Transmission ratio

In the next figures the comparatives between analytical and numerical models are summarized evaluating discrete positions of the slide. The slide displacements compared are equal to: 5 mm, 10 mm, 15 mm, 20 mm and 25 mm. Analytical results are obtained by the “Analytical cinematic model” fixing a constant sliding coefficient SL equal to -2% but this is a simplifying assumption because this coefficient isn’t constant in realty.

Figure A: Transmission ratio comparison with slide displacements of 5 and 10 mm

Figure B: Transmission ratio comparison with slide displacements of 15 and 20 mm

Figure C: Transmission ratio comparison with slide displacement of 25 mm

The output shaft angle δ indicates the locked gear angular position respect the output shaft axis, as it’s possible to see in the next figure.

Figure D: Definition of the described angle

In every output shaft turn everyone of the 4 pinions satellites is locked for 90° of output shaft angle so in every output shaft turn the transmission ratio trend reported in figures above repeats 4 times.

As described in paragraph “Analytical Cinematic Model” the analytical results fit quite well the numerical ones, but there is a relevant difference in the first output shaft angles, where the reference pinion satellite is being locked. In fact, in the initial locking wheel transitory, the unilateral bearing has a wide sliding in the forbidden verse which bring to power losses and to an unwanted maximum point of the transmission ratio. Then the bearing is locking gradually.

The differences between numerical and analytical model increases for increased slide displacements; this is due to greater angular velocity oscillations of the lateral shafts in the rotations about their axis and about disk axis.

In both the analytical and numerical model, transmission ratio oscillates widely when the slide displacement increases and so when the input-output shafts offset raises; when the slide displacement is small these oscillations are reduced.

Next tables summarize the results obtained from the analysis of the analytical and numerical transmission ratio; the tables report the mean values of the transmission ratio, its maximum and minimum values and the relative deviations obtained subtracting the max\min values from the mean values.

Plotting previous results:

Figure E: Correlation between slide displacement and mean transmission ratio

The last graph shows that the differences between the mean analytical and the mean numerical results are low, typically of 1.5%.

The numerical model presents greatest differences between maximum/minimum and mean values than the analytical model. These differences are accentuated in the numerical model for the relevant angular sliding of the unilateral bearings which belongs to the virtual model working as described in the modeling problem. Probably analytic results describe more realistically the real CVT behavior.

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