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L. Igumnov et al.
Fig. 12.13 Bifurcation diagrams with frequency parameter p for γ = 4
а
b
Fig. 12.14 The existence and stability region D(1,1) of periodic motions with alternate PS impacts
a(k 1 = 0, ,k = 0), b( k 1 = 0.1, ,k = 0.1)
parameter value; at 0.104 ≤ p ≤ 0.112 a chaotic mode is observed; at 0.1 ≤ p ≤
0.104m 1 = 2, m 2 = 2.
Figure 12.13 shows that the main mode is observed at 0.15 ≤ p ≤ 0.21, 0.13 ≤
p ≤ 0.15m 1 = 3, m 2 = 2, 0.21 ≤ p ≤ 0.22m 1 = 4, m 2 = 1, while at 0.1 ≤ p ≤
0.13, a chaotic mode exists.
Figure 12.14 presents the stability region in the plane with parameters ( p, R),
where μ = 0.1, ε = 0.02, γ = 4, φ = 0, 52, λ 1 = 0, λ 2 = 0, while in
Fig. 12.14a k 1 = 0, ,k = 0(without accounting for anvil heights), in Fig. 12.14b
k 1 = 0.1, ,k = 0.1(with accounting for anvil heights).
Figures 12.16a, b present the bifurcation diagrams with the same set of parameters,
as in Fig. 12.14a, b but for R = 0.25.
The analysis of the diagrams and stability regions showed that if the anvil heights
k 1 , k 1 + are accounted for, this leads to a change in the configuration of the
existence region of periodic motion modes. Thus, it is seen from Fig. 12.15 that the
periodic mode for the selected parameter values exists at 0.15 ≤ p ≤ 0.205 (without
accounting for the anvil heights), and Fig. 12.16 shows that the periodic mode exists
at 0.16 ≤ p ≤ 0.195.
The numerical experiments led to the conclusion that parameters ε, φ, k 1 , ,k have
the most significant effect on the dynamics of the mechanism.
L. Igumnov et al.
Fig. 12.13 Bifurcation diagrams with frequency parameter p for γ = 4
а
b
Fig. 12.14 The existence and stability region D(1,1) of periodic motions with alternate PS impacts
a(k 1 = 0, ,k = 0), b( k 1 = 0.1, ,k = 0.1)
parameter value; at 0.104 ≤ p ≤ 0.112 a chaotic mode is observed; at 0.1 ≤ p ≤
0.104m 1 = 2, m 2 = 2.
Figure 12.13 shows that the main mode is observed at 0.15 ≤ p ≤ 0.21, 0.13 ≤
p ≤ 0.15m 1 = 3, m 2 = 2, 0.21 ≤ p ≤ 0.22m 1 = 4, m 2 = 1, while at 0.1 ≤ p ≤
0.13, a chaotic mode exists.
Figure 12.14 presents the stability region in the plane with parameters ( p, R),
where μ = 0.1, ε = 0.02, γ = 4, φ = 0, 52, λ 1 = 0, λ 2 = 0, while in
Fig. 12.14a k 1 = 0, ,k = 0(without accounting for anvil heights), in Fig. 12.14b
k 1 = 0.1, ,k = 0.1(with accounting for anvil heights).
Figures 12.16a, b present the bifurcation diagrams with the same set of parameters,
as in Fig. 12.14a, b but for R = 0.25.
The analysis of the diagrams and stability regions showed that if the anvil heights
k 1 , k 1 + are accounted for, this leads to a change in the configuration of the
existence region of periodic motion modes. Thus, it is seen from Fig. 12.15 that the
periodic mode for the selected parameter values exists at 0.15 ≤ p ≤ 0.205 (without
accounting for the anvil heights), and Fig. 12.16 shows that the periodic mode exists
at 0.16 ≤ p ≤ 0.195.
The numerical experiments led to the conclusion that parameters ε, φ, k 1 , ,k have
the most significant effect on the dynamics of the mechanism.