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A study of the bone machining process—Orthogonal cutting
.4 STUDY OF THE BONE MACHINING ORTHOGONAL CUTTING*
PROCESS-
C. H. JACOBS?. M. H. POPE:. J. T. BERRY$and F. HOAGLCSD UniLersitk of Vermont. Burlington. Vermont 05401. U.S.;\ Abstract--Thee appears to be no record of any orthogonal cutting anal>& of bone in the literature. although many surgical procedures using cutting tools are performed ever) da>. This paper describes a series of two-component cutting dynamometer experiments at constant speed using bovine bone as the workpiece for an orthogonal cutting analysis. The bone samples were taken from the mid-diaphysis of bovine tibiae and \\cre cut in three mutually perpendicular directions: across. parallel and transverse to the preferred osteon direction. Microscopic and SEM photographs are presented detailing ths tivc different chip types categorized b) the authors. Precutting (i.e. plastic deformation) studies were conducted and A theor) for precutting bchaxior based on hydroxyapatite crystallite interlocking is postulated. The Merchant analysis of orthogonal cutting is shokvn to ha\c limited applicability to bone material.
1. IKTRODUCTIOS
Since the early Lvork of Wertheim (1517) and Rauber (1576) and others. many studies have been made of the mechanical properties of bone substance. These have been well summarized by Evans (1964) and Kraus ( 1967). In view of the importance of machining bone in many operative procedures. particularly in orthopaedies. it is perhaps surprising that little work has been done in investigating the basic niechanisms involved in the bone machining process. Other aspects of the problem have been studied. for example: Orell(1959) investigated the cooling of bone drills and saws whilst Bowden (1955) and Thompson i 1958) have looked at metallic transfer in drilling. More recently Costich i 196-l) investigated high speed drilling instruments and Moss (1964) performed the first thermal necrosis study. Most of this tvork dealt Lvith dental drills (which rotate at a considerably higher speed than orthopaedic drills) and tooth substance, rather than bone. Brooks (1970) investigated stress concentration effects in drilled holes and found that a single hole can reduce overall bone strength by 30 per cent. Burstein’s (1972) recent work shotved the relationship between drilled holes, screws and breaking strength. Perhaps bvas that of research the most significant Matthews and Hirsch (1972) who. for the first time. established a basis for thermal necrosis of bone. These * Receicrd 17 September 1973. t M.S.M.E.. Department of Mechanical Engineering. : Ph.D.. Departments of Orthopaedic Surgery and Mechanical Engineering. P Ph.D.. Department of hlechanical Engineering. M.D.. Department of Orthopaedic Surgery.
workers shotved that the very high local increase of temperature present in drilling can destroy bone cell viabilit! in the area surrounding a hole. In view of the potential for cell damage and microcrack (Pope. 1972) formation there was obviously a need to optimize machining parameters. The study reported herein attempts to establish the basic mechanisms operative during the orthogonal cutting process and to optimize the parameters, The orthogonal cutting process has been chosen since it is fundamental to all other machining processes (drilling, tapping. sawing, etc.).
2.
SPECI\IESS
A.SD PREP.ARhTION
The specimens were taken from mature bovine tibiae, with a high content of haversian. rather than plexiform. bone. The tibiae were obtained from a local abbatoir immediately following slaughter. For the orthogonal machining tests rectangular specimens approximately 0.019 x 0.038 x 0.0076 m were cut out in three mutually perpendicular directions: from the middiaphysis of the bone: across, parallel and transverse to the preferred osteon direction (Fig. 1). The samples were kept frozen (- IO’C) and when used were kept immersed in lactated Krebs-Ringers solution. following the guidelines previously established by Sedlin and Hirsch (1966). 3. PRECLTTISG
STUDIES
The initial contact of anl; cutting tool with a specimen results in a deflection of the workpiece without rupture. Most cutting studies have ignored this stage 131
C. H. J.ACOBS.$1. H. POPE. J. T. BERRY and F. HOAGLUND
Inltlal‘
where cutting had taken place. This probably represented the effects of the high residual tensile stresses from the tool (Ramalingam, 1967). The identification of a ‘shear plane’ in this manner is of interest since a similar zone has been identified in continuous chip formation in orthogonal metal cutting viz.Merchant (1945) and Piispanen (1948).
lndentotion -L
Tool
Bone
3.2 Plastic beharior
removed
pollwed
to remove
Collagen itores length
swath the
Fiy. I. Precutting
return
deformatton
/
to orlginol
removal
behavior
of OHAP
of bone.
with the rationale that the cutting edge produces a stress concentration factor that will put the contact stress above the strength of the material. McKenzie (1960), in his wood-cutting studies, found that this stage is negligible only with very sharp tools and high rake angles. This conclusion is shared by the present authors on their work with bone substance. For example, in cutting parallel to the osteon orientation it has been found in some cases that indentation becomes so pronounced that very high tensile stresses are produced parallel to the osteon directions. The net result is the fracture characterized by the authors as type V which is due to failure in tension across the fibers. The following work attempts to investigate this behavior in more detail.
Burstein et nl. (1972) have recently pointed out the significance of the so-called plastic deformation in bone substance. It was also noted that much of the deformation is such that when the load is released, the deformation will return to zero as a function of time. This behavior is consistent with the model of bone as proposed by Sedlin (1965). To investigate the plastic phenomenon and its limitation when applied to orthogonal cutting, the experimental arrangement as shown in Fig. 3 was utilized. The sample of bone was held in a vise with the direction of the osteons parallel to the direction of cutting tool travel. The crosshead was moved down to a point where no cutting had occurred but a permanent deformation could be recognized. The specimens were then polished and decalcified (2’; HNOJ for 24 hr. then dewatered with ethanol). After the decalcification procedure it was noted that a mirror image of the deformed surface was formed, i.e. the surface at the point of tool contact was distinctly raised above the surrounding surface. This phenomenon can be explained if one considers the deformation to be ‘locked’ into the matrix perhaps by interactions of the hydroxyapatite (OHAp) crystals that are dispersed along the collagen fibres. It would appear that the first stage of plastic deformation in orthogonal cutting is recoverable and can be attributed to the prefailure behavior of the mucopolysaccharide. The second stage, which is a permanent deformation, is due to OHAp interactions. 4. CUI-IINC
STUDIES
3.1 Prefiihli-e beharior
4.1 Equipment
To investigate prefailure behavior cuts were made in a bone sample parallel to the preferred osteon direction. The cuts were stopped before they were completed and the sample was then polished in the plane of the chip and stained with basic fuchin. Staining was evident in the chip. terminating in a ‘shear plane’ along’ the chip root from tool tip to workpiece surface (Fig. 2). The damage suffered by the chip is indicative of stress of @7 tf (failure stress) or above. (It has previously been established that increased permeability occurred at stresses of this order (Pope, 1972)) There was also a thin layer of stained material on the surface
The orthogonal cutting was done on a Brown and Sharpe No. 2 milling machine (Fig. 4) with a fixed ground double ended tool composed of AISI M2 molybdenum high-speed steel with available rake angles of - 5, 0, 15, 35 and 45 degrees. Force measurements were made with a Cook, Smith and Associates Two-Component Milling Dynometer using a San-Ei type 6L4 Strain Amplifier and Dixon Visigraph-P Oscillograph as indicating and recording instruments respectively. These instruments were calibrated using dead weights and showed a linear input/output relation for the applied loads.
Fi*=. -1 1 Fig. 3.
Fig 6. Type I chip (B.T.O.) Fio. _ 7. Type II chip (B.T.O.)
j. 1600. 100.
Fig. 8. T>pz it1 chip (B.T.O.)
.. 1000.
Fig. 9. Type
‘.: 1000.
IV chip @.A.O.j
Fig. 10. Type V chip (B.P.O.)
x250.
.A stud>
of the bone
machming
1:;
process
4.3 Renrlts
Sample size variation was a difficult) bvhen anal!+ ing bone data. Therefore all tabulated force values for the three materials used are shown for a theoretical piece of material 0.234 m in width. Thar is, the force value measured on the oscillograph tracings was divided by the sample width to allow for a uniform base of comparison. The force values are shown in Fig. 5.
+=I *x
cut paroilei to osteone (8. P 01
Bane
5. I Mechanics Bone cut
transverse (B.T.0. I
.3one c9t ( B.A.0 )
across
osteone
** Fig. -1.
I. .~S.+LFSIS
** Preferred * Cvttlng
oste0r.e
to
3steone dlrection
drrectror
Schematic ofcutting sample locations from 3 axes.
4.2 Procedures As stated, samples were cut from the three mutually perpendicular axes of the bone, thereby enabling cutting data to be obtained parallel, perpendicular and transverse to the predominant osteon directionality. After the samples were prepared and placed in the dynamometer they were all cut at a constant velocity of O-47m/min (18-35 in/mint using the various angIes available and at the foIlowing depths of cut: I2. 24, 36, 43 x 10e6m. As the samples were cut the oscillograph recorded deflections indicative of the horizontal and vertical forces acting to cut the material. These deflections were then measured and evaluated using the pre-established calibration curves. The resultant chip thickness was measured using a standard micrometer and was recorded along with horizontal and vertical forces, cutting velocity, depth of cut and tool rake angle for analysis. As is evident from the literature there are some elastic elements functioning in bone tissue and for this reason and because no other cutting theory for bone exists, the Merchant analysis was used to analyse the data. The chips were collected and at various magnifications using ordinary light microscopy and scanning electron microscopy (SEAL). Chips were prepared for the S.E.M. by sputtering with carbon followed by gold palladium.
OF THE CLmiNG
PROCESS
of rhe process
Ttvo factors. the anisotropy of bone substance and the change of variables in the cutting tests. resulted in substantial changes in the chip types from the diffkent tests. In all. five different
chip types iyere identified.
S.E.M.‘s of these chip forms are shown in Figs. 6-10 and are tabulated in Table L. The t>-pe I chip was a smooth. curved chip, that was formed at low depths of cut and high rake angles (I) in all cutting directions. It is thought that there was little precutting deformation due, in part, to the low resisting forces and partly due to the high tool rake angle. This particular cutting situation most closely represented rhat suggested in classical Merchant theory. The t>pe II chip was a smooth to fairly smooth Hat chip with little break up. It was seen with low depths of cut and low angles in the across osteon and parallel to the fiber (osteon) directions. In this case it is thought that there was more precutting deformation due to a *BOG lBT.0.
17co
,,/’ 5
,y
3.T.0.
:5
35
II 3c
coo
;
900
:2 d r z i 0
800 7;o
6OC 500 COO I 330 i 130 4 230 0
6
iz
24
Depth of cut, direction
r9
m )(8:“
cutting force for bovine and rake angle r~ depth of cut).
Fig. 5. Measured mean resultant bone (cuttine
36
C.
134
H. J.ACOBS.M.
H. POPE.J. T. BERRYand F. HO.AGLLSD
Fig. I I. Artist’s rendition of cutting done transverse-the predominant osteon direction.
Fig. 12. Artist’s rendition of cutting bone across-the dominant osteon direction.
tool resulting in a more compressed (and fatter) chip of inferior surface quality to the type I. The type III chip was seen exclusively during cutting transverse to theosteon where the depth ofcut was high or when the rake angle was low. The type III form was a very segmented chip. At best (high depth of cut, low I) it leas a very ragged. segmented chip and at worse it was almost a pile of fiber-like material (Fig. 11). Due to the low interosteon strength cracks also exist between the osteons. Maj and Toajari (1937) were probably the first to point out that failures tend to be parallel to the predominant direction of the fibrous matrix of the bone. Values of fracture energy now available show that it is energetically favorable for bone to break in a longitudinal. rather than a transverse, direction. It was found that there is a preference in bone for the crack to propagate beuvsen the osteons. thus indicating the existence ofa weak interface between the osteons. This is because the boundaries between osteons are not crossed by collagen fibers and because the cementing substance (mucopolysacchnride) is much weaker than collagen.
The type IV chip was seen in cutting across the osteons. Again. the chip type probably resulted from osteon deflection before rupture and the segmented nature of the chip was due to the low interosteon strength (Fig. 12). The type V chip was obtained in cutting parallel to the osteons. It \vas seen at high depths of cut. Essentially it was a series of fractures with the crack running ahead of the cutter and the resultant chip breaking as a cantilever beam (Fig. 13).As 1 was decreased the chip became rougher due to the more severe precutting deformation.
‘blunter’
pre-
5.2 Prediction of cutting forces
The IMerchant analysis (1945) is concerned with the geometric relationships existing between the forces in
Table 1. Chip types for various cutting conditions Cutting direction
Depth of cut
BTO
High Low High Low High Low
B.40 BP0
Chip type Large Small 1 I III I IV I V I
III III IV II V II
Fig. 13. Artist’s rendition of cutting bone parallel-the dominant osteon direction.
pre-
A srudl; of the bone machining process
the shear zone. on the tool face and those normally measured during cutting (using dynamometers). The measured quantities are horizontal and vertical cutting force and chip thickness. Other parameters, normally held constant. are the tool rake angle, depth of cut and the cutting speed. The horizontal cutting force can be shown to be: P, =
where: 5,) = j? = x= 0 = b= r= ;i =
r,bt cos(p - 3) sm 4 cos(qb + b - 2)
shear stress at failure on the shear zone friction angle = arc tan p tool rake angle shear plane angle work piece width nominal chip thickness (depth of cut) friction coefficient between tool face and chip.
Appropriate values for the shear stress (rO) can be obtained from the work of Crowninshield (1972) and Evans I 1964). It is of importance to note that not only must the value selected be appropriate to the strain exhibited at the shear zone, it must also be appropriate to the strain rate and mean temperature. Because the cutting tool was ground but not polished. a value for ~1(from which B is derived) was taken to be equal to 0.75. i.e. ‘sticking friction’. This value for p is within the values calculated from experimental data. Tool rake angle (I) and depth of cut (t) values are as shown in Table 1. (Sample width is 0.254 m.) The shear plane angle (4) was derived using the Ernst->lerchant relationship (Alexander and Brewer, 1963): ?I$ + p - 1 = 90’ which permits some elastic behavior in the workpiece and is based upon work minimization in the cutting (Appendix A is a sample calculation of the horizontal cutting force). It is apparent from the calculation in Appendix A and the comparison of theoretical results with experimental results in Table 2 that there is limited agreement. Table 2 Curling direction
Depth of cut ( tom6 m)
angle
Rake
BAO BTO BP0
12 12 I).
15’ 15’ 15’
P,’
p,+
34s 616 260
252 252 252
* Horizontal Force (Experimental, Nm x lo-‘). + Horizontal Force (Theoretical. N,‘m x lo-‘).
135
The agreement existing between measured and predicted tool forces depends. at least in part. upon orientation. reflecting the anisotropy of bone and also the general insensitivity to this effect inherent in Merchant’s theory. 6. GENERALDISCCSSIOShED COSCLCSIONS Currently available metal cutting theories would lead to the exclusive use of high rake angle tools if cutting forces were to be minimized and if tool wear and replacement costs were of no importance. Since this is contrary to current surgical practice the findings of this study merit careful examination. However. such theories are of assistance in the understanding of bone machining since the experimental dynamometry techniques used to develop them are excellent for evaluating the cutting forces. It has been shown that the classic Merchant analysis gives some limited agreement between the predicted cutting forces and the experimental results. This is because the Merchant analysis assumes an isotropic material which shears in a planar fashion. Bone is, of course. markedly anisotropic and its failure mechanisms in cutting clearly demonstrates this. Furthermore. we have no exact knoa-ledge of strain rates and temperature fields occuring in cutting bone. This must be at hand before a theory appropriate to an anisotropic medium can be developed. However, it should be noted that many surgical cutting operations upon bone substance embrace an ‘averaging’ of cutting in several different directions. Consequently, the above calculations using the Merchant theory- should provide good general guidance in tool design. Finally, it is appropriate to note that cutting speed, which in turn affects strain rate. temperature and therefore flow stress, was not one of the variable parameters in the current investigation; due to available equipment constraints. Cutting speed would normally be expected to affect cutting forces and thus will be studied in future experimental work. In addition to these effects. cutting speed (i.e. strain rate) can also effect crack propagation. indeed there is evidence due to Piekarski (1970) that crack initiation energy is decreased significantly by an increase in strain rate. One of the present authors has also indicated a similar trend for fracture energy (Pope, 1972). Consequently an increased cutting speed might lead to a change in mode of failure in the so-called stress zone, as well as a change in cutting energy requirements. The exact nature of the total energy requirement change is difficult to envisage since an increased strain rate would normally involve increased stress energy on one hand. while on the other it would
136
C.
H.
JACOBS. M. H. POPE. J. T. BERRY
lead to a decreased energy requirement if cracking or spIitting in the stress zone became the dominant failure mode. In conclusion, the practical application of the present work is a defence for the use of truly sharpened tools for orthopaedic surgery. tinder the experimental conditions studied cutting forces can be markedly decreased when using tools with rake angles on the order of 45’. This recommendation is diametrically opposed to that of Ekchtol (1959). It is understood that Bethtol’s manufacturing guidelines are currently being followed for orthopaedic drill manufacture. These guidelines recommend drill rake angles of zero degrees or slightly negative. Currently work is being performed at the University of Vermont to determine what the optimum combination of tool rake angle geometry and
cutting speed should be in orthopaedic
drills.
Acknowledgements-The authors would like to rake this opportunity to thank those individuals without whose assistance this project would not have been possible: The Society of Manufacturing Engineers, Mr. D. Cheng. Professor B. F. von Turkovich, The Orthopaedic Research Education Foundation and certain others who shall remain anonymous. Our special thanks to Mrs. K. Hoyt for her perseverance in preparing this manuscript. REFERESCES
Burstein, A. H., Currey, J., Frankel. V. H., Heiple, K. G.. Lunseth. P. and Vesselv. J. C. (1972) Bone strennth. The effect of’screw holes. J.-bone J~nf Surg. 54-A, 1l&l 156. Burstein, A. H., Cutrey, J. D., Frankel, V. H. and Reilly, D. T. (1972) The ultimate properties of bone tissue: the effects of yielding. J. Biomechanics ql), 3>45. Costich, E. R.. Youngblood, P. and Walden, J. M. (1964) A study of high speed rotary instruments on bone repair in dogs. Oral Mrd. Ural Path. 17, j63-571. Crowninshield, R. D. (1973) The response of anisotropic bone to tensile impact. LVevew England Bioengineering Conference. Burlington, Vermont. Evans, F. G. (1964) Significant differences in the tensile strength of adult human compact bone. Proc. Isr European Bone and loozh Symp., pp. 319-331. Pergamon Press, Oxford.
and F.
HO.AGLGSD
Kraus, H. (1967) On the mechanical properties of human compact bone. .ddcances in Biomed. Engng Xed. Phys. Maj, E. and Toajoari, E. (1937) La resistanza meccanica del tessuto oseeo lamellare compatto misurata on varie direzioni. Bo[l. Sot. ftal. BioL Sper. 12. 83. Matthews. L. S. and Hirsch C. (1974) Temperatures measured in human cortical bone when drilled. J. Bone Jnr Sury. To be published. McKenzie, W. M. (1960) Wood cutting process. Forest Prod. J. 9,4&F456. Merchant, M. E. (1945) Mechanics of the metal cutting process. J. appl. Phys. 16, 267-324. Moss. R. (1964) Histopathologic reaction of bone to surgical cutting. Oral Surq. Oral Zfed. Oral Pathol. 17.405-414. Orell. S.-(1954) Drilling and sawing of bone and cooling of insrrument. ll’ormed 27. 1549-1552. Pickarski, J. (1970) Fracture of bone. J. appl. Phys. 41, 1. Piispanen. V. (1948) Theor- of formation of metal chips. J. appi. Phys. 19, 876-881. Pope. M. H. (1972) On the fracture of bone substance, Ph.D. dissertation, University of Vermont, Burlington, Vermont. Pope, M. H. and Outwater. J. 0. (1972) The fracture characieristics of bone substance. J. Biomechanics 5, 457-465. Ramalineam. S. (1967) Plastic deformation in metal cuttine. Ph.D. ldissertaiion, ‘University of Illinois. Rauber. A. (1876) Elasricifare and fesrigkeir der knochen. Engelmann, Leipzig. Sedlin. E. D. 119651A oheolonical model for corrical bone. Acta. Orthob. S&d.‘Suppl.
&I, OOWlOO.
Sedlin, E. D. and Hirsch, C. (1966) Factors affecting the determination of the physical properties of femoral cortical bone. Acta. Orthop. Stand. Suppl. 37, 1918. Thompson, H. C. (1958) Effects of drilling into bone. J. Oral Surq. 16. 22-30. Wertheim, M. G. (I 847) Memoire sur I’elasticity ei la cohesion des principaux tissus du carp humain. Ann. Chim. Phgs. 21, 385-414. APPESDJX A P, = rd br
+cos(B - z);sin d. Ib + p - z) -’ p where ~1= 0.75 (Sticking friction) ; 1 :“7ri
(A)
I = 15’ b = 0.003 in.
Q = 3$+(yrnl
thegof;nst-Merchant
Relationship:
sd = 16,260 psi. (In order to evaluate this work static shear stress (z,,) has been taken from rhe independent work of Evans (1964) and increased to a dynamic shear stress value (id) with data taken from Crowninshield (1973) appropriate to the strain values measured in the experiments assuming that: rd = 50 aid=0 where a,,; a0 are static and dynamic (strain of lO/sec) normal stress respectively.) By substitution into (A) the theoretical horizontal force (P,,) is: 252 N/m x IO-‘.
PROCESS-
C. H. JACOBS?. M. H. POPE:. J. T. BERRY$and F. HOAGLCSD UniLersitk of Vermont. Burlington. Vermont 05401. U.S.;\ Abstract--Thee appears to be no record of any orthogonal cutting anal>& of bone in the literature. although many surgical procedures using cutting tools are performed ever) da>. This paper describes a series of two-component cutting dynamometer experiments at constant speed using bovine bone as the workpiece for an orthogonal cutting analysis. The bone samples were taken from the mid-diaphysis of bovine tibiae and \\cre cut in three mutually perpendicular directions: across. parallel and transverse to the preferred osteon direction. Microscopic and SEM photographs are presented detailing ths tivc different chip types categorized b) the authors. Precutting (i.e. plastic deformation) studies were conducted and A theor) for precutting bchaxior based on hydroxyapatite crystallite interlocking is postulated. The Merchant analysis of orthogonal cutting is shokvn to ha\c limited applicability to bone material.
1. IKTRODUCTIOS
Since the early Lvork of Wertheim (1517) and Rauber (1576) and others. many studies have been made of the mechanical properties of bone substance. These have been well summarized by Evans (1964) and Kraus ( 1967). In view of the importance of machining bone in many operative procedures. particularly in orthopaedies. it is perhaps surprising that little work has been done in investigating the basic niechanisms involved in the bone machining process. Other aspects of the problem have been studied. for example: Orell(1959) investigated the cooling of bone drills and saws whilst Bowden (1955) and Thompson i 1958) have looked at metallic transfer in drilling. More recently Costich i 196-l) investigated high speed drilling instruments and Moss (1964) performed the first thermal necrosis study. Most of this tvork dealt Lvith dental drills (which rotate at a considerably higher speed than orthopaedic drills) and tooth substance, rather than bone. Brooks (1970) investigated stress concentration effects in drilled holes and found that a single hole can reduce overall bone strength by 30 per cent. Burstein’s (1972) recent work shotved the relationship between drilled holes, screws and breaking strength. Perhaps bvas that of research the most significant Matthews and Hirsch (1972) who. for the first time. established a basis for thermal necrosis of bone. These * Receicrd 17 September 1973. t M.S.M.E.. Department of Mechanical Engineering. : Ph.D.. Departments of Orthopaedic Surgery and Mechanical Engineering. P Ph.D.. Department of hlechanical Engineering. M.D.. Department of Orthopaedic Surgery.
workers shotved that the very high local increase of temperature present in drilling can destroy bone cell viabilit! in the area surrounding a hole. In view of the potential for cell damage and microcrack (Pope. 1972) formation there was obviously a need to optimize machining parameters. The study reported herein attempts to establish the basic mechanisms operative during the orthogonal cutting process and to optimize the parameters, The orthogonal cutting process has been chosen since it is fundamental to all other machining processes (drilling, tapping. sawing, etc.).
2.
SPECI\IESS
A.SD PREP.ARhTION
The specimens were taken from mature bovine tibiae, with a high content of haversian. rather than plexiform. bone. The tibiae were obtained from a local abbatoir immediately following slaughter. For the orthogonal machining tests rectangular specimens approximately 0.019 x 0.038 x 0.0076 m were cut out in three mutually perpendicular directions: from the middiaphysis of the bone: across, parallel and transverse to the preferred osteon direction (Fig. 1). The samples were kept frozen (- IO’C) and when used were kept immersed in lactated Krebs-Ringers solution. following the guidelines previously established by Sedlin and Hirsch (1966). 3. PRECLTTISG
STUDIES
The initial contact of anl; cutting tool with a specimen results in a deflection of the workpiece without rupture. Most cutting studies have ignored this stage 131
C. H. J.ACOBS.$1. H. POPE. J. T. BERRY and F. HOAGLUND
Inltlal‘
where cutting had taken place. This probably represented the effects of the high residual tensile stresses from the tool (Ramalingam, 1967). The identification of a ‘shear plane’ in this manner is of interest since a similar zone has been identified in continuous chip formation in orthogonal metal cutting viz.Merchant (1945) and Piispanen (1948).
lndentotion -L
Tool
Bone
3.2 Plastic beharior
removed
pollwed
to remove
Collagen itores length
swath the
Fiy. I. Precutting
return
deformatton
/
to orlginol
removal
behavior
of OHAP
of bone.
with the rationale that the cutting edge produces a stress concentration factor that will put the contact stress above the strength of the material. McKenzie (1960), in his wood-cutting studies, found that this stage is negligible only with very sharp tools and high rake angles. This conclusion is shared by the present authors on their work with bone substance. For example, in cutting parallel to the osteon orientation it has been found in some cases that indentation becomes so pronounced that very high tensile stresses are produced parallel to the osteon directions. The net result is the fracture characterized by the authors as type V which is due to failure in tension across the fibers. The following work attempts to investigate this behavior in more detail.
Burstein et nl. (1972) have recently pointed out the significance of the so-called plastic deformation in bone substance. It was also noted that much of the deformation is such that when the load is released, the deformation will return to zero as a function of time. This behavior is consistent with the model of bone as proposed by Sedlin (1965). To investigate the plastic phenomenon and its limitation when applied to orthogonal cutting, the experimental arrangement as shown in Fig. 3 was utilized. The sample of bone was held in a vise with the direction of the osteons parallel to the direction of cutting tool travel. The crosshead was moved down to a point where no cutting had occurred but a permanent deformation could be recognized. The specimens were then polished and decalcified (2’; HNOJ for 24 hr. then dewatered with ethanol). After the decalcification procedure it was noted that a mirror image of the deformed surface was formed, i.e. the surface at the point of tool contact was distinctly raised above the surrounding surface. This phenomenon can be explained if one considers the deformation to be ‘locked’ into the matrix perhaps by interactions of the hydroxyapatite (OHAp) crystals that are dispersed along the collagen fibres. It would appear that the first stage of plastic deformation in orthogonal cutting is recoverable and can be attributed to the prefailure behavior of the mucopolysaccharide. The second stage, which is a permanent deformation, is due to OHAp interactions. 4. CUI-IINC
STUDIES
3.1 Prefiihli-e beharior
4.1 Equipment
To investigate prefailure behavior cuts were made in a bone sample parallel to the preferred osteon direction. The cuts were stopped before they were completed and the sample was then polished in the plane of the chip and stained with basic fuchin. Staining was evident in the chip. terminating in a ‘shear plane’ along’ the chip root from tool tip to workpiece surface (Fig. 2). The damage suffered by the chip is indicative of stress of @7 tf (failure stress) or above. (It has previously been established that increased permeability occurred at stresses of this order (Pope, 1972)) There was also a thin layer of stained material on the surface
The orthogonal cutting was done on a Brown and Sharpe No. 2 milling machine (Fig. 4) with a fixed ground double ended tool composed of AISI M2 molybdenum high-speed steel with available rake angles of - 5, 0, 15, 35 and 45 degrees. Force measurements were made with a Cook, Smith and Associates Two-Component Milling Dynometer using a San-Ei type 6L4 Strain Amplifier and Dixon Visigraph-P Oscillograph as indicating and recording instruments respectively. These instruments were calibrated using dead weights and showed a linear input/output relation for the applied loads.
Fi*=. -1 1 Fig. 3.
Fig 6. Type I chip (B.T.O.) Fio. _ 7. Type II chip (B.T.O.)
j. 1600. 100.
Fig. 8. T>pz it1 chip (B.T.O.)
.. 1000.
Fig. 9. Type
‘.: 1000.
IV chip @.A.O.j
Fig. 10. Type V chip (B.P.O.)
x250.
.A stud>
of the bone
machming
1:;
process
4.3 Renrlts
Sample size variation was a difficult) bvhen anal!+ ing bone data. Therefore all tabulated force values for the three materials used are shown for a theoretical piece of material 0.234 m in width. Thar is, the force value measured on the oscillograph tracings was divided by the sample width to allow for a uniform base of comparison. The force values are shown in Fig. 5.
+=I *x
cut paroilei to osteone (8. P 01
Bane
5. I Mechanics Bone cut
transverse (B.T.0. I
.3one c9t ( B.A.0 )
across
osteone
** Fig. -1.
I. .~S.+LFSIS
** Preferred * Cvttlng
oste0r.e
to
3steone dlrection
drrectror
Schematic ofcutting sample locations from 3 axes.
4.2 Procedures As stated, samples were cut from the three mutually perpendicular axes of the bone, thereby enabling cutting data to be obtained parallel, perpendicular and transverse to the predominant osteon directionality. After the samples were prepared and placed in the dynamometer they were all cut at a constant velocity of O-47m/min (18-35 in/mint using the various angIes available and at the foIlowing depths of cut: I2. 24, 36, 43 x 10e6m. As the samples were cut the oscillograph recorded deflections indicative of the horizontal and vertical forces acting to cut the material. These deflections were then measured and evaluated using the pre-established calibration curves. The resultant chip thickness was measured using a standard micrometer and was recorded along with horizontal and vertical forces, cutting velocity, depth of cut and tool rake angle for analysis. As is evident from the literature there are some elastic elements functioning in bone tissue and for this reason and because no other cutting theory for bone exists, the Merchant analysis was used to analyse the data. The chips were collected and at various magnifications using ordinary light microscopy and scanning electron microscopy (SEAL). Chips were prepared for the S.E.M. by sputtering with carbon followed by gold palladium.
OF THE CLmiNG
PROCESS
of rhe process
Ttvo factors. the anisotropy of bone substance and the change of variables in the cutting tests. resulted in substantial changes in the chip types from the diffkent tests. In all. five different
chip types iyere identified.
S.E.M.‘s of these chip forms are shown in Figs. 6-10 and are tabulated in Table L. The t>-pe I chip was a smooth. curved chip, that was formed at low depths of cut and high rake angles (I) in all cutting directions. It is thought that there was little precutting deformation due, in part, to the low resisting forces and partly due to the high tool rake angle. This particular cutting situation most closely represented rhat suggested in classical Merchant theory. The t>pe II chip was a smooth to fairly smooth Hat chip with little break up. It was seen with low depths of cut and low angles in the across osteon and parallel to the fiber (osteon) directions. In this case it is thought that there was more precutting deformation due to a *BOG lBT.0.
17co
,,/’ 5
,y
3.T.0.
:5
35
II 3c
coo
;
900
:2 d r z i 0
800 7;o
6OC 500 COO I 330 i 130 4 230 0
6
iz
24
Depth of cut, direction
r9
m )(8:“
cutting force for bovine and rake angle r~ depth of cut).
Fig. 5. Measured mean resultant bone (cuttine
36
C.
134
H. J.ACOBS.M.
H. POPE.J. T. BERRYand F. HO.AGLLSD
Fig. I I. Artist’s rendition of cutting done transverse-the predominant osteon direction.
Fig. 12. Artist’s rendition of cutting bone across-the dominant osteon direction.
tool resulting in a more compressed (and fatter) chip of inferior surface quality to the type I. The type III chip was seen exclusively during cutting transverse to theosteon where the depth ofcut was high or when the rake angle was low. The type III form was a very segmented chip. At best (high depth of cut, low I) it leas a very ragged. segmented chip and at worse it was almost a pile of fiber-like material (Fig. 11). Due to the low interosteon strength cracks also exist between the osteons. Maj and Toajari (1937) were probably the first to point out that failures tend to be parallel to the predominant direction of the fibrous matrix of the bone. Values of fracture energy now available show that it is energetically favorable for bone to break in a longitudinal. rather than a transverse, direction. It was found that there is a preference in bone for the crack to propagate beuvsen the osteons. thus indicating the existence ofa weak interface between the osteons. This is because the boundaries between osteons are not crossed by collagen fibers and because the cementing substance (mucopolysacchnride) is much weaker than collagen.
The type IV chip was seen in cutting across the osteons. Again. the chip type probably resulted from osteon deflection before rupture and the segmented nature of the chip was due to the low interosteon strength (Fig. 12). The type V chip was obtained in cutting parallel to the osteons. It \vas seen at high depths of cut. Essentially it was a series of fractures with the crack running ahead of the cutter and the resultant chip breaking as a cantilever beam (Fig. 13).As 1 was decreased the chip became rougher due to the more severe precutting deformation.
‘blunter’
pre-
5.2 Prediction of cutting forces
The IMerchant analysis (1945) is concerned with the geometric relationships existing between the forces in
Table 1. Chip types for various cutting conditions Cutting direction
Depth of cut
BTO
High Low High Low High Low
B.40 BP0
Chip type Large Small 1 I III I IV I V I
III III IV II V II
Fig. 13. Artist’s rendition of cutting bone parallel-the dominant osteon direction.
pre-
A srudl; of the bone machining process
the shear zone. on the tool face and those normally measured during cutting (using dynamometers). The measured quantities are horizontal and vertical cutting force and chip thickness. Other parameters, normally held constant. are the tool rake angle, depth of cut and the cutting speed. The horizontal cutting force can be shown to be: P, =
where: 5,) = j? = x= 0 = b= r= ;i =
r,bt cos(p - 3) sm 4 cos(qb + b - 2)
shear stress at failure on the shear zone friction angle = arc tan p tool rake angle shear plane angle work piece width nominal chip thickness (depth of cut) friction coefficient between tool face and chip.
Appropriate values for the shear stress (rO) can be obtained from the work of Crowninshield (1972) and Evans I 1964). It is of importance to note that not only must the value selected be appropriate to the strain exhibited at the shear zone, it must also be appropriate to the strain rate and mean temperature. Because the cutting tool was ground but not polished. a value for ~1(from which B is derived) was taken to be equal to 0.75. i.e. ‘sticking friction’. This value for p is within the values calculated from experimental data. Tool rake angle (I) and depth of cut (t) values are as shown in Table 1. (Sample width is 0.254 m.) The shear plane angle (4) was derived using the Ernst->lerchant relationship (Alexander and Brewer, 1963): ?I$ + p - 1 = 90’ which permits some elastic behavior in the workpiece and is based upon work minimization in the cutting (Appendix A is a sample calculation of the horizontal cutting force). It is apparent from the calculation in Appendix A and the comparison of theoretical results with experimental results in Table 2 that there is limited agreement. Table 2 Curling direction
Depth of cut ( tom6 m)
angle
Rake
BAO BTO BP0
12 12 I).
15’ 15’ 15’
P,’
p,+
34s 616 260
252 252 252
* Horizontal Force (Experimental, Nm x lo-‘). + Horizontal Force (Theoretical. N,‘m x lo-‘).
135
The agreement existing between measured and predicted tool forces depends. at least in part. upon orientation. reflecting the anisotropy of bone and also the general insensitivity to this effect inherent in Merchant’s theory. 6. GENERALDISCCSSIOShED COSCLCSIONS Currently available metal cutting theories would lead to the exclusive use of high rake angle tools if cutting forces were to be minimized and if tool wear and replacement costs were of no importance. Since this is contrary to current surgical practice the findings of this study merit careful examination. However. such theories are of assistance in the understanding of bone machining since the experimental dynamometry techniques used to develop them are excellent for evaluating the cutting forces. It has been shown that the classic Merchant analysis gives some limited agreement between the predicted cutting forces and the experimental results. This is because the Merchant analysis assumes an isotropic material which shears in a planar fashion. Bone is, of course. markedly anisotropic and its failure mechanisms in cutting clearly demonstrates this. Furthermore. we have no exact knoa-ledge of strain rates and temperature fields occuring in cutting bone. This must be at hand before a theory appropriate to an anisotropic medium can be developed. However, it should be noted that many surgical cutting operations upon bone substance embrace an ‘averaging’ of cutting in several different directions. Consequently, the above calculations using the Merchant theory- should provide good general guidance in tool design. Finally, it is appropriate to note that cutting speed, which in turn affects strain rate. temperature and therefore flow stress, was not one of the variable parameters in the current investigation; due to available equipment constraints. Cutting speed would normally be expected to affect cutting forces and thus will be studied in future experimental work. In addition to these effects. cutting speed (i.e. strain rate) can also effect crack propagation. indeed there is evidence due to Piekarski (1970) that crack initiation energy is decreased significantly by an increase in strain rate. One of the present authors has also indicated a similar trend for fracture energy (Pope, 1972). Consequently an increased cutting speed might lead to a change in mode of failure in the so-called stress zone, as well as a change in cutting energy requirements. The exact nature of the total energy requirement change is difficult to envisage since an increased strain rate would normally involve increased stress energy on one hand. while on the other it would
136
C.
H.
JACOBS. M. H. POPE. J. T. BERRY
lead to a decreased energy requirement if cracking or spIitting in the stress zone became the dominant failure mode. In conclusion, the practical application of the present work is a defence for the use of truly sharpened tools for orthopaedic surgery. tinder the experimental conditions studied cutting forces can be markedly decreased when using tools with rake angles on the order of 45’. This recommendation is diametrically opposed to that of Ekchtol (1959). It is understood that Bethtol’s manufacturing guidelines are currently being followed for orthopaedic drill manufacture. These guidelines recommend drill rake angles of zero degrees or slightly negative. Currently work is being performed at the University of Vermont to determine what the optimum combination of tool rake angle geometry and
cutting speed should be in orthopaedic
drills.
Acknowledgements-The authors would like to rake this opportunity to thank those individuals without whose assistance this project would not have been possible: The Society of Manufacturing Engineers, Mr. D. Cheng. Professor B. F. von Turkovich, The Orthopaedic Research Education Foundation and certain others who shall remain anonymous. Our special thanks to Mrs. K. Hoyt for her perseverance in preparing this manuscript. REFERESCES
Burstein, A. H., Currey, J., Frankel. V. H., Heiple, K. G.. Lunseth. P. and Vesselv. J. C. (1972) Bone strennth. The effect of’screw holes. J.-bone J~nf Surg. 54-A, 1l&l 156. Burstein, A. H., Cutrey, J. D., Frankel, V. H. and Reilly, D. T. (1972) The ultimate properties of bone tissue: the effects of yielding. J. Biomechanics ql), 3>45. Costich, E. R.. Youngblood, P. and Walden, J. M. (1964) A study of high speed rotary instruments on bone repair in dogs. Oral Mrd. Ural Path. 17, j63-571. Crowninshield, R. D. (1973) The response of anisotropic bone to tensile impact. LVevew England Bioengineering Conference. Burlington, Vermont. Evans, F. G. (1964) Significant differences in the tensile strength of adult human compact bone. Proc. Isr European Bone and loozh Symp., pp. 319-331. Pergamon Press, Oxford.
and F.
HO.AGLGSD
Kraus, H. (1967) On the mechanical properties of human compact bone. .ddcances in Biomed. Engng Xed. Phys. Maj, E. and Toajoari, E. (1937) La resistanza meccanica del tessuto oseeo lamellare compatto misurata on varie direzioni. Bo[l. Sot. ftal. BioL Sper. 12. 83. Matthews. L. S. and Hirsch C. (1974) Temperatures measured in human cortical bone when drilled. J. Bone Jnr Sury. To be published. McKenzie, W. M. (1960) Wood cutting process. Forest Prod. J. 9,4&F456. Merchant, M. E. (1945) Mechanics of the metal cutting process. J. appl. Phys. 16, 267-324. Moss. R. (1964) Histopathologic reaction of bone to surgical cutting. Oral Surq. Oral Zfed. Oral Pathol. 17.405-414. Orell. S.-(1954) Drilling and sawing of bone and cooling of insrrument. ll’ormed 27. 1549-1552. Pickarski, J. (1970) Fracture of bone. J. appl. Phys. 41, 1. Piispanen. V. (1948) Theor- of formation of metal chips. J. appi. Phys. 19, 876-881. Pope. M. H. (1972) On the fracture of bone substance, Ph.D. dissertation, University of Vermont, Burlington, Vermont. Pope, M. H. and Outwater. J. 0. (1972) The fracture characieristics of bone substance. J. Biomechanics 5, 457-465. Ramalineam. S. (1967) Plastic deformation in metal cuttine. Ph.D. ldissertaiion, ‘University of Illinois. Rauber. A. (1876) Elasricifare and fesrigkeir der knochen. Engelmann, Leipzig. Sedlin. E. D. 119651A oheolonical model for corrical bone. Acta. Orthob. S&d.‘Suppl.
&I, OOWlOO.
Sedlin, E. D. and Hirsch, C. (1966) Factors affecting the determination of the physical properties of femoral cortical bone. Acta. Orthop. Stand. Suppl. 37, 1918. Thompson, H. C. (1958) Effects of drilling into bone. J. Oral Surq. 16. 22-30. Wertheim, M. G. (I 847) Memoire sur I’elasticity ei la cohesion des principaux tissus du carp humain. Ann. Chim. Phgs. 21, 385-414. APPESDJX A P, = rd br
+cos(B - z);sin d. Ib + p - z) -’ p where ~1= 0.75 (Sticking friction) ; 1 :“7ri
(A)
I = 15’ b = 0.003 in.
Q = 3$+(yrnl
thegof;nst-Merchant
Relationship:
sd = 16,260 psi. (In order to evaluate this work static shear stress (z,,) has been taken from rhe independent work of Evans (1964) and increased to a dynamic shear stress value (id) with data taken from Crowninshield (1973) appropriate to the strain values measured in the experiments assuming that: rd = 50 aid=0 where a,,; a0 are static and dynamic (strain of lO/sec) normal stress respectively.) By substitution into (A) the theoretical horizontal force (P,,) is: 252 N/m x IO-‘.