More importantly, both the transformation algorithm of the helix angle and the arc-selecting  principle are proposed. Compared to the measuring results and time consumption of the  profilometer, the maximum error for the measured radius and contact angle of the system  proposed in this paper is 1.5μm and 35′, and the measuring efficiency is increased by 15.8%,  58.6% and 67.5% for 1, 5 and 20 continuous raceways, respectively, which shows a good  performance in accuracy, repeatability and efficiency. Moreover, the system is also capable of  measuring the pitch diameter and lead error of ballscrew, which is significant for classifying the  accuracy of the ballscrew raceway profile and improving the machining precision.



Ball screws, which are widely used in CNC machine tools, have a great performance on reliability, rigidity and bearing capacity. The parameters of ballscrew raceway profile directly  determine the load distribution in ball screws, and therefore affect the contact stiffness and friction  characteristics. With the development of the modern manufacturing industry, the positioning  accuracy and precision retention are becoming increasingly important, which confirms the  indispensability of machining accuracy detection for ball screws.Most of the modern  manufacturing companies have relied on the roughness profilometers launched by industrial  measuring corporations.

Measurement, the profile usually was measured along the normal section of the ballscrew raceway. Although this method can achieve relatively high accuracy, the probe must be adjusted  for the measurement of each raceway. That is, it is not applicable in the batch tests due to the low  efficiency, and more importantly, the surface with poor roughness is more likely to cause the  probe wear. Therefore, existing non-contact measuring methods still cannot realize continuous  measurement.

Contact measurement is not suitable for batch tests, and non-contact measurement by the  industrial camera is likely to be affected by lens distortion and image processing. Considering the  accuracy of the optical measurement, three kinds of optical sensors are studied in this paper,  namely confocal laser, triangular laser, and LED sensor, of which the applications and measuring  principles are shown in Fig. 1, Fig. 2 and Fig. 3. When using the confocal laser (Fig. 1 (a)) or  triangular laser (Fig. 2(a)), to scan the 60 ballscrew raceway profile along the side generatrix, the  laser should be set parallel to the Y-axis. And the two-dimensional (2D) mobile station is used to  adjust the measuring distance of the sensor both along the X-axis and the Y-axis. When using the  LED sensor (Fig. 3(a)), if the optical path is set parallel to the Y-axis, the projection of partial  profile along upper side or lower side cannot be perceived by the receiver due to the light  occlusion caused by the helical surface of the ballscrew. To avoid the image distortion and  acquire the complete profile, the LED sensor should be rotated at a helix angle from the Y-axis,  making the optical path consistent with the tangential direction of the helical line on the measured  raceway. To find the most suitable optical sensor, preliminary experiments were carried out.

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