Table 1.

Description of symbols in Fig. 1.

Symbol	Explanation
m1, m11	The masses of the front and rear drums
m2, m10	The masses of the front and rear ranging arms
m3, m7	The masses of the front and rear haulage units
m12, m13	The masses of the front and rear walking units
m5, m8	The masses of the front and rear supporting units
m6	The mass of the shearer body
z3, z7	The vibration displacements of the front and rear haulage units
z5, z8	The vibration displacements of the front and rear supporting units
z12, z13	The vibration displacements of the front and rear walking units
z6	The vibration displacement of the shearer body
Iz3, Iz7	The rotational inertia of the front and rear haulage unit
ηz3, ηz7	The vibration swings of the front and rear haulage unit
αz1, αz11	Initial angle of the front and rear ranging arms to the haulage unit
βz1, βz11	The vibration swings of the front and rear drums
γz2, γz10	The vibration swings of the front and rear ranging arms
Rx1, Rz1	Cutting load on the front drum in the traction direction and axial direction
kz2, kz10	Equivalent rigidities of the front and rear ranging arms
kzz2, czz2, kzz10, czz10	Front and rear ranging arms- haulage unit joint rigidities and resistances
kzz5, czz5, kzz8, czz8	Front and rear supporting units—haulage unit joint rigidities and resistances
kzz12、czz12、kzz13, czz13	Front and rear walking units—haulage unit joint rigidities and resistances
kqpz, cqpz, khpz, chpz	Front and rear supporting units—middle groove joint rigidities and resistances
kqdz, cqdz, khdz, chdz	Front and rear guidance sliding boots inner face-pin rail contact rigidities and resistances
kqdm, cqdm, khdm, chdm	Front and rear guidance sliding boots inner top face-pin rail contact rigidities and resistances
kcms, ccms, kcmx, ccmx	The equivalent rigidities and resistances of the upper and lower hydraulic rods on the coalface side
kcks, ccks, kckx, cckx	The equivalent rigidities and resistances of the upper and lower hydraulic rods on the goaf side
e	The radius of gyration of the gravity center of the ranging arm
p	The distance between the gravity centers of the drum and ranging arm
j	THE width of the haulage unit
r	the length of the haulage unit