Model for Reciprocating Sawing
,”
ASME J. Manuf. Sci. Eng.
,
130
(
5
), pp.
151
157
.
21.
Jacobs
,
C. H.
,
Pope
,
M. H.
,
Berry
,
J. T.
, and
Hoaglund
,
F.
, 1974, “
A Study of the Bone Machining Process—Orthogonal Cutting
,
J. Bio. Mech.
,
7
(
2
), pp.
131
136
.
22.
Krause
,
W. R.
, 1976, “
Mechanical Effects of Orthogonal Bone Cutting
,” Ph.D. Dissertation, Clemson University, Clemson, SC.
23.
Wiggins
,
K. L.
, and
Malkin
,
S.
, 1978, ”
Orthogonal Machining of Bone
,”
J. Biomech. Eng.
,
100
, pp.
122
130
.
24.
Malak
,
S.
, and
Anderson
,
I.
, 2008, “
Orthogonal Cutting of Cancellous Bone with Application to the Harvesting of Bone Autograft
,”
Med. Eng. Phy.
,
30
, pp.
717
724
.
25.
Plaskos
,
C.
,
Hodgson
,
A. J.
, and
Cinquin
,
P.
, 2003, “
Modeling and Optimization of Bone-Cutting Forces in Orthopaedic Surgery
,
Lect. Notes Comp. Sci.
,
2878
, pp.
254
261
.
26.
Yeager
,
C.
,
Nazari
,
A.
, and
Arola
,
D.
, 2008, “
Machining of Cortical Bone: Surface Texture, Surface Integrity and Cutting Forces
”,
Mach. Sci. Technol.
,
12
, pp.
100
118
.
27.
Albrecht
,
P.
, 1960, “
New Development in the Theory of Metal-Cutting Process, Part I. The Ploughing Process in Metal Cutting
,
ASME J. Eng. Ind.
,
82
, pp.
348
357
.
28.
Basuray
,
P. K.
,
Misra
,
B. K.
, and
Lal
,
G. K.
, 1977, “
Transition from Ploughing to Cutting During Machining With Blunt Tools
,”
Wear
,
43
(
3
), pp.
341
349
.
29.
Waldorf
,
D. J.
,
DeVor
,
R. E.
, and
Kapoor
,
S. G.
, 1998, “
A Slip-Line Field for Ploughing During Orthogonal Cutting
,”
ASME J. Manuf. Sci. Eng.
,
120
(
4
), pp.
693
699
.
30.
Waldorf
,
D. J.
,
DeVor
,
R. E.
, and
Kapoor
,
S. G.
, 1999, “
An Evaluation of Ploughing Models for Orthogonal Machining
,”
ASME J. Manuf. Sci. Eng.
,
121
(
4
), pp.
550
558
.
31.
Woon
,
K. S.
,
Rahman
,
M.
,
Neo
,
K. S.
, and
Liu
,
K.
, 2008, “
The Effect of Tool Edge Radius on the Contact Phenomenon of Tool-Based Micromachining
,”
Int. J. Mach. Tools. Manuf.
,
48
, pp.
1395
1407
.
32.
Liu
,
K.
,
Li
,
X. P.
, and
Liang
,
S. Y.
, 2001, “
Modeling of Ductile Cutting of Tungsten Carbide
,”
Trans. North Am. Manuf. Res. Inst. SME
, pp.
251
258
.
33.
Liu
,
K.
,
Li
,
X .P.
, and
Liang
,
S. Y.
, 2007, “
The Mechanism of Ductile Chip Formation in Cutting Brittle Materials
,”
Int. J. Adv. Manuf. Technol.
,
33
, pp.
875
884
.
34.
Venkatachalam
,
S.
, and
Liang
,
S. Y.
, 2007, “
Effects of Ploughing Forces and Friction Coefficient in Microscale Machining
,”
Trans. ASME
,
129
, pp.
274
280
.
35.
Son
,
S. M.
,
Lim
,
H. S.
, and
Ahn
,
J. H.
, 2005, “
Effects of the Friction Coefficient on the Minimum Cutting Thickness in Micro Cutting
,”
Int. J. Mach. Tools Manuf.
,
45
, pp.
529
535
.
36.
Bhushan
,
B.
, 1999,
Principles and Applications of Tribology
,
Wiley
,
New York
, p.
369
.
37.
Johnson
,
K. L.
, 1987,
Contact Mechanics
,
Cambridge University Press
,
New York
.
38.
Shigley
,
J. E.
, and
Mischke
,
C. R.
, 1989,
Mechanical Engineering Design
,
5th ed.
,
McGraw-Hill
,
New York
.
39.
Reilly
,
D. T.
, and
Burstein
,
A. H.
, 1974, “
The Mechanical Properties of Cortical Bone
,”
J. Bone Joint Surg. Am.
,
56
, pp.
1001
1022
.
40.
Toksvig-Larsen
,
S.
,
Ryd
,
L.
, and
Lindstrand
,
A.
, 1991, “
On the Problem of Heat Generation in Bone Cutting: Studies on the Effects of Liquid Cooling
,”
J. Bone Joint Sur. Br.
,
73-B
, pp.
13
15
.
41.
Eriksson
,
A. R.
, and
Albrektsson
,
T.
, 1983, “
Temperature Threshold Levels for Heat-Induced Bone Tissue Injury: A Vital-Microscopic Study in the Rabbit
,”
J. Prosthetic Dentistry
,
50
(
1
), pp.
101
107
.
42.
Wachter
,
R.
, and
Stoll
,
P.
, 1991, “
Increase of Temperature During Osteotomy: In Vitro and In Vivo Investigations
,”
Int. J. Oral Maxillofacial Sur.
,
20
(
4
), pp.
245
249
.
43.
Krause
,
W. R.
,
Bradbury
,
D. W.
,
Kelly
,
J. E.
, and
Lunceford
E. M.
, 1982, “
Temperature Elevations in Orthopaedic Cutting Operations
,”
J. Biomech
,
15
(
4
), pp.
267
275
.
You do not currently have access to this content.