A turbocharger comprising: a compressor wheel ; a shaft coupled to the compressor wheel ; a bearing housing through which the shaft extends, and which includes an inner housing surface extending circumferentially around an axis of the shaft , wherein the inner housing surface comprises an axially central region surrounded by first and second axially outer regions; a floating ring that rotatably supports the shaft in the bearing housing and which rotates relative to the bearing housing and the shaft , the floating ring having an outer bearing surface that extends circumferentially around the axis and that faces the inner housing surface ; characterized in that the inner housing surface has a geometry that varies in radial dimension moving circumferentially about the axis of the bearing housing and also moving axially there along, wherein the inner housing surface is formed of a rigid material and has an inner housing cross-sectional shape that in the first axially outer region of the inner housing surface is non-circular perpendicular to the axis, decreases in area moving axially toward a first axial end of the floating ring , and forms a first outer fluid film interface with the outer bearing surface of the floating ring , and in that the inner housing cross-sectional shape includes peaks and valleys that extend axially toward the first axial end, wherein in the first axially outer region, the peaks have a peak radial dimension measured from the axis that is constant moving axially toward the first axial end, and the valleys have a valley radial dimension measured from the axis that is greater than the peak radial dimension and that reduces moving axially toward the first axial end. a compressor wheel ; a shaft coupled to the compressor wheel ; a bearing housing through which the shaft extends, and which includes an inner housing surface extending circumferentially around an axis of the shaft , wherein the inner housing surface comprises an axially central region surrounded by first and second axially outer regions; a floating ring that rotatably supports the shaft in the bearing housing and which rotates relative to the bearing housing and the shaft , the floating ring having an outer bearing surface that extends circumferentially around the axis and that faces the inner housing surface ; characterized in that the inner housing surface has a geometry that varies in radial dimension moving circumferentially about the axis of the bearing housing and also moving axially there along, wherein the inner housing surface is formed of a rigid material and has an inner housing cross-sectional shape that in the first axially outer region of the inner housing surface is non-circular perpendicular to the axis, decreases in area moving axially toward a first axial end of the floating ring , and forms a first outer fluid film interface with the outer bearing surface of the floating ring , and in that the inner housing cross-sectional shape includes peaks and valleys that extend axially toward the first axial end, wherein in the first axially outer region, the peaks have a peak radial dimension measured from the axis that is constant moving axially toward the first axial end, and the valleys have a valley radial dimension measured from the axis that is greater than the peak radial dimension and that reduces moving axially toward the first axial end. <EOS>