*Effect of Different Material Properties on the Nonlinear Dynamics Phenomenon… DOI: http://dx.doi.org/10.5772/intechopen.112795*

speeds and follower guides' clearances since there will be an energy dissipation outside the envelope of phase-plane diagram. The non-periodic motion of the follower displacement is shown in **Figure 3c** and **d** when the follower starts multi-impacts since the follower variation is increased with the increasing of cam speeds. The Poincare' maps investigate the chaotic motion of the follower due to multi-impact in one cycle of the cam rotation [10]. **Figure 4** shows the Poincare' maps when the contact condition is nylon for follower guide's clearance (16.10-3 mm). Poincare' map represents that the follower motion reached the steady state (periodic motion) as shown in **Figure 4a** based on the single dot in Poincare' map for the given displacement and velocity. **Figure 4b** reflects the periodic motion of the follower displacement at (55 and 59.5 mm) while the non-periodic motion is occurred when the black dots are stationed around one area inside Poincare' map. The more black dots in Poincare' maps, the more detachment heights between the cam and the follower. The non-periodic motion of the follower displacement is indicated in **Figure 4d**. The quasi-periodic motion of the follower displacement is shown in **Figure 5a** and **b** at follower displacement (27 mm), and (30.5 to 31 mm). The non-periodic motion of the follower displacement is shown in **Figure 5d**. The black dots are increased with the increasing of cam speeds and with the increasing of follower guides' clearances. SolidWorks software is used to calculate the follower displacement and follower velocity at different contact conditions, different cam speeds, and different follower

**Figure 6.**

*Follower displacement mapping when the contact condition is nylon for follower guide's clearance (17.10-3 mm).*

guides' clearances. Follower guide clearances (C = 1610-3, 1710-3, 1810-3, and 1910-3 mm) are used in the simulation while the cam is rotating at constant speed (100, 300, 500, and 700 rpm). **Figure 6** shows the mapping of follower displacement when the contact condition is nylon at different cam speeds and follower guide's clearance (17.10-3 mm). The cam and the follower are in permanent contact as shown in **Figure 6a** in which it indicates periodic motion. The quasi-periodic motion of the follower displacement is shown in **Figure 6b**. The detachment of the follower is shown in **Figure 6c** in which it indicates non-periodic motion and chaos as shown in **Figure 6d**. **Figure 7** shows the mapping of follower displacement when the contact condition is steel greasy at different cam speeds and follower guide's clearance (17.10-3 mm). The cam and the follower are in permanent contact as shown in **Figure 7a** and **b** which indicates periodic motion for the follower displacement. The quasi-periodic motion of the follower displacement is shown in **Figure 7c** in which the detachment is occurred between the cam and the follower. **Figure 7d** shows the nonperiodic motion and chaos for the follower displacement due to the high speed of the cam. **Figure 6d** indicates non-periodic motion and chaos over all the periods of time

#### **Figure 7.**

*Follower displacement mapping when the contact condition is steel greasy for follower guide's clearance (17.10-3 mm).*

*Effect of Different Material Properties on the Nonlinear Dynamics Phenomenon… DOI: http://dx.doi.org/10.5772/intechopen.112795*

#### **Figure 8.**

*Follower displacement mapping when the contact condition is steel greasy for follower guide's clearance (17.10-3 mm).*

#### **Figure 9.**

*Follower displacement mapping for follower guide's clearance (19.10-3 mm) at different contact conditions.*

while in **Figure 7d** the motion of the follower displacement is divided between periodic and non-periodic motion and chaos over some periods of time. It can be concluded from all the contact conditions that the non-periodic motion starts at (N = 300 rpm) except for the contact condition of nylon material properties where the non-periodic motion starts sometimes earlier after (N = 100 rpm). All the contact conditions have periodic motion at (N = 100 rpm). **Figure 8** shows the follower displacement mapping when the contact condition is steel greasy for follower guide's clearance (17.10-3 mm) while **Figure 9** shows the follower displacement mapping for follower guide's clearance (19.10-3 mm) at different contact conditions. **Figure 10** shows the follower displacement mapping when the contact condition is aluminum greasy at different guides' clearances.

**Figure 10.** *Follower displacement mapping when the contact condition is aluminum greasy at different guides' clearances.*
