Heating and cooling will more and more rely on heat pumping in order to enable a more rational use of energy. The further development of domestic and small industrial multi-stage heat pumps with enhanced performance is impaired by the presence of oil mixed with the refrigerant and its migration through the hermetic loop. Oil-free directly driven small-scale turbomachinery has been identified as a technology that will allow a significant performance surge in refrigeration and heat pump applications. A proof of concept compressor unit has been designed, built and successfully tested, demonstrating the technical feasibility of such a system. Directly driven turbocompressors are composed of several components, involving different specialization fields like compressor aerodynamics, bearing and rotordynamic design as well as the electric layout of the motor and its drive. Fragmentation is the commonly used procedure for designing complex and interdisciplinary systems. The splitting into submodules certainly simplifies the design process of the individual components, it leads, however, to conservative designs and makes it more complex to keep track of the mutual interactions between the submodules. Only an integrated and simultaneous design of the complete system ensures an optimum solution. The models of the different components have been linked together to build a global system, enabling its integrated optimization. Compared to a unit that has been designed using fragmented design, the overall efficiency could be increased by 16 points by using the proposed integrated design procedure. In order to be able to predict the system's performance, losses, critical speeds and stability margins the different components have been modeled in a modular and generic way. As the system operates with a vapor close to the saturation line, both the impeller and the gas-bearing models include real gas effects. The bearing model additionally incorporates rarefaction and clearance distortion effects resulting from centrifugal growth and thermal influence. Models for calculating the windage losses occurring in the bearings and in the gap between the rotor and the stator of the electric motor have been introduced as well. In order to enable the calculation of the whirl speeds and the corresponding stability margins, a rotordynamic model has been developed specifically for gas bearing supported rotors. The model has been extended with a forced response module that allows to predict the orbits of the rotor as a function of a given unbalance and vice-versa. A vapor phase test rig for measuring the compressor performance has been built. The oil free gas bearing supported radial turbocompressor with a tip diameter of 20 mm could be tested to speeds up to 210 krpm, reaching pressure ratios higher than 3.2 and powers of 1.7 kW. Internal isentropic compressor efficiencies in excess of 80% have been measured. A detailed comparison between the measured and the predicted compressor map shows excellent agreement.