Double Ball Bar Research Articles

A modified method for measuring geometric errors of rotary axes based on sensitivity analysis and error simulation

Complicated measurement for machine tools geometric errors limits the high-accuracy machining processes. This research is aimed at measuring and identifying geometric errors of rotary axes efficiently by designing and optimizing measurement method using double ballbar. First, the conical and tangential measurement patterns are designed to reduce the installation times of the double ballbar. Secondly, the effect of installation errors is reduced by analyzing the coefficient matrix to avoid error accumulation. Thirdly, measurement trajectories affected by position-independent geometric errors are simulated and eliminated. Finally, the error measurement and validation experiments were performed on a dual-turntable five-axis machine tool, and the machining precision was improved by 34.09%-48.89%. The results indicated that the scheme can effectively identify the geometric errors of rotary axes and has the advantages of high efficiency and accuracy.

Research on positioning accuracy of the swivel head of milling and turning complex machining center

Abstract This article focuses on the swivel head of a milling-turning complex machining center and establishes a geometric error model between the rotary axes based on the multi-body system theory and the homogeneous coordinate transformation method. The double ball bar (DBB) is used to identify the geometric errors of the machine tool swivel head position-independent by measuring circular trajectories. The impact of PIGEs on the measurement trajectory is simulated. The swivel head is rotated at four angles (B0°, B45°, B90°, B-15°), and the laser tracker is used to analyze and study the linear axis straightness, perpendicularity, and the center coordinates and plane errors of the swivel head movement along the XZ plane. A swivel head rotation accuracy test fixture is designed to correct the positioning accuracy of a swivel head with a 45° inclination of the rotation axis. The research results show that the fluctuation of the center plane degree of freedom of the swivel head moving along the XZ plane is small, and the maximum value is 0.0086mm. Under the 45° angle posture of the swivel head, both the center coordinate error value and the plane error value are the largest. The simulation results of the swivel head position error are fairly consistent with the center coordinate error of the swivel head plane movement. A backward tilt displacement of 0.01mm~0.015mm of the machine column during assembly can reduce the influence of the weight of the swivel head on the perpendicularity and straightness of the vertical reciprocating motion, and adding auxiliary support near the base of the swivel head zero position can reduce machine straightness error.

A novel identification method for all geometric errors of rotary axis based on boundaryless constraint optimization method

For the redundancy in definition of position independent geometric errors(PIGEs) and position dependent geometric errors(PDGEs), it is difficult to identify all geometric errors of rotational axis simultaneously. A novel identification method using boundaryless constraint optimization method(BCOM) is established to improve PIGEs and PDGEs identification accuracy of rotary axis. For PIGEs, the two different dimension errors are identified separately based on least square method through appropriate measurement direction by double ball bar(DBB), and thus decrease condition number of identification matrix. For PDGEs, the B-spline curve is applied to fit the geometric errors and the objective function has been established. Several measurement paths are conducted and geometric errors are figured out by iterations of objective function. Furthermore, setup errors of DBB are investigated and discussed based on the sensitivity analysis. Finally, Simulations and experiments are conducted and their results demonstrate the effectiveness of the proposed method.

Geometric error compensation method using the Laser R-test

Traditional methods for measuring geometric errors in machine tools, including interferometry and Double Ball Bar (DBB), are known to be expensive and time-intensive. Consequently, a non-contact calibration system called the “Laser R-test” has been developed. This innovative system is designed to measure both position-independent geometric errors (PIGEs) and position-dependent geometric errors (PDGEs) efficiently. Since its development in 2000, this tool has been instrumental in analyzing eccentricity errors, angular position errors, and simultaneous trajectory errors. Through extensive research, it has been determined that the total error in a five-axis machine tool can be controlled to below 40 µm after compensating for eccentricity parameters and angular position errors. However, reducing this error to below ± 10 µm is challenging, primarily due to wobble errors in the orientation of the rotary axis without compensating. In this study, a new methodology based on Laser R-test and Rodrigues’ rotation formula has been developed to establish a PIGE model of rotary axis. Based on the methodology, the 8 PIGEs can be analyzed by measuring 5 coordinate positions. The compensation of 8 PIGEs in the rotary axis is completed within 30 min using the inspection path. Compatibility with ISO-10791–6 standards for BK1, BK2, and BK4 path tests is confirmed, validating the compensation effects. A precision of below ± 10 µm is achieved, with inspection time reduced by over 50%. This system can complete multiple errors by simply using the different paths. This greatly reduces the setup time for future users, enhancing its commercial applicability.

Fast detection of geometric errors for three-axis machine tools with combined double-ball bars based on spatial circle detection

The geometric accuracy of the CNC machine tools determines the quality of the sculptured mechanical parts. Measuring and compensating the geometric errors of machine tools can effectively improve the machining accuracy. However, traditional measurement methods using a double-ball bar (DBB) can only detect the error along the rod length direction and thus require multiple measurements in three orthogonal planes of the machine tool. This work proposes a fast error detection method for the three-axis machine tools using combined double-ball bars (C-DBBs) based on the spatially circular detection (SCD) path. The test path of this method requires the simultaneous linkage of three linear axes of the machine tools and thus could identify 21 geometric errors of three-axis machine tool. Firstly, the measuring principle of the SCD method is introduced, and the mathematical model for detecting 21 geometric errors of the machine tool based on the SCD method is established. Then, the detection experiment based on the SCD method is carried out, and it is shown that 21 geometric errors of the three-axis machine tool are obtained. Finally, the verification experiment using a traditional DBB is conducted to validate the effectiveness of the proposed SCD method. The radial errors in three orthogonal planes measured by traditional DBB exhibit a good agreement with those predicted using 21 geometric errors obtained by the SCD method. Compared with the traditional DBB method, the proposed SCD method could detect 21 geometric errors of three-axis machine tools in a single measurement. This work provides an effective and efficient methodology for detecting all geometric errors of the three-axis machine tool.

A New Kinematic Synthesis Model of Spatial Linkages for Designing Motion and Identifying the Actual Dimensions of a Double Ball Bar Test Based on the Data Measured

This paper presents the new synthesis models of spatial linkages for designing measurement motion functions and ranges and identifying the actual dimension parameters. The spatial five-bar linkage is first introduced for the kinematic model of a double ball bar test of a two-axis rotary table. To design the ideal measurement motion and motion range of the double ball bar test, a novel saddle synthesis model of a spatial four-bar linkage RRSS is readily presented. Based on the output data measured from the double ball bar test, a new saddle synthesis model of a spatial five-bar linkage RRSPS is logically proposed for identifying their actual dimensions. Finally, three test cases and their results indicate that the new synthesis models presented in the paper can conveniently and efficiently calculate the measurement motion function and range and accurately identify the actual dimensions of the double ball bar test, which provides a suitable mathematical model for improving the accuracy of the double ball bar tests of a two-axis rotary table of machine tools.

A novel method for measuring radial and axial errors in a cylindrical coordinate system using a combined double ball bar

Multiaxis machine tools are widely used in manufacturing. The measurement of motion error is important to improve the machining accuracy of machine tools. A double ball bar (DBB), as a high-precision single-dimensional position reading device, is widely used to measure the motion error of the circular path of machine tools. However, the motion errors contain the cylindrical radial and axial errors with respect to the circular path plane. Therefore, the measurement results of the DBB are incomplete because they do not contain axial errors. To measure the motion error of the circular path accurately, completely and concisely, a novel measurement method based on the combined DBB (C-DBB) is proposed in this paper, which can directly measure the radius and axial motion error of the circular path in one measurement. First, the measuring principle of the C-DBB method is introduced, and the measurement model of the radius and axial motion error of the circular path is established. Then, a measuring device using the C-DBB method was designed based on the lever principle, and the error parameters of the designed device were analyzed. According to the error analysis results, the measurement results of the C-DBB method were compensated and corrected. Finally, the C-DBB method is used to measure the circular path on the vertical CNC milling machine, and the results are compared with the measurement results using the DBB method. It is shown that the proposed C-DBB method can obtain high-precision multidimensional motion error in a single measurement, and the designed measuring device based on the C-DBB method has high repeatability and good circular path measuring ability. The proposed method provides an effective method for machine tool multidimensional motion error measurement and compensation.

Identification and compensation of position independent geometric errors of dual rotary axes for hybrid-type five-axis machine tool based on unit dual quaternions

This paper presents a novel synchronous motion trajectory based on the unit dual quaternion (UDQ) to identify the position-independent geometric errors (PIGEs) of the dual rotary axes of a hybrid five-axis machine tool using a Double ball-bar (DBB). A general irregular trajectory equipartition method is presented to deal with the asynchronous matching between DBB data sampling and trajectory points. The kinematic model is effectively simplified by redefining the PIGEs of linear/rotary axes. The installation errors of the DBB are obtained by circular/spherical fitting trajectories, which are brought into the error model for elimination. The simulation of the UDQ kinematic model combined with preset error value shows that the non-uniform variation of DBB motion will lead to the deviation of PIGEs decoupling results. A compensation strategy of major orientation errors based on the UDQ is proposed, which is verified by simulation and compensation experiments.

A new method to identify the position-independent geometric errors in the rotary axes of five-axis machine tools

Position-independent geometric errors (PIGEs), caused by assembly imperfection, affect the machine tool's accuracy. Moreover, the rotary axes of five-axis machine tools introduce more PIGEs during parts machining, hence, the need to identify them to improve the accuracy. However, the identification of rotary axes centerlines and the use of extension bars, using double ball bar (DBB), introduce additional setup errors and uncertainties during error measurements and sometimes make the process tedious. This work proposes a new method to identify the eight (8) PIGEs in the rotary axes of a five-axis machine tool with a tilting table. The homogeneous transformation matrix (HTM) was used to construct the relative motion matrix to the established coordinate systems and then deduced the error model. Three different DBB installation setups were employed for the identification of the PIGEs for both rotary axes using the planar test, the recorded DBB length data was substituted into the model to obtain the PIGEs. The results show that the proposed PIGEs identification method is accurate and can improve the accuracy of the five-axis machine tool effectively, and this method has some advantages over some existing methods of identification in terms of simplicity which shows a good improvement in the manufacturing industry.

Virtual sensor for monitoring the geometric and kinematic accuracy of machine tools

The performance of machine tools depends on their working accuracy. The paper presents a new approach for in-process monitoring the geometric and kinematic accuracy of a machine tools. This approach utilizes a virtual sensor for capturing displacements at the tool center point (TCP). The virtual sensor is set up by using a data-driven approach based on extended transmissibility functions. The input data for monitoring are the NC internal data. The transmissibility functions are established via standard experimental procedures such as double ball bar (DBB) tests tests and estimation of frequency response functions (FRF). The data from the virtual sensor can be used for process monitoring and troubleshooting when launching a new process.

Telescopic ball bar with an indexing joint for measuring machine tool error

Measurement and compensation of these errors can improve the machining accuracy of a machine tool. Double ball bar is one of the traditional instruments for measuring machine tool errors, whose measurement range depends on the length of the bar since the sensor has a stretching range of only 2 mm. Some extension bars are usually used to extend the measuring range, but each replacement of an extension bar requires recalibration and installation. In this paper, a novel measuring equipment based on telescopic ball bar with an indexing joint (IJ-TBB) is proposed, which has six measuring ranges after a single installation. First, the basic structure and measuring principle of the IJ-TBB are introduced. Then, the effect of structural errors of IJ-TBB on the measurement accuracy is studied. Next, the error amplification characteristic and measurement resolution of the IJ-TBB are analyzed. Finally, an experiment was carried out to validate the accuracy of the IJ-TBB. The results reveal that the IJ-TBB has high precision and high efficiency. It is valuable to extend the measurement range and improve the measurement efficiency of machine tools.

All position-independent and position-dependent geometric error measurement and identification of the precision of a horizontal boring machine tool

Geometric error is the main obstacle that affects the quasi-static accuracy of horizontal boring machine tools. To improve quasi-static performance, the error terms of all position-independent geometric errors (PIGEs) and position-dependent geometric errors (PDGEs) must be measured and identified precisely. This study proposes a novel method for measuring and identifying the above two types of geometric errors based on double ballbar for the rotary axis. The error terms of the linear axis are identified from the measurement model based on the exponential product method and a preset measure trajectory, and the measure coordinate system is combined with the reference coordinate to lower the uncertainty in the identification accuracy. Then, the elastic net method and improved weight function IGG3-LTS method are established to identify the PIGEs and PDGEs of the rotary and linear axes, respectively. This method has the advantage that measurement with the built-in sensor method synchronously does not interfere with the running state of the machine tool, and neither the inaccuracy of reference-frame misalignment nor installation error of the measuring instrument affects the geometric error identification results of the linear axis. Moreover, all PIGEs and PDGEs, particular to the rotary axis of the horizontal boring machine tool, are determined accurately. The measurement and identification strategy is demonstrated by experimental comparison on a four-axis precision horizontal boring machine tool. The minimum compensation rate of each precision index of the test specimen is 40.0%, the average compensation rate is 52.7%, and the maximum compensation rate is 62.5%.

Geometric error identification of five-axis machine tools using dual quaternion

A universal identification method for position independent geometric errors (PIGEs) of dual rotary axes of five-axis machine tools with arbitrary rotary axis position structures is proposed based on the unit dual quaternion (UDQ). The PIGEs of translational/rotary axes are redefined based on UDQ transformation, which effectively reduces the transformation parameters and avoids the unitization process of UDQ compared with the existing UDQ kinematics model. Based on the redefined PIGEs, a kinematic error model of a five-axis machine tool is established for error identification. Taking the cradle-type five-axis machine too with non-intersecting rotary axes as the research objective, a novel method for identifying PIGEs through the synchronous motion of dual rotary axes using a double ball bar (DBB) is proposed. Compared with BK1 and BK2 in ISO10791-6 and other existing methods, the advantage of the proposed method is that it can greatly reduce the complexity of the experiment and the operation steps by directly constructing the relative kinematic relationship between the tool and the workpiece based on the error model. Only one installation and one measurement trajectory are needed to simultaneously identify the eight PIGEs of the dual rotary axes. In addition, a trajectory equalization algorithm is proposed to effectively solve the asynchronous problem of motion and data sampling in DBB trajectory operation. By combining the simplified error model with the sampling data of DBB, the pseudo-inverse matrix is used for decoupling. The effectiveness of the proposed method is verified by DBB compensation comparison experiment. The proposed error identification method can be applied to other types of five-axis machine tools with a few changes in the configural parameters, which is ideal for periodic checks and calibration to ensure the machining accuracy.

Identification method for the dynamic motion error of the rotary axis based on circular and elliptical test piece cutting

The rotary axis is crucial for the machining accuracy of five-axis machines, and its motion accuracy is significantly influenced by the dynamic motion error. A test of circular and elliptical test piece cutting is proposed to identify and analyze the dynamic motion error of the rotary axis. The influence of the feed rate on the dynamic motion accuracy is explained. The dynamic motion error can be divided into two types, depending on its source and manifestation: dynamic error inside the servo loop (DEIS) and dynamic error outside the servo loop (DEOS). At different feed rates, elliptical test piece cutting and kinetics analyses are conducted to identify the DEIS, and circular test piece cutting together with double ball bar (DBB) tests are conducted to identify the DEOS. On-machine inspection and the coordinate measuring machine (CMM) calibration are performed. By combining the DBB test and kinetics analysis results, the DEIS and DEOS are identified and analyzed. The experimental verification shows that the DEIS and DEOS change according to the feed rate and can be determined from the machining error of the test piece. Consequently, the proposed method offers an effective reference for improving the motion accuracy of the rotary axis.

A method of identifying geometric errors for machine tools with 3 axes based on a set of sine functions using double ballbar

A method of identifying geometric errors for machine tools with 3 axes based on a set of sine functions using double ballbar

Various methods of circular interpolation performance analysis

The paper discusses the possibilities and methodology of utilizing software, designed to be used with a double ball bar device to analyze CNC machine tool positioning performance, to analyze measurements measured by a different method. The Renishaw Ballbar system is a special tool designed to allow rapid and highly effective checks of positioning performance of any numerically controlled cartesian structure, such as a CNC machine tool, and at the same time allows monitoring its condition and to some extent predict its future development. The system uses sophisticated algorithms to decompose the overall measured inaccuracy of examined machine to values of individual errors and offers possible actions to remove such errors. The ability to push different measurements of circularity, such as measurement of circularity of machined surface on a coordinate measuring machine, would allow checking the presence of various errors without the necessity to measure with a double ball bar device. Therefore, the paper presents the custom software, that shows such possibilities, which was developed at the Department of Automation and Production Systems, Faculty of Mechanical Engineering, University of Zilina.

Phase-to-Coordinates Calibration for Fringe Projection Profilometry Using Gaussian Process Regression

In the task of 3-D topography measurement by fringe projection profilometry (FPP), it is crucial to establish mapping from the phase map to the 3-D coordinates, known as 3-D calibration. The traditional methods are prone to select some specific functions to fit the phase-to-coordinates’ relationship, which needs to make a compromise between measurement accuracy and efficiency. This article proposes a novel calibration method based on the Gaussian process (GP) regression to solve this problem. In this work, according to the geometric and other systemic constraints, a pixel-dependent semiparameterized calibration model is derived to guarantee the efficiency of computation and data storage. Based on the spatial correlations of the calibration data, the GP regression method is applied to enhance the fitting ability and flexibility of the calibration model without any specific functions and parameters. The GP regression method is also applied to remove random noise from the phase map, which further improves the accuracy of 3-D coordinates. The experimental results of measuring a whiteboard and a double ball bar demonstrate the superiority of the proposed GP-based calibration model in terms of accuracy and robustness when compared with the traditional models.

Positioning Errors Measurement of CNC Machine Tools Based on J-DBB Method

Due to the errors of the servo system and the errors of the ball screw drive system, the positioning errors inevitably occur in the process of CNC machine tools. The measurement of traditional equipment is limited by a fixed measurement radius and a single degree of freedom, which can only be measured within a fixed plane. In this paper, four different positioning errors of CNC machine tools are first measured at full scale by using J-DBB (a modified double ball bar with one spherical joint connecting two bars) method. The J-DBB device uses a three-degree-of-freedom spherical joint as a connecting part, which realizes that the measurement radius can be continuously changed, and the measurement space is a spatial sphere. First, the principle of the J-DBB method is briefly introduced. Next, four typical positioning errors of CNC machine tools are analyzed and examined, which contain the uniform contraction error of ball screw and linear grating, periodic error of the ball screw and linear grating, interference of measurement devices error, and opposite clearance error. In the end, the trajectories of the CNC machine tool spindle with a single positioning error are simulated by using the J-DBB method. The results reveal that this method can be used for the positioning error of machine tools, which helps to better understand the spatial distribution of CNC machine tool errors and provides guidance for the reasonable selection of working areas to improve the machining accuracy of parts.

Modelling and indirect measurement of machine tool equivalent joint compliances

Machine tools require high geometric accuracy and stiffness. Both of these characteristics affect the radius of a radially loaded circular test. By using various loads, the machine's volumetric compliance can be studied as a function of position, orientation, and load. Further processing of the data using a kinematic and compliance model of the machine allows the equivalent joint compliances to be estimated. This model also allows to produce the characteristic patterns of loaded telescopic double ball bar readings associated with each compliance term. The compliance model contains numerous superfluous and confounded terms that are pruned from the model. The analytical model is then used to produce a numerical identification Jacobian that is further applied to estimate the compliances from test data gathered at various force levels. By using all force data at once global compliance values are estimated whereas using only adjacent force level data allows observing the change in compliance with force. The new nomenclature is introduced where each compliance term has three subscripts. The first subscript is the direction of the displacement, the second subscript is the applied force direction, and the third subscript is the relevant joint or axis. The dominant compliances are the X-axis on-axis compliance C XXX (confounded with the lateral compliance of the Y-axis C XXY ) and C YYY (confounded with C YYX ). It is observed that as the load increases from 76 to 706 N (by increments of 126 N), the dominant compliances increase by around 5%. Type A uncertainties of the calculated compliances are estimated from repeated measurements and are found to be relatively small. Some non-dominant compliances, such as the torsional compliance of the Y-axis C CCY account for deflection of less than 0.5% of that for the main compliances and has a negative value which is mechanically unexpected. It is explained in detail in the results and discussion section.

Quasi-Static Compliance Calibration of Serial Articulated Industrial Manipulators

This article presents a procedure for the quasi-static compliance calibration of serial articulated industrial manipulators. Quasi-static compliance refers to the apparent stiffness displayed by manipulators at low-velocity movements, i.e., from 50 to 250 mm/s. The novelty of the quasi-static compliance calibration procedure lies in the measurement phase, in which the quasi-static deflections of the manipulator’s end effector are measured under movement along a circular trajectory. The quasi-static stiffness might be a more applicable model parameter, i.e., representing the actual manipulator more accurately, for manipulators at low-velocity movements. This indicates that the quasi-static robot model may yield more accurate estimates for the trajectory optimization compared with static stiffness in the implementation phase. This study compares the static and apparent quasi-static compliance. The static deflections were measured at discretized static configurations along circular trajectories, whereas the quasi-static deflections were measured under circular motion along the same trajectories. Loads of different magnitudes were induced using the Loaded Double Ball Bar. The static and quasi-static displacements were measured using a linear variable differential transformer embedded in the Loaded Double Ball Bar and a Leica AT901 laser tracker. These measurement procedures are implemented in a case study on a large serial articulated industrial manipulator in five different positions of its workspace. This study shows that the measured quasi-static deflections are bigger than the measured static deflections. This, in turn, indicates a significant difference between the static and apparent quasi-static compliance. Finally, the implementation of the model parameters to improve the accuracy of robots and the challenges in realizing cost-efficient compliance calibration are discussed.