It is not sufficient to devise a feasible procedure for a desired component or commodity. The procedure must be economically justified. The variables affecting the economics of a machining operation are numerous which include the tool material, machine tool capacity and the cutting conditions. As these variables are readily accessible on the machine tool, their selection has been traditionally considered part of the machine operators duties. How­ever the economical selection of the cutting condition involves techni­cal and cost data which are not readily available to the operator, so that an optimum selection can seldom be achieved by this app­roach. Taylor stressed this point some years ago and suggested that an optimum can only be approached, if the selection is made by a planning engineer with access to all relevant information.

The manufacturing situation is usually a complex operation and a single machining operation is seldom carried out on a compo­nent by one manufacturer.   Thus the true economic optimum for any machining operation must take into account the other processes to be performed on that component. Establishing conditions to give a certain production rate at one stage of the manufacture will influence the production rate at other stages and will also influence storage costs for components. The situation is further complicated by the fact that in general, most manufacturing machine tools are used for more than one type of component and these may give different economic returns. The manufacturing company is interes­ted in the overall profit in a given time interval. Thus, it is concer­ned with the product mix and the production rate a” each manu­facturing state which give the greatest return on the over head in­vestment, and the running costs, including both raw material cost and the machine: operating cost.

In selecting economic operating conditions, machine tool cap­abilities must be taken into account. Often the desired conditions may not be attainable on the machine-tool proposed for particular operation. It is then necessary to either change the operating condition or review the machine tool selection by a cost compari­son, to se» if a change in machine tool is economically justified. The change may involve purchase of new machine or possibly modifying the existing machine. The capacity limits of a machine tool limiting the selection of machining conditions may be listed as-follows ;

(1)   Machine tool maximum feed.

(2)   Machine tool maximum speed.

(3)   Machine tool maximum power.

(4)   Maximum allowable cutting or thurst force.

(5)   Feed and speed limits for the desired component surface finish.

(6)   Machine tool feed and speed steps.

Cost per component, production rate, and profit-rate. The machining cost per component is made up of a number of different costs.   For simplicity, single pass case will be considered.

(i) Non-productive cost per component (C1). ,It includes the cost of loading and unloading component, the ideal time cost and other non-cutting time costs not included in the total cost per com­ponent. This cost is determined by adding all non-productive time T1 and multipling it by the cost rate x. The cost rate includes the labour and over head cost rates.   Thus

                                            C1= xT1

(ii) The cost of machining time (C2). It is found by multiply­ing the cost x, by the machining time per component  Te. The machining time is the times required for the tool to traverse the component (feed engaged), whether the tool is continuously in con­text with the work or not.   The cost C2 is therefore given by

 

(iii) The tool-changing time cost (C3). It is found by multiply­ing the cost rate by the total tool-changing time per component. This time is the time required to change a cutting edge (Td) multiplied by the number of tool changes per.component, hence

C3= x.T(Tae /T)

The number of tool changes depends on the actual cutting time per component (Tae) and the tool life T.

(iv) The tool cost per component (C4). It is equal to the tool cost per cutting edge by y times the number of cutting edges used per component

C4 = y ((Tae /T)

The tool cost per cutting edge depends on the type of tool used. For a brazed tool tip the cost per cutting edge is given by

Y =   Cost of tool  /No. of resharpening  + l

For the throw away tips

   Y= Cost of insert  / Number of cutting edges  + Number of cutting edges in one life of tool holder

Other costs, such as coolant cost, tool inventory cost and work  material cost, may also be included, although the first two costs may (be incorporated in the overhead costs. The cost per component becomes

CT=C1+C2+C3+C4+(Material cost C5)                                          ……..(1)

Excluding the material cost

                              C  = x.TL+ x .Te +x.Td   ( Tae / T)                                                 ……..(2)

Considering equation  (2), it is seen that the cost per component can be reduced by decreasing the loading and unloading time, idle time and the tool changing time. Here a combination of technical and management methods can prove useful. Thus impro­ved jigs and fixtures, inspecting gauges, and tool holders design together with method study can reduce costs. Improved tool materials and tool geometry which can give longer tool-life would reduce the number of tool replacements and grinding costs per com­ponent, and hence lower the cost per component. Overhead costs cannot normally be expected to drop (although this would help), so that cost reduction will have to be based on improved techniques. The cost per component can also be lowered by decreasing the machining time Te . Increase in the cutting speed or feed reduces the machining time Te, but at the same time reduces the tool life at a faster rate ; as

Te  ά 1 / V and   T ά 1 / V 1/m

Thus increasing the cutting speeds has opposing effects on the cost per component, since C2 decreases while the total tool cost (C3+C4) increases. The effect of the speed on the cost per component can be represented by the diagram (24.29).

It is interesting to note that an optimum cost occurs due to the increasing tool costs -an ideal tool which does not wear would give an ever-decreasing cost per component as the speed increases. Although it is unlikely that such an ideal tool will ever be discover­ed  i.e. tool materials which can resist high speeds, giving longer tool-life values. This means that greater demands on machine-tool capabilities will result from improved tool materials

The production rate is inversely proportional to the product­ion time per component. The time per component is given by

                             TT=TL+Te+Td (Tae / T).

 

The production rate is dependent on the cutting conditions and the tool life. For the optimum cost, decreases in TL and Td will increase the production rate. Increase in cutting speed will reduce Te  and increase the tool changing time per component, a minimum time per component or maximum production rate will therefore result as seen in Fig. 24.29 (b). Here again, improved tool materials will increase the optimum speed.

The profit rate (Pr) is expressed by

Pr = Income per component—Cost per component  / Time per component

The variables which reduce the cost per component and increase the production rate will increase profit rate. In view of the fact that variations in cutting speed will give the optimum values of cost per component and production rate, a maximum profit rate will also occur. In general, the speed for maximum profit rate will differ from those for minimum cost and maximum production rate.