In the 1st report, the authors presented two formulae of cutting force for two cutting mechanisms, that are the crack type and the shear type. And the applicable ranges for these two formulae are discussed.
In this report, the authors attempt to generdize these two formulae and to apply them to the results of experiments in two dimensions, using various gypsum and sand mixtures and a coal sample.
The generalized formulae are as follows,
P=2/
n+2
St·
t·cos (α-φ)√1+2Stcos2φ/(n+2) Sc-cos (α-φ) for crack type cutting mechanism,
P=2/n+1
St·
t·cos (α-φ)·cosec1/2 (
k+α-φ)/cos1/2 (
k+α+φ)-cot
k·sin1/2 (
k+α+φ) for shear type cutting mechanism,
where
P=cutting force by unit length of blade
t=depth of cut
St=tensile strength of sample
Sc=compressive stength of sample
φ=friction angle between blade and chip
α=rake angle of cutting tool
n=stress distribution factor
cot
k=
Sc2-16
St2/8
Sc·
StSubstituting experimental data in
Sc,
St, φ, and
k, the authors estimate the stress distribution factor “
n” by means of each set of experimental values of
P/tandα.
In this culculation, W. E. DEMING'S method of statistical adjustment of data is applied. And then the applicable ranges of these two generalized formulae are discussed.
Under the experimentalconditions in this report, it is concluded that the formula for shear type cutting mechanism has a good agreement with the experimental results, but that the formula for crack typecutting mechanism does not agree with the experimental results.
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