Research on Online Measurement and Evaluation of Axial Straightness Errors for Deep-hole Parts

doi:10.3969/j.issn.1004-132X.2025.09.013

Abstract

Abstract:

To realize the accurate online measurement of axis straightness errors for deep-hole parts， a multi-sensor integrated measurement system was constructed by eddy current displacement sensors， electromagnetic ultrasonic transducer， rotary encoder and laser interferometer. By analyzing the arrangement and distribution of spatial sample points， a rough error filtering method was proposed based on sine and cosine distribution characteristics， and the influences of random errors were reduced by Kalman filtering method， and data information closer to the real contour of parts was obtained. Based on the principle of approaching the minimum area， the evaluation of axis straightness errors was transformed into a parameter optimization problem， and the IZOA was adopted to solve this problem. In the comparative measurement experiments of commercial laser trackers， the measurement error of the developed measurement system is only 0.053 mm in the length range of 1500 mm deep-hole parts（with an inner diameter of 150 mm）， and the straightness measurement errors are less than 0.065 mm/m， which meets the requirements of enterprises（0.15 mm/m） and may effectively guide the machining processes of deep-hole parts.

Key words: deep-hole part, axis straightness error, multi-sensor integrated online measurement, improved zebra optimization algorithm （IZOA）

摘要：

为实现深孔零件轴线直线度误差的精准在线测量，融合电涡流位移传感器、电磁超声换能器、旋转编码器和激光干涉仪构建了一种多传感器集成式在线测量系统。通过分析空间样点集的排列分布状态，提出了基于正余弦分布特性的粗大误差过滤法，并利用卡尔曼滤波法降低了随机误差的影响，获得了更接近零件真实轮廓的数据信息。以逼近最小区域为原则，将轴线直线度误差评定转化为参数优化问题，并采用改进斑马优化算法对该问题进行求解。经商用激光跟踪仪的对比测量实验，开发测量系统在1500 mm的深孔零件（内径为150 mm）长度范围内的测量误差仅为0.053 mm，直线度测量误差小于0.065 mm/m，满足企业要求的直线度误差0.15 mm/m，能够有效指导深孔零件的加工过程。

关键词: 深孔零件, 轴线直线度误差, 多传感器集成式在线测量, 改进斑马优化算法

CLC Number:

TH161.12

Wenhua SHEN, Xibin WANG, Yonghao QIAN, Zhibing LIU, Ci SONG. Research on Online Measurement and Evaluation of Axial Straightness Errors for Deep-hole Parts[J]. China Mechanical Engineering, 2025, 36(9): 2011-2021.

沈文华, 王西彬, 钱泳豪, 刘志兵, 宋慈. 深孔零件轴线直线度误差的在线测量与评定技术研究[J]. 中国机械工程, 2025, 36(9): 2011-2021.

Figures/Tables 14

Fig.1 Schematic diagram of axis straightness error

Fig.2 Multi-sensor integrated online measurement system

Tab.1 Repeatability and indication error of each sensor

传感器	重复性	示值误差
电涡流位移传感器	1 μm	0.015 mm
旋转编码器	1 $″$	20 $″$
激光干涉仪	0.01 μm	0.5 μm/m

Tab.1 Repeatability and indication error of each sensor

传感器	重复性	示值误差
电涡流位移传感器	1 μm	0.015 mm
旋转编码器	1 $″$	20 $″$
激光干涉仪	0.01 μm	0.5 μm/m

Fig.3 Structure of self-adaptive distance adjustment mechanism

Fig.4 Lift-off distance control principle of self-adaptive distance adjustment mechanism

Fig.5 Gross error and random error

Fig.6 Data filtering

Fig.7 Flow chart of ZOA

Fig.8 Simulation test results

Fig.9 Comparison of error evaluation algorithms

Fig.10 Sampling of measuring points of laser tracker

Fig.11 Experimental site

Fig.12 Extraction axes of two measurement systems

Tab.2 Axis straightness errors measured by two measurement systems

测量长度	轴线直线度误差
测量长度	在线测量系统	激光跟踪仪	标准值
900	0.452	0.419	0.430
1200	0.581	0.603	0.590
1500	0.717	0.664	0.670

References 20

[1]	李超，孔令飞，梁炎眀，等. 基于刀具振动模式特征的深孔圆度误差预测方法［J］. 兵工学报， 2018， 39（2）：364-372.
	LI Chao， KONG Lingfei， LIANG Yanming， et al. Prediction Method for Roundness Error of Machined Deep-hole Based on Vibration Behaviors of Cutting Tools［J］. Acta Armamentarii， 2018， 39（2）：364-372.
[2]	孔令飞，牛晗，侯晓丽，等. 错齿内排屑刀具深孔加工中的刀具振动特性对孔圆度形貌的作用机制［J］. 兵工学报， 2016， 37（6）：1066-1074.
	KONG Lingfei， NIU Han， HOU Xiaoli， et al. Influence of Tool Vibration Characteristics on the Hole Roundness Morphology in BTA Deep-hole Drilling［J］. Acta Armamentarii， 2016， 37（6）：1066-1074.
[3]	KONG Lingfei， CAO Shuai， CHIN J H， et al. Vibration Suppression of Drilling Tool System during Deep-hole Drilling Process Using Independence Mode Space Control［J］. International Journal of Machine Tools and Manufacture， 2020， 151：103525.
[4]	CHANG T Y， LIAO Y S， LIU W C. Development of a Micro Hole Measuring System Based on the Capacitance Principle［J］. Measurement Science and Technology， 2009， 20（10）：105104.
[5]	CHEN Yuanliu， NIU Zengyuan， MATSUURA D， et al. Implementation and Verification of a Four-probe Motion Error Measurement System for a Large-scale Roll Lathe Used in Hybrid Manufacturing［J］. Measurement Science and Technology， 2017， 28（10）：105004.
[6]	DENKENA B， BERGMANN B， KAISER S， et al. Process-parallel Center Deviation Measurement of a BTA Deep-hole Drilling Tool［J］. Procedia Manufacturing， 2018， 24：229-234.
[7]	YOKOTA M， KOYAMA T， TAKEDA K. Digital Holographic Inspection System for the Inner Surface of a Straight Pipe［J］. Optics and Lasers in Engineering， 2017， 97：62-70.
[8]	倪骁骅. 形状误差评定和测量不确定度估计［M］. 北京：化学工业出版社， 2008.
	NI Xiaohua. Evaluation of Shape Error and Estimation of Measurement Uncertainty［M］. Beijing：Chemical Industry Press， 2008.
[9]	LEI Xianqing， ZHANG Chunyang， XUE Yujun， et al. Roundness Error Evaluation Algorithm Based on Polar Coordinate Transform［J］. Measurement， 2011， 44（2）：345-350.
[10]	张春阳，雷贤卿，李济顺，等. 基于几何优化的圆度误差评定算法［J］. 机械工程学报， 2010， 46（12）：8-12.
	ZHANG Chunyang， LEI Xianqing， LI Jishun， et al. Method for Roundness Error Evaluation Based on Geometry Optimization［J］. Journal of Mechanical Engineering， 2010， 46（12）：8-12.
[11]	ZHU L M， DING H， XIONG Y L. Distance Function Based Algorithm for Spatial Straightness Evaluation［J］. Proceedings of the Institution of Mechanical Engineers， Part B：Journal of Engineering Manufacture， 2003， 217（7）：931-939.
[12]	ZHU L M， DING Y， DING H. Algorithm for Spatial Straightness Evaluation Using Theories of Linear Complex Chebyshev Approximation and Semi-infinite Linear Programming［J］. Journal of Manufacturing Science and Engineering， 2006， 128（1）：167-174.
[13]	DING Y， ZHU L M， DING H. A Unified Approach for Circularity and Spatial Straightness Evaluation Using Semi-definite Programming［J］. International Journal of Machine Tools and Manufacture， 2007， 47（10）：1646-1650.
[14]	DING Y， ZHU L M， DING H. Semidefinite Programming for Chebyshev Fitting of Spatial Straight Line with Applications to Cutter Location Planning and Tolerance Evaluation［J］. Precision Engineering， 2007， 31（4）：364-368.
[15]	ZHANG Cong， DUAN Fajie， FU Xiao， et al. Research of Intelligent Segment-fitting Algorithm for Increasing the Measurement Accuracy of Quadrant Detector in Straightness Measuring System［J］. Optics & Laser Technology， 2020， 125：106062.
[16]	陈晖，刘志兵，王西彬. 旋转投影法评定孔类零件轴线直线度误差［J］. 哈尔滨工业大学学报， 2020， 52（7）：147-152.
	CHEN Hui， LIU Zhibing， WANG Xibin. Evaluation of Axis Straightness Error of Hole Parts by Rotating Projection Method［J］. Journal of Harbin Institute of Technology， 2020， 52（7）：147-152.
[17]	CHO S， KIM J Y. Straightness and Flatness Evaluation Using Data Envelopment Analysis［J］. The International Journal of Advanced Manufacturing Technology， 2012， 63（5）：731-740.
[18]	HUANG J. An Exact Minimum Zone Solution for Three-dimensional Straightness Evaluation Problems［J］. Precision Engineering， 1999， 23（3）：204-208.
[19]	TROJOVSKÁ E， DEHGHANI M， TROJOVSKÝ P. Zebra Optimization Algorithm：a New Bio-inspired Optimization Algorithm for Solving Optimization Algorithm［J］. IEEE Access， 2022， 10：49445-49473.
[20]	SONG C， WANG X B， LIU Z B， et al. Evaluation of Axis Straightness Error of Shaft and Hole Parts Based on Improved Grey Wolf Optimization Algorithm［J］. Measurement， 2022， 188：110396.