A turbocharger (100, 200) comprising: a compressor wheel; a shaft coupled to the compressor wheel; a bearing housing (140, 240) through which the shaft extends, and which includes an inner housing surface (144, 244) extending circumferentially around an axis of the shaft, wherein the inner housing surface (144, 244) comprises an axially central region surrounded by first and second axially outer regions; a floating ring (150, 250) that rotatably supports the shaft in the bearing housing (140, 240) and which rotates relative to the bearing housing (140, 240) and the shaft, the floating ring (150, 250) having an outer bearing surface that extends circumferentially around the axis and that faces the inner housing surface (144, 244); characterized in that the inner housing surface (144, 244) has a geometry that varies in radial dimension moving circumferentially about the axis of the bearing housing (140, 240) and also moving axially there along, wherein the inner housing surface (144, 244) 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 (144, 244) is non-circular perpendicular to the axis, decreases in area moving axially toward a first axial end of the floating ring (150, 250), and forms a first outer fluid film interface with the outer bearing surface of the floating ring (150, 250), 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 (140, 240) through which the shaft extends, and which includes an inner housing surface (144, 244) extending circumferentially around an axis of the shaft, wherein the inner housing surface (144, 244) comprises an axially central region surrounded by first and second axially outer regions; a floating ring (150, 250) that rotatably supports the shaft in the bearing housing (140, 240) and which rotates relative to the bearing housing (140, 240) and the shaft, the floating ring (150, 250) having an outer bearing surface that extends circumferentially around the axis and that faces the inner housing surface (144, 244); characterized in that the inner housing surface (144, 244) has a geometry that varies in radial dimension moving circumferentially about the axis of the bearing housing (140, 240) and also moving axially there along, wherein the inner housing surface (144, 244) 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 (144, 244) is non-circular perpendicular to the axis, decreases in area moving axially toward a first axial end of the floating ring (150, 250), and forms a first outer fluid film interface with the outer bearing surface of the floating ring (150, 250), 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.