- Original Article
- Open Access
High Resolution Clinometers for Measurement of Roll Error Motion of a Precision Linear Slide
© The Author(s) 2018
- Received: 18 April 2018
- Accepted: 22 October 2018
- Published: 1 November 2018
This paper proposes a new method for measurement of the roll error motion of a slide table in a precision linear slide. The proposed method utilizes a pair of clinometers in the production process of a precision linear slide, where the roll error motion measurement will be carried out repeatedly to confirm whether the surface form errors of slide guideways in the linear slide are sufficiently corrected by hand scraping process. In the proposed method, one of the clinometers is mounted on the slide table, while the other is placed on a vibration isolation table, on which the precision linear slide is mounted, so that influences of external disturbances can be cancelled. An experimental setup is built on a vibration isolation table, and some experiments are carried out to verify the feasibility of the proposed method.
- Linear slide
- Rotational error motion measurement
In recent, precision linear slides are playing important roles in various ultra-precision machines, such as ultra-precision machine tools or coordinate measuring machines (CMMs) [1–3], in which both a long stroke on the order of several meters and high positioning accuracy on the order of sub-micron to several-tens nanometer are required. For the achievement of such a high positioning accuracy, a closed-loop control with a sufficient position sensor is required. Therefore, most of the precision linear slides are equipped with position sensors such as linear encoders or laser interferometers . Especially, linear encoders are preferred to be employed in linear slides in terms of their low cost, robustness and a high measurement resolution .
Rotational error motions of the slide table are induced by the surface form errors of the linear guideways. Therefore, the guideway surfaces are required to be compensated by repeating measurement of the rotational error motions and the form error correction of the guideways in the manufacturing process of linear slides. Although the hand scraping-based error correction is very time-consuming, it is an essential in the production process of the precision linear slides .
For measurement of the yaw error motion, laser interferometers, laser Doppler scales or laser autocollimators  have been employed. Especially, autocollimators are often employed in the manufacturing process of linear slides since they can continue their measurement even if their measurement laser beams are interrupted by operators for the hand scraping process. In addition, autocollimators have advantage of high measurement resolution on the order of sub arc-second [17–21]. In the case of measuring the yaw error motion by using an autocollimator, a small mirror reflector will be mounted on a slide table, while an optical sensor head of the autocollimator will be aligned in such a way that the optical axis will be parallel with the motion axis of the slide table. The setup for this measurement is not so difficult since the required size of the reflector is small.
However, on the other hand, measurement of roll error motion requires a long precision mirror, which has the same length as the stroke of the slide. Furthermore, when the stroke of the slide table becomes longer, a disturbance of refractive index in the long optical path influences measurement results. Therefore, it is difficult for a laser autocollimator to carry out measurement of the roll error motion of a linear slide having a long stroke. Meanwhile, a clinometer is another candidate for measurement of the roll error motion. There are three major types of clinometers; the mechanical pendulum-based type [22, 23], the accelerometer-based type , and the fluid-based type [25, 26]. The mechanical pendulum-based clinometers and the accelerometer-based clinometers have advantages of high resolution, large measurement range and small size. Some of those mechanical gravity-based clinometers are designed in a compact size of smaller than 75 mm × 40 mm × 45 mm, while achieving high resolution up to 0.1 arc-second with a good stability . However, they are not suitable for measurement in the manufacturing process of the linear slides since these pendulum-based clinometers have the disadvantages of high cost, and heavy weight owing to its complex mechanism. Meanwhile, on the other hand, the fluid-type clinometers, which detect the direction of the gravity with a liquid surface , has the advantages of low cost, small size, and light weight compared with other types of clinometers. In addition, fluid-based type clinometers are robust against external vibration because of its non-mechanical structure. Therefore, the fluid-based type clinometers are suitable to be applied for the manufacturing process of the linear slides. Differing from the autocollimators, the fluid-based type clinometer does not require a mirror reflector because its angle reference is the level of liquid enclosed inside of the sensor body [27, 28]. By utilizing the feature of the clinometer, a setup for measurement of the roll error motion of the slide table in a long-stroke linear slide can therefore be established in a compact size; this is a great advantage from the viewpoint of the production line of the linear slides.
This paper proposes a new measurement method for evaluation of the roll error motion of a precision linear slide by using a high resolution fluid-based type clinometer in the production process of the stage system. The clinometer used in this research is developed based on a commercially-available fluid type clinometer , which detects the surface level of the liquid enclosed inside of the sensor body. Since the clinometer detects the absolute angle with respect to the direction of gravitational vector, clinometer detects not only the roll error motion of a slide table but also external inclination such as tilt angle of a vibration isolation table where the linear slide is mounted. In order to remove the influence of the external inclinations, in this paper, another clinometer is directly mounted on the vibration isolation table. By taking a differential output signal of the two clinometers, the roll error motion of the slide table can be evaluated, while eliminating the influence of the external disturbances mainly from the vibration isolation table. An experimental setup employing the pair of clinometers is developed, and experiments are carried out to verify the feasibility of the proposed method.
With this simple operation, the influence of the external disturbances can be removed, in principle.
3.1 Calibration of the Clinometers
3.2 Roll Error Measurement for a Linear Slide
By using the calibrated clinometers, the roll error motion of the precision linear slide was then evaluated in experiments. The setup shown in Figure 10 was also employed in the experiments. As shown in the figure, the Sensor 1 was mounted on the slide table, while the Sensor 2 was directly fixed on the vibration isolation table. Since the measurement range of each clinometer was set to be small for enhancement of the measurement resolution, Sensor 1 and 2 were mounted on different manual tilt stages independently. The stage roll error motion was evaluated by using both the developed clinometers and the commercial laser autocollimator, which was employed as a reference in the experiments. Since the commercial autocollimators cannot measure roll motion of a linear slide with a long stroke due to the absence of a precision mirror having a length comparable with the slide, a linear stage with a short stroke of 45 mm was employed in this paper. A precision reflective mirror with the length of 100 mm was also mounted on the slide table so that slide roll motion could be measured by the commercial laser autocollimator.
For measurement of roll error motion of a slide table in a precision linear slide during its manufacturing process, a new measurement method using a pair of clinometers has been proposed, and its feasibility has been verified in experiments. At first, the sensitivities of the clinometers have been calibrated by using the precision air spindle having a precision rotary encoder. The linearity error of each sensor has been verified to be within 0.001°. The differential output of the two clinometers has also been calibrated, and the output difference between the two clinometers has been verified to be within 0.0015°. Finally, the roll error motion of the slide table has been evaluated by using the proposed method. By taking the differential of the sensor outputs, the roll error motion of the slide has successfully been measured, while eliminating the influence of the external disturbances.
YS was in charge of the whole trial; SK assisted with sampling and laboratory analyses; and YS and WG wrote the manuscript. All authors read and approved the final manuscript.
Yuki Shimizu received his bachelor and MS degrees from Tohoku University, Japan, in 2000 and in 2002, respectively. He received his PhD degree from Department of Mechanical Engineering, Nagoya University, Japan, in 2009. He is currently an associate professor at Nano-Metrology and Control Laboratory, Department of Finemechanics, Tohoku University, Japan.
Satoshi Kataoka is currently a master candidate at Nano-Metrology and Control Laboratory, Department of Finemechanics, Tohoku University, Japan.
Wei Gao received his bachelor degree in precision engineering from Shanghai Jiao Tong University, China, in 1986 and MS and PhD degrees in engineering from Tohoku University, Japan, in 1991 and 1994, respectively. He is currently a professor and a director of Research Center for Precision Nanosystems, Department of Finemechanics, Tohoku University, Japan. His research interests include optical sensors, precision dimensional metrology and motion control. He is a member of JSPE, JSME, CIRP and a Fellow of The International Society for Nanomanufacturing. He is serving as the Chairman of The Scientific Technical Committee Precision Engineering and Metrology of CIRP. He is the author of the book Precision Nanometrology published by Springer.
This project was supported by Japan Society for the Promotion and Science (JSPS). The authors would like to thank Mr. Satoshi Nakagawa for his valuable comments and suggestions on our experiments.
The authors declare that they have no competing interests.
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
- K Sato. High-precision and high-speed positioning of 100G linear synchronous motor. Precision Engineering, 2015, 39: 31–37.View ArticleGoogle Scholar
- M Week. Linear magnetic bearing and levitation system for machine tools, CIRP Annals-Manufacturing Technology, 1998, 47(1): 311–314.View ArticleGoogle Scholar
- K Erkorkmaz, M Gorniak. Precision machine tool X–Y stage utilizing a planar air bearing arrangement. CIRP Annals-Manufacturing Technology, 2010, 59(1): 425–428.View ArticleGoogle Scholar
- H Kunzmann, T Pfeifer, J Flügge. Scales vs. laser interferometers performance and comparison of two measuring systems. CIRP Annals-Manufacturing Technology, 1993, 42(2): 753–767.View ArticleGoogle Scholar
- W Gao, S W Kim, H Bosse, et al. Measurement technologies for precision positioning. CIRP Annals-Manufacturing Technology, 2015, 64(2): 773–796.View ArticleGoogle Scholar
- J B Bryan. The Abbe principle revisited - an updated interpretation. Precision Engineering, 1979, 1(3): 129–132.View ArticleGoogle Scholar
- W Knapp. Measurement uncertainty and machine tool testing. CIRP Annals-Manufacturing Technology, 2002, 51(1): 459–462.View ArticleGoogle Scholar
- H Schwenke, W Knapp, H Haitjema, et al. Geometric error measurement and compensation of machines - an update. CIRP Annals-Manufacturing Technology, 2008, 57(2): 660–675.View ArticleGoogle Scholar
- Y Shimizu, S Goto, S Ito, et al. Fabrication of large-size SiC mirror with precision aspheric profile for artificial satellite. Precision Engineering, 2013, 37: 640–649.View ArticleGoogle Scholar
- W Gao, Y Arai, A Shibuya, et al. Measurement of multi-degree-of-freedom error motions of a precision linear air-bearing stage. Precision Engineering, 2006, 30(1): 96–103.View ArticleGoogle Scholar
- W Gao. Precision nanometrology. Springer, London, 2010.View ArticleGoogle Scholar
- X Li, W Gao, H Muto, et al. A six-degree-of-freedom surface encoder for precision positioning of a planar motion stage. Precision Engineering, 2013, 37: 771–781.View ArticleGoogle Scholar
- K C Fan, M J Chen. A 6-degree-of-freedom measurement system for the accuracy of X–Y stages. Precision Engineering, 2000, 24(1): 15–23.View ArticleGoogle Scholar
- S L Tan, Y Shimizu, T Meguro, et al. Design of a laser autocollimator-based optical sensor with a rangefinder for error correction of precision slide guideways. International Journal of Precision Engineering and Manufacturing, 2015, 16(3): 423–431.View ArticleGoogle Scholar
- Heidenhain. Exposed linear encoders. Heidenhain, 2016.Google Scholar
- W R Moore. Foundations of mechanical accuracy. The Moore Special Tool Co., MIT Press, 1970.Google Scholar
- W Gao, Y Saito, H Muto, et al. A three-axis autocollimator for detection of angular error motions of a precision stage. CIRP Annals-Manufacturing Technology, 2011, 60(1): 515–518.View ArticleGoogle Scholar
- Y Shimizu, S L Tan, D Murata, et al. Ultra-sensitive angle sensor based on laser autocollimation for measurement of stage tilt motions. Optics Express, 2016, 24(3): 2788–2805.View ArticleGoogle Scholar
- Y L Chen, Y Shimizu, Y Kudo, et al. Mode-locked laser autocollimator with an expanded measurement range. Optics Express, 2016, 24(14): 15554–15569.View ArticleGoogle Scholar
- Y L Chen, Y Shimizu, J Tamada, et al. Optical frequency domain angle measurement in a femtosecond laser autocollimator. Optics Express, 2017, 25(14): 16725–16738.View ArticleGoogle Scholar
- J Tamada, Y Kudo, Y L Chen, et al, Determination of the zero-position for an optical angle sensor. Journal of Advanced Mechanical Design, Systems, and Manufacturing, 2016, 10(5): 00072.View ArticleGoogle Scholar
- K C Fan, T H Wang, S Y Lin, et al. Design of a dual-axis optoelectronic level for precision angle measurements. Measurement Science and Technology, 2011, 22(5): 055302.View ArticleGoogle Scholar
- K Venkateswara, C A Hagedorn, M D Turner, et al. A high-precision mechanical absolute-rotation sensor. Review of Scientific Instruments, 2014, 85(1): 015005.View ArticleGoogle Scholar
- F S Alves, R A Dias, J M Cabral, et al. High-resolution MEMS inclinometer based on pull-in voltage. Journal of Microelectromechanical Systems, 2015, 24(4): 931–939.View ArticleGoogle Scholar
- H Ueda, H Ueno, K Itoigawa, et al. Development of micro capacitive inclination sensor. IEEJ Transactions on Sensors and Micromachines, 2006, 126(12): 637–642.View ArticleGoogle Scholar
- Y Shimizu, S Kataoka, T Ishikawa, et al. A liquid-surface-based three-axis inclination sensor for measurement of stage tilt motions. Sensors, 2018, 18: 398.View ArticleGoogle Scholar
- Sherbome Sensor, LSOP-LSOC-2013 Iss1. Sherborne Sensors, 2013.Google Scholar
- S L Tan, S Kataoka, T Ishikawa, et al. An ultra-precision electronic clinometer for measurement of small inclination angles. Journal of the Korean Society of Manufacturing Technology Engineers, 2014, 23(6): 539–546.View ArticleGoogle Scholar
- S Kataoka, T Ishikawa, Y Shimizu, et al. Measurement of angular error motions of a precision linear stage by using a high resolution clinometer. Proceedings of the 8th International Conference on Leading Edge Manufacturing in 21st Century, 2015: https://doi.org/10.1299/jsmelem.2015.8._1505-1_.Google Scholar