Optimization of the cutting regims and estimation of possibilities of efficiency rise at the face milling

There are presented the results of the cutting regimes optimization on the criteria of the prime price, the productivity and multiplicative association of these criteria at the face milling. The coefficients of intercommunication between of the cutting regimes, expected on the different criteria of optimization, are grounded. Analytical dependences of optimum values of feed and cutting speed are allowing to calculaty the optimum cutting regims for any machining terms. Got dependences provide the quantitative estimation of the cutting regims intensification at the use of the hard-alloy cutting tool with wearproof coverages. The efficiency estimation is executed on basis of the productivity rise and of the prime price decline at the face milling by the hard-alloy cutting tool with wearproof coverages. There are presented the results of experimental and theoretical researches of the cutting tool life, cutting temperature and work surface roughness at the face milling by the cutting tool with wearproof coverages. The comparative analysis of the possibilities of the productivity rise and of the prime price decline is executed due to the cutting tool life increase, the cutting temperature and the work surface roughness lowering at the use of the cutting tool with different wearproof coverages.


Introduction
The rise of the manufacturing efficiency is the major problem of the modern engineer. This problem successfully decides based on the application of the hard-alloy cutting tool with wearproof coverages including the face milling cutters [1] and ground of optimum terms it exploitation. It is known the method of the optimization of the cutting regimes at the face milling on the criteria of the productivity and the prime price [2,3]. There is of interest the use for the face milling of multiplicative association of these criteria, applied before at the turning [4].
It is known the method of the cutting regimes optimization on the different criteria and estimation of efficiency of the cutting tools with wearproof coverage's at the turning [5]. The method is based on the estimation of the possibilities of intensification of the optimum cutting regimes due to the increase of the tool with wearproof coverages life, declines of cutting temperature and roughness of the treated surface. There is of interest further development of this method as it applies to other types of the machining and foremost to the face milling, which is the most widespread method of the flat surfaces treatment.
The purpose of the presented work is the optimization on the different criteria of the cutting regimes at the face milling and analysis of possibilities of it efficiency rise due to the use the hardalloy cutting tool with wearproof coverages.

General information
In presented work the there are used followings generally accepted criteria of the optimization: productivity P, prime price C, association of these criteria СМ = Р/С [4]. The objective functions expresses dependence of the optimization criteria on the cutting speed V and the feed S [4]: ; kV = 1/m -1; kS = yv/m -1; tc -the restoration time of the tool; T -the cutting tool life period; А -the expenses for 1 minute of the equipment work; Аиthe expenses for 1 the cutting tool life period; t -the cutting depth; B -the milling width; z -the number of the milling cutter tooth; Dthe diameter of milling cutter; CV, KVfactors and xv, uv,pv, qv, yv, mthe indexes characterizing degree of influence of the depth t, milling width B, feed S and cutting tool life T for cutting speed V; К = о/ -coefficient of the necessary decline of the cutting temperature at exceeding by it possible level о [4]. Two-parameter graphs of the relative objective functions of the productivity Рr, prime price Cr and association of these criteria CrM depending on the cutting speed V and the feed S, which are presented on the figure 1 testify to the presence of extremums of objective functions. There are set analytical dependences of the optimum feed Sо and cutting speed Vо from the face milling parameters, which allow for any terms treatments to expect the optimum cutting regimes. At the rough milling optimum feed Sо1 regardless of the optimization criterion is determined coming from the limitations on the cutting plate strength, at the finish milling the optimum feed is determined coming from the limitations on the work surface roughness: where CP, KP -factors and xp, yp, np -the indexes characterizing degree of influence of cutting depth t, feed S and cutting speed V for cutting force Pz; Кφ = (sin60 o /sin φ) -factors taking into account the tool
The calculations of the optimum cutting regimes are resulted for two variants of the machining (the rough face milling and the finish face milling) of the construction steel by the sintered hard alloy cutting tool. The geometrical parameters are: major cutting edge angle  = 67, rake angle = -11; diameter of milling cutter D = 125mm; milling width B = 85mm; cutting tool life period T = 180min. Definition of the optimum cutting regimes at the rough milling is executed for following terms: cutting depth t = 3mm; width of the cutting plate c = 4.76mm. Definition of the optimum cutting regimes at the finish milling is executed for following terms: cutting depth t = 1mm; work surface roughness Ra.= 2.5мкм. The dependences of the work surface roughness Ra from the cutting process parameters at the face milling Ra = 11.6S 1.62 [2].   At the face rough milling the optimum cutting speeds are determined taking into account the optimization criterion: VоР1for criterion of the maximum productivity, VоС1for criterion of the minimum prime price, VоМ1for criterion of the multiplicative association of these criteria.
As a result of the comparison of these optimum cutting speeds it is set that optimum at productivity cutting speed is on 30% higher, than optimum on the prime price speed and on 9% higher, than optimum on criterion of the association. In general case, the indicated coefficients can be expected: At the face finish milling it is necessary to take into account the temperature limitations in case that determined taking into account the optimization criterion: VоР2for the productivity criterion, VоС2for prime price criterion, VоМ2for the association of these criteria: where СΘ -factors and nt, yt, xtthe indexes characterizing degree of influence of cutting speed V, feed S and depth t for the cutting temperature Θ; КoP, КoC, КoMthe border value of coefficient of cutting temperature decline for different optimization criterion: for criterion of the maximum productivity, for criterion of the minimum prime price, for criterion of the multiplicative association of these criteria accordingly.   Graphs of change of the optimum cutting speeds Vо depending on the optimum feed Sо for the different optimization criterion at the rough milling are presented on the figure 6. Graphs of change of the border value of coefficient of the cutting temperature decline KΘо depending on the optimum feed Sо for the different optimization criterion at the finish milling are presented on the figure 7. The dependences of the cutting temperature from the cutting process parameters at the face milling of construction steel  =302V 0.23 S 0.21 [2].
The presented graphs illustrate conformities to law of changeoptimum on the different criteria cutting regimes and present recommendations on a choice optimum feed Sо and cutting speeds Vо under various conditions of the rough and face finish milling. Analytical dependences of optimum values of feed (3) and cutting speed (4) are allowing to calculatу the optimum cutting regims for any machining terms.
For the before indicated machining terms following optimum cutting regimes at the rough milling are defined: optimum feed Sо = 0.12mm/t; optimum cutting speed VоP1 = 160m/min; VоС1 = 121m/min; VоM1 = 147m/min; at the finish milling are defined: optimum feed Sо = 0.06mm/t; optimum cutting   Got analytical dependences of optimum cutting regimes provide the quantitative estimation of the cutting regims intensification at the use of the hard-alloy cutting tool with wearproof coverages. Efficiency of the face milling at the use of the cutting tool with different wearproof coverages is arrived at an account the cutting tool life increase Тcov, the cutting temperaturecov and the work surface roughness lowering Racov by comparison to them indexes for cutting tool without coverages: where КТ, К, КRcoefficients of the cutting tool life Т increase, the cutting temperature and the work surface roughness Ra decline. The quantitative estimation of the cutting regims intensification at the use of the hard-alloy cutting tool with wearproof coverages is provided based on coefficients change of the feed KS and cutting speed KV, which are presented on the figure 8 and figure 9:  The quantitative estimation of increase of the machining efficiency at the face milling at the use of the cutting tool with different wearproof coverages is executed based on coefficients of the productivity rise KP and of the prime price decline KC:   Coefficients of the cutting tool life increase КТ, the cutting temperature KΘ and the work surface roughness decline КR of the face milling at the use of the cutting tool with different wearproof coverages are determined based on experimental researches. Experiments were executed for next terms: the face milling of the construction steel by sintered hard alloy cutting tool with two variants of the wearproof coverages -titanium carbid TiC and titanium nitrid TiN (cutting depth t = 2mm; feed S = 0.3mm/rev).
It is set that at the face milling for the indicated machining terms a cutting temperature does not exceed a possible level Θ = 800 o . Consequently coefficients of the cutting temperature KΘ < 1 and optimum cutting regimes can be determined without account of the temperature limitations.
As a result of experiment there are set coefficients of the cutting tool life increase КТ at the face milling of the cutting tool with coverages TiC -КТ TiC = 2.2; with coverages TiN -КТ TiN = 3.3. As a result of experiment there are set coefficients of the work surface roughness decline КR at the face milling of the cutting tool with coverages TiC -КR TiC = 0.95; with coverages TiN -КR TiN = 0.9. Results of efficiency estimation of face milling cutters with wearproof coverages based on experimental researches are presenting in the table 1.  The results of researches testify that more effective is the use of coverages from of titanium nitrid TiN. Productivity is in 1.4 times higher and prime price is in 1.4 times below, than tools without coverages.
Results of efficiency estimation of face milling cutters with wearproof coverages on the basis of known literary data [1] are presenting in the table 2.

Conclusion
Multi-layered coverages have substantial advantage before one-layered coverages and cutting tools without coverages. Productivity of the face milling cutters with three-layered wearproof coverages TiCN-TiZrN-TiN is in 1.7 times higher and prime price is in 1.7 times below, than without coverages. Thus the comparative analysis of the possibilities of the productivity increase and of the prime price decline is executed due to the cutting tool life increase, the cutting temperature and the work surface roughness lowering at the use of the cutting tool with different wearproof coverages.