Efficiency analysis

During its operating, Edyson CVT absorbs an entering power and returns it reduced by a mechanical efficiency as output power with different values of rotational velocity and torque. In the numerical model, mechanical power losses regard unilateral bearings, cylindrical bearings through which the base and the slide support the input and output shafts, lateral shafts sliding along disk slopes, supports revolution around input shaft, friction between gear teeth.

Most relevant losses derive from unilateral bearings working. As discussed in “The modelling problem”, most of mechanical losses in these bearings recorded in virtual model simulations are caused by small relative rotations of their rings in the sense ideally impeded by the device. These rotations happen when bearing should lock lateral shaft when it transmits power from principal gear to disk and output shaft. During this phase lateral shaft is subjected to high torque, so even if its relative rotational velocity is small, the power loss is not negligible.

Numerical results here reported derive from simulations made on the virtual model where the free wheel mechanism is been built with a simplified model of unilateral bearing. Efficiency depends strongly by the modeling parameters choice. All analysis shown refers to the same particular set of these which is been chosen because it returns good mean efficiency values in a large range of working conditions. However it does not coincide with the real solution at all and a real Edyson variator could work with efficiency values even better.

Even when the gearbox is set to work in stable conditions, mechanical elements of the transmission never operate in stationary conditions. In this situation is hard to define the efficiency in a proper way to study power losses. Anyway, one can define efficiency as:

In this way, giving constant TIN = 100Nm, C = 3 m2 Kg/(rad s) and a fixed slide position with 20 mm of shafts offset one can obtain the results reported in the image below in term of η. Efficiency trends are all qualitatively similar varying  TIN and C for not null shafts offsets.

Figure A: Efficiency with slide displacement magnitude equal to 20 mm

Mean value of η, calculated in a revolution period of the output shaft (0.284 seconds), is 0.972 but it oscillates between 0.930 and 0.992. These variations in η values derive from not stationary working of the CVT and so they are associated to inertia effects, elastic potential energy stores and other causes.

Steepest efficiency drops, which repeats 4 times in an output shaft revolution, are due to transitory period between unlocking of one lateral shaft and locking of the next. In fact unilateral bearing needs some time, when loaded, to pass from free to locked configuration. In this phase it is loaded by increasing torque but its locking is progressive and this brings to a maximum in power losses which then decrease as the relative angular sliding reduces gradually.

Even if output shaft revolution period is 0.284 seconds, efficiency trend has a periodicity of 0.284/4 = 0.071 seconds. In fact lateral arms in the model geometry are symmetric and in a 360° revolution period of the output shaft everyone of the 4 lateral wheels transmits torque for an angular interval of about 90° of the disk.

Aligning input and output shafts, the revolution multiplier assumes velocity ratio τ = 1. In this configuration all lateral gears remains locked and rotate rigidly with supports. In this case transmission working is effectively stationary in all its parts so, eliminated a first transitory interval time, no locking processes of unilateral bearings occur during the CVT operating. Without these events the periodical efficiency drops do not verify and total power dissipation is related to the angular sliding of locked unilateral bearings and to all other small friction losses.

So mechanical efficiency of the gearbox in the configuration with transmission ratio τ = 1 is constant in stable conditions and it is equal to 0.995 if calculated by numerical simulation setting TIN = 100 Nm and C = 3 m2 Kg/(rad s).

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