Double mechanism

In this section of analysis, a more complex system is simulated. It contains two single mechanisms joined properly to have the output shaft of the first mechanism welded with the input shaft of the second one. The aim of this type of solution is broadening the range of transmission ratios reachable with a fixed maximum displacement of the slide, and so permits a wider range of possible transmission ratio maintaining the same global dimensions.

Figure A: Single mechanism

Figure B: Double mechanism

The modeling of this system repeats that is described on the previous part of this work, so it is not analyzed here; all the components of the second subsystem are identical to those relative to the first subsystem. The friction forces, inserted to model losses in the mechanism, are added in the new elements maintaining the same friction coefficients that are used for the single mechanism.

The next videos illustrate how the double mechanism works when a constant input velocity is applied.

Double mechanism working with constant input velocity

Transmission ratio comparison with same slide position

The first analysis made on double mechanism is a comparative between the double system and the single system with an identical position of the slide, with the aim of analyzing the difference in terms of transmission ratio reached.

In this analysis is assumed for both mechanisms:

  • Slide position = 10 mm
  • Input torque = 100 Nm
  • Angular damping at output shaft = 5 m2 Kg/(rad s)

For the conditions described previously, the single mechanism reaches a mean transmission ratio of about 0.854; the double mechanism instead reaches a mean value of 0.729. The oscillations of the values are written in the next table:

The transmission ratio of the double mechanism is theoretically equal to:

From the analysis it’s possible to observe that this relation is also correct for the numerical model, so it’s possible to say that the numerical model of the double mechanism works correctly. Another important observation is that the double mechanism presents bigger oscillations than the single mechanism at the same transmission ratio. In fact the double mechanism has two pinions satellites blocked at time, one of the first mechanism and one of the second, and then the effect of oscillation in the output entities is about the double of the same effect in the single mechanism, as it is possible to see in the previous table.

Efficiency comparison with same mean transmission ratio

The second analysis is a comparative between the two systems with an identical mean transmission ratio, with the aim of analyzing the difference in terms of efficiency as defined in the paragraph “Efficiency Analysis”; the double mechanism reaches a certain transmission ratio with smaller displacement of the slide, but it presents more elements with friction losses, therefore one cannot predict easily which system provides the higher efficiency.

In this analysis is assumed for both systems:

  • Mean transmission ratio = 0.854
  • Input torque = 100 Nm
  • Angular Damping at output shaft = 5 m2 Kg/(rad s)

The single mechanism reaches this transmission ratio for a displacement of the slide equal to 10 mm as can be seen in the previous analysis; the same transmission ratio in the double mechanism is obtained with a slide displacement equal to 5.65 mm.

In the first case mean efficiency is equal to 98.3% and in the second case it reaches a value of 97.2 %; in conclusion the single mechanism has better efficiency respect to the other when working at the same transmission ratio. This is probably due to higher number of mechanical losses sources in the double mechanism than in the single one; as advantage the double mechanism reaches the same transmission ratio with lower displacement of the slide and so when the maximum displacement is fixed it is possible to obtain a bigger range of possible transmission ratio values.

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