- Original Article
- Open Access
New Measurement Method for Spline Shaft Rolling Performance Evaluation using Laser Displacement Sensor
© The Author(s) 2018
- Received: 30 August 2016
- Accepted: 6 August 2018
- Published: 20 August 2018
In order to control the quality of spline shaft in rolling process, an efficient measurement method for rolling performance evaluation is essential. Here, a newly developed on-machine non-contact measurement prototype based on laser displacement sensor and rotary encoder is proposed. The prototype is intended for the automated evaluation of the spline shaft rolling performance by measuring the dimensional change of tooth root, which is correlated with the surface residual stress and micro-hardness. Laser displacement sensor and rotary encoder are used to record the polar radius and polar angle of each point on measuring section. Data are displayed in a polar coordinate system and fitted in a gear. Through multipoint curvature method, the roots of spline shaft are recognized automatically. Then, the dimensional change can be calculated by fitting the radius of the tooth root circle before and after rolling. Systematic error covering offset error is also analyzed and calibrated. At last, measurement test results show that the system has advantages of simple structure, high measurement precision (radius error < 0.6 μm), high measurement efficiency (measuring time < 2 s) and automatic control ability, providing a new opportunity for the efficient evaluation of various spline shafts in high-precision mechanical processing.
- Laser measurement
- Spline shaft
- Rolling performance
- Dimensional change
Spline shaft is an important part of a machine to transmit power or bear torque. Its section contour is like a gear. It suffers from great loads and alternating stress during the runtime. The tooth root of the spline shaft has a risk of fracture due to fatigue stress [1–4]. Thus, it is essential to conduct a surface hardening process such as rolling after machining. In order to control the quality of product, a rolling performance evaluation becomes essential. The commonly used evaluation parameters of surface integrity involve the surface roughness, the surface residual stress and the micro-hardness. However, measurement of surface roughness or through-thickness residual stresses in difficult locations or complex geometries is not easy. Many measurement techniques are destructive, such as the centre-hole drilling method, the ring core method and the block removal method. There are non-destructive techniques (e.g., X-ray and neutron diffraction, optical, magnetic or ultrasonic methods) , but they often require the off-machine measuring. Note that for the rolling process, it is an efficient alternative to conventional cutting processes to manufacture spline shaft as it possesses several advantages i.e. shorter process times, no material loss and no chip disposal, high surface quality . The residual stress is only induced by the residual strain and the residual strain appears as the dimensional change in the macroscopic view. Therefore, it is probably feasible to use the dimensional change of tooth root as an alternative evaluation parameter.
The dimensional change of the tooth root is about 20 μm after rolling. Thus, the measurement precision of the conventional mechanical measuring instrument is not enough and it is time-consuming due to the complexity of the spline shaft. In order to solve such problems, it is necessary to develop a new measuring system with high efficiency and high precision. The laser triangulation displacement sensor (LDS) is a common-used tool in high precision and short-distance measuring, which can measure the displacement change of an object without any contact. It is mainly used in automatically measuring the geometrical parameter such as thickness, distance, diameter, etc [7–10]. Over a period of time there were several novel measuring systems by combining it with other devices, such as identification of location error of rotary axes for five-axes machine tools , on machine measurement of RFQS , automated inner dimensional measurement system for long-stepped pipes  and piston secondary motion measurement . For spline shaft measuring system, a rotary encoder is needed to record the rotation angle. Together with the radius recorded by the laser displacement sensor, the section contour of the spline shaft is obtained by plotting each point of the measuring section in a polar coordinate system.
The section contour of the spline shaft is like a gear, but the method used in gear measurement cannot be directly applied to our system, because most of them require the workpiece to be measured off-machine . Besides, for gear measurement, researchers usually care more about the tooth thickness, tooth pitch , tooth flank  and cutting error . While in the spline shaft measuring, the position of the tooth roots and their dimensional change should be focused, which are different from the previous gear measurement.
In this paper, a newly developed on-machine non-contact measurement prototype based on laser displacement sensor and rotary encoder is proposed. Firstly, by using this prototype, the section contour of spline shaft is quickly measured. Then, through multipoint curvature method (MCM), the roots of spline shaft can be recognized automatically. At last, the dimensional change can be calculated by fitting the radius of the tooth root circle before and after rolling. The offset error and its calibration method were also discussed in this paper. Measurement test results show that the system has advantages of simple structure, high measurement precision, high measurement efficiency and automatic control ability.
It can be seen that both of the dimensional change ΔR and the residual stress σ0 are the function of residual strain ε0. Therefore, there is a corresponding relationship between the dimensional change ΔR and the residual stress σ0. Although it is difficult to establish an equation for them through theoretical analysis, it is available to fit a formula through the measurement experiments.
The details of each module are described as follows. The data acquisition module consists of the laser displacement sensor (LDS) and the rotary encoder. Laser displacement sensor is mounted on the worktable. Rotary encoder is mounted on spindle to record the angle of rotation. The motion control module consists of the worktable and the spindle, which are controlled by the CNC system of the rolling machine. The data processing module consists of the data acquisition card (DAQ card) and the computer. The DAQ card performs data synchronous acquisition work and sends the data of displacement and angle to the computer. The captured data are calculated in time by the program installed in the computer. Accordingly, the section contour of the spline shaft is displayed on the screen and the radius of the tooth roots can be calculated.
4.1 Acquisition of the Data
4.2 Recognition of the Tooth Roots
In the computer image processing, the feature points play a very important role in characteristic recognition. Feature points, such as angular point, tangency point and inflection point, are the basic units to characterize a specific shape. They can be applied to senior visual processing such as pattern recognition, shape matching and dimension measurement, etc. For the spline shaft measuring, the feature points are the tooth roots and tooth crests.
Curvature is the rate of change (at a point) of the angle between a curve and a tangent to the curve. The greater the curvature, the sharper the line bend. Based on the phenomenon that curvature on feature point changes dramatically, the feature point can be recognized when given a threshold. In the curvature method, continuous three points and their coordinate values are used to calculate the curvature of each point on a line. But, its curvature calculation range is too narrow to avoid the effect of vibration. This problem can be handled by the multipoint curvature method, which expands its curvature calculation range thus showing robust recognition performance. In fact, the value calculated by multipoint curvature method is not the true curvature of a point, but an approximate value.
4.3 Calculation of the Dimensional Change
5.1 Calculation Result
Angles of the tooth roots
5.2 Results of Joint Least Squares Fitting
Parameters fitting results for each section
Crest circle radius
Root circle radius
0.0127 ± 0.0005
24.8831 ± 0.0006
23.0695 ± 0.0003
0.0156 ± 0.0003
24.8867 ± 0.0006
23.0657 ± 0.0005
0.0183 ± 0.0013
24.8905 ± 0.0005
23.0602 ± 0.0006
0.0257 ± 0.0007
24.8958 ± 0.0009
23.0509 ± 0.0005
The dimensional change of the tooth roots can be achieved by calculating the radius of tooth root circle before and after rolling. The relationship between the dimensional change and the residual stress should be established by rolling experiments in the future. Accordingly, the spline shaft rolling performance can be rapidly evaluated using the dimensional change as an alternative evaluation parameter. It is also worth noting that a hydraulic servo system should be used to generate accurate pressures in the future experiments and the residual stress will be measured using the X-ray diffraction (XRD).
An on-machine non-contact measurement method for spline shaft rolling performance evaluation is proposed. To verify the validity of this method, a measurement prototype mainly consisted of a laser displacement sensor and rotary encoder was built on a rolling machine. Using the prototype established, a spline shaft is scanned and its section figure is obtained.
Through multipoint curvature method (MCM) and joint least square fitting method, the roots of the spline shaft were recognized automatically. The dimensional change can be calculated by fitting the radius of the tooth root circle before and after rolling. The offset error was also analyzed and calibrated in data processing.
Measurement test results show that the proposed method is feasible with high measurement precision (radius measuring error less than 0.6 μm), high measurement efficiency (measuring time less than 2 s) and automatic control ability (auto evaluation of rolling performance). Moreover, the method can cover the measurement needs of different spline shafts and has potential to analyze various gears machining process.
Z-QL and X-BW were in charge of the whole trial; H-WL and J-JP wrote the manuscript; LJ and L-JX assisted with sampling and laboratory analyses. All authors read and approved the final manuscript.
Hong-Wei Li, born in 1974, is currently a PhD candidate at Key Laboratory of Fundamental Science for Advanced Machining, Beijing Institute of Technology, China. He also is currently a researcher at Beijing North Vehicle Group Corporation, China. His research interests include advanced machining technology, and rolling and measurement. E-mail: firstname.lastname@example.org.
Zhi-Qiang Liang, born in 1984, is currently an associate professor at Key Laboratory of Fundamental Science for Advanced Machining, Beijing Institute of Technology, China. He received his PhD degree on mechanical engineering from Beijing Institute of Technology, China, in 2011. His research interests include advanced machining technology, cutting and grinding technique. Tel: +86-10-68911214; E-mail: email@example.com.
Jia-Jie Pei, born in 1987, is currently a PhD candidate at Key Laboratory of Fundamental Science for advanced Machining, Beijing Institute of Technology, China. His research interests include advanced machining technology. E-mail: firstname.lastname@example.org.
Li Jiao, born in 1975, is currently an associate professor at Key Laboratory of Fundamental Science for Advanced Machining, Beijing Institute of Technology, China. She received his PhD degree on mechanical engineering from Beijing Institute of Technology, China, in 2002. His main research interests include high efficiency machining technology, digital process planning, rapid production preparation and group technology. E-mail: email@example.com.
Li-Jing Xie, born in 1971, is currently an associate professor at Key Laboratory of Fundamental Science for Advanced Machining, Beijing Institute of Technology, China. She received his PhD degree on mechanical engineering from Karlsruhe Institute of Technology, Germany, in 2004. His main research interests include cutting and grinding of difficult-to-cut materials, ultra-high speed cutting, database of high efficiency processing technology. E-mail: firstname.lastname@example.org.
Xi-Bin Wang, born in 1958, is currently a professor and a PhD candidate supervisor at Key Laboratory of Fundamental Science for Advanced Machining, Beijing Institute of Technology, China. He received his PhD degree on mechanical engineering from Xi’an Jiaotong University, China, in 1994. His main research interests include advanced machining technology, grinding, cutting and green manufacturing. E-mail: email@example.com.
The authors declare that they have no competing interests.
Supported by Industrial Technology Development Program of China (Grant Nos. JCKY2017208C005, A0920132008), and National Natural Science Foundation of China (Grant No. 51575049).
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.
- A V Guimaraesa, P C Brasileirob, G C Giovanni, et al. Failure analysis of a half-shaft of a formula SAE racing car. Case Studies in Engineering Failure Analysis, 2016, 7: 17–23.View ArticleGoogle Scholar
- I Barsoum, F Khan, Z Barsoum. Analysis of the torsional strength of hardened splined shafts. Materials and Design, 2014, 54: 130–136.View ArticleGoogle Scholar
- L J Shen, A Lohrengel, G Schäfer. Plain–fretting fatigue competition and prediction in spline shaft-hub connection. International Journal of Fatigue, 2013, 52: 68–81.View ArticleGoogle Scholar
- Y J Li, W F Zhang, C H Tao. Fracture analysis of a castellated shaft. Engineering Failure Analysis, 2007, 14: 573–578.View ArticleGoogle Scholar
- N S Rossini, M Dassisti, K Y Benyounis, et al. Methods of measuring residual stresses in components. Materials and Design, 2012, 35: 572–588.View ArticleGoogle Scholar
- K Guptaa, R F Laubschera, P J Davimb, et al. Recent developments in sustainable manufacturing of gears: a review. Journal of Cleaner Production, 2016, 112(4): 3320–3330.View ArticleGoogle Scholar
- Y C Zhang, J X Han, X B Fu, et al. Measurement and control technology of the size for large hot forgings. Measurement, 2014, 49: 52–59.View ArticleGoogle Scholar
- J Rejc, U Cinkelj, M Munih. Dimensional measurements of a gray-iron object using a robot and a laser displacement sensor. Robotics and Computer-Integrated Manufacturing, 2009, 25: 155–167.View ArticleGoogle Scholar
- Y Gao, Q Feng, J Y Cui. A simple method for dynamically measuring the diameters of train wheels using a one-dimensional laser displacement transducer. Optics and Lasers in Engineering, 2014, 53: 158–163.View ArticleGoogle Scholar
- J H Sun, J Zhang, Z Liu. A vision measurement model of laser displacement sensor and its calibration method. Optics and Lasers in Engineering, 2013, 51: 1344–1352.View ArticleGoogle Scholar
- C Hong, S Ibarkai. Non-contact R-test with laser displacement sensors for error calibration of five-axis machine tools. Precision Engineering, 2013, 37: 159–171.View ArticleGoogle Scholar
- Y Kondo, K Hasegawa, H Kawamata, et al. On-machine non-contact dimension-measurement system with laser displacement sensor for vane-tip machining of RFQs. Nuclear Instruments and Methods in Physics Research A, 2012, 667: 5–10.View ArticleGoogle Scholar
- F M Zhang, X H Qu, J F Ouyang. An automated inner dimensional measurement system based on a laser displacement sensor for long-stepped pipes. Sensors, 2012, 12: 5824–5834.View ArticleGoogle Scholar
- Y C Tan, Z M Ripin. Technique of measuring piston secondary motion using laser displacement sensors. Experimental Mechanics, 2012, 52: 1447–1459.View ArticleGoogle Scholar
- E S Gadelmawla. Computer vision algorithms for measurement and inspection of spur gears. Measurement, 2011, 44: 1669–1678.View ArticleGoogle Scholar
- M A Younes, A M Khalil, M N Damir. Automatic measurement of spur-gear dimensions using laser light. Part 1: measurement of tooth thickness and pitch. Optical Engineering, 2005, 44: 1–13.Google Scholar
- P F Su, L J Wang, M Komori. Design of laser interferometric system for measurement of gear tooth flank. Optic, 2011, 122: 1301–1304.Google Scholar
- W Gao, M Furukawa, S Kiyono. Cutting error measurement of flexspline gears of harmonic speed reducers using laser probes. Precision Engineering, 2004, 28: 358–363.View ArticleGoogle Scholar
- E J Hearn. Mechanics of materials volume 1: an introduction to the mechanics of elastic and plastic deformation of solids and structural materials. 3rd ed. Musselburgh: Butterworth-Heinemann; 1997.Google Scholar
- J H Han, T Poston. Chord-to-point distance accumulation and planar curvature: a new approach to discrete curvature. Pattern Recognition Letters, 2001, 22: 1133–1144.View ArticleMATHGoogle Scholar