A New Model of the Fractional Order Dynamics of the Planetary Gears

Figure 10

Four eigen fractional modes, 𝜉₁(𝛼,𝑡), 𝜉₂(𝛼,𝑡), 𝜉₃(𝛼,𝑡), and 𝜉₄(𝛼,𝑡) presented by surfaces.

(a) First mode of the planetary gear system 𝜉₁(𝛼,𝑡)

(b) Second mode of the planetary gear system 𝜉₂(𝛼,𝑡)

(c) Third mode of the planetary gear system 𝜉₃(𝛼,𝑡)

(d) Fourth mode of the planetary gear system 𝜉₄(𝛼,𝑡)