Calculation of the basic parameters of planetary hydraulic motor.

Annotation

A schematic diagram of the planetary gearing is shown. The calculation of the main parameters of a planetary hydraulic motor such as torque, working volume, output power, total and volumetric efficiency is presented in this article.

Hydraulic motor is a hydraulic machine designed to convert the hydraulic energy of a droplet liquid stream into the mechanical energy of the output link (shaft). The planetary is a high-torque, low-speed, volume-type hydraulic motor whose displacement system is the internal gearing of the two gears.

The torque of the hydraulic motor is given by the formula:

q – working capacity, cm3

ΔР – differential pressure of the hydraulic motor, MPа

ηhm – hydromechanical efficiency.

The working chamber in hydraulic motors of this type is limited by the profile of the teeth of the inner and outer gears, and the places of their contact. The sum of the volumes of the filled working chambers is the working volume:

Rн – radius of the outer gear, m

Rш – radius of the inner gear, m

Zн – number of teeth of outer gear

Zш – number of teeth of inner gear

rн – radius of the tooth of the outer gear, m

rш – radius of the tooth of the inner gear, m

b – width of gears, m

The teeth of the outer gear are always one more than the teeth of the inner gear.

Substituting (2) in (1) we obtain the expanded form of the equation of torque:

Equation (3) shows that a lot of factors influence the torque. An increase in any geometric parameter will directly increase the moment, but will lead to an increase in the mass and dimensions of the hydraulic machine. The pressure drop, to a greater extent, depends on the pump supplying this hydraulic motor. Hydromechanical efficiency reflects the influence of friction and other intrasystem processes.

The power on the shaft of the hydraulic motor is determined by the formula:

Having determined the power on the shaft of the hydraulic motor by the formula (4) and knowing the characteristics of the electric drive motor, we can determine the overall efficiency of the hydraulic drive.

ηv – volumetric efficiency

In turn, the volumetric efficiency is found by the formula:

Qм.r. – liquid consumption in a real hydraulic machine (taking into account volume losses ΔQм);

Qм – liquid consumption in an ideal hydraulic machine; is equal to the product of the working volume by the rotational speed of the hydraulic machine.

Reference

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