A study of the bone machining process—Drilling

A STUDY OF THE BONE MACHINING

PROCESS-DRILLING*

C. H. JACOB and J. T. BERRY School of Mechanical Engineering, Georgia Institute of Technology. GA 30331. U.S.A.

M. H. POPE and F. T. HOAGLUND Departments of Orthopaedic

Surgery and Mechanical Engineering, University of Vermont. VT. USA

Abstract-Internal fixation of fractures with screws is a common procedure that has been an historical fact for a number of years. Unfortunately little research has been reported on the action of drilling when preparing for screw insertion. This paper presents some results of a study wherein bovine tibia mid-shaft sections were drilled using several commercially available and experimental drill point geometries under different conditions of feed rate and rotational speed while measuring torque and thrust. Results indicate that drill point geometry is critical when attempting to minimize drilling forces and that there appears to be a softening effect in bone when drilled at relatively high speeds.

1. INTRODUCTION Internal fixation of fractures with screws is a common

procedure that has been an historical fact for a number of years. It is. however, only within the last 20 years that any investigative work has been done regarding the actual drilling process that must be done before a screw can be inserted. The principal authors in this area are: Ore11 (1959), Bowden (1955), Thompson (19%X),Costich (1964) and Moss (1964). Primarily these authors used dental drills or burrs (which rotate at considerably higher speeds than current orthopaedic tooling) and tooth substance rather than bone. Analysis of drilling in bone, as done in orthopaedic surgery, has a much more limited history. Eechtol et al. (1959) presented a set of guidelines for drilling in bone and for the manufacture of drill points. More recently, Sneath (1967) reported the results of a similar study which produced recommendations for drill point configuration which are opposed to those of Bechtol et al. Matthews and Hirsch (1972) measured the temperature changes in bone during in vitro drilling. This work established the temperature distribution around a hole related to drill rotational speed. Work by Jacobs (1973) described the interrelationships between cutting forces, osteonal orientation and cutting tool geometry for single edge tools. This information was then used as a basis for a complete evaluation of the bone drilling process: it is to the results of this study that this paper is addressed.

a drill can be considered to be formed from two single edge tools wrapped around a common axis. Single edge cutting analysis has been used to predict the energy to shear (cut) a material. This formation can be used to help develop an approximate equation for drilling forces, if the mode of fracture is by shear, as presented by Cook (1966). For example, the power force Fp acting on the main cutting edges (in the plane perpendicular to the rotational axis) of a drill is: Fp = ubt = u(d/2)(f/2). where: u = total energy per unit volume consisting of shear energy (~3 required to produce gross deformation, the friction energy (ul) of the chip sliding past the tool and certain other minor energies; h = d/(2cosa,,): the width of cut; d = drill dia.; x(p= function of the drill point angle; t = cf/Z)(cos ze): the depth of cut; ,f = feed rate per revolution.

2. SINGLE EDGE ORTHOGONAL CUITING OF BONE

It can be shown that when friction effects are considered the total energy term above is of the form (Jacobs, 1974 after Cook): u = ISU, Cook has also shown that shear energy (u,) is actually the product of strain (y) (change of length) and flow (or shear) stress (r). Therefore the cutting energy term (u) can be used to estimate and evaluate the flow stress in bone through the following approximation: I4 = 1.5u, = 1.5(l;r). (A more detailed development of the Cook equations is presented in Appendix I).

AND ITS RELATIONSHIP TO DRILLING

Work by Jacobs et al. (1974) has shown that tool rake angle is a critical factor when cutting bone, i.e. the more severe the angle the lower the cutting forces regardless of the direction the bone is cut. In general L * Received 24 June 1974. 343

3. SPECIMENS AND PREPARATION Drilling specimens were taken from mature bovine tibiae (mixed breed dairy cattle), with a high content of haversian, rather than plexiform, bone. The tibiae

C. H. JACOB,J. T. BERRY,M. H. POPE and F. T.

344

were obtained from a local slaughter house within 2 hr of the animal’s death. For this study full section slabs (0.125m) in width were cut with a band saw after all soft tissue had been removed. The samples were kept frozen (- 10°C) and when used were kept immersed in lactated Krebs-Ringer solution, following guidelines previously established by sedlin and Hirsch (1966). 4. EXPERIMENTAL

EQUIPMENT

4.1 Measurement and recording device The factors controlled in this-study were as follows: drill geometry, rotational speed and feed rate, while the measured factors are: drill torque and thrust. Torque and thrust were measured using a 2 component drilling dynamometer (non-interactive straingauge type). The output signal from this device was processed with a strain-gauge signal amplifier and recorded on a,galvanometric oscillograph with a flat frequency response of 500 Hz. The dynamometer was equipped with a specimen support plate which allowed the torque and thrust force components to remain physically separated before being applied to the dynamometer itself (Fig. 1). 4.2 Dn’ve mechanism A 1 h.p. variable speed d.c. electric motor was fixed to the cross-head of an Instron Universal Testing Machine. This machine has available cross-head feed rates of 0.0127-5.08 m/min (0.05-20.0 in/min). A spindle (supported in two heavy duty ball bearings) and drill chuck assembly were rigidly attached to the: motor support and the dynamometer was fixed to the main frame of the Instron Universal Testing Machine. The motor unit had controllable rotation from 100 to 2360 rev/min. This system was thus capable of varying both feed and speed for drilling over a very broad spectrum. Thus the equipment was an improvement over that used by Matthews and Hirsch (1972) in that feed rate rather than feed load could be investigated, and it was also more sophisticated than the system used by Sneath (1967). 4.3 Drill point supply All drills used in this study were commercially available surgical drills with the exception of two., Photographs of the various geometric point cofigurations are shown in Figs. 2 and 3. Drill dia. of 2.8, 3.2,5.2 and 6.3 mm (7/&l, l/8, 13/64, l/4 in.) were used. In all, seven drills were studied for a total of twelve combinations (Table 1). The two non-surgical drills were: (1) a standard metal cutting drill (Fig. 3b) and (2) an experimental point design (Fig. 3~). In some respects the experimental work was a product comparison and as a result, complete anonymity of manufacturer has been maintained. * See Appendix 2.

HOAGLUND

Table 1. Available drill points used CODE

* l* 01x D 01x E OlX F 02X D 02X E 02X F 04X D

Qu E 94X E TlX E TlX E T4X E P6X E x4x E NlXE UZfE

DIAMETER h/m. .125/3.2 .125/3.2 .125/3.2 .250/6.3 .250/6.3 .250/6.3 .109/2.8 .125/3.2 .109/2.8 .125/3.2 .125/3.2 .109/2.8 .203/5.2 .109/2.8 .125/3.2 .250/6.3

POINTIIliCLE go0 900 go* 90. 90' 909 91* 110. 1100 88' 86' 53.7;$*** 40' 113. 113.

HXLIXANCLF 23. 23' 23' 23. 23. 23' 23' 24' 24' 27' 17.2' 16.5' 19.50 10.5. 13.5. 13.50

l

Feed Rate Code.D-0.0254mhin. E-0.0508mimin.F-O.112mhin .**

5. EXPERIMENTAL

PROCEDURE

After the bone sample had been prepared it was fixed in a vise on the dynamometer support plate, the periosteum removed and test holes (6-20 depending on drill dia. and specimen size) were drilled. Feed rate was maintained at 0.254, 0.508 or 1.27 m/min (1.0, 2.0, 50in/min) and rotational speeds controlled at 100, 250, 500, 75Q 1000, 1500, 1750, 2ooO or 2360 rev/min. Typically, 3-5 holes* were drilled for any speed-feed combination with any one drill geometry. Krebs-Ringer solution was applied to the bone surface at all times to prevent drying of the tissue, and may have also acted as a lubricant. 5.1 Data reduction ‘To facilitate the data analysis, a series of computer programs were written, All drilling data, i.e. torque and thrust deflections, were tagged with a 4 character code identifying drill type (point geometry) diameter, rotational speed, and feed rate, e.g. a code of 02AE signified an ‘0’ type drill, 6.3 mm dia., 100 rev/min with a 0.508 m/min feed rate. This raw data was converted to actual force values using the computer programs, then statistically evaluated using a standard curve fitting regression analysis. All data points and the regression curves were then plotted by the computer. 6. RESULTS As previously noted, a variety of drill types were studied (7 in all) and complete results are available elsewhere (Jacobs, 1974). Therefore, the results for 4 different drills of the same diameter will be presented here. The test conditions were: 0.508 m/min feed rate, 3.2 mm dia. (2 in/mm, l/8 dia. respectively) and rotational speeds from 100 to 2360 rev/min.

6.1 ‘M type drill form This drill is a standard high carbon machine shop drill (Fig. 3b) of the type used for surgical purposes

. 1. Test apparatus:

Facing p. 344)

1 h.p. drive and chuck assembly with dynameter for clarity).

(torque plate sepal

Fig. 2. (a) ‘Q-type’. (b) ‘O-type’.

(c) ‘X-type’. (d) ‘T-type’.

Fig. 3. (a) ‘Y-type’.

(b) ‘M-type’.

(c) ‘F-type’.

345

A study of the bone machining process

difficulties may have been due to the relatively long length of the drill. Torque and thrust curves for this drill are given in Figs. 5(a and b). Feed rate 0 0.0508 m/mln (2OOlpm)

6.3 ‘(2’ type drill form

This drill was found to be in terms of force considerations the others studied (see Fig. 8). angle of. 110” and a helix of

the best overall drill when compared with The drill has a point

24’ (Fig. ?a). There was little. if any, heating observed when using this drill although at speeds less than 5OOretjmin

0

0

8

0

I

500

,

I

I

IGCO

Drill rotational

I .3-

I

Ix0 speed.

2coo

J

the drill could be difficult to start if it was not perpendicular to the bone surface. This is due to the fact that there is no appreciable point on the drill bit. Torque and thrust curves are given in Figs. 6(a and b).

2mJ

rev/mm

6.4 ‘0’ type drill form

This drill (Fig. 2b) has a point angle of 90’ and a helix angle of 23”. The main cutting edge angle

(b)

0

Feed rate 0 0.0508 m/mm WJOipm)

15-

Feed rate loo

aO.O!308 m/mm (200 ipm)

s 83

t 0

I 500

I

I

1006

Drill ratatianal

1506

speed.

I

2ouJ rev/min

Fig. 4. (a) Force regression. (b) Torque regression. 3.2 mm (l/8 in.) dia. ‘M.-type drill.

031 Drill rotational

in the past. It was used in this study as an example of another drill point geometry. This drill has a point angle of 113” and a helix angle of 13.5”. During actual drilling there was some heating due to friction and workpiece shear deformation at the higher drill speeds. This heating was not as severe as in other

speed.

rev/mm

(b) 1.a

t Feed rote 0 0.0508 m/mm (2.00 Ipm)

CWS.* The torque and thrust curves for this drill configuration are shown in Figs. 4(a and b).

6.2 ‘r

type drill form

This drill has a point angle of 86’ and a helix angle of 17.2” (Fig. 3a). Below speeds of 1500 rev/min this drill was somewhat difficult to start and produced some heating effects at greater speeds. The starting * “Heating”, as used here, is a qualitative descriptive term indicating that there was some localized boiling of the Ringer’s solutions applied to keep the specimen moist. Obviously, boiling would qualitatively indicate a temperature in excess of 100°C.

0

0

I 500

I coo

Drill rotatiwl

I

I

I500

zmo

speed.

I

2%x

rev/mln

Fig. 5. (a) Force regression. (b) Torque regression. Using a 3.2 mm (l/8 in.) dia. ‘Y.-type drill.

C. H. JACOB,J. T. BERRY, M. H. POPE and

l

F. T. HOAGLUND

ml analysis indicates that this relationship form

(a)

is of the

F = A -t BRX,

where F = Torque or thrust value; A = Asymptote value; B = Change in “F” as “x” passes from zero to infinity; R = The factor by which the deviation of ‘%” from its asymptote value is reduced for each incremental change in “x”. (a more detailed description of this statistical analysis may be found in Dixon, 1971 and Stevens. 1951). The value of the exponent “X” is of importance as it is a dimensionless parameter consisting of a drill velocity term (a function of rotational speed) and the drill feed rate term (mimin). This relationship is of the form: x = f(rev/min) Drill rotattonal speed,

rev/min

D

=

I

X (Feedrate)- 1 1

rev’mm ’ 12.K ’ DFI(I2.K)

(b)

1.5

Feed rate 00.508 m/min

Feed rate Y 0.0254 m/min (1.OOipm) 0 0.0508 m/min (2,OOimpI 0 0.127 m/min (5.OOipm)

I0

I

I

500

KKXJ

I 1500

Drill rotatianal speed.

I 2ooo

2

rev/mm

Fig. 6. Force regression. (b) Torque regression. trsing a 3.2 mm (l/8 in.) dia. ‘0’~type drill.

1

(rake angle; see Jacobs et al., 1974) has been blunted so that there is an effective rake angle of negative l-3”. The forces associated with this drill were the highest. There was a great deal of adverse heating at all drilling speeds in excess of 750 rev/min as indicated by steam being ejected from the hole with the chips produced. If Ringer’s solution was not continuously present at the drilling site there was evidence of severe thermal necrosis; this was apparent upon removal of the drill from the hole with brown or blackened chips impacted in the flutes. Torque and thrust curves for this drill are given in Figs. 7(a and b). 6.5 Overall data summary It is apparent from that the drilling force asymptotic form. That forces are much higher

review of the data presented speed-feed relationship is of is, at lower rotational speed, than at higher speeds. Statisti-

1

I

0

I

wo

1000

I 1503

Drill rotatlonol speed,

I 2cca

I 2500

rev/mm

x 0.0254 m/mln (I.00 ipm) 0 0.0508 m/mm (2.00 1pm1 A 0.127 m/min (5.00 ipm)

I

0

I

I

5w

000

Drlll

rotatim

1 1500

speed.

2ooo

I

2500

rev/mm

Fig. 7. (a) Force regression. (b) Torque regression. Using a 3.2 mm Cl/8 . in.)I dia. ‘0’~tvw _. drill.

347

A study of the bone machining process Droll form key

Torque

I , 0 IIn

28 Drill dia.

Fig. 8. Comparison

where: D = drill dia.; DF = down K = metric conversion factor.

of asymptotic

feed-rate

and

The asymptote value is then of importance for comparison of the various drill forms. The lower asymptote values (at high values of “X”) indicate lower cutting forces, which are associated with lower cutting energies. Lower cutting energy is associated with less residual damage in the cutting region and is therefore important in terms of thermal damage and physical damage (i.e. residual stress and cracking). This has been described by many workers, see Matthews and Hirsch (1972). An overall view of the asymptote force values for the drills used in this study is shown in Fig. 8. This shows the dramatic change in cutting forces as a function of tool geometry. The “p” drill form is obviously the best available drill configuration of those studied.

7. DISCUSSION

7.1 Rake angle considerations

As noted above it has been shown by Jacobs et al. (1974) that in order to lower cutting forces it is

necessary to have a sharp (positive) rake angle on the cutting tool. From review of the drills illustrated and the data presented this thesis is justified, that is, a drill with a rake angle on the main cutting edge consumes leas energy than one without an appreciable rake angle (compare the ‘0’ type drill with the ‘Q type). 7.2 Theoretical analysis The introductory portion of this paper presents an approximate theoretical model for drilling as developed by Cook based on a shear failure criteria. Although fracture, rather than shear failure has been

3.2

6.3

5.2

mm

drilling forces for all drills studied.

noted in single edge cutting (Jacobs et al., 1974) the vast majority of chips recovered indicated shear as the mechanism of failure. It is of interest to relate this generalized form more specifically to drilling in bone. This is done through the utilization of appropriate material properties. As indicated in Section 1, the specific energy ‘u’ term can be utilized to help predict cutting forces when combined with geometric considerations of the drill point. This specific energy . term can be developed from an independently evaluated term: the flow (shear) stress (r). In machining operations, the action of the tool results in either a shearing or a fracture process. (Layers of material appear to slide over one another; see e.g. Merchant, 1945.) This implies that for incipient permanent deformation (Sow or fracture) to occur at a specific strain, the localized shear stress must reach a critical or maximum flow (shear) stress. If one assumes bone to be either an ideal plastic, or an elastic-ideal plastic material (where the plastic strain is large, i.e. a cutting situation) the shear stress (r) will be constant over a wide range of strain (y) values up to a *maximum strain at fracture (7,) (Cook, 1966). The flow stress of bone, however, is also sensitive to both orientation and loading rate as many workers have reported. (See Pope er al., 1974; Crowninshield and Pope, 1974.) Flow stress values (parallel to the predominant osteonal direction) determined by Crowninshield and Pope (1974) increase from 7300 kg/m’ (ISo psi) to 172000 kg/m2 (35000 psi) as the strain rate increased at room temperature. Values of flow stress in this range were selected and utilized in a computer modeled solution of the Cook equations. A limiting value of two was used for the strain. This value was selected from the results of earlier work (Jacobs, 1973) where it was clearly

C. H. JACOB, J. T. BERRY, M. H. POPE and F. T. HOAGLUND

348

03

(0) Sheor

stress

values

I 20,cQo PSI 2.30,ooo psr 02 t

Drill

c (

I50

roiotlC+lOI

speed,

rev/mln

Sheor

stress value

3D,cxo

It is important to note the degree of mismatch between the two data sets. At the lower rotational speeds, the predictions using the higher shear stress value bracket the experimental results, while at the higher speeds, the predictions using the lower value bracket the measured results. While the choice of shear stress is purely arbitrary, the fact that there is agreement in this manner is vital to an understanding of the material behavior of bone during this type of drilling (variable feed/revolution). There appears to be significant softening of the bone at higher rotational speeds indicated by the lower shear stress value.

b)

PSI

8. CONCLUSIONS

\

8.1 Theoretical considerations

(cl Shwr stnss value 2O.OW psi I

(1) The ability to correlate theoretical models to real situations is ideal from the design standpoint in any, mechanical processing operation. It is then possible to evaluate new tool and equipment designs without having to perform full scale evaluations with the actual apparatus per se. It is fortunate that the agreement between the experimental data for bone drilling and the Cook approximate model is sufficient to provide reasonable guidance in predetermining at least order of magnitude values of expected torque and thrust for drilling. (2) Subtleties of tool design cannot as yet be described in anything more than a semi-quantitative way, e.g. by referring to single edge orthogonal cutting studies of the type performed by Jacobs (1973). (3) The rheology of bone, being as complex as it is, leads one to suggest that further work is necessary to handle particular features such as the effect of temperature on flow stress or the flow stress dependency on strain and strain rate. 8.2 &sign reconmenddons

Drill

rototl~nd

speed.

rw/mIn

Fig. 9. (a) Comparison of Cook model simulation of drilling in bone with experimental data (torque). (b) Thrust. (c) Thrust.

indicated that bone was unable to support strains of more than this magnitude in orthogonal cutting over a wide range of parameters. The drill geometry simulated with this model was that of the ‘0’ type, described in Table 1. The results of the model simulation are shown along with experimental data in Figs. 9(a-c). While the model does not allow for “work hardening” effects or relaxation effects due to localized heating, it is possible to vary the shear stress parameter (while limiting shear strain) as shown in Section 2.

This study would not be complete without some suggestions as to how orthopaedic drill design and use might be improved. It is apparent from all the material discussed that drills designed following recommendations prepared by Bechtol require greater cutting forces and increased energy than those of other configurations, therefore the following suggestions for design and use are presented. (1) Bone drills must have an appreciable rake angle (25-35”). (2) A point angle on the drill is desirable to prevent the drill from “walking” on the surface. (Similar to the ‘0’ type form.) (3) Drilling should be done in the 750-1250 rev/min range (the knee of the force curves presented) to take advantage of the decrease in flow stress of the material at these speeds. At these speeds and above, a drill of the Q’ configuration will not “walk” on the surface and thus becomes an excellent tool.

349

A study of the bone machining process (4) Coolant, in the form of sterile saline, should flood the entire drilling field. Cold saline would possibly allow for drilling at higher speeds than indicated in (3) above. (5) The periosteum should be reflected away from the point where the drill will enter the bone. This prevents the chips (being ejected from the hole) being forced under this tissue and clogging the flutes of the drill. (6) Drill flutes should, for compact bone, be steep enough to remove the chips at an even rate. Acknowledgements-This work was partially supported by a grant from the Orthopaedic Research and Education Fund. Several well-known orthopaedic equipment manufacturers kindly supplied drill bits and other equipment.

REFERENCES Bechtol, C. O., Ferguson, A. B. and Laing, P. G. (1959) Metals ana’ Engineering in Bone and Joint Surgery. Williams & Wilkins, Baltimore. Bowden, F. P., Williamson, F. R. and Williamson, J. B. (1955) Metallic transfer in drillinn: sianificance in orthopaedie surgery. Nature, Land. 17;, 8%. Cook, N. H. (1966) Manujbcturing Analysis. Addison-Wesley; Reading MA. Costich, E. R., Youngblood, B. J. and Walden, J. M. (1964) A study of the effects of high speed rotary instruments on bone repair in dogs. O&l St&g. 17, 563. Crowninshield. R. D. and Pane. M. H. (1974) Annals of Bioengineer&, Vol. 2, The’response of compact bon; in tension at various strain rates. p. 217. Dixon, W. J. (Ed.) (1971) Biomedical Computer Programs, D. 297. Univ. of Calif. Press. CA. Jacobs, C. H. (1973) Machining characteristics of bovine bone. M.D. Thesis, University of Vermont: Burlington, VT. Jacobs, C. H. (1974) An analysis of the drilling characteristics of bovine bone. Ph.D. Dissertation. University of Vermont: Burlington, VT. (Available from University Microfilm: Ann Arbor. Michigan). Jacobs, C. H., Pope, M. H.. Berry. J. T. and Hoaglund. F. T. (1974) A study of the bone machining process-orthogonal cutting. J. Biomechanics 7, 131.- _ Matthews. L. S. and Hirsch. C. (19721 Temnerature measured in human cortical bone when hrilledrJ. Bone Jnt Surg. 54, 297.

Merchant, M. E. (1945) Mechanics of the metal cutting process. J. appl. Phys. 19, 876.

Moss, R. (1964) Histopathologic reaction of bone to surgical cutting. Oral Surg. 17, 405. Orell, S. (1954) Drilling and sawing of bone and cooling of instrument Normed 27, 1549. Pope, M. H. and Outwater. J. 0. (1974) Mechanical properties of bone as a function of position and orientation. .I. Biomechanics 7, 61. Sealin. E. D. and Hirsch, C. (1966) Factors affecting the determination of the physical properties of femoral cortical bone. Acta Orthop. Stand..371 29. Sneath. R. S. (1967) The determination of ontimum twist ’ drill shape for bone. Hosp. Engr. 21. Stevens. W. L. (1951) Asymptotic regression. Biomerrics. 7, 247. Thompson, H. C. (1968) The effect of drilling into bone. J. Oral Surg. 16, 22. APPENDIX lAfter Cook (1966) The horizontal power forces F, acts at the midpoint of each cutting edge thereby creating a torque force: M = ud2f/8 Where: u = total energy; d = drill dia.; f = feed rate/rev. A drill contacts material on both the chisel edge and main cutting edges, this results in a two-component thrust force r The main edge concentration T, is given as:

r, = K, cos aph(d/z)(f/z)

and the component due to the chisel edge T, is given as: T2=K2

F.

where: K, and K, are tool geometry parameters; d’ is the chisel edge length and T* is the flow stress term. APPENDIX 2 The

standard deviations for typical data from the various tests is given below for four different tool geometries studied. S.D. Range Torque Thrust [email protected] OIXE 0.234.8 TIXE o.m.12 0.23-2.3 QIXE 0.0-0.18 0.00-0.40 MIXE 0.0-0.28 0.38-2.19 O.&o.19 YIXE 0.28-1.22 Each entry is given for the full speed range tested (1tX1-2360 rev/min) and indicates the variation of the experimental data. * See Table 1 for code explanation. Test Condition*