Lesson 5 of Process Industrial Engineering ONLINE Course (Module)
Lesson 48 of Industrial Engineering ONLINE Course
IE Research by Taylor - Productivity of Machining - Part 1 - Part 2 - Part 3 - Part 4 - Part 5
Lesson 48 of Industrial Engineering ONLINE Course
IE Research by Taylor - Productivity of Machining - Part 1 - Part 2 - Part 3 - Part 4 - Part 5
Lesson 49 - Productivity Science of Machining V
Paper Published in the Proceedings of IISE 2020 Annual Conference.
Frameworks for Productivity Science of Machine Effort and Human Effort
Rao, Kambhampati Venkata Satya Surya Narayana. IIE Annual Conference. Proceedings; Norcross (2020): 429-434.
IE Research by Taylor - Productivity of Machining: Variables Discussed: depth of cut, duration of cut
(F) depth of cut: 1 with 1/2 inch depth to 1.36 with 1/8 inch depth of cut;
284 (F) The depth of the cut; or, one-half of the amount by which the forging or casting is being reduced in diameter in turning.
Proportion is as 1 with 1/2 inch depth of cut to 1.36 with 1/8 inch depth of cut.
(G) duration of cut: 1 with 1.5 hour cut to 1.20 with 20-minute cut;
285 (G) The duration of the cut; i. c., the time which a tool must last under pressure of the shaving without being reground.
Proportion is as 1 when tool is to be ground every 1.5 hour to 1.207 when tool is to be ground every 20 minutes.
284 (F) The depth of the cut; or, one-half of the amount by which the forging or casting is being reduced in diameter in turning.
Proportion is as 1 with 1/2 inch depth of cut to 1.36 with 1/8 inch depth of cut.
EFFECT OF FEED AND DEPTH OF CUT ON CUTTING SPEED
THE EFFECT OF VARYING THE FEED AND THE DEPTH OF THE CUT UPON THE CUTTING SPEED
The following are the principal conclusions arrived at on this subject:
729 (A) With any given depth of cut metal can be removed faster, i. e., more work can be done, by using the combination of a coarse feed with its accompanying slower speed than by using a fine
feed with its accompanying higher speed. (See paragraphs 743 to 751)
730 For example, by referring to any of the sets of experiments in cutting steel, described in paragraphs 743 to 772, it will be noted that if with a combination of inch depth of cut and r inch feed, the hardness of the metal were of such a quality, for instance, that just 100 pounds of chips would be cut off in an hour by using the same tool on the same forging at its proper cutting speed corresponding to a feed of inch, the metal would then be removed at the rate of 250 pounds per hour. In most cases it is not practicable for the operator to take the coarsest feeds, owing either to the lack of pulling power of the machine or the elasticity of the work. Therefore, the above rule is only of
course a broad general statement.
731 (B) The cutting speed is affected more by the thickness of the shaving than by the depth of the cut. (See paragraphs 761 to 763) A change in the thickness of the shaving has about three times as
much effect on the cutting speed as a similar or proportional change in the depth of the cut has upon the cutting speed. Dividing the thickness of the shaving by 3 increases the cutting speed 1.8 times,
while dividing the length that the shaving bears on the cutting edge by 3 increases the cutting speed 1.27 times. (See paragraphs 303 to 306)
732 (C) Expressed in mathematical terms, the cutting speed varies with our standard round nosed tool approximately in inverse proportion to the square root of the thickness of the shaving or of the
feed; (See the various formula from paragraphs 770 to 787)
733 (D) With the best modern high speed tools, varying the feed and the depth of the cut causes the cutting speed to vary in practically the same ratio whether soft or hard metals are being cut. (See paragraphs 1062 and 815 to 828)
734 (E) The same general formula expresses the laws for the effect of depth of cut and feed upon the speed, the constants only requiring to be changed. (See paragraphs 769 to 770) This is a matter of very great importance, as it enables us to use a single slide rule as a means of finding the proper combination of speed and depth of cut and feed for all qualities of metal which may be cut. (See
paragraph 772)
736 (F) The same general type of formula expresses the laws governing the effect of the feed and depth of cut upon the cutting speed when using our different sized standard tools. This is also fortunate as it simplifies mathematical work in the final solution of the speed problem. (See paragraph 772)
IMPORTANCE OF THE STUDY OF EFFECT OF FEED AND DEPTH OF CUT UPON CUTTING SPEED AND THE DIFFICULTIES ATTENDING THESE EXPERIMENTS
737 A study of the effect of the feed and depth of cut upon the cutting speed constitutes in our judgment the most important element in the rt of cutting metals. As pointed out in the opening
paragraphs of this paper, the three questions which must be answered each day in every machine shop by every machinist who is running a metal cutting machine, such as a lathe, planer, etc., are:
WHAT TOOL SHALL I USE?
WHAT CUTTING SPEED SHALL I USE?
WHAT FEED SHALL I USE?
738 Having already established in a shop standards for the shape and quality of the tools, there remain but two of these questions to be answered, namely, as to the cutting speed and the feed. And the decision as to the cutting speed will depend more upon the depth of cut and feed which are chosen than upon any other element.
739 Experiments upon these two elements can only be undertaken after practically all of the other elements in the art of cutting metals have been standardized. A standard quality of tool steel and
its proper heat treatment must have been established. A standard curve for the cutting edge of the tools, with standard lip angles, back slope and side slope, must have been established. The effect of the quality of the metal which is to be cut upon the pressure on the tool and of the pressure on the tool upon the pulling or driving power of the machine must be known before it is possible to decide upon the depth of cut and feed.
740 The depth of cut and feed, then, are of necessity almost the last elements to be experimented upon, and with the exception of determining the combination of the best tool steel and its proper heat
treatment, they constitute the two elements to which we have given the largest amount of time and study. We have undertaken many sets of experiments upon this subject since 1881 when we first
began its investigation, and as discussed in paragraph 213 the accurate determination of these laws is rendered especially difficult owing to the necessity for making such a large number of experiments
in cutting pieces of test metal which are uniform in quality. We have found it difficult to obtain large enough masses of uniform metal to accurately determine these laws, and each improvement in the
quality of the tool steel which gives higher cutting speeds calls for larger and larger masses of uniform test metal, thus greatly increasing the difficulty and expense of these experiments.
741 Moreover, each change in almost any one of our important standards involves in the end a more or less elaborate investigation as to what modification the new standard has made in the effect that a
change of feed or depth of cut has upon the cutting speed. Time after time the absolutely necessary changes in standards have forced us to reinvestigate the effect of feed and depth of cut upon cutting
speed; and viewed from the point of expense alone, such an investigation is truly a serious undertaking. It is a matter of doubt to the writer whether with our accumulated experience it would be possible even now for us to make a consistent series of experiments either upon steel or cast iron with these two elements at a smaller cost than $5000.
742 All of these facts emphasize the desirability for the greatest care and consideration in adopting shop standards, and indicate the importance of not changing shop standards when once adopted except from imperative necessity.
PRACTICAL TABLES GIVING CUTTING SPEEDS CORRESPONDING TO DIFFERENT DEPTHS OF CUT AND THICKNESS OF FEED ON HARD, MEDIUM
AND SOFT STEEL AND ON HARD, MEDIUM AND SOFT CAST
IRON, WHEN BEST MODERN HIGH SPEED TOOLS OF OUR
STANDARD SHAPES ARE USED
743 Before starting to discuss the experiments upon this subject and the formuh which we have developed to represent the conclusions drawn from them we give the following:
744 Folder 24, Figs. 143-154, are practical working tables which will be found useful by machine shop foremen and machinists as a general guide to determining what cutting speed to use under several of the usual or typical conditions met with in ordinary machine shop practice. The cutting speeds given in these tables are based upon the use of our standard tools, shown on Folder 5, Figs. 24 and 28, for cutting hard steel and cast iron, and those shown in Folder 5, Figs. 24 and 20b for cutting medium and soft steel. In making these tables we also assumed the use of the best quality of high speed tool as represented by tool No. 1 (Folder 20, Table 138),treated in the best manner, as described by us in paragraphs 979 to 994. The tables were also based upon cutting three different qualities of steel, having the following chemical and physical properties, and the following cutting
speeds when cut with our standard inch tool, x cut, for standard 20-minute cut.
745 HARD STEEL Cutting speed, 45 ft. per minute; Class No. 21k,
(such for instance as is used in a hard locomotive tire)
Carbon ................................ 0.64 per cent
Manganese ............................. 0.70 per cent
Silicon ................................ 0.21 per cent
Phosphorus ............................. 0.044 per cent
Tensile strength ......................... 118,500 lbs.
Elastic limit ............................. 70,000 lbs.
Percentage of stretch ..................... 14
746 MEDIUM STEEL Cutting speed, 99 ft. per minute; Class No. 13.
Carbon ................................ 0.34 per cent
Manganese ........................... 0.60 per cent
Silicon ................................ 0.183 per cent
Sulphur ............................... 0.032 per cent
Phosphorus ............................. 0.035 per cent
Annealing heat...................... 1275 degrees Fahr.
Tensile strength ........................... 72,830 lbs.
Elastic limit ............................... 34,630 lbs.
Per cent of stretch ......................... 30
Per cent of contraction ...................... 48.73
747 SOFT STEEL Cutting speed, 108 ft. per minute; Class No. 5.
Carbon ................................ 0.22 per cent
Manganese ............................. 0.42 per cent
Silicon ................................ 0.07 per cent
Sulphur ............................... 0.025 per cent
Phosphorus ........................... 0.022 per cent
Annealing heat..................... 1200 degrees Fahr.
Tensile strength ........................... 56,250 lbs.
Elastic limit .............................. 26,590 lbs. Per cent of stretch ........................ 35.50
Per cent of contraction ...................... 56.26
753 This section of the paper is entitled "The Effect of Varying the Feed and the Depth of the Cut upon the Cutting Speed." It should be noted that a change in feed produces a change in the thickness of the chip which is cut by the tool, and that it is the actual thickness of the chip as it crosses the line of the cutting edge of the tool which causes or produces the change in cutting speed. The thinner the chip or shaving the higher the cutting speed, and the thicker the chip the slower the cutting speed. (See paragraphs 292 to 297, explaining the causes for wear on tools and the effect of the pressure of the chip upon the tool.)
754 Now the actual thickness of the chip is dependent not only upon the coarseness of the feed that is, the advance of the tool for each revolution of the work, but also:
a upon the shape of the cutting edge of the tool, and
b upon the position of the tool in the tool post; i. e., the angle at which the cutting edge of the tool is set with relation to the center line of the work.
758 In paragraphs 307 to 311 we have pointed out, and in Folder 16, Fig. 112, we illustrate, the fact that with all curved line cutting edges the chip must necessarily vary in thickness at all points, and that a straight line is the only shape for the cutting edge of a tool in which the thickness of the shaving is uniform throughout its length.
759 The experiments on the effect of feed and depth of cut which are of the greatest practical interest, and the results of which are required for everyday use refer to our standard round nosed tools; but, as just explained, with our standard round nosed tools the actual thickness of the shaving is affected by a change in the depth of the cut as well as by a change in the feed, therefore any investigation made with these standard tools must necessarily include at the same time both the effect of a change in the feed and in the depth of cut upon the cutting speed.
760 With but little thought, therefore, it becomes evident that for the primary or more fundamental investigation as to the effect which the thickness of the chip or shaving has upon the cutting speed, it is desirable to experiment first upon shavings which are uniform in thickness throughout their whole length, and therefore we first describe our experiments with different thicknesses of shaving
uniform throughout their length.
285 (G) The duration of the cut; i. c., the time which a tool must last under pressure of the shaving without being reground.
Proportion is as 1 when tool is to be ground every 1.5 hour to 1.207 when tool is to be ground every 20 minutes.
HOW LONG SHOULD A TOOL BE RUN WITHOUT REGRINDING?
711 It is clear that we have on the one hand the main fact that the more often we are willing to grind the tool the higher the cutting speed at which the tool can be run, and therefore the larger the
amount of work which will be turned out by the machine. On the other hand, there are four opposing considerations all of which tend toward a greater expense the more frequently the tools are ground.
These considerations are:
712 (A) The time required to remove the worn-out tool from the tool-post; get another sharp tool; set and clamp it into the tool-post; and again start the roughing cut to exactly the proper size. For
exact figures see, Folder 15, Table 108.
713 (B) The time of the tool grinder and the grinding machine and the wear on the emery wheel each time a tool is ground, which can be expressed in terms of the time of the lathe hand and his lathe time. For exact figures see, Folder 15, Fig. 108.
714 (C) The cost of the smith's and helper's wages, and fire, blast, etc., in the smith shop, for dressing a tool; which cost should be divided by the total number of times the tool is ground before it
requires redressing. And this fraction of the dressing cost can then be expressed also in terms of the time of the lathe hand and his lathe. For exact figures see, Folder 15, Fig. 108.
715 (D) The cost of the tool steel which is lost every time a tool is redressed. This cost should also be divided by the total number of times the tool is ground, and expressed in terms of the time of the
lathe hand and lathe. For exact figures see, Folder 15, Fig. 108.
716 This problem has been put into definite mathematical form and solved by us as follows: Let us assume that the cost of the grinder's wages plus the cost of the grinding machine is the same per
hour or minute as the cost of the lathe in which the work is being done plus the wages of the lathe hand for lathes using certain sized tools; and that for lathes using larger sized tools the grinding machine cost is proportionally smaller, while for lathes using smaller tools the grinding machine cost is proportionally larger. Also, in a similar way the cost of the smith and his helper and of the fuel are expressed in terms of the time of the lathe hand and his machine, as stated above. This enables us then to arrive at the following mathematical solution of the problem.
717 Folder 15, Table 108, we have given the time required to dress and grind the various sized tools, and also the time required to place them in the machine, remove them from the machine, and start
the cut. These data have been compiled from accurate observations made in each case by a competent observer with a stop watch, while the grinder, the lathe hand, and the smith were working at their
proper normal speeds. In the same table we have also given the average number of times that each of the sizes of our standard tools can be reground before requiring to be redressed. The cost of the
tool steel used each time a tool is dressed is also found in the same table.
Updated on 16 July 2021
Pub 4 July 2020
Productivity Impact of Depth of cut: 1 with 1/2 inch depth to 1.36 with 1/8 inch depth of cut;
284 (F) The depth of the cut; or, one-half of the amount by which the forging or casting is being reduced in diameter in turning.
Proportion is as 1 with 1/2 inch depth of cut to 1.36 with 1/8 inch depth of cut.
EFFECT OF FEED AND DEPTH OF CUT ON CUTTING SPEED
THE EFFECT OF VARYING THE FEED AND THE DEPTH OF THE CUT UPON THE CUTTING SPEED
The following are the principal conclusions arrived at on this subject:
729 (A) With any given depth of cut metal can be removed faster, i. e., more work can be done, by using the combination of a coarse feed with its accompanying slower speed than by using a fine
feed with its accompanying higher speed. (See paragraphs 743 to 751)
730 For example, by referring to any of the sets of experiments in cutting steel, described in paragraphs 743 to 772, it will be noted that if with a combination of inch depth of cut and r inch feed, the hardness of the metal were of such a quality, for instance, that just 100 pounds of chips would be cut off in an hour by using the same tool on the same forging at its proper cutting speed corresponding to a feed of inch, the metal would then be removed at the rate of 250 pounds per hour. In most cases it is not practicable for the operator to take the coarsest feeds, owing either to the lack of pulling power of the machine or the elasticity of the work. Therefore, the above rule is only of
course a broad general statement.
731 (B) The cutting speed is affected more by the thickness of the shaving than by the depth of the cut. (See paragraphs 761 to 763) A change in the thickness of the shaving has about three times as
much effect on the cutting speed as a similar or proportional change in the depth of the cut has upon the cutting speed. Dividing the thickness of the shaving by 3 increases the cutting speed 1.8 times,
while dividing the length that the shaving bears on the cutting edge by 3 increases the cutting speed 1.27 times. (See paragraphs 303 to 306)
732 (C) Expressed in mathematical terms, the cutting speed varies with our standard round nosed tool approximately in inverse proportion to the square root of the thickness of the shaving or of the
feed; (See the various formula from paragraphs 770 to 787)
733 (D) With the best modern high speed tools, varying the feed and the depth of the cut causes the cutting speed to vary in practically the same ratio whether soft or hard metals are being cut. (See paragraphs 1062 and 815 to 828)
734 (E) The same general formula expresses the laws for the effect of depth of cut and feed upon the speed, the constants only requiring to be changed. (See paragraphs 769 to 770) This is a matter of very great importance, as it enables us to use a single slide rule as a means of finding the proper combination of speed and depth of cut and feed for all qualities of metal which may be cut. (See
paragraph 772)
736 (F) The same general type of formula expresses the laws governing the effect of the feed and depth of cut upon the cutting speed when using our different sized standard tools. This is also fortunate as it simplifies mathematical work in the final solution of the speed problem. (See paragraph 772)
IMPORTANCE OF THE STUDY OF EFFECT OF FEED AND DEPTH OF CUT UPON CUTTING SPEED AND THE DIFFICULTIES ATTENDING THESE EXPERIMENTS
737 A study of the effect of the feed and depth of cut upon the cutting speed constitutes in our judgment the most important element in the rt of cutting metals. As pointed out in the opening
paragraphs of this paper, the three questions which must be answered each day in every machine shop by every machinist who is running a metal cutting machine, such as a lathe, planer, etc., are:
WHAT TOOL SHALL I USE?
WHAT CUTTING SPEED SHALL I USE?
WHAT FEED SHALL I USE?
738 Having already established in a shop standards for the shape and quality of the tools, there remain but two of these questions to be answered, namely, as to the cutting speed and the feed. And the decision as to the cutting speed will depend more upon the depth of cut and feed which are chosen than upon any other element.
739 Experiments upon these two elements can only be undertaken after practically all of the other elements in the art of cutting metals have been standardized. A standard quality of tool steel and
its proper heat treatment must have been established. A standard curve for the cutting edge of the tools, with standard lip angles, back slope and side slope, must have been established. The effect of the quality of the metal which is to be cut upon the pressure on the tool and of the pressure on the tool upon the pulling or driving power of the machine must be known before it is possible to decide upon the depth of cut and feed.
740 The depth of cut and feed, then, are of necessity almost the last elements to be experimented upon, and with the exception of determining the combination of the best tool steel and its proper heat
treatment, they constitute the two elements to which we have given the largest amount of time and study. We have undertaken many sets of experiments upon this subject since 1881 when we first
began its investigation, and as discussed in paragraph 213 the accurate determination of these laws is rendered especially difficult owing to the necessity for making such a large number of experiments
in cutting pieces of test metal which are uniform in quality. We have found it difficult to obtain large enough masses of uniform metal to accurately determine these laws, and each improvement in the
quality of the tool steel which gives higher cutting speeds calls for larger and larger masses of uniform test metal, thus greatly increasing the difficulty and expense of these experiments.
741 Moreover, each change in almost any one of our important standards involves in the end a more or less elaborate investigation as to what modification the new standard has made in the effect that a
change of feed or depth of cut has upon the cutting speed. Time after time the absolutely necessary changes in standards have forced us to reinvestigate the effect of feed and depth of cut upon cutting
speed; and viewed from the point of expense alone, such an investigation is truly a serious undertaking. It is a matter of doubt to the writer whether with our accumulated experience it would be possible even now for us to make a consistent series of experiments either upon steel or cast iron with these two elements at a smaller cost than $5000.
742 All of these facts emphasize the desirability for the greatest care and consideration in adopting shop standards, and indicate the importance of not changing shop standards when once adopted except from imperative necessity.
PRACTICAL TABLES GIVING CUTTING SPEEDS CORRESPONDING TO DIFFERENT DEPTHS OF CUT AND THICKNESS OF FEED ON HARD, MEDIUM
AND SOFT STEEL AND ON HARD, MEDIUM AND SOFT CAST
IRON, WHEN BEST MODERN HIGH SPEED TOOLS OF OUR
STANDARD SHAPES ARE USED
743 Before starting to discuss the experiments upon this subject and the formuh which we have developed to represent the conclusions drawn from them we give the following:
744 Folder 24, Figs. 143-154, are practical working tables which will be found useful by machine shop foremen and machinists as a general guide to determining what cutting speed to use under several of the usual or typical conditions met with in ordinary machine shop practice. The cutting speeds given in these tables are based upon the use of our standard tools, shown on Folder 5, Figs. 24 and 28, for cutting hard steel and cast iron, and those shown in Folder 5, Figs. 24 and 20b for cutting medium and soft steel. In making these tables we also assumed the use of the best quality of high speed tool as represented by tool No. 1 (Folder 20, Table 138),treated in the best manner, as described by us in paragraphs 979 to 994. The tables were also based upon cutting three different qualities of steel, having the following chemical and physical properties, and the following cutting
speeds when cut with our standard inch tool, x cut, for standard 20-minute cut.
745 HARD STEEL Cutting speed, 45 ft. per minute; Class No. 21k,
(such for instance as is used in a hard locomotive tire)
Carbon ................................ 0.64 per cent
Manganese ............................. 0.70 per cent
Silicon ................................ 0.21 per cent
Phosphorus ............................. 0.044 per cent
Tensile strength ......................... 118,500 lbs.
Elastic limit ............................. 70,000 lbs.
Percentage of stretch ..................... 14
746 MEDIUM STEEL Cutting speed, 99 ft. per minute; Class No. 13.
Carbon ................................ 0.34 per cent
Manganese ........................... 0.60 per cent
Silicon ................................ 0.183 per cent
Sulphur ............................... 0.032 per cent
Phosphorus ............................. 0.035 per cent
Annealing heat...................... 1275 degrees Fahr.
Tensile strength ........................... 72,830 lbs.
Elastic limit ............................... 34,630 lbs.
Per cent of stretch ......................... 30
Per cent of contraction ...................... 48.73
747 SOFT STEEL Cutting speed, 108 ft. per minute; Class No. 5.
Carbon ................................ 0.22 per cent
Manganese ............................. 0.42 per cent
Silicon ................................ 0.07 per cent
Sulphur ............................... 0.025 per cent
Phosphorus ........................... 0.022 per cent
Annealing heat..................... 1200 degrees Fahr.
Tensile strength ........................... 56,250 lbs.
Elastic limit .............................. 26,590 lbs. Per cent of stretch ........................ 35.50
Per cent of contraction ...................... 56.26
753 This section of the paper is entitled "The Effect of Varying the Feed and the Depth of the Cut upon the Cutting Speed." It should be noted that a change in feed produces a change in the thickness of the chip which is cut by the tool, and that it is the actual thickness of the chip as it crosses the line of the cutting edge of the tool which causes or produces the change in cutting speed. The thinner the chip or shaving the higher the cutting speed, and the thicker the chip the slower the cutting speed. (See paragraphs 292 to 297, explaining the causes for wear on tools and the effect of the pressure of the chip upon the tool.)
754 Now the actual thickness of the chip is dependent not only upon the coarseness of the feed that is, the advance of the tool for each revolution of the work, but also:
a upon the shape of the cutting edge of the tool, and
b upon the position of the tool in the tool post; i. e., the angle at which the cutting edge of the tool is set with relation to the center line of the work.
758 In paragraphs 307 to 311 we have pointed out, and in Folder 16, Fig. 112, we illustrate, the fact that with all curved line cutting edges the chip must necessarily vary in thickness at all points, and that a straight line is the only shape for the cutting edge of a tool in which the thickness of the shaving is uniform throughout its length.
759 The experiments on the effect of feed and depth of cut which are of the greatest practical interest, and the results of which are required for everyday use refer to our standard round nosed tools; but, as just explained, with our standard round nosed tools the actual thickness of the shaving is affected by a change in the depth of the cut as well as by a change in the feed, therefore any investigation made with these standard tools must necessarily include at the same time both the effect of a change in the feed and in the depth of cut upon the cutting speed.
760 With but little thought, therefore, it becomes evident that for the primary or more fundamental investigation as to the effect which the thickness of the chip or shaving has upon the cutting speed, it is desirable to experiment first upon shavings which are uniform in thickness throughout their whole length, and therefore we first describe our experiments with different thicknesses of shaving
uniform throughout their length.
Productivity Impact of duration of cut: 1 with 1.5 hour cut to 1.20 with 20-minute cut;
285 (G) The duration of the cut; i. c., the time which a tool must last under pressure of the shaving without being reground.
Proportion is as 1 when tool is to be ground every 1.5 hour to 1.207 when tool is to be ground every 20 minutes.
HOW LONG SHOULD A TOOL BE RUN WITHOUT REGRINDING?
711 It is clear that we have on the one hand the main fact that the more often we are willing to grind the tool the higher the cutting speed at which the tool can be run, and therefore the larger the
amount of work which will be turned out by the machine. On the other hand, there are four opposing considerations all of which tend toward a greater expense the more frequently the tools are ground.
These considerations are:
712 (A) The time required to remove the worn-out tool from the tool-post; get another sharp tool; set and clamp it into the tool-post; and again start the roughing cut to exactly the proper size. For
exact figures see, Folder 15, Table 108.
713 (B) The time of the tool grinder and the grinding machine and the wear on the emery wheel each time a tool is ground, which can be expressed in terms of the time of the lathe hand and his lathe time. For exact figures see, Folder 15, Fig. 108.
714 (C) The cost of the smith's and helper's wages, and fire, blast, etc., in the smith shop, for dressing a tool; which cost should be divided by the total number of times the tool is ground before it
requires redressing. And this fraction of the dressing cost can then be expressed also in terms of the time of the lathe hand and his lathe. For exact figures see, Folder 15, Fig. 108.
715 (D) The cost of the tool steel which is lost every time a tool is redressed. This cost should also be divided by the total number of times the tool is ground, and expressed in terms of the time of the
lathe hand and lathe. For exact figures see, Folder 15, Fig. 108.
716 This problem has been put into definite mathematical form and solved by us as follows: Let us assume that the cost of the grinder's wages plus the cost of the grinding machine is the same per
hour or minute as the cost of the lathe in which the work is being done plus the wages of the lathe hand for lathes using certain sized tools; and that for lathes using larger sized tools the grinding machine cost is proportionally smaller, while for lathes using smaller tools the grinding machine cost is proportionally larger. Also, in a similar way the cost of the smith and his helper and of the fuel are expressed in terms of the time of the lathe hand and his machine, as stated above. This enables us then to arrive at the following mathematical solution of the problem.
717 Folder 15, Table 108, we have given the time required to dress and grind the various sized tools, and also the time required to place them in the machine, remove them from the machine, and start
the cut. These data have been compiled from accurate observations made in each case by a competent observer with a stop watch, while the grinder, the lathe hand, and the smith were working at their
proper normal speeds. In the same table we have also given the average number of times that each of the sizes of our standard tools can be reground before requiring to be redressed. The cost of the
tool steel used each time a tool is dressed is also found in the same table.
Updated on 16 July 2021
Pub 4 July 2020
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