Roughness measurements inside tiny nozzles

Due to their long-term accuracy and excellent repeatability, small nozzles have been used in a number of industrial and scientific applications for gas and fluid flow measurements such as, e.g., calibration standards. In the case of the sonic nozzles, the flow rate remains constant over the nozzle when the differential pressure exceeds a certain minimum value. The smaller the flow rate, the smaller the diameter of the corresponding nozzle must be. With smaller nozzles, however, the topography of the inner surface has an increased influence on the flow behaviour and the flow rate. For nozzles with a diameter below 1.5 mm, significant deviations from the above-mentioned ideal relation between the differential pressure over the nozzle and the flow rate may occur, depending on the specimen considered; these deviations can turn out to be extremely disturbing in practice and their source in connection with the inner topography are not understood yet. Measuring the inner surface of such small nozzles with conventional tactile and optical measuring instruments is, however, very difficult.

PTB, in cooperation with the Forschungsinstitut für Mikrosensorik und Photovoltaik (Microsensor systems and photovoltaics research institute – CiS) in Erfurt and the Institut für Halbleitertechnologie (Institute of Semiconductor Technology – IHT) of Braunschweig Technical University, has developed a profilometer for roughness measurements on surfaces of microcomponents with a high aspect ratio. Its key component is a long silicon cantilever with an integrated tip and a full-bridge piezoresistive strain gauge for deflection detection. The cantilevers are available in different lengths (1.5 mm, 3 mm, 5 mm) and widths (30 μm, 100 μm, 200 μm) and with tip heights of up to 70 μm. The sensor is mounted into a measuring head with a travel of 800 μm × 800 μm × 250 μm. Three laser interferometers (resolution: 1 nm) are also integrated; they virtually measure the position of the tip. A coarse motorized 3D moving stage allows the precise positioning of samples. Numerous comparison measurements of step heights and of PTB roughness standards proved that the deviations of the profilometer for step heights as well as the roughness the arithmetic mean value Ra lie within ± 10 nm (2 σ).

Diverse nozzles manufactured by different methods (e.g. turning or electrical discharge machining) have been measured by the profilometer. Their diameters varied from 200 μm to 800 μm, the measuring depth from 1.5 mm to 7 mm. It is the first time that the inner surface of sonic nozzles with diameters in the micrometer range has been successfully characterized.

Hereby, in some nozzles, manufacturing defects were detected which explained the deviation of the flow rate experiments performed earlier. This also confirms the assumption that the shape and the roughness of the inner surfaces have a strong influence on the flow rate properties of the nozzles. It is expected that the calibration uncertainty and the quality control of such nozzles with diameters in the micrometre range can be improved by the measurement results of the profilometer.