(Under construction.)
Run-out means variations of cutting edge positions on a milling cutter.
Run-out consists of static and dynamic components.
- Static components are run-outs which can be measured without rotating.
- Dynamic components are run-outs which can be only measured with rotating.
Thus, when you measure run-out with a dial-gauge and your hand, it is a static run-out.
And then, run-outs consist of radial and axial directions.
It is important to distinguish these two direction.
The conventional evaluation method for run-outs is explained.
Following equations are used.
\( \Delta R_{conv} = max(R_{1}, R_{2},...,R_{n}) - min(R_{1}, R_{2},...,R_{n}) \)
\( \Delta H_{conv} = max(H_{1}, H_{2},...,H_{n}) - min(H_{1}, H_{2},...,H_{n}) \)
\( \Delta R_{conv} \): Conventional radial run-out
\( \Delta H_{conv} \): Conventional axial run-out
\( R_{n} \): Radial cutting edge position of "N"-th edge
\( H_{n} \): Axial cutting edge position of "N"-th edge
I think that these two values lose important information.
You can not evaluate effects to cutting forces and surface roughness by using these two values.
It is the reason why this calculation function is made.
How to evaluate effects to cutting forces by run-outs is explained.
A simple cutting force equation is shown as follows;
\( F_{c} = K_{c} a_{p} f_{z} \)
\( F_{c} \): Cutting force
\( a_{p} \): Axial depth of cut
\( f_{z} \): Feed per tooth
\( K_{c} \): Cutting force co-efficient
In a milling cutter, a undeformed chip section of a current edge is affected by relative positions between a current edge and a previous edge.
Relative positions are shown as follows;
\( \Delta R_{relative,n} = R_{n} - R_{n-1} \)
\( \Delta H_{relative,n} = H_{n} - H_{n-1} \)
\( \Delta R_{relative,n} \): Adjacent radial radial run-out
\( \Delta H_{relative,n} \): Adjacent axial radial run-out
\( R_{n} \): Radial cutting edge position of "N"-th edge
\( R_{n-1} \): Radial cutting edge position of "N-1"-th edge
\( H_{n} \): Axial cutting edge position of "N"-th edge
\( H_{n-1} \): Axial cutting edge position of "N-1"-th edge
In a provisional manner, these relative positions are called adjacent run-outs.
By combining these equations, a following equation is obtained.
\( F_{c,n} = K_{c} (a_{p} + \Delta H_{relative,n}) (f_{z} + \Delta R_{relative,n}) \)
Axial depth of cut is 1 mm-order.
Feed per tooth is 0.1 mm-order.
Axial depth of cut is 10 times larger than feed per tooth.
However, run-outs are from 0 um to 40um.
When you set a feed per tooth 0.1 mm/t, radial run-outs / feed per tooth is from 0 % to 40 %.
When you set an axial depth of cut 1 mm, axial run-outs / axial depth of cut is from 0 % to 4 %.
Thus, adjacent radial run-outs is important for evaluating cutting forces.
How to evaluate effects to a surface roughness by run-outs is explained.
A surface roughness is affected by axial cutting edge positions, the shape of a minor cutting edge, the length of a minor cutting edge, the feed per tooth and the number of teeth.
The feed per rotation is calculated from a feed per tooth and the number of teeth.
When the feed per rotation is larger than the length of the minor cutting edge, the surface roughness become bad.
So, this effect must be considered.
Let's assume the following conditons;
- The number of teeth: 8
- The conventional axial run-out: 15 um
- Feed per rotation: 0.125 mm/rev
- Feed per rotation: 1.0 mm/rev
- The length of a minor cutting edge: 0.5 mm
Case1: Axial positons of No.1 and No.2 edges are -15 um. Those of others are 0 um.
Case2: Axial positons of No.1 and No.5 edges are -15 um. Those of others are 0 um.
Both of case have the same axial run-outs.
However, surface roughnesses of each case are different.
In case 1, a minor cutting edge of No.2 finishes at No.6.
In case 2, a minor cutting edge of No.1 finishes at No.5. And a minor cutting edge of No.5 finishes at No.1.
Thus, in case 2, minor cutting edges of No.1 and No.5 are connected on a workpiece surface.
It means that the combination of cutting edge positions are important.
It is the reason why the effective axial run-out is made.
In this value, axial cutting edge positions, the length of a minor cutting edge, the feed per tooth and the number of teeth is considered.
The shape of a minor cutting edge and the angle of a minor cutting edge is omitted.
Because it is difficult to measure these two values.
How to evaluate effects to a cutting section by run-outs is explained.
The simple cutting force equation is used already.
In the model, adjacent run-out is only used.
It is not precise.
Because, when axial cutting edge positions of No.1, No.2 and No.3 are 0 um, 0 um and -15 um, an underformed chip section of No.3 is affected by No.1 and No.2.
In evaluation of the underformed chip section, these effects are also considered.