Figure 5
The figure contains six finite element deformation plots of the same shaft-and-wheel assembly arranged in three rows and two columns. In each subplot, the meshed shaft with flanges at both ends is shown in a deformed shape, bending or twisting differently. The surfaces are colored with a rainbow contour from blue through green to red to indicate “U, Magnitude”, with a small legend in the upper left of each plot listing displacement values for the color scale. Row 1: In the left plot, the shaft bends downward in a smooth arc between the two wheels, with a noticeable tilt of the left wheel. The color map starts with blue near the right wheel, changes through green along most of the shaft, and becomes yellow to red around the left wheel and at the right wheel rim, indicating increasing displacement toward those regions. The color scale ranges from positive 1.729 e minus 04 (blue) to positive 5.859 e minus 02 (red). In the right plot, the shaft bends in an S-like shape, with the central part deflecting in one direction and the right wheel tipped in the opposite direction. Here, the color map shows blue at portions of the shaft near the center, transitioning to green and yellow along the span, and reaching orange to red around the rims of both wheels and at one end of the shaft. The color scale ranges from positive 2.256 e minus 05 (blue) to positive 6.639 e minus 02 (red). Row 2: In the left plot, the right wheel and shaft remain almost straight and uniformly dark blue, while the left wheel is highly twisted into a looped, knot-like shape. The color-spreading trend runs from dark blue on the undeformed-looking shaft to green, yellow, and then bright red on the most twisted portions of the left wheel rim. The color scale ranges from positive 1.772 e minus 09 (blue) to positive 1.245 e minus 01 (red). In the right plot, both wheels and the shaft are bent into an S-shaped curve. The bending trend shows the shaft curving downward then upward between the two wheels, with both wheels slightly tilted relative to the shaft. The color starts with blue around the central shaft, changes to green and yellow along the curved span, and reaches orange to red at the rim of the right wheel and at the free end of the left shaft section. The color scale ranges from positive 8.537 e minus 05 (blue) to positive 1.364 e minus 01 (red). Row 3: In the left plot, the shaft bends in a gentle S-shaped curve between the two wheels. The bending trend shows the shaft deflecting upward near the left wheel, then downward at midspan, and slightly upward again toward the right wheel. The color starts with dark blue near the right wheel and central regions, transitions through cyan and green along the curved shaft, and becomes yellow to red at the free shaft tip on the left. The color scale ranges from positive 2.899 e minus 05 (blue) to positive 1.817 e minus 01 (red). In the right plot, the left wheel region is highly twisted into a helical or corkscrew-like deformation, while the shaft to the right and the far-right wheel remain almost straight and dark blue. The color trend runs from dark blue on the mostly undeformed right shaft and wheel to green, yellow, and bright red on the twisted sections around the left wheel rim and adjacent shaft. The color scale ranges from positive 8.626 e minus 09 (blue) to positive 1.491 e minus 01 (red).Modal vibration mode diagram of wheel set. Source: Authors’ own work