Run-out Error Research Articles

Improved Design of Imaging System for Online Detection of Large-Sized Step-Shaft Runout Errors

Large-sized step shafts are important devices for supporting and transferring heavy parts, and online inspection equipment for runout errors is affected by the environment and is subject to coaxiality errors and center-position errors, leading to problems such as reduced measurement accuracy in imaging systems. In view of the above problems, this paper proposes an improved optical imaging system design for runout error detection based on the plane-mirror-group correction method. Zemax was used to optimize the structure and simulate the optical path of the optical imaging system. The total length of the structure was 50 mm, and the MTF function for each field of view was greater than 0.3 at the spatial level up to a frequency of 42 lp/mm. The system was applied to a test platform for runout error detection, achieving the detection of runout errors of a large size in the radial direction and at the end face with a diameter range of 500–700 mm. The measurement repeatability was less than 30 μm, and the system corrected the coaxiality error of the stepped-shaft online inspection equipment considered in this paper.

Design and Study of Machine Tools for the Fly-Cutting of Ceramic-Copper Substrates.

Ceramic-copper substrates, as high-power, load-bearing components, are widely used in new energy vehicles, electric locomotives, high-energy lasers, integrated circuits, and other fields. The service length will depend on the substrate's copper-coated surface quality, which frequently achieved by utilising an abrasive strip polishing procedure on the substrate's copper-coated surface. Precision diamond fly-cutting processing machine tools were made because of the low processing accuracy and inability to match the production line's efficiency. An analysis of the fly-cutting machining principle and the structural makeup of the ceramic-copper substrate is the first step in creating a roughness prediction model based on a tool tip trajectory. This model demonstrates that a shift in the tool tip trajectory due to spindle runout error directly impacts the machined surface's roughness. The device's structural optimisation design is derived from the above analyses and implemented using finite element software. Modal and harmonic response analysis validated the machine's gantry symmetrical structural layout, a parametric variable optimisation design optimised the machine tool's overall dimensions, and simulation validated the fly-cutterring's constituent parts. Enhancing the machine tool's stability and motion accuracy requires using the LK-G5000 laser sensor to measure the guideway's straightness. The result verified the machine tool's design index, with the Z- and Y-axes' straightness being better than 2.42 μm/800 mm and 2.32 μm/200 mm, respectively. Ultimately, the device's machining accuracy was confirmed. Experiments with flying-cut machining on a 190 × 140 mm ceramic-copper substrate yielded a roughness of Sa9.058 nm. According to the experimental results, the developed machine tool can fulfil the design specifications.

An Intelligent Detection System for Surface Shape Error of Shaft Workpieces Based on Multi-Sensor Combination

As the main components of mechanical products and important transmission components of mechanical motion, shaft workpieces (SW) need to undergo high-speed motion while also withstanding high torque motion, which has high processing requirements. At the same time, the processing quality of the workpieces determines the success of the entire processing process, and the quality-inspection methods and the accuracy of the technology directly affect the evaluation of the product. This paper designs an intelligent detection system for the surface shape error (SSE) of SW that combines multiple sensors. Based on the principle of sensor use and specific experimental status, the overall scheme of the detection system is designed, followed by research on the spatial positioning algorithm and surface measurement algorithm of the workpiece to be tested. We then compensate and correct the errors with the algorithm. The effectiveness of the system is verified by measuring the surface size of the workpiece. Finally, the radial circular runout error is taken as an example to verify the detection system. The results show that the measurement error is less than 5%, and the accuracy of the system is high.

High-precision radius and sphericity measurement for microspheres of micro-CMM probe tip

The microsphere profile of probe tips has to be measured and compensated to improve the measurement accuracy of micro-coordinate measuring machines (micro-CMMs) to less than several hundred nanometers. A high-precision radius and sphericity measurement method for the microsphere of the CMM probe tip is proposed in this article. Different circumferences of the tested microsphere are measured, and the true radius of any measuring point on the surface can be obtained after separating the runout errors. Then the sphericity of the tested microsphere can be evaluated by the minimum zone sphere method. A corresponding measuring system is developed based on the analysis of the primary error model and mechanical model, and verification experiments are conducted using a ruby microsphere (A-5000-7801, Renishaw Corporation) as the reference, whose claimed diameter and sphericity are 700 µm and 130 nm, respectively. Six groups of repeated experiments are performed, and 18 000 measurement points on 15 circumferences are recorded in each group of experiments. Results show that the average radius of the tested microsphere is 350.003 µm, and the average sphericity error is 208 nm with a standard deviation of 5.3 nm. Finally, the expanded uncertainty of the measurement results of the developed system is calculated as 209 nm (k = 1.96, normal distribution). The proposed method and system can be used in the precision measurements and compensations for probe tips of micro-CMMs and other parts, such as microspheres used in micro-bearings and micro-manufacturing machines.

MACHINING OF TOOTH PROFILES ON CNC MACHINES

Conventional methods of tooth machining using worm modular milling cutters, gear wheels and gear combs have common disadvantages - they require specialized equipment, are characterized by complex readjustment and relatively low productivity, which are eliminated in skiving. This paper views the possibilities for machining tooth profiles by means of skiving on CNC turning and milling machines. A new version of the kinematics of the process upon cutting inclined teeth has been implemented, where the feed is in the direction of the tooth, no correction in the angular speed is required and a skiving tool profiled according to the profile of the machined surface is used. Meshing of a tooth pair with crossed axes is reproduced. As a result of the crossing, slipping of the profiles occurs, which is the main cutting motion. The cutting speed, as a determining mode factor, can vary widely and depends on a number of design and technological parameters. Single-factor experiments have been conducted to determine the influence of the conditions of the implementation of the skiving process (the crossing angle of the tool axes and the workpiece, determining the magnitude of the cutting speed, and feed rate) on the quality parameters of the machined surfaces (tooth profile deviation, tooth direction deviation, accumulated pitch error, largest pitch difference and radial runout error) and the corresponding graphical dependencies have been constructed. A 7- 12 degree of accuracy of the machined tooth profiles has been ensured.

Five-degrees-of-freedom error motion measurement method of precision rotary table based on BMPES

It is essential to obtain the five-degrees-of-freedom (5-DOF) error motion of a rotary table to reconstructthe real trajectory of the rotating shaft, but there are many error coupling problems when measuring the error motion of a rotary table. In order to improve the measurement accuracy of the 5-DOF error motion of the rotary table, a method of measuring the error motions based on bidirectional multi-point error separation (BMPES) is proposed. First, by analyzing the motion characteristics of the rotary table with multiple degrees of freedom error during the rotation, a detection system with a double-layer structure probe arrangement is designed. Then, the three-point method is used in the radial direction to separate the roundness error of the measuring disk, which improves the measurement accuracy of radial error. Finally, the coupling relationship between the mixing errors collected by the axial probes is researched, and a face-four-point error separation method is proposed, which can separate the flatness error of the lower surface of the measuring disk and complete the decoupling of the tilt error and the axial runout error. Simulation results show that for the measurement of radial, tilt and axial errors, the measurement errors of the BMPES method proposed in this paper are reduced by 97.89%, 68.40% and 99.99%, respectively, compared with the five-point method, and when eccentricity errors exist, the measurement errors of the radial and tilt errors are reduced by 99.06% and 85.67%, which verifies that the method can accurately obtain the 5-DOF motion of the rotary table errors.

Straightening of the rollers of planetary roller screw — Design of straightening die and experimental validation

The roller of a Planetary Roller Screw (PRS) is prone to bending deformation and runout error after carburizing, which results in the uneven transmission performance, increased transmission friction, and decreased service life. Traditional grinding methods used to rectify these errors have high costs and low efficiency and furthermore reduce the thickness of the carbon layer of the roller. This paper proposed a new radial feed-in straightening method to correct the geometric errors of carburized PRS rollers. Trial tests are first performed to explore the feasibility of different straightening techniques, as well as to discover key factors for the rational design of a straightening die. Based on the trial tests, a new tooth profile model of the straightening die for the PRS roller is proposed. Finite element models are developed to analyze the material flow feature of the straightening process, as well as to verify the effectiveness of the proposed tooth profile model of the straightening die. For mass production needs, experimental tests are performed to further examine the performance of the proposed straightening method. It is found that reducing the tooth contact interference between the roller and die can effectively increase the quality of the straightened workpiece. Results show that the bending deformation and runout error of the carburized PRS roller are effectively corrected by the proposed straightening process. Furthermore, the smoothness of the tooth surface of the roller is significantly increased, and all the tested samples meet production quality standards after straightening. A comparison of transmission performance under 0.3 million cycles shows that the maximum friction torque (1.82 N·mm) of the PRS product with straightened rollers is much better than without straightening (105.70 N·mm).

Kinematic modeling of a planetary roller screw mechanism considering runout errors and elastic deformation

Kinematic modeling of a planetary roller screw mechanism considering runout errors and elastic deformation

Comparison of GUM and Monte Carlo Methods for the Measurement Uncertainty Circular Runout Error of Shafts

Measurement uncertainty is one of the most important concepts. The ISO IEC 17025:2005 standard: describes harmonized policies and procedures for testing and calibration laboratories. Guide to the expression of uncertainty in measurement (GUM) is a direct uncertainty analysis method, which calculates the combined standard uncertainty and expanded uncertainty by law of propagation of uncertainty. Monte Carlo Method (MCM) as presented by the (GUM S1) involves the propagation of the distributions of the input sources of uncertainty by using a model to provide the distribution of the output. By random sampling, the probability density function of the input quantities. In this paper, present measurement uncertainty to circular runout error. By use shaft standard with a diameter of 32 mm., length 100 mm. From the experiment results, Comparison of GUM and MCM showed no differences. The cases the estimated uncertainty using the GUM approach slightly overestimated the results obtained with the MCM. However, the use of numerical methods such MCM as a valuable alternative to the GUM approach. The practical use of MCM it has proven to be a fundamental tool, being able to address more complex measurement problems that were limited by the GUM approximations.

Application of active magnetic bearings in control and estimation of geared-rotor faults in high speed offset spur gear transmission system

This study is focused on the mathematical modelling, analysis, active transverse vibration control and fault analysis of a single-stage spur geared-rotor system. It uses Active Magnetic Bearings (AMBs) as an auxiliary bearing in addition to the conventional mechanical bearing in rotor fault detection considering the dynamic model with gyroscopic effects. The change in dynamic forces primarily due to the mesh deformation, gear runout, and variable transmission error are considered, which causes unwanted vibration and noise. To prevent the damage of gears and other supporting structures, these forced vibrations and control currents are meticulously investigated. From the dynamic responses of geared-rotor, the AMB control the stiffness and damping to minimize the transmission of forced vibrations to the mountings by closed-loop feedback control system. For an accurate modelling the dynamic transmission error is taken in two orthogonal transverse directions, which has asymmetric transmission error characteristics. Full spectrum is used for frequency domain analysis with tilting phenomena of the gears at high spin speed. An identification algorithm is developed for fault detection and estimation of system parameters from vibration and current of the proposed geared-rotor-AMB system. The robustness of the proposed algorithm is verified with different added percentage of noise and modeling errors.

The Modelling and Analysis of Micro-Milling Forces for Fabricating Thin-Walled Micro-Parts Considering Machining Dynamics

In the fabrication process of thin-walled micro-parts, both micro-cutting tools and thin-walled micro-parts have the characteristics of small size and low stiffness. Therefore, the regenerative chatter during the machining process cannot be ignored. The influence of the tool runout error and actual trochoidal trajectories of the cutting edge on micro-milling forces should also be considered comprehensively. In this paper, the tool runout error in the micro-milling process is first analysed, and an instantaneous undeformed chip thickness model is established considering the runout error. On this basis, the dynamic deformation of the micro-cutting tool and thin-walled micro-part is studied, and an instantaneous, undeformed, chip-thickness model is proposed with the consideration of both the runout error and dynamic deformation. The dynamic parameters of the machining system are obtained using the receptance coupling method. Finally, thin-walled micro-part machining experiments are carried out, and the obtained results of micro-milling force simulation based on the proposed model are compared with the experimental results. The results indicate that the micro-milling force modelling, by taking the influence of machining dynamics into account, has better prediction accuracy, and the difference between the predicted resultant forces and the experimental results is less than 11%.

Astigmatism correction of convex aspheres using the subaperture stitching hindle test

We propose an astigmatism correction method for the subaperture stitching Hindle test to measure hyperbolic convex aspheres. Astigmatic wavefront errors arise from misaligned Hindle setups, mechanical runout errors of the rotational motion for stitching, and the surface error of the target itself. Because these errors are combined, they cannot be separated in the conventional subaperture stitching Hindle tests. We exploited the rotational periodicity of each error to distinguish the surface figure error from other astigmatic error sources and rectified the Hindle test results with a third-order astigmatism. Using the subaperture stitching Hindle test, we averaged two sets of measurement data with a 180° rotational phase difference between them to calculate the astigmatic surface error. The proposed method was verified experimentally by comparing it with the results from a commercial stitching interferometer from QED Technologies; only subnanometer differences in the root-mean-square values were obtained. Therefore, the proposed method calibrated the system errors from the test surface wedge and the rotational decenter easily, thereby reducing the mechanical costs and alignment efforts and making it more accessible than a sophisticated mechanism.

New Radius and Roundness Measurement for Microspheres Using a High-Precision Run-Out Error Separation Method

Roundness is a kind of form error in geometrical measurement in laboratory and industry and contributes significantly to the uncertainty of the measurement instruments using precision spheres, especially microspheres. A new radius and roundness measurement method for microspheres is proposed in this paper. Using this method, not only can separate different run-out errors from the measuring results, but also can obtain the true radii in different directions of the tested microsphere, which are necessary for the roundness evaluation according to ISO 1101. A new roundness measurement system has also been developed, which is mainly composed of two miniaturized Michelson interferometer (MI) systems, two elastic mechanisms, and a precision rotating stage. Repeated measurements have been performed using a ruby microsphere manufactured by Renishaw Corporation as the reference, which has a claimed diameter and roundness of 700 μm and 130 nm respectively. Experimental results show that the average radius of the tested microsphere is 349.99 μm with a maximum error of 65 nm and an expanded uncertainty of 94.0 nm (k=2). The proposed method and system can be used in the precision contact measurements of parts with micro circular characteristics such as microspheres and micro cylinders.

Influences of circular runout errors and processing parameters for slotting on the accuracy of harmonic reducer

Influences of circular runout errors and processing parameters for slotting on the accuracy of harmonic reducer

Flatness on-machine measurement system of chemical mechanical polishing process for large-caliber tin plates

In planar optics machining, surface flatness is a critical requirement for making high-quality optical devices. Chemical mechanical polishing (CMP) is an important process of smoothing surfaces for hard and brittle planar optics. Thus, there are growing interests in developing high-precision flatness on-machine measurement system for tin plate CMP process. However, the traditional evaluation measurement cannot meet the measurement accuracy requirement of approximate 2 μm. In this study, we propose an effective on-machine measuring system for the large-caliber optical tin plate, which consists of linear guideway, rotary table, and measuring sensor. In the system, the straightness error of the guideway and the axial runout error of the rotary table are compensated using a spiral method and the Keyence LK-G5000 measuring sensor. First, the spiral measuring path is formed by the movement of the line guideway and rotary table, which can prevent from multiple calibration. Then, the 3D flatness error of the dressing process is measured by linear movement of the LK-G5000 and the rotation of the tin plate. After the primary measurement process, the obtained 3D flatness error is compensated for straightness and axial runout error in sequence. To verify the accuracy of the flatness measurement, the tin plate is dressed by the natural diamond tool according to the measured 3D flatness error. After the dressing process, the peak-valley value of the remeasured flatness error can achieve 2.12 μm through a single-step dressing. The experimental results provide the accuracy and reliability of the high-precision on-machine flatness measurement system for the large-caliber tin plate.

Developing a rotation device in radio frequency systems for improving the heating uniformity in granular foods

A major obstacle for industrial radio frequency (RF) treatments is non-uniform and thermal runaway heating. This study aimed to improve the RF heating uniformity in granular products using a rotation device with sample mixing. After the run-out error of the rotation device met the allowable tolerance range, the RF heating uniformity was evaluated for mung bean, coix seed, peanut kernel and almond kernel under different rotating speeds, volume ratios and moisture contents (MCs). The results showed that the RF heating uniformity index decreased and then increased with increasing rotation speed, whereas the volume ratio presented the opposite effect. The RF heating uniformity index raised with increasing MCs. The heating uniformity in mung beans was the best because of their smallest particle size among the four selected samples. Therefore, the laboratory-scale rotation device applied in the RF system could provide a solid foundation for further large-scale industrial applications.

Modeling and sphere constrained calibration of a vision coordinate measurement machine

A new vision coordinate measurement machine (v-CMM) is proposed by integrating a binocular stereo vision tracking device and a 1D distance sensor to measure the surface. Using a standard sphere, the calibration process is carried out in two steps. Fewer points on the sphere are measured and the linear calibration model is used to calculate the approximated transformation. More points are collected and the radius-difference based optimization model is used to calculate the accurate transformation. Using the Monte Carlo method, the calibration uncertainty is analyzed by deriving the relationship between calibration uncertainty and tracking random errors. The effectiveness of the calibration algorithm is verified by analyzing the situation where the center error and tracking error mix. Two experiments are carried out: One is the calibration experiment, which will obtain the structure parameters of v-CMM with uncertainty. In the experiment, the measured runout error of the sphere is 0.024 mm, which is able to evaluate the accuracy of the calibration process. The other experiment is that a part with three cylindrical bars is measured. Key sizes of the part are calculated, containing bars radiuses and the distances between them. The experimental results show that after calibrating, the measuring precision of v-CMM is highly improved. The v-CMM is suitable in specific scenarios, like transparent media surface measuring.

A comprehensive method for controlling the electrical runout of the rotor for a geared centrifugal compressor

The internal high-speed geared rotor is the most important component of centrifugal compressors. The electrical runout error of the rotor including mechanical and electrical ones can greatly affect the working performances of the centrifugal compressors. To overcome this problem, this work proposes a practical comprehensive method for controlling the electrical runout of the rotor of a geared centrifugal compressor. An elastic-plastic deformation calculation method based on the slice approach is presented to determine the applied load range calculation for controlling the cross-sectional deviation of the rotor profile. In this method, the demagnetism and remanence detection should be provided to obtain a small residual magnetism value before the mechanical runout detection. A combined method including cold extrusion processing and slight impact processing is proposed to reduce the electrical runout of the rotor. A case study is carried out to validate the proposed method. To avoid the effect of the rotation precision and clearance of the support system on the detection results, a rigid support system is used to detect the mechanical runout of the rotor. Note that single cold extrusion or impact processing cannot completely eliminate the electrical runout. Finally, the results show that the proposed combined method can be a helpful approach in controlling the electrical runout of the rotors.

Transverse Vibration of Geared-Rotor Integrated With Active Magnetic Bearings in Identification of Multiple Faults

Abstract This paper presents a novel concept of the modeling, active control of transverse vibration responses, and identification of fault parameters in a geared-rotor system integrated with active magnetic bearings (AMBs). The sources of error in gears while in the operation are the gear mesh deformation, transmission error, and runout, resulting in dynamic forces, excessive vibration, and noise. To avoid any undesirable effect on the gear-pair and other supporting structures, it is essential to investigate these forced vibrations in time and frequency domain. Hence, an approach to monitor and control the transverse vibration of mating gears is presented with the help of AMBs. The AMBs are capable of suppressing the vibration of the system (transients as well as steady-state) by controlled electromagnetic forces considering the rotor vibrational displacement with a closed-loop feedback system. A mathematical model has been developed with geared rotor faults, like the mesh deformation, gear run-out, and asymmetric transmission error. The transmission error has been modeled as the sum of mean and varying components of error in two orthogonal transverse directions. Based on the mathematical model, an identification algorithm has been developed. Considering full spectrum analysis of the rotor vibration and AMB current information, estimation of system parameters, i.e., the equivalent mesh stiffness, mesh damping, gear runouts, the mean and varying transmission error magnitude and phase angles, and the current and displacement constants of AMBs has been performed. Gaussian noise in responses and modeling errors in mathematical models have been added to test the robustness of the proposed algorithm to comply with the experimental settings.

Simulation-based surface roughness modelling in end milling

The surface topography often is an important quality criterion for the manufacturing of milled workpieces as it often defines their functional behaviour. In machining both, the kinematics of the process and the stochastic influences deriving from the machine tool, workpiece and the surrounding environment affect the workpiece’s surface roughness. This paper presents a simulation-based method for flank milling, which considers kinematic and stochastic influences including run-out errors and tooth length variations. The simulation results are used in combination to predict the surface roughness depending on the chosen process parameters. Hence, also making in possible to choose appropriate process parameters to achieve a defined surface roughness.