1.1.3.2angle conversion from main section to any sectionWhen θ＝0: tanγθ=tanλs，γθ＝λswhenθ＝90°－kr，the longitudinal rake angleγp:tanγp=tan γ0.cos kr＋tan λs.sin kr whenθ＝180°－kr，the transverse rake angleγf:（1.11）tanγf=tan γ0.sin kr＋tan λs.coskr（1.12）the maximum rake angleγg obtained by differential quotient of formula 1.10tan γg＝tan2?0?tan2?sor tan γg＝（1.13）（1.14）tan?f?tan?p221.1.3.2angle conversion from main section to any sectionThe angle formed by the plane where the maximum angle is and the cutting edge projected on the reference plane θmax：tan?0tan θmax＝tan?swhenθ＝90°－kr：whenθ＝180°－kr:（1.15）similarly，the clearance angle of any given sectionαθ：cot?p?cot?0.coskr?tan?s.sinkr(1.17)cot?f?cot?0.sinkr?tan?s.coskr(1.18)1.1.4 working angles
1.1.1.4 working angles influenced by feed motion
(1) Transverse turning shown as Fig.5.15:
In cut-off turning, without
considering feed motion，the cutting path is circular,while considering the feed motion, it becomes helical, and cutting edge plane changes from Ps to Pse，the angle variation is η。The working angles in the reference
system（Pre、Pse、P0e）are：γ0e ＝γ0+η; α0e=α0－η。
(1) Transverse turningη is the resultant cutting speed angle，formed by the main cutting speed and resultant speed. From the definition：tanη＝vfvcf= (1.19)?dWheredistheworkpiecediameterchangedwiththetoolfeeding.ηbecomesbiggerwhenthecuttingtoolapproachesthecenterofthework；whenthecuttingtoolis1mmfarawayfromtheworkcenterundernormalfeedrate,η＝1°40′；goingfurther,ηincreasessuddenly,andclearanceanglebecomes negative.（2）Longitudinal turning
Similarly, the working angles will change because of the resultant speedη
in longitudinal turning ，shown as 1.16，supposing λs＝0，
without considering feed motion, the marked angles are γ0、α0；otherwise the
working cutting edge plane Pse is
tangent to the helical surface and the tool working system （Pse、Pre）has an inclination angleη，the
working angles in working feed section are：γfe＝γf+η；ααf－η
fe＝