Measurement Strategies and Standardization in Manufacturing

Journal Name	Impact Factor	CiteScore	Launched Year	First Decision (median)	APC
Applied Sciences applsci	2.5	5.3	2011	17.8 Days	CHF 2400	Submit
Journal of Manufacturing and Materials Processing jmmp	3.3	5.1	2017	14.7 Days	CHF 1800	Submit
Materials materials	3.1	5.8	2008	15.5 Days	CHF 2600	Submit
Metrology metrology	-	-	2021	28.5 Days	CHF 1000	Submit
Sensors sensors	3.4	7.3	2001	16.8 Days	CHF 2600	Submit
Standards standards	-	-	2021	37.9 Days	CHF 1000	Submit

18 pages, 5886 KiB

Open AccessArticle

Interior Profile Accuracy Assessment Method of Deep-Hole Parts Based on Servo Drive System

by Jintao Liang, Kaixin Wang, Xiaotian Song and Xiaolan Han

Sensors 2024, 24(20), 6554; https://doi.org/10.3390/s24206554 - 11 Oct 2024

Viewed by 341

Dimensional and profile measurements of deep-hole parts are key processes both in manufacturing and product lifecycle management. Due to the particularity of the space conditions of deep-hole parts, the existing measurement instruments and methods exhibit some limitations. Based on the multi-axis, highly precise [...] Read more.

Dimensional and profile measurements of deep-hole parts are key processes both in manufacturing and product lifecycle management. Due to the particularity of the space conditions of deep-hole parts, the existing measurement instruments and methods exhibit some limitations. Based on the multi-axis, highly precise servo drive system, a novel measuring device is developed. The laser displacement sensors are fed by the flux-switching permanent magnet linear motor, and the part is rotated by the servo motor. On this basis, the assessment methods of roundness, straightness, and cylindricity are proposed by employing the least square method (LSM). Additionally, considering the axial center deviation between the sensors and the part, the rotating center coordinate is optimized by the gradient descent algorithm (GDM). Then, the measurement system is constructed and the experiment study is conducted. The results indicate favorable evaluation error of the LSM fitting and GDM iteration. Compared with the coordinate measuring machine (CMM), the measured results show good consistency. In the error analysis, the angle positioning error of measured point is less than 0.01°, and the axial positioning error is less than 0.05 mm. The proposed system and assessment method are regarded as a feasible and promising solution for deep-hole part measurements. Full article

(This article belongs to the Topic Measurement Strategies and Standardization in Manufacturing)

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21 pages, 1293 KiB

Open AccessReview

A Review of Friction in Low-Stress Mechanics of Fibrous Flexible Materials

by Liang Luo and George Stylios

Materials 2024, 17(15), 3828; https://doi.org/10.3390/ma17153828 - 2 Aug 2024

Viewed by 487

Abstract

The structure of a fabric is a highly complex assembly of fibres, which have order and regularity as well as disorder and randomness. The complexity of the structure poses challenges in defining its mechanical behaviour, particularly at low stress, which is typical to [...] Read more.

The structure of a fabric is a highly complex assembly of fibres, which have order and regularity as well as disorder and randomness. The complexity of the structure poses challenges in defining its mechanical behaviour, particularly at low stress, which is typical to end uses. The coexistence of multiple deformations and the high degree of nonlinearity of the fabric due to fibre friction make its stress–strain relationship complicated. This article reviews the literature on friction related to the low-stress mechanics of fabrics, and it establishes its range and regularity to help with finding a unified reference model, in which although the physical meanings of fabric tensile, shear, and bending vary, they follow consistent mathematical regularities. So, invariably, their disorder and randomness needed in defining them can be obtained from fabric measurement data. It defines the scope and patterns of friction to facilitate the development of a unified reference model. It argues that although the physical interpretations of fabric tensile, shear, and bending characteristics may differ, they adhere to consistent mathematical regularities within this model, and hence extracting disorder and randomness from fabric measurement data may be achievable. This paper concludes with a number of recommendations, postulating that hysteresis caused by friction between fibres in a fabric is an important component of mechanical information, and it coexists with its purely elastic component, but it cannot be obtained directly by measurement. Seeking means to effectively decompose the friction hysteresis and pure elastic components contained in fabric mechanics measurement data will provide an accurate characterization of fabric mechanical properties and hence an accurate modelling and simulation of its behaviour, and will impact many traditional and industrial textile end uses. Full article

(This article belongs to the Topic Measurement Strategies and Standardization in Manufacturing)

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20 pages, 30344 KiB

Open AccessArticle

A Single-Camera-Based Three-Dimensional Velocity Field Measurement Method for Granular Media in Mass Finishing with Deep Learning

by Jie Zou, Chunyue Tian, Yiqun Liu, Junfei Ding and Wenhui Li

Sensors 2024, 24(15), 4790; https://doi.org/10.3390/s24154790 - 24 Jul 2024

Viewed by 642

Abstract

Surface treatment processes such as mass finishing play a crucial role in enhancing the quality of machined parts across industries. However, accurate measurement of the velocity field of granular media in mass finishing presents significant challenges. Existing measurement methods suffer from issues such [...] Read more.

Surface treatment processes such as mass finishing play a crucial role in enhancing the quality of machined parts across industries. However, accurate measurement of the velocity field of granular media in mass finishing presents significant challenges. Existing measurement methods suffer from issues such as complex and expensive equipment, limited to single-point measurements, interference with the flow field, and lack of universality in different scenarios. This study addresses these issues by proposing a single-camera-based method with deep learning to measure the three-dimensional velocity field of granular flow. We constructed a complete measurement system and analyzed the accuracy and performance of the proposed method by comparing the measurement results with those of the traditional DIC algorithm. The results show that the proposed method is very accurate in measuring spatial displacement, with an average error of less than 0.07 mm and a calculation speed that is 1291.67% of the traditional DIC algorithm under the same conditions. Additionally, experiments in a bowl-type vibratory finishing machine demonstrate the feasibility of the proposed method in capturing the three-dimensional flow of granular media. This research not only proposed a novel method for three-dimensional reconstruction and velocity field measurement using a single-color camera, but also demonstrated a way to combine deep learning with traditional optical techniques. It is of great significance to introduce deep learning to improve traditional optical techniques and apply them to practical engineering measurements. Full article

(This article belongs to the Topic Measurement Strategies and Standardization in Manufacturing)

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22 pages, 2363 KiB

Open AccessArticle

Evaluation of Air Pollution Levels in Agricultural Settings Using Integrated Weather Variables and Air Pollutants

by Saad S. Almady, Saleh M. Al-Sager, Abdulrahman A. Al-Janobi, Samy A. Marey and Abdulwahed M. Aboukarima

Appl. Sci. 2024, 14(13), 5713; https://doi.org/10.3390/app14135713 - 29 Jun 2024

Cited by 1 | Viewed by 715

Abstract

Research on the quality of the air in rural areas is essential for determining base emissions of air pollutants, evaluating the effects of dust pollutants particular to rural areas, modeling the dispersion of pollutants, and developing appropriate pollution mitigation systems. The absence of [...] Read more.

Research on the quality of the air in rural areas is essential for determining base emissions of air pollutants, evaluating the effects of dust pollutants particular to rural areas, modeling the dispersion of pollutants, and developing appropriate pollution mitigation systems. The absence of a systematic review based on the assessment of air quality levels in agricultural settings based on integrated weather variables and air pollutants in the literature draws attention to the deficiencies and the necessity of further research in this area. Hence, our study aimed to develop an Arduino monitoring system with related sensors to acquire some air pollutants and weather parameters. Additionally, we proposed an innovative solution to compare air quality levels by suggesting a new criterion called an integrated indicator for air quality assessment (IAQA). It was created based on the weighted average method to combine the investigated air pollutants and weather parameters. This criterion was evaluated while conducting field measurements in 29 environmentally different agricultural regions located within the Kingdom of Saudi Arabia. To determine the integrated indicator, all the values of the variables were normalized between 0 and 1. The agricultural setting with the lowest integrated indicator was the best environmentally. The lowest and highest values of the integrated indicator ranged from 37.03% and 66.32%, respectively, with an arithmetic average of 48.24%. The developed criterion can change its value depending on the change in the weight value of the variables involved, and it is suitable for application to any other agricultural or non-agricultural setting to evaluate the pollution level in the air. Although similar research has been published, this paper presents novelty findings based on integrated values of air pollutants and weather variables for defining a new criterion called IAQA. Additionally, this paper presents original results for air pollutants and weather aspects in different agricultural settings. Full article

(This article belongs to the Topic Measurement Strategies and Standardization in Manufacturing)

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14 pages, 9983 KiB

Open AccessCommunication

The Importance of Dimensional Traceability in Microfluidic Systems

by Elsa Batista, João Alves e Sousa, Fernanda Saraiva, André Lopes, Vania Silverio, Rui F. Martins and Luis Martins

Metrology 2024, 4(2), 240-253; https://doi.org/10.3390/metrology4020015 - 6 May 2024

Viewed by 1058

Abstract

Dimensional measurements are fundamental in microfluidic device manufacturing and performance. The main focus of this study is the measurement of the connection port sizes in microfluidic devices and components and, accordingly, the possible existence of fluid leaks determined using the flow rate error. [...] Read more.

Dimensional measurements are fundamental in microfluidic device manufacturing and performance. The main focus of this study is the measurement of the connection port sizes in microfluidic devices and components and, accordingly, the possible existence of fluid leaks determined using the flow rate error. The sizes associated with three different microfluidic systems were determined using laser interferometry and through an optical measuring instrument, with metrological traceability to national length standards. It was possible to infer the method with the greatest accuracy and lowest measurement uncertainty for characterizing this kind of system. In conclusion, the results of this work directly address the current lack of dimensions measuring methods of microfluidic components by providing a comprehensive comparison of different protocols, ultimately suggesting a preferred option for immediate application within the microfluidic industry. Full article

(This article belongs to the Topic Measurement Strategies and Standardization in Manufacturing)

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15 pages, 6475 KiB

Open AccessArticle

Development of a Six-Degree-of-Freedom Analog 3D Tactile Probe Based on Non-Contact 2D Sensors

by José Antonio Albajez, Jesús Velázquez, Marta Torralba, Lucía C. Díaz-Pérez, José Antonio Yagüe-Fabra and Juan José Aguilar

Sensors 2024, 24(9), 2920; https://doi.org/10.3390/s24092920 - 3 May 2024

Viewed by 1204

Abstract

In this paper, a six-degree-of-freedom analog tactile probe with a new, simple, and robust mechanical design is presented. Its design is based on the use of one elastomeric ring that supports the stylus carrier and allows its movement inside a cubic measuring range [...] Read more.

In this paper, a six-degree-of-freedom analog tactile probe with a new, simple, and robust mechanical design is presented. Its design is based on the use of one elastomeric ring that supports the stylus carrier and allows its movement inside a cubic measuring range of ±3 mm. The position of the probe tip is determined by three low-cost, noncontact, 2D PSD (position-sensitive detector) sensors, facilitating a wider application of this probe to different measuring systems compared to commercial ones. However, several software corrections, regarding the size and orientation of the three LED light beams, must be carried out when using these 2D sensors for this application due to the lack of additional focusing or collimating lenses and the very wide measuring range. The development process, simulation results, correction models, experimental tests, and calibration of this probe are presented. The results demonstrate high repeatability along the X-, Y-, and Z-axes (2.0 µm, 2.0 µm, and 2.1 µm, respectively) and overall accuracies of 6.7 µm, 7.0 µm, and 8.0 µm, respectively, which could be minimized by more complex correction models. Full article

(This article belongs to the Topic Measurement Strategies and Standardization in Manufacturing)

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21 pages, 5605 KiB

Open AccessArticle

Validation of a Manual Methodology for Measuring Roundness and Cylindricity Tolerances

by Enrique García-Martínez, Narciso García-González, María Carmen Manjabacas and Valentín Miguel

Appl. Sci. 2023, 13(17), 9702; https://doi.org/10.3390/app13179702 - 28 Aug 2023

Cited by 1 | Viewed by 1808

Abstract

This paper describes a practice-based methodology applied to roundness and cylindricity concepts. Traditionally, technicians encounter difficulties in understanding this topic, especially when they analyze the tolerances involved due to the complexity of their graphic interpretation. Additionally, it is mandatory for industrial engineers to [...] Read more.

This paper describes a practice-based methodology applied to roundness and cylindricity concepts. Traditionally, technicians encounter difficulties in understanding this topic, especially when they analyze the tolerances involved due to the complexity of their graphic interpretation. Additionally, it is mandatory for industrial engineers to acquire competencies that allow them to validate form and make decisions in this field. With the goal of enhancing the handling of measurement techniques involved in this topic and analyzing the results obtained, a methodology has been designed to address the roundness and cylindricity tolerance evaluation from different perspectives. Firstly, based on a conceptual analysis, an analytical procedure is introduced. Secondly, an engaging manual practice is implemented by using simple measuring instruments that allow the user to be involved in the development of the procedure applied. The conditions that tried to optimize the manual procedure to get good results were analyzed. Moreover, the results obtained under this perspective allow us to ensure that better skills can be acquired regarding the typical method based on the coordinate measuring machines. This experience has been validated based on the practice with ongoing users under a training period. Full article

(This article belongs to the Topic Measurement Strategies and Standardization in Manufacturing)

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18 pages, 2717 KiB

Open AccessArticle

Metrics Related to Confusion Matrix as Tools for Conformity Assessment Decisions

by Dubravka Božić, Biserka Runje, Dragutin Lisjak and Davor Kolar

Appl. Sci. 2023, 13(14), 8187; https://doi.org/10.3390/app13148187 - 14 Jul 2023

Cited by 7 | Viewed by 1947

Abstract

Conformity assessment refers to activities undertaken to check whether some product, service or process meets certain criteria and specifications given by internationally accepted standards. The decision on whether a property of interest is aligned with the set standards is made based on measurement. [...] Read more.

Conformity assessment refers to activities undertaken to check whether some product, service or process meets certain criteria and specifications given by internationally accepted standards. The decision on whether a property of interest is aligned with the set standards is made based on measurement. However, uncertainty associated with the measurement results may lead to incorrect decisions. Measurement results may be falsely rejected as non-conforming, although they meet specifications. This is referred to as the producer’s risk. If the measurement result that does not meet the required specifications is accepted as conforming, this is referred to as the consumer’s risk. This paper covers calculations of global consumer's and producer's risk using the Bayesian approach and deals with the application of metrics related to confusion matrices in conformity assessments. These techniques have been used to assess the conformity of the bearing ring diameter with the given specifications. Based on the behavior of these metrics, the optimal length of the guard band was determined with the aim of minimizing the global consumer’s and producer’s risk. Full article

(This article belongs to the Topic Measurement Strategies and Standardization in Manufacturing)

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27 pages, 6597 KiB

Open AccessArticle

An Efficient Improved Harris Hawks Optimizer and Its Application to Form Deviation-Zone Evaluation

by Guangshuai Liu, Zuoxin Li, Si Sun, Yuzou Yang, Xurui Li and Wenyu Yi

Sensors 2023, 23(13), 6046; https://doi.org/10.3390/s23136046 - 29 Jun 2023

Viewed by 1022

Abstract

Evaluation of the deviation zone based on discrete measured points is crucial for quality control in manufacturing and metrology. However, deviation-zone evaluation is a highly nonlinear problem that is difficult to solve using traditional numerical optimization methods. Swarm intelligence has many advantages in [...] Read more.

Evaluation of the deviation zone based on discrete measured points is crucial for quality control in manufacturing and metrology. However, deviation-zone evaluation is a highly nonlinear problem that is difficult to solve using traditional numerical optimization methods. Swarm intelligence has many advantages in solving this problem: it produces gradient-free, high-quality solutions and is characterized by its ease of implementation. Therefore, this study applies an improved Harris hawks algorithm (HHO) to tackle the problem. The average fitness is applied to replace the random operator in the exploration phase to solve the problem of conflicting exploration strategies due to randomness. In addition, the salp swarm algorithm (SSA) with a nonlinear inertia weight is embedded into the HHO, such that the superior explorative ability of SSA can fill the gap in the exploration of HHO. Finally, the optimal solution is greedily selected between SSA-based individuals and HHO-based individuals. The effectiveness of the proposed improved HHO optimizer is checked through a comparison with other swarm intelligence methods in typical benchmark problems. Moreover, the experimental results of form deviation-zone evaluation on primitive geometries show that the improved method can accurately solve various form deviations, providing an effective general solution for primitive geometries in the manufacturing and metrology fields. Full article

(This article belongs to the Topic Measurement Strategies and Standardization in Manufacturing)

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15 pages, 18063 KiB

Open AccessArticle

Geometric Error Parameterization of a CMM via Calibrated Hole Plate Archived Utilizing DCC Formatting

by Ming-Xian Lin and Tsung-Han Hsieh

Appl. Sci. 2023, 13(10), 6344; https://doi.org/10.3390/app13106344 - 22 May 2023

Cited by 1 | Viewed by 1761

Abstract

This study implemented the measurement results and administrative information obtained from the hole plate into the Digital Calibration Certificate (DCC). The DCC comprises three parts: Norms and Standards, Hierarchical Structure, and XML as Exchange Format. DCCs play a significant role in the field [...] Read more.

This study implemented the measurement results and administrative information obtained from the hole plate into the Digital Calibration Certificate (DCC). The DCC comprises three parts: Norms and Standards, Hierarchical Structure, and XML as Exchange Format. DCCs play a significant role in the field of metrology and statistics by ensuring data interoperability, correctness, and traceability during the conversion and transmission process. The hole plate is a length standard used for two-dimensional geometric error measurements. We evaluated the accuracy of the high-precision coordinate measuring machine (CMM) in measuring a hole plate and compared the measurement error results obtained from the hole plate with those of the laser interferometer, autocollimator, and angle square. The results show that the maximum difference in linear error is −0.30 μm, the maximum difference in angle error is −0.78″, and the maximum difference in squareness error is 4.54″. The XML is designed for machine-readability and is modeled and edited using the XMLSpy 2022 software, which is based on information published by PTB. The administrative management and measurement results tasks are presented in PDF format, which is designed for human-readability and ease of use. Overall, we implemented the measurement results and information obtained from the hole plate into the DCC. Full article

(This article belongs to the Topic Measurement Strategies and Standardization in Manufacturing)

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16 pages, 5063 KiB

Open AccessArticle

Thermal Calibration of Triaxial Accelerometer for Tilt Measurement

by Bo Yuan, Zhifeng Tang, Pengfei Zhang and Fuzai Lv

Sensors 2023, 23(4), 2105; https://doi.org/10.3390/s23042105 - 13 Feb 2023

Cited by 7 | Viewed by 3170

Abstract

The application of MEMS accelerometers used to measure inclination is constrained by their temperature dependence, and each accelerometer needs to be calibrated individually to increase stability and accuracy. This paper presents a calibration and thermal compensation method for triaxial accelerometers that aims to [...] Read more.

The application of MEMS accelerometers used to measure inclination is constrained by their temperature dependence, and each accelerometer needs to be calibrated individually to increase stability and accuracy. This paper presents a calibration and thermal compensation method for triaxial accelerometers that aims to minimize cost and processing time while maintaining high accuracy. First, the number of positions to perform the calibration procedure is optimized based on the Levenberg-Marquardt algorithm, and then, based on this optimized calibration number, thermal compensation is performed based on the least squares method, which is necessary for environments with large temperature variations, since calibration parameters change at different temperatures. The calibration procedures and algorithms were experimentally validated on marketed accelerometers. Based on the optimized calibration method, the calibrated results achieved nearly 100 times improvement. Thermal drift calibration experiments on the triaxial accelerometer show that the thermal compensation scheme in this paper can effectively reduce drift in the temperature range of −40 °C to 60 °C. The temperature drifts of x- and y-axes are reduced from −13.2 and 11.8 mg to −0.9 and −1.1 mg, respectively. The z-axis temperature drift is reduced from −17.9 to 1.8 mg. We have conducted various experiments on the proposed calibration method and demonstrated its capacity to calibrate the sensor frame error model (SFEM) parameters. This research proposes a new low-cost and efficient strategy for increasing the practical applicability of triaxial accelerometers. Full article

(This article belongs to the Topic Measurement Strategies and Standardization in Manufacturing)

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23 pages, 7638 KiB

Open AccessArticle

Research on Image Measurement Method of Flat Parts Based on the Adaptive Chord Inclination Angle Algorithm

by Tao Liu, Xingchen Lv and Min Jin

Appl. Sci. 2023, 13(3), 1641; https://doi.org/10.3390/app13031641 - 27 Jan 2023

Cited by 1 | Viewed by 1315

Abstract

To accurately measure the critical dimensions of flat parts using machine vision, an inspection method based on the adaptive chord inclination angle progressively screening the segmentation points of graphic elements was proposed in this study. The method doubled the size of the part [...] Read more.

To accurately measure the critical dimensions of flat parts using machine vision, an inspection method based on the adaptive chord inclination angle progressively screening the segmentation points of graphic elements was proposed in this study. The method doubled the size of the part image using bicubic interpolation, extracted the single-pixel contour with more detailed information, and designed an adaptive step size to obtain the front and back chord inclination angles of the contour. The method of complementing the front and back chord inclination angles was employed to avoid the negative effects of contour jaggedness, thereby obtaining the contour segmentation points after the initial screening. The segmentation points obtained in the initial sieving were divided into different point clusters according to the distance, and the contour, which was segmented by two segmentation points in different point clusters, was fitted using the least squares. The fitting results were evaluated, and all the fitting results were selected using the improved non-maximum suppression (NMS) algorithm to obtain the precisely selected segmentation points of the graphic elements. Consequently, the segmented individual graphic elements were fitted with the segmentation points as constraints to obtain the key dimensions of the closed part. The developed method could accurately find the contour segmentation points, and the relative error was less than 0.6%. Full article

(This article belongs to the Topic Measurement Strategies and Standardization in Manufacturing)

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18 pages, 3691 KiB

Open AccessArticle

Calibration Procedure of a Multi-Camera System: Process Uncertainty Budget

by Ibai Leizea, Imanol Herrera and Pablo Puerto

Sensors 2023, 23(2), 589; https://doi.org/10.3390/s23020589 - 4 Jan 2023

Cited by 3 | Viewed by 3304

Abstract

The Automated six Degrees of Freedom (DoF) definition of industrial components has become an added value in production processes as long as the required accuracy is guaranteed. This is where multi-camera systems are finding their niche in the market. These systems provide, among [...] Read more.

The Automated six Degrees of Freedom (DoF) definition of industrial components has become an added value in production processes as long as the required accuracy is guaranteed. This is where multi-camera systems are finding their niche in the market. These systems provide, among other things, the ease of automating tracking processes without human intervention and knowledge about vision and/or metrology. In addition, the cost of integrating a new sensor into the complete system is negligible compared to other multi-tracker systems. The increase in information from different points of view in multi-camera systems raises the accuracy, based on the premise that the more points of view, the lower the level of uncertainty. This work is devoted to the calibration procedures of multi-camera systems, which is decisive to achieve high performance, with a particular focus on the uncertainty budget. Moreover, an evaluation methodology has been carried out, which is key to determining the level of accuracy of the measurement system. Full article

(This article belongs to the Topic Measurement Strategies and Standardization in Manufacturing)

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20 pages, 4523 KiB

Open AccessArticle

A Designed Calibration Approach for the Measurement-While-Drilling Instrument

by Zongwei Liu, Kan Lei, Jiancheng Song, Linbo Li and Tao Li

Appl. Sci. 2023, 13(1), 61; https://doi.org/10.3390/app13010061 - 21 Dec 2022

Cited by 3 | Viewed by 1562

Abstract

The Measurement-While-Drilling (MWD) system, composed of a tri-axial magnetometer and a tri-axial accelerometer, is widely used in the Horizontal Directional Drilling machine in coal mines. This system can provide attitude information of each measuring point in the borehole, which will eventually allow the [...] Read more.

The Measurement-While-Drilling (MWD) system, composed of a tri-axial magnetometer and a tri-axial accelerometer, is widely used in the Horizontal Directional Drilling machine in coal mines. This system can provide attitude information of each measuring point in the borehole, which will eventually allow the trajectory of the borehole to be drawn. The attitude information, however, showed a low-level accuracy, due to the sensor’s imperfection and mounting errors. The accuracy worsened when low-cost sensors were employed, as they had higher random noise. Therefore, an exploration of ways to eliminate the sensor imperfection and mounting tolerance as well as to suppress the noise is needed. In this paper, a feasible calibration approach was designed to address these issues. This new approach combined three foundational calibration algorithms, including the ellipsoidal fitting method, the planar fitting method, and the inner product invariance method. The traditional ellipsoidal fitting method and planar fitting method were optimized by using the recursive least square criterion and omitting the steps of sample data acquisition, respectively. In addition, the noise suppression method was involved in our approach to improve the calibration accuracy. The numerical simulation results showed that the number of sampling points decreased significantly, but the accuracy of the azimuthal angle and the pitch angle fully met the engineering requirements. The experimental results showed that the pitch angle error was reduced by less than 0.5°, and the azimuth error was also reduced by less than 2.5°. It should be noted that this new approach could be implemented without the help of other expensive auxiliary equipment. Full article

(This article belongs to the Topic Measurement Strategies and Standardization in Manufacturing)

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