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Helical rake flank is an important structure of helical broach tools. Its perfect sharpening is crucial to maintain the working performance of the tool and prolong the tool life, which is obtained via proper wheel orientation and suitable grinding processes. In practical, wheels with diverse profiles are adopted to satisfy the sharpening for various rake flanks. Therefore, wheel orientation identification methods with strong robustness are expected to deal with general helical rake flank sharpening tasks. Besides, proper grinding processes should be devoted to helical rake flank sharpening to improve the quality of broach tool. This study developed a wheel orientation calculation method that combing the specific process for helical rake flank sharpening with involving discrete enveloping. Firstly, a general model for grinding wheel is established, and the swivel-tilt-based orientation and positioning parameters of wheel are given. Then, through approximating the grinding motion as a serial of discrete wheels, the machined profile on the broach tool axial-section is expressed as the external enveloping profile of the intersection curves between the wheels and the tool axial-section. After distinguishing the enveloping profile by points along radial direction, the derivation of the instant contact line was provided. Furthermore, the mathematic model of the specific process about helical broach rake flank sharpen is established to enhance the wheel orientation identification algorithm. At last, both experiments and simulations are implemented to verify the effectiveness of this method and to investigate the influences of the process constrains via solution space.

Form error deflects the assembly surfaces and thus greatly affects the assembly accuracy of precision mechanical systems. Based on rigid motion, this paper proposes a prediction method for assembly surface contact considering form error to improve the simulation accuracy of virtual assembly. The method estimates the assembly equilibrium state by simulating the realistic behaviour of surfaces in assembly process: Firstly, one surface is fixed and the other is transferred along the assembly direction until the first contact occurs. Then, the other surface is rotated according the assembly force and the previous contact positions to successively reach the second and third contacts. The rotation operation is repeated until the assembly equilibrium conditions are finally met. Particularly, a space slicing algorithm is put forward to achieve faster calculation of the rotation information including rotation axis, rotation direction and rotation angle. This method can be applied in the field of assembly simulation and assembly verification. At the end of this paper, an assembly case of two rectangular plates is carried out to prove the feasibility and effectiveness of the method.

Previous works have shown that only relying on measurement data is generally insufficient to identify root causes of the dimensional variation for the complex manufacturing system. It is also well known that for underdetermined multistage assembly processes (MAPs), the number of measurements is less than that of process errors so that the traditional methods are not available for the variation source identification. Therefore, there exists a substantial challenge for fault diagnosis of underdetermined MAPs, especially for the case with multiple fault patterns. To tackle this problem, a novel approach that integrates statistical analysis with domain knowledge is proposed in this paper. First, the variation propagation model is employed to reveal the inherent relationship between key control characteristics and key product characteristics, and then the corresponding variance model is constructed to interpret process faults by means of the abnormal variance of process errors. Considering that the probability of less process faults is far higher than that of more process faults in MAPs, the problem of fault diagnosis is further transformed into searching the sparse solution of abnormal variance changes for process faults. Afterwards, based on the non-negative property of the covariance matrix, an enhanced Bayesian hierarchical model is developed to favor sparse estimation of the variance for the underdetermined system in MAPs. Finally, experimental results of both the numeric simulation and practical case study demonstrate the proposed diagnosis methodology can effectively identify the process faults for different patterns with system noise.

The traditional finite element method has the advantages of strong versatility and high calculation accuracy. Thus it is widely applied in various numerical simulation problems. Although the traditional finite element method for solving the shaft-hole assembly problem can obtain better solution accuracy, the process of modeling and calculation take a long time and thus cannot meet the engineering application requirements when the equilibrium position after the assembly needs to be obtained quickly to guide the subsequent process. In this paper, an iterative method based on the spring contact model is proposed. Firstly, the actual form error of the shaft and hole is characterized by the Fourier series expansion method; Then, in the contact surface, we established a discrete spring contact model and obtained the equivalent stiffness of the coupling spring through the discrete solid model. The balance iterative calculation based on the form errors and contact deformation force can finally determine the equilibrium position after the assembly. Compared with the calculation results of the finite element model, the equilibrium position of the shaft-hole assembly can be quickly solved under the condition of sacrificing certain precision. From this aspect it can be estimated that this method has a good potential for engineering application.

Purpose This paper aims to develop a theoretical method to analyze the rotation accuracy of rotating machinery with multi-support structures. The method effectively considers the geometric errors and assembly deformation of parts. Design/methodology/approach A method composed of matrix and FEA methods is proposed to do the analysis. The deviation propagation analysis results and external loads are set as boundary conditions of the model which is built with Timoshenko beam elements to calculate the spatial pose of the rotor. The calculation is performed repeatedly as the rotation angle increased to get the rotation trajectories of concerned nodes, and further evaluation is done to get the rotation accuracy. Additionally, to get more reliable results, the bearing motion errors and stiffness are analyzed by a static model considering manufacturing errors of parts. Findings The feasibility of the proposed method is verified through a case study of a high-precision spindle. The method reasonably predicts the rotation accuracy of the spindle. Originality/value For rotating machinery with multi-support structures, the paper proposes a modeling method to predict the rotation accuracy, simultaneously considering geometric errors and assembly deformation of parts. This would improve the accuracy of tolerance analysis.

Contact scanning probes have higher accuracy than non-contact probes in industrial applications. But changes of the measured surface and adjustment of velocity and acceleration may cause random measurement deviations, which are mainly determined by dynamic characteristics of the probe system. To realize the prediction of measurement deviations related to scanning parameters, this paper proposes a simpler detection method of dynamic performance. In this article, the dynamic response characteristics of the probe to diverse external stimuli are studied theoretically and experimentally on the basis of the original probe design. Under different scanning variables including the amplitude, spacing and shape of the surface, velocity and acceleration, the integration of the second-order vibration model and external excitation forms the theoretical basis for quantitative analysis of the system response, and numerical simulation and three sets of experiments are designed to effectively verify the deviation distribution of the system response caused by different scanning parameters in the time and frequency domains.

Input uncertainties inevitably result in the output error for parallel mechanisms, which will lead to significant influence on good work performance. To control the output error within the specification boundary, this article proposes a novel approach of input tolerance design based on the level set method for the driving joint. The implementation of the proposed method can be divided into two subtasks. First, using the level set method, the exact input error boundary is determined by means of evolving an initial input error interface with a defined normal speed field, thereby transforming the problem of exploring the exact boundary into solving a partial differential equation with initial value. On this basis, according to the equal and scaled principles, the tolerance width of each input is evaluated in an intuitionally geometrical manner, that is, searching the maximum geometry corresponding to the principle inside the exact input error boundary. Finally, two planar parallel mechanisms with different degrees of freedom are introduced as numerical examples to demonstrate the execution and effectiveness of the proposed method.

Accuracy is of great importance for deployable mechanisms because it greatly determines the performance of the antenna. The main purpose of this paper is to propose a method to analyze the angular errors of the multi-closed-loop deployable mechanism of the planar synthetic-aperture radar antenna considering link deviations and joint clearances. First, a two-link unit is explored to calculate the position errors of the joints due to the manufacturing imperfection only in the assembly process. On this basis, conducting a geometrical analysis, the formulations of the studied angular errors of two planar antenna panels after the introduction of clearances are established. Utilizing the rotatability law of the single-loop linkage, the worst-case scenario associated with a chaotic clearance-induced uncertainty is reduced to a purely geometrical problem. Accordingly, the maximum angular errors caused by these two error sources are obtained in an intuitive manner. Finally, the proposed method is demonstrated by a numerical example of the deployable mechanism and verified by experimental measurements.

Because of the existence of link errors, assembly deviations, and redundant constraints, link adjustments for deployable structures must be implemented during the assembly process to ensure accurate performance and deployable reliability. Thus, this study proposes an optimization method to conduct quantitative link adjustments for spatial multi-loop deployable structures considering redundant constraints. First, the equations of the deformation compatibility are derived based on static analysis. Second, by formulating the objective functions of surface accuracy and strain energy, a multiobjective discrete optimization model of link adjustment, subjected to the equations of the deformation compatibility and adjustable scopes of the support links, is established accordingly. Third, the optimization model is solved using the successive Taguchi approach, which uses the grey relational analysis coupled with principal component analysis as the multicriteria decision-making model, leading to the optimal adjustment for each link. Finally, a numerical example is presented to verify the validity of the proposed method.

Strict requirements for concentricity of the multistage high pressure rotor of an aero-engine are employed to guarantee performances such as vibration. Tedious and time-wasting trial assembly by adjusting the installation angles of stages is needed to meet the requirements due to the lack of effective analysis methods. Furthermore, there is no quick way to find out where the problem is and how to repair the parts when the installation-angle-adjusting method fails. This article focuses on a solution to optimize the installation angle of each stage and to make repair decisions in the assembly process. The run-out data are processed by least square method to get the spatial positions and attitudes of flanges and a deviation propagation analysis model is built by virtue of homogeneous coordinate transformation theory to predict the accumulative errors of each stage. The eccentricities of stages are evaluated with reference to the common axis and the installation angles of stages are optimized by minimizing the sum of eccentricities. Sensitivities of eccentricity, eccentric angle and parallelism of each stage are analyzed and repair decisions for parts are made to meet more strict requirements. An example of a three-stage subassembly is presented to demonstrate the solution.

Time-dependent system kinematic reliability of robotic manipulators, referring to the probability of the end-effector’s pose error falling into the specified safe boundary over the whole motion input, is of significant importance for its work performance. However, investigations regarding this issue are quite limited. Therefore, this work conducts time-dependent system kinematic reliability analysis defined with respect to the pose error for robotic manipulators based on the first-passage method. Central to the proposed method is to calculate the outcrossing rate. Given that the errors in robotic manipulators are very small, the closed-form solution to the covariance of the joint distribution of the pose error and its derivative is first derived by means of the Lie group theory. Then, by decomposing the outcrossing event of the pose error, calculating the outcrossing rate is transformed into a problem of determining the first-order moment of a truncated multivariate Gaussian. Then, based on the independent assumption that the outcrossing events occur independently, the analytical formula of the outcrossing rate is deduced for the stochastic kinematic process of robotic manipulators via taking advantage of the moment generating function of the multivariate Gaussian, accordingly leading to achievement of the time-dependent system kinematic reliability. Finally, a six-degrees-of-freedom (6-DOF) robotic manipulator is used to demonstrate the effectiveness of the proposed method by comparison with the Monte Carlo simulation and finite-difference-based outcrossing rate method.

Kinematic reliability is an essential index assessing the work performance of robotic manipulators. In general, the kinematic reliability of robotic manipulators is defined as the probability of the pose or position error falling into a specified tolerant region. Therefore, this work proposes an efficient method to conduct kinematic reliability analysis for robotic manipulators under rectangular and spherical allowable safe boundaries in terms of dimension and input uncertainties. First, based on the Baker–Campbell–Hausdorff formula and Lie group theory, the mean and covariance matrix of the distribution of the pose error are analytically determined. Then, the expectation propagation of the multivariate Gaussian and saddlepoint approximation method are employed to calculate the probabilities of kinematic reliability under the rectangular and spherical safe boundaries, respectively. The proposed method takes into account the boundness of the random error variable and is available for arbitrarily distributed errors. Finally, a spatial six degrees-of-freedom industrial robot is used as an example to demonstrate the effectiveness of the proposed method by comparison with other methods. The comparison results indicate that the proposed method has higher accuracy and efficiency.

As a particular two degree of freedom generating method, skiving is effective to manufacture the periodically distributed internal and external profiles, and its cutting edge design is a foundational problem. In order to avoid the singularity in analytical methods, this paper studied a discrete surface assisted universal method to identify the cutting edge of skiving cutter and simulate the machining process by discrete cutting points. Firstly, the kinematic model of skiving was constructed in aspects of the parametrical modeling of the cutter and workpiece as well as the machining configuration. The principle of cutting edge identification was investigated based on the conjugation process of skiving in the following. Then, the entire procedure for cutting edge calculation was presented in detail. Therefrom, according to the profile generation during cutting action, the skiving spatial contacts were analyzed through reasonable coordinate frame transformation. At last, an external skiving for involute gear was taken, the cutting edges for two kinds of rake flank were calculated, and the machining error between the machined profile and desired profile was compared to proof the correctness of calculated cutting edges. Besides, the analysis of the spatial contact motions for these cases validated the effectiveness and the practicality of the proposed method.

The assembly process for planar closed-loop mechanisms is full of complexity and uncertainty due to joint clearance, link coupling and probable redundant constraint. In order to ensure assembly precision, an algorithm of predicting accuracy for planar closed-loop mechanisms in view of joint clearance and redundant constraint is proposed. Firstly by analyzing the assembly process of a planar fivebar closed-loop mechanism, three components of single-fixed, two-connected and redundant-inserted links are proposed to describe the assembly process of arbitrary planar closed-loop mechanisms which is regarded as successive stacking of those components. Then error models of those components are established based on the linear kinematics and principle of virtual work. Subsequently, an algorithm of precision prediction for planar closed-loop mechanisms is constructed by combining those error models. Finally the extendible support structure of the SAR antenna is used as the numerical example to verify the validity and generality of the proposed algorithm.

This paper proposes a measurement and adjustment procedure for virtual pivot errors using the R-test and investigates the influence of virtual pivot errors to the surface profile in bonnet polishing. Initially, kinematic modeling is carried out for describing the location errors of rotary axes and defining overall errors of the virtual pivot arm. Then, the R-test is introduced to measure the three-dimensional displacement of a sphere located at the virtual pivot point and identify location errors. The adjustment procedure for virtual pivot errors is developed by means of mathematical analysis. The measurement and adjustment approach is applied to an ultra-precision polishing machine, on which an adjustment experiment was conducted to validate the proposed method. Based on this, a contrastive polishing experiment on a concave lens is carried out under good and poor virtual pivot errors. The experiment result shows that the maximum form deviation of the polished surface profile is reduced from 241.0 nm to 89.6 nm when good alignment of virtual error is achieved. Analytical simulation based on a material removal model of the bonnet polishing tool and machine is implemented to reveal the influence of virtual pivot errors to polishing quality.

Time-dependent positional reliability, mathematically defined as the probability of the positional error falling inside a specified safe boundary over a time interval, is of importance for robotic manipulators. This work proposes an enhanced moment-based approach integrating the Lie-group theory, series expansion simulation, sparse grid Gauss-Hermite integration technique and chi-square approximation to attacking this problem. The novelties of this work lie in two points. On the one hand, different from previous methods that compute the first to fourth order moments directly using the original limit-state function, the proposed method takes advantage of the Lie group theory, PCE and EOLE to transform the original limit-state error function into a simple surrogate one for moment calculation, which helps to get rid of repeatedly calling the original error function and therefore results in a great enhancement in efficiency. On the other hand, the proposed method first introduces the non-central chi-square approximation to rebuild the extreme value distribution of the positional error, by which the accuracy of time-dependent positional reliability analysis is highly enhanced. Finally, a 6-DOF robotic manipulator is showcased to demonstrate the effectiveness and advantages of the proposed approach.

This paper introduces a novel modelling method for variation propagation calculation of 3-D assemblies taking into account geometric variation and part deformation, which are neglected in most models in tolerance analysis. Initially, numerical studies are carried out in order to illustrate the characteristics of strain distribution in components and contact forces on the mating surfaces of a 3-D assembly. According to these characteristics, a linear equivalent model using springs to represent the elastic mating surfaces with geometric variation was presented. Then, the equilibrium criterions corresponding to actual contact situations and iterative searching algorithm of the equilibrium status of contacting were developed. The proposed modelling and calculation method were finally applied to the assembly of two machined parts, on which finite-element analyses and experimental tests were conducted to validate the effectiveness and accuracy. This linear contact model also shows an important advantage on mode...

Machining stiffness, which serves the overall stability of a machine tool, plays a significant role in determining the resulting machining errors in a machine tool. Therefore, the machine tools can thus be improved to get high levels of precisions directly from what we behold as the most important determinant, the overall stiffness. In this paper, a novel approach modeling the static stiffness field of the machining space is being discussed. Within this method, a parametric model, considering six-directional static stiffness, is established to design and evaluate the static stiffness model of a high-performance computerized numerical control (CNC) machine tool. The result is then used for further discussions on the estimating and reducing of the machining errors. The machining errors are predicted by using the same CNC model under various load bearings considering the practical machining positions and stress conditions. Moreover, the effect of the six-directional static stiffness on the machining errors according to each position in the machining space is researched, where we investigate the possible solutions to reduce the machining errors with the processing technology put into consideration. In the end, by experimenting on boring-milling machining center, we verify the accuracy and efficiency of the proposed error prediction method by comparing the results from experimental data and those from finite element analysis. The proposed model is then proved to have great efficiency in optimizing the machine tool’s layout and structural design based. This improved modeling strongly suggests a favorable application for future manufacturing processes of machine tools.

This paper introduces a novel approach for measurement process planning in machine tool assembly by applying the observability principle of state space model which is widely used in control engineering. Initially, state space modeling was carried out for describing the variation propagation and accumulation of assembly process. Then, a mathematical explanation of measurement uncertainty accumulation was presented by means of optimal estimation using Kalman filter. Based on this, an analysis algorithm is developed to find an optimal solution with small estimation errors and money and working time costs, so as to provide designers with feasible measurement plans in assembly. When such method is used, a quantitative approach could be offered to the evaluation of uncertainties of measurement process, which is totally different from traditional methods dependent on experiences. The suggested approach was finally applied to the assembly of a horizontal machining center, on which numerical analyses was conducted to validate the proposed method, and some guidance for measurement planning is summarized from this example analysis.

Time-dependent system kinematic reliability of the planar parallel manipulator refers to the probability of the pose error falling into the allowable safe region over the whole specified trajectory, which is essential for its work performance. However, works regarding this issue are quite limited. Consequently, this study conducts time-dependent kinematic reliability analysis for planar parallel manipulators considering joint clearance, input uncertainty, and manufacturing imperfection based on the first-passage method. First, the limit-state pose error function is established by means of the Baker–Campbell–Hausdorff formula and the theory of the Lie group and Lie algebra. Then, the analytical solution to the outcrossing rate of the non-stationary vector stochastic kinematic process is derived by employing the expectation propagation and closed-form properties of conditional and marginal statistical moments (mean and covariance) of the multivariate Gaussian. On this basis, the time-dependent system kinematic reliability is calculated upon the assumption that the outcrossing events are independent. Finally, the planar 3- R RR parallel manipulator is used to demonstrate the proposed method, and its effectiveness is validated by comparison with the Monte Carlo simulation method.

Kinematic reliability and surface accuracy are of importance for the deployable structure in that the former directly determines whether the deployment is successful or not and the latter is greatly associated with the performance of the space antenna. These two key indexes are generally guaranteed by adjusting the length of the support link. To this end, this study proposes an enhanced method of quantitatively resizing support links for a planar closed-loop overconstrained deployable structure. First, the relationship between the successful unfolding and the combination of link adjustments is derived by taking advantage of the support vector machine to train the motion data that is collected from rigid-flexible dynamic simulations. Then, resorting to structural mechanics, the system of equilibrium equations in terms of stretching and bending is established, thereby leading to the implicit mapping from link deviations to the angular errors of the satellite panels. Thereon, a discrete optimization model with two objectives ensuring the deployable reliability and accuracy performance for link adjustment is completely developed. This optimization model is solved by an improved successive Taguchi approach, which uses the grey relational analysis coupled with principal component analysis as the multicriteria decision-making model. Finally, the implementation of the proposed method and its effectiveness are comprehensively demonstrated by a numerical example.

This study proposes a generalized approach to error space calculation for parallel/hybrid manipulators resulting from joint clearance, input uncertainty, and manufacturing imperfection. First, the local pose deviation caused by each error is parameterized using exponential coordinates, and the distribution is defined as a Gaussian on the motion group. Second, the linear relationship between the local pose error caused by the disturbance of the passive joint and that by other error sources is derived based on the Baker–Campbell–Hausdorff formula. Third, closed-form formulas are developed for error propagation on independent and non-independent group elements, thereby determining the covariance and mean of the pose error distribution of the end-effector. Fourth, the error space and maximum deviation along/about each axis are extracted from the covariance matrix and mean at the designated confidence level. Finally, four numerical cases are presented to demonstrate the effectiveness and advantages of the proposed method. The experimental evidence indicates that the proposed method can be applied to planar and spatial parallel/hybrid manipulators and has a significantly high computation speed.