9.9: Nomenclature

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a, \(\ \tau_\mathrm{a}\)	Adhesive shear strength	kPa
A	Adhesive force on the blade	kN
c, \(\ \tau_\mathrm{c}\)	Cohesive shear strength	kPa
c’	Pseudo cohesive shear strength	kPa
C	Cohesive force on shear plane	kN
E_sp	Specific energy	kPa
F	Force	kN
F_h	Horizontal cutting force	kN
FD	Drag force on chisel (horizontal force)	kN
F_v	Vertical cutting force	kN
FN	Normal force on chisel (vertical force)	kN
g	Gravitational constant (9.81)	m/s²
G	Gravitational force	kN
h_i	Initial thickness of layer cut	m
h_b	Height of the blade	m
h_b,m	Mobilized height of the blade in case Curling Type	m
K₁	Grain force on the shear plane	kN
K₂	Grain force on the blade	kN
I	Inertial force on the shear plane	kN
N₁	Normal grain force on shear plane	kN
N₂	Normal grain force on blade	kN
p_1m	Pore pressure in the shear plane	kPa
p_2m	Pore pressure on the blade	kPa
P_c	Cutting power	kW
Q	Production	m³
r	Adhesion/cohesion ratio	-
r₁	Pore pressure on shear plane/cohesion ratio	-
r₂	Pore pressure on blade/cohesion ratio	-
r_z	Ratio hydrostatic pressure to cohesion	-
R	Radius of Mohr circle	kPa
R₁	Acting point on the shear plane	m
R₂	Acting point on the blade	m
S₁	Shear force due to internal friction on the shear plane	kN
S₂	Shear force due to external friction on the blade	kN
T	Tensile force	kN
UCS	Unconfined Compressive Stress	kPa
v_c	Cutting velocity	m/s
w	Width of the blade	m
W₁	Force resulting from pore under pressure on the shear plane	kN
W₂	Force resulting from pore under pressure on the blade	kN
α	Blade angle	rad
β	Angle of the shear plane with the direction of cutting velocity	rad
\(\ \tau\)	Shear stress	kPa
\(\ \tau_\mathrm{a}\), a	Adhesive shear strength (strain rate dependent)	kPa
\(\ \tau_\mathrm{c}\), c	Cohesive shear strength (strain rate dependent)	kPa
\(\ \tau_\mathrm{s1}\)	Average shear stress on the shear plane	kPa
\(\ \tau_\mathrm{s2}\)	Average shear stress on the blade	kPa
σ	Normal stress	kPa
σ_c	Center of Mohr circle	kPa
σ_T	Tensile strength	kPa
σ_min	Minimum principal stress in Mohr circle	kPa
σ_N1	Average normal stress on the shear plane	kPa
σ_N2	Average normal stress on the blade	kPa
φ	Angle of internal friction	rad
δ	Angle of external friction	rad
λ	Strengthening factor	-
λ₁	Acting point factor on the shear plane	-
λ₂	Acting point factor on the blade	-
λ_HF	Flow Type/Crushed Type horizontal force coefficient	-
λ_VF	Flow Type/Crushed Type vertical force coefficient	-
λ_HT	Tear Type/Chip Type horizontal force coefficient	-
λ_VT	Tear Type/Chip Type vertical force coefficient	-
λ_HC	Curling Type horizontal force coefficient	-
λ_VC	Curling Type vertical force coefficient