1881.] 



The Action of Cutting Tools. 



137 



which they cut, and at the same time may have smaller values for 

 given to them than when held in any other way with which I am 

 acquainted. The general conclusion to which the foregoing remarks 

 point are : — 



(1.) Work has to be expended in dividing substances merely because 

 the necessary forces cannot be applied locally enough ; the more local 

 the application of the force, the less is the travel, and therefore the 

 work required to effect the separation. 



(2.) All ordinary tools act by shearing the substance on which they 

 operate in a plane inclined at an angle of less than 45° to the plane 

 or surface swept out by the edge of the tool. 



(3.) To remove a given volume of material requires nearly the same 

 amount of work, as far as the tool itself is concerned, whether it be 

 removed in few cuts or many ; but the constant friction of the 

 machinery always makes the thicker cuts more economical in practice. 



(4.) Tools for heavy work should be so shaped that the resultant 

 force on them may lie nearly in the direction of motion. In order that 

 this may be the case, must be determined by equation (C). 



If a less value for than this be adopted, less work will be required 

 to effect the same cut, but the tool will have a tendency to dig. 



(5.) In tools which are merely required to leave a good surface and 

 not to take cats of any appreciable depth, the angles are unimportant. 



One curious point connected with the subject of cutting tools is the 

 manner in which their action is facilitated by lubricants. Lubricants 

 seem to act by lessening the friction between the face of the tool and 

 the shaving, and the difficulty is to see how the lubricant can get there, 

 since the only apparent way is round the edge of the tool, and there it 

 might be expected that the contact between the tool and the substance 

 would be too close to admit of its passage. Somehow or other, how- 

 ever, some of the lubricant does find its way between the shaving and 

 the tool, and perhaps also into the substance of the shaving. 



Some metals, copper for instance, when unlubricated, actually refuse 

 to slide over the face of the tool, and the metal is then driven before 

 the tool in a growing lump, as stiff mud would be before a board 

 pushed through it (fig. 6). The separation in these cases does not take 

 place at the edge of the tool, but some distance beneath it. 



Note 1. — On Mr, Babhage's Taper on the Principles of Tools for 

 Turning and Planing Metal. 



Mr. Babbage, in the paper above referred to, assumes that 

 the force required to remove a shaving of constant width may be 

 expressed in terms of its thickness by the series A + B£+C£ 3 + &c, 

 and this of course is perfectly true. But in his application he reduces 

 this series to two terms only, viz., A and C£ 3 ; of these he says that A 

 is the constant force "necessary to tear along the whole line of section 



l 2 



