FIG 1 slotting cutter rake angle profile error caused by If the involute profile in the II - II section of the figure is used as the reference, the thickness of the crest is thinned by Δ f a on each side in the III - III section. Similarly, the root will increase by Δ f f . Equivalent to an increase in the rounding pressure angle, which will cause a large tooth shape error. θ y = inv α y Where cos α y = r bo / r y Figure 2 Analysis of the tooth profile error of the pinion cutter The equation for the projection of the cutting edge on the base surface can be obtained by the following method. Take any point M on the cutting edge, the radius is r y , the section is I - I, and the distance from the base plane OO is Δ b , then there is Δ b =( r a - r y ) tg | γ | M point is rotated by Δ φ angle with respect to M ′ point, and its value is Where β y is the flank angle of the flank surface with radius r y The polar coordinate equation of any point M on the cutting edge (ie the equation of the cutting edge projected on the base surface) is θ y = θ y - Δ φ Next page Measuring Tape,Metric Tape Measure,Rolling Tape Measure,Metric Tape SHANGQIU CHAOYUE MEASURING TOOLS CO., LTD , https://www.calibrateds.com
2, by inserting the distal end surface of the cutter blade as top end section OO, the CD have involute, to OO (base surface) is the polar coordinate plane, so that the axis O o y C involute starting point, Then the polar coordinate equation of the involute is 
= θ y -( r a - r y ) tg | γ | tg α o tg α e / r o ( 1 )
When the gear is cut by the shaper cutter, the surface of the track on which the cutting edge moves up and down is meshed with the gear to be machined, so the projection of the cutting edge on the base surface should be involute without causing a principle error. The shaper blade has a front angle and a back angle, and the tooth side surface of the shaper blade is an involute spiral surface. If the rake angle of the top edge of the shaper blade is γ = 0° , the shape of the rake face is involute. It does not cause machining tooth shape error; if the top edge rake angle γ < 0° , the rake face tooth shape is the intersection of the conical surface and the tooth side surface, and the projection of the cutting edge on the base surface is not an involute, so This will cause a tooth profile error (see Figure 1 ).