In case you use two equal milling tools spaced as the normal base pitch (fig.12A) (fig.13U) , you will machine at one time two different surfaces on adiacent tooth, relative to 2 different curvature radius according to:.

For better understand what happens with two milling tools, it is necessary to define Krc ratio that represents cut-lenght operated by rear milling tool and whole cut lenght:

That shows covering action of rear milling tool.

In case of two milling tools in continous mode, active path of front tool may begin at an intermediate position, since rear tool has already machined initial path during cut before.

Best condition occours when Krc value is exactly 0,50 , that means that both tools begin active cut at the same time other than along the same path lenght.

Obviously the first cut for each axial set of cut must be done along a whole path.

In this way machining time may be reduced up to 50%, expecially when Feed value along X must be kept constant, and the reduction is anyway good also when it is possible to fit feed value according to current curvature radius of REAR tool.

In fact, the position difference over profile path corresponding to a fixed difference of curvature radius becomes smaller as curvature radius lowers, so that with feed auto-fitting the front tool has a real feed over profile lower than optimal one.

Cut starting position of front tool along the path may be reached with a high feed with correct X position, or with a small tool desplacement along X .

- For values of krc up to 0,50 (fig.27A) the first contact is done by front tool, and feed fitting may be referred to front tool position; As rear tool begins to cut, feed must reduced since must be referred to rear tool position; Milling path along X is constant for any value of krc.

- For values of krc over 0,50 (fig.28A) the first contact is done by rear tool, and whole feed fitting is referred to its position.

For example, in case of gears in example we have following machining time for each cut path, for a reference feed on profile = 100 mm/min in both fitted and not-fitted feed (values T100P and T100C in (fig.25A) (fig.26A) ):.

:                  WITH NO fit       WITH fit
: PINION:
:  with 1 tool  :     0,901           0,609
:  with 2 tool  :     0,522           0,424
:
: WHEEL:
:  with 1 tool  :     0,649           0,581
:  with 2 tool  :     0,380           0,357

It is clear that feed fitting is more convenient in case of pinion, when curvature radius changes very much in relativ value, and then use of 2 tools is more convenient for machining wheels, since both front and rear cut move along the profile with small real feed differences.

Best machining results occour when krc value is close to 50% and it is possible to fit feed value continously.

Warning: feed fitting is not a matter of CNC performances ( since it is always possible to share cut path into 10-20 steps and assign a proper feed value to each one ) but depends upon the position error of B-X axes when feed changes: it shouldn't be a problem for a modern machine, but it could be the same.

Instead of in order to reduce machining time, second tool might be placed a little more spaced and be used for reducing material stock to be removed by front tool along the external path ( usually corresponding to greatest amount of over-stock).

In this case whole path must be run by front tool, even with a certain penalty since rear tool commands feed value anyway.

In this case the second tool allows to reduce the number of cuts, and each cut operates at two different curvature radius on two following teeth.

Since tool distance is strictly defined, the cuts planning must be optimized in reference to front tool or rear tool extreme positions, so that the number of cuts for a certain form error doesn't succeed in reaching the half value (fig.06A) (fig.09A) (fig.07A) (fig.11A) .

Also in this case the value krc leads to refer planning mode to front or rear tool extreme positions.

A simple simulation shows that the distance between two cuts ( for an assigned form error ) become larger as curvature radius reduces: this means that a cut planning referred to rear tool will be certainly satisfying if properly translated to front tool.

It is only necessary to check relative position between innest rear tool position and outest front tool position.

For values of krc over 0,5 it is better to plan cuts in reference to tip circle curvature radius ( (fig.10A) with plan edge=Re).

For values of krc up to 0,5, it is better to plan cuts in reference to a virtual external circle corresponding to innest cuvature radius + 2 x [base normal pitc] * COS(beta).

in order to assure complete covering to front tool position ( (fig.11A) with plan edge=ri+2*P).

For example, we show cut plannigs and their form error for gears in example:

:                  n=8   n=7   n=6   n=5   n=4   n=3   n=2
: PINION:
:       1 tool :  0,071 0,095 0,131 0,196 0,327 0,634 1,769
:       2 tools:  0,023 0,031 0,044 0,065 0,108 0,210 0,584
:
:  WHEEL:
:       1 tool :  0,016 0,021 0,030 0,045 0,074 0,146 0,403
:       2 tools:  0,005 0,006 0,008 0,012 0,020 0,039 0,108

That shows how second tool is convenient also in multi-plane mode.