confidence level of 90 % in the identification of the significant factors of the process。

= - 630。54 – 2172。50 。 a  +  2128。33 。 p  +  7600 。 a 。 p (4)

Another model that it can be proposed, in agreement with the tendency of the current researches, is the potential model according with Eq。 5。

= 2156。5 。 a 0。7 + 47。4 。 p – 0。7 (5)

Using the Eq。 1 and 4 for the feed rate and cutting depth factors and calculating the relation the residual stresses and the penetration cutting, is possible to obtain the graphs illustrated on the Fig。 7。

Fig。 7。 Relation between the residual stresses and the penetration force as function of the feed rate and cutting depth

Applying the ratio (Residual Stress/Penetration Force) to the factorial analysis for two factors (feed rate (mm/rev) and cutting depth (mm) under two levels of the experiment, it’s possible to identify a linear empirical model for this relationship; Applying the estimated coefficients, resulted  in the Eq。 6:

res   = 20。56 – 57。77 。 f -  87。77 。 p + 31。33 。 f 。 p (6)

The Fig。 8 shows the graph for the Eq。 6。

Fig。 8。 Relationship between the residual stresses and the penetration force

The Eq。 3 and 5 were treated in terms of level curves and represented by the Fig。 9, 10 and 11。

Fig。 9。 Level curve for the variation of the penetration force with the feed rate and the cutting depth。

Fig。 10。 Level curve for the variation of the residual stresses with the feed rate and the cutting depth。

Fig。 11。 Level curve for the correlation between the residual tensions and the penetration forces。

The measured values of the penetration force were always the largest between the cutting forces, and the feed rate and cutting depth were the most significant factors under the penetration force。

The penetration force grows with the increase of the feed rate and the cutting depth。

To resultant cutting forces behaves in the same way that by penetration force, with relationship to the feed rate  and  cutting depth parameters。

It was not possible to find structural transformations on the current phases and consequent “white layers” formation in the domain of the experiments of this work。

The relationship between the feed rate and cutting depth  with the penetration force could be described through linear and potential equations。

The feed rate and cutting depth were the  most  significant factors on the circunferentials residual stresses introduced in the surface of the bodies tests。

The residual stresses were of compression in all the bodies test measurements, in the domain of the experiments of this work。

The residual stresses are so much more compressive as larger the feed rate and the and smaller the cutting depths parameters。

The obtained experimental results allowed the proposition of equations of the linear and potential type。

A correlation between the residual stress and the penetration force was established。

The authors would like to thanks the FAG Bearings-Brazil。

[1] Y。 Matsumoto, M。 M。 Barash, C。 R。 Liu, Effect of hardness on the surface integrity of AISI 4340 steel。 Transactions of the ASME - Journal of Engineering for Industry 108 (1986) 169-175。

[2] J。D。 Thiele, S。N。 Melkote,  R。A。  Pascoe,  T。R。  Walkins, Effect of cutting-edge geometry and workpiece hardness on surface residual stresses in finish hard turning of AISI 52100 steel。 Transactions of the ASME – Journal of Manufacturing Science and Engineering 122/4 (2000) 642-649。 弯曲处的残余应力模型英文文献和中文翻译(7):http://www.youerw.com/fanyi/lunwen_84316.html