( )( )

The bush wear ( )τwu and the shaft temperature ( )τθ ,r are defi ned through the following equations [3]:

where

∑ (2.5)

mμ (m=1,2,3,…) are the roots of characteristic equation 0)(J-)(BiJ 10 =μμμ . In (2.1)–(2.5), the following nondimensional quantities are introduced

(2.6)

where

(2.7)

and l0 is the no stretched spring length, l1 is the length of the compressed spring for 02 =ϕ , (k* > 0), E1 is the elasticity modulus, ν1 is the Poisson coeffi cient, 1α is the coeffi cient of thermal expansion of the shaft, Tα is the heat transfer coeffi cient, a1 is the thermal diffusivity, 1λ is

the heat transfer coeffi cient, ( )t2ϕ is the angle of bush rotation, Kw is the wear coeffi cient, η denotes the part of heat energy associated with wear [ ]1,0∈η , tc is the time of contact (0 < t < tc, P(t) > 0).