Friction Sawing

Friction Sawing M. C. S h a w (1). P r o f e s s o r of E n g i n e e r i n g , A r i z o n a State U n i v e r s i t y , Tempe, A2 85287 / U S A R e c e i v e d on D e c e m b e r 16,1987

Summary The friction sawing operation in which a soft steel tool moving a t very high speed i s used to cut a hard o r soft steel workpiece i s analyzed based upon an assumed melting mechanism. Key Words Sawing, cut-off, friction sawing, melting, processing

Introduction Friction sawing i s an alternative t o the abrasive cut-off operation i n which a soft steel disk or band travelling at very high speed i s forced into a stationary hard or soft workpiece. The frictional energy at the interface causes material t o be removed from the stationary workpiece while the disk o r band experiences relatively l i t t l e wear due t o the very high speed of the disk or band relative to the penetration velocity. The friction sawing operation i s not new as indicated by the following quotation published in London a long time ago (Lardner, 1833). "Another experiment in cutting steel i s s t i l l more curious. Mr. Barnes of Cornwall, i n America, having occasion to repair a cross-cut saw, recollected having heard that the religious sect called Shakers sometimes made use of what he called a buzz to cut iron. He therefore made a circular plate of soft sheet iron, fixed an axis to it, and put it on his lathe, which gave i t a very rapid rotatory motion. He then applied to it, when in motion, a common file, t o make i t perfectly round and smooth but t h e f i l e w a s c u t in t w o by it, while i t received itself no impression. He then applied a piece of smoky quartz, which produced the desired effect. He then brought under it the saw-plate, which in a few minutes was neatly and completely cut through longitudinally. When he stopped the buzz, he found it had not been worn by the operation, and that he could immediately apply his finger t o i t without perceiving much heat. During the operation, there appeared a band of intense fire around the buzz, which continually emitted sparks of fire with great violence. He afterwards marked the saw for the teeth, and i n a short time cut them out by the same means. The foregoing narrative of what had been done in America having appeared i n Sillimann's Journal, Mr. Perkins met w i t h it and tried the experiment w i t h success in London. The writer of this paragraph too, willing to satisfy himself by ocular demonstration of so curious a fact, attached to the spindle of a common lathe a disc of soft sheet iron, not thicker than that of which t i n utensils are commonly made, and only about three inches in diameter: on applying the sharp edge of a hardened steel chisel, the iron was cut by it; but on causing the disc t o revolve very rapidly, it presently overcame the tool, evidently by tempering it at the point of contact: when the cutting had once commenced, i t was easily continued until a deep s l i t was produced produced in the steel. The theory of this phenomenon has been considered of difficult solution - some persons even referring it t o magnetism To the present writer i t appears t o be Simply an effect of attrition, upon the principle of which we frequently see a soft body wear away a harder, when the impetus of motion i s given almost entirely t o the former. A familiar illustration may often be witnessed i n the works of an old clock, the click, although of steel o r case hardened iron, w i l l often be worn completely through by i t s operation on the teeth of the ratchet wheel, the latter being merely made of brass, and hardly worn at all. I t was clear, however, in the experiment alluded to,

Annals of the ClRP Val. 37/1/1988

that no operation of the iron upon the steel took place until the latter had become softened by the friction of the disc, as an intense bluing accompanied the line of section. I t appears that cast iron does not, in the same manner, yield to the action of soft iron. "An iron worker, in a communication t o the editor of the New York Journal above named, says - 'Having occasion, a short time since, to cut a plate of cast iron three eighths of an inch thick, i t was thought that the plan recommended for cutting steel might succeed i n this case. Accordingly a disc of sheet iron was placed on an axis, and adapted t o a water lathe in such a manner as t o revolve w i t h great rapidity. This disc would cut hardened or soft steel, or wrought iron, w i t h much facility, but produced not the slightest effect on the cast iron. I confess I am quite at a loss to explain this difference in the action of the disk."' In modern times, the friction sawing operation i s employed in steel m i l l s t o remove the ends of ingots and in this case very large wheels up to 5 feet (1.5 m) diameter are operated at surface speeds as high as 25000 ft/min (125 m/sec). In the case of these large saws, the rate of penetration through the ingot i s relatively high as i s the horsepower dissipated (up t o 200 hp = 150 kW). Another modern application of friction sawing is i n cutting off individual parts from the central stem in a precision (lost wax) casting operation using a high speed soft steel band operating at speeds up t o I5000 fpm (80 mps) I t i s the purpose of this paper to consider theory that explains the friction sawing operation. Important questions t o be answered are the following: .Why a relatively soft wheel can cut through a much harder workpiece .Why the wheel i s cool t o the touch after use even though it has essentially the same thermal properties as the workpiece which i s obviously heated t o a high temperature as may be seen from the oxidation colors that appear on either side of a cut .The relation between the power consumed and the rate of cut-off .The theoretical upper l i m i t of grinding ratio of work removed vol of wheel consumed

= yo1

.Why the process gray cast iron

works

for

steel

but

not

for

The premise adopted i s that friction sawing involves substantial melting of the workpiece but l i t t l e or no melting of the wheel since this i s consistent w i t h the fact that the wheel may be softer than the work. This i s i n contrast t o grinding where it i s essential that the abrasive be much harder than the material ground. Since thermal energy i s involved in friction sawing, it i s prudent to begin by reviewing the behavior of a high speed moving heat source.

33 1

Movino Heat Source Theorv Jaeger ( 1942) has presented a very useful two dimensional solution to the moving heat source problem. A perfect insulator O f length P w i t h a constant heat source of intensity q (cal/cm*.seC) at i t s lower surface moves w i t h constant velocity V across a semi-infinite stationary body having thermal conductivity k and volume specific heat pC (Fig. la). Figure I b shows the variation Of nondimensional temperature number versus nondimensional distance along the moving conductor for different Peclet numbers [L = -1. For a relatively high speed (L > 20). the variation of k temperature along the interface I s approximately linear and the mean temperature rise w i l l be as follows to a good approximation.

e = 0.754IA- 1 0 . ~

(1)

V(kpC)

(a)

While the thermal quantity of importance in this case (kpC)O.’ does not have a name, i t Is recognized as the geometric mean of thermal conductivity and volume specific heat and hence may be referred t o as the geometric mean thermal property (GMTP).

If the slider Is also a Conductor of heat, the interface temperature may be obtained by substituting Rij for 4 in equation 1 where R i s the fraction of the total energy going t o the (stationary) member. The fraction of the total heat going t o the moving number w i l l then be 1 - R.

Fig. 2a) Friction sawing operation 2b) Enlargement of interface between wheel and work showing black molten zone

Thermal Analvsis - Friction Sawing Figure 2a shows a friction saw in operation while Figure 2b shows the region of contact ignoring curvature of the wheel. The molten region i s shown black i n Figure 2b. After a steady state has been reached, a l l of the work done per unit time F t v s + Fr a, Ncm/s) w i l l be divided between wheel and work and the thermal energy going t o the work w i l l cause melting of solid material that i s at the melting temperature.

Fig. 3. Heat transfer model for two sliding surfaces i n contact w i t h a stationary heat source The f i r s t two effects cancel and hence the partltlon of thermal energy between wheel and work i s independent of veloclty and depends only on the GMTP values for wheel and work. It has been shown (Ramanath and Shaw. 1988) that in general, the thermal partitition coefficient R is

0

where s pertains t o the upper member (saw) and w pertains t o the lower member (work). For friction sawing involving a steel disk and steel workpiece, R = 0.5 That is, equal amounts of heat w i l l flow into wheel and work but much more superficially in the case of the wheel than in the case of the work due t o the large difference in velocities pertaining.

4 b)

.,

Assuming adiabatic melting

4

-2

-I

0

X

Fig. la) Two dimensional slider (perfect insulator) moving over semi-infinite body w i t h velocity V (after Jaeger) Ib) Temperature distribution curves for a non-conducting slider of infinite width moving on a plane conducting surface for different Peclet numbers L = k Figure 3 shows a stationary heat source i n black w i t h two moving surfaces on either side. The amount of heat flowing from the stationary heat source into each of the moving sources W i l l depend on oarea traversing the heat source per unit (- velocity) otime of contact w i t h heat source (- I/velocity) OGMTP = (kpC)O.’ of materlal

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time

where ,h i s the heat of fusion z 315 cal/cc for steel

and J = mechanical equivalent of heat = 418.5 cal/J

where P i s the total power consumed i n kW. Substituting into equation (3) w i t h R = 0.5 P/Pb = (21239) (3 15); = 2 . 6 4

where Q , b are in cm and d i s the rate of down feed i n cm/s.

Assuming a wheel speed of 12700 cm/s (25000 fpm) for the two examples previously given:

The specific energy required (u) w i l l be For the f i r s t example, G = ( 1270011 )0.5= 1 13

u = 100

m, P N/m,

or Pa

(6)

For the second example, G ( 1 2700/0.5)0.5 = 160 Both of these values are relatively high for a cut-off operation

Examples First, consider a large friction saw cutting a relatively large cross section [Q = 10 cm (3.94 in), b = 1 cm (0.394in)l using a high wheel speed (12700 cm/s = 25000 fpm) at a downfeed rate of 1 cm/s (0.394ips) From equation 5, the total power required would be 26.4 kw (35.6 hp) . For a relatively small cut (0 = 1 cm, b = 0. I cm) at a downfeed rate of 0.5 cm/s (12 ipm), the required power would be only 0.132 kW (0.18 hp). This second case is consistent w i t h the situation that might have existed in the 1830s when friction sawing was used t o rough in the teeth of a hand saw. The specific energy (u) for both the large and small cuts i s the same x 109= 2640 MPa (383000 in.lb/cu.in) u= 10 which is nearly four times that required i n an abrasive cut-off operat ion.

a

Grindina Ratio Of work removed ) i s a useful The grinding ratio (volume volume of wheel consumed measure of relative wheel wear i n grinding operations. The grinding ratio for an ideal friction sawing situation involving melting w i l l be

G

meltina f rom wor k Volume melted from wheel

(7)

It i s reasonable t o assume that the ratio of the volume melted from the work t o the volume melted from the wheel w i l l approximately equal the ratio of the penetration of the thermal front into the work t o the penetration of the thermal front into the wheel.

From the theory of heat transfer (Incropera, 1985)

where BS = constant temperature of surface 9, = temperature at distance y from surface after an

elapsed time t from initial contact 8, = ambient temperature

a = thermal diffusivity = k/pC erf = error function

Remarks Based on the foregoing analysis, it appears that unlike fine grlnding, the friction sawlng Operation involves material removal by melting whlch explains how a soft tool can cut a much harder workplece. The tool i s cool after cutting because the depth of penetratlon of heat into the tool i s superficial due t o the speed of the wheel belng so high. The heat entering the wheel during contact w l t h the work i s completely extracted during the noncontacting portlon of a revolutlon. This i s also the case i n fine grlnding as discussed in (Ramanath and Shaw, 1988). The manner of estimatlng the relation between the rate of cuttlng and the power required based on the assumed melting mechanism has been given together w i t h a method of estimating the grinding ratio to be expected. All of these results appear t o be i n agreement w i t h values to be expected In practice. An item not explained i s why friction sawing i s not practical for cast Iron. Thls Is not due to differences between steel and cast iron w i t h regard to meltlng tremperature, heat of fusion or GMTP since differences i n these values are not very great. The difference in performance appears to Ile In the relatlve values of vlscosity Just after m e l w f o r steel and cast Iron. Since the wheel and work are separated by a f i l m of molten metal In a friction sawing operation, a hydrodynamlc bearlng Is lnvolved and of course vlscosity plays a dominant role in such a case. Since thls does not appear to be a suitable place t o discuss the hydrodynamic aspects of the problem thls w i l l be the subject of another paper submitted t o the Journal of Tribology (Trans. AWE).

References

I . Incropera, F. P., 1985, Fundamentals of Heat and Mass Transfer,J. Wiley, New York. 2. Jaeger, J. C., 1942, Moving Sources of Heat and Temperature at Sliding Contacts, Proc. of the Royal SOC. of New South Wales, 76: 222. 3. Lardner, D.L., 1833, The Cabinet CvcloDaedia - A Treatise on the Proaressive lmorovement and Present State of the Manufacturers i n Metal. Vol II Iron and Steel. Longman, Rees, Orme, Brown, Green and Longman, London, pp 156- 157. 4. Ramanath, S. and Shaw, M.C., 1988, Abrasive Grain Temperature at the Beginning of a Cut in Fine Grinding, Soon t o be published in Jour. of Eng. f o r Industry (Trans. ASME).

From this, the depth of melting ym should be proportional to (at)0.5where t i s the contact time which varies as (velocity)-’. Thus, since ci i s approximately the same for wheel and work

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