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Surface deviations of parts have vital impact on the function and performance of products, and should be controlled in manufacturing. Deviation representation facilitates the analysis of product function and performance, as well as the control of manufacturing process. In this paper, a novel deviation representation method for cylindrical surface i...
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Citations
... The surface deviation of each mating plane was modelled to acquire the non-ideal morphologies required by the POD computation. A modelling method from the perspective of manufacturing errors was employed to describe the actual morphologies of each mating plane [18,31,32]. Consequently, the surface deviations of each mating plane were generated by the deviation functions corresponding to the manufacturing errors, as shown in Equation (5). ...
The occurrence of position and orientation deviations (PODs) during the assembly of rigid components, which is caused by non-ideal morphologies on the manufactured surface, directly affects the performance of the mechanical product. Moreover, the generated PODs are influenced by the deformation of the contact points because of the assembly force. Therefore, to control the product performance in the design stage, the PODs should be computed considering both the non-ideal morphologies of the mating surfaces as well as the forces acting on the assembly. However, most existing approaches to POD computation ignore the effects of the assembly force. Moreover, they often focus on assemblies with a single mating plane. To address this problem, a force constraint-based approach is proposed in this study, which considers both the non-ideal morphologies of multiple mating planes and the assembly forces. The principle of force balance is employed to determine whether the assembly is completed. Different tentative positions and orientations are determined according to the strategies of progressively approaching position and orientation, and recursion of degrees of freedom (DOFs). An unbalance indicator was established in this study to determine whether the force balance in the direction of each DOF is satisfied. As long as the force balance of all DOFs to be constrained is achieved, the assembly of parts is considered to be finalised, and the final PODs are acquired. Finally, the PODs of a typical assembly with multi-mating planes and the guiding accuracy of a sliding workbench are computed according to the non-ideal morphologies modelled from the perspective of manufacturing errors, thereby validating the proposed approach.
... The PODs are directly affected by the surface deviations. For consistency of the surface deviations and the actual morphologies of each mating plane, a modeling method from the perspective of manufacturing errors is employed [31][32][33]. The deviation functions corresponding to manufacturing errors over the process of machining each mating plane are established, and the surface deviation model of each mating plane is acquired by accumulating the deviation functions. ...
Position and orientation deviations (PODs), being affected by surface deviations, occur after parts are assembled, which directly affects the performance of mechanical products. Moreover, mechanical parts are generally assembled with multiple constraint planes, and the generated PODs are influenced by the type of positioning. Therefore, the PODs of multiple planes should be computed in the design stage according to the predicted surface deviations, to control the product performance. However, even though the POD computation of multiple planes has been researched, the effects of surface deviations and multiple types of positioning cannot be considered simultaneously. To address this problem, this study proposes a point-by-point-contact-based approach. The six-point positioning principle is employed to determine the possible number of contact points on each mating plane. The surface deviations are modeled from the perspective of manufacturing errors. Furthermore, the contact points on each mating plane are determined successively using both the strategies of progressively approaching position and of the orientation and recursion of contact points. As a result, the PODs are acquired. The feasibility and usefulness of the proposed approach are verified through a case study. Herein, effects of surface deviations and multiple types of positioning on PODs are unified as contact point variations. Consequently, this approach is expected to assist with accurately controlling the POD influence on the performance of mechanical products in the design stage.
... And Wang and Liu 7 presented a tolerance simulation for the TC2B assembling based on numerical model of TC2B and SDT model. Additionally, Qiao et al. 8 proposed the definition of curvilinear coordinate system on ideal surface and introduced the deviation dimension in the orthogonal direction to directly describe morphology deviations. These expression methods above facilitated the modeling and simulation analysis of non-ideal surface. ...
Performance of mechanical product is highly influenced by assembly deviation. Due to manufacturing errors, the real part surface is machined with morphology deviations, which would cause mating surface deviating from ideal position in assembly behavior, consequently leading to assembly deviation. Meanwhile, the random variation of relative position and orientation between two non-ideal parts also affects the assembly deviation. To efficiently obtain the maximum assembly deviation considering the comprehensive influence of two factors above for circumferential grinding plane, an assembly deviation calculation method based on surface deviation modeling is proposed in this paper. In this method, morphology deviations models of part surfaces are firstly established from the deviation function. The randomness of two factors are represented by a multivariate group with randomness containing deviation function coefficients and three deflected parameters. Then based on surface deviation modeling method, differential evolution algorithm is applied to search the maximum assembly deviation, which involves the construction of fitness function by implementing optimized progressive contact method and iterative operations of mutation, crossover and selection. Finally, the effectiveness of this method is illustrated by an assembly in the end.
... Therefore, various methods for representing the deviation have been researched. For example, Qiao et al. proposed a deviation representation method for cylindrical surfaces [4]. Semere et al. illustrated how variations can be obtained from a skin model in the form of vectoral deviations or as small displacement torsors [5]. ...
Various tolerance analysis and numerical analyses based on skin model shapes have been conducted and developed in recent years. If skin model shapes with features such as a machining path and a cutting trace are generated randomly, the design and manufacturing parameters can be rationally determined based on the analysis of results. Considering the fact that characteristic processing marks have multiscale properties, we have developed a skin model shape generation method using discrete wavelet transform. However, the skin model shape generated by the method has the problem of forming an undesired seam. In this study, we developed a method that applies the dual-tree complex wavelet transform, which has an approximate shift invariance property. The effectiveness of the method is observed using test data, and the problem is solved.
... This concept uses discrete geometry representation schemes for the representation of part geometry considering all different kinds of geometric deviations (Schleich et al., 2016) and could be used to specify geometrical defects with numerous mathematical descriptions. Qiao et al. (2016) developed a deviation coordinate system to represent the non-ideal cylindrical surface by adding a deviation dimension in the curvilinear coordinates instead of applying the Cartesian coordinate system. This description method is convenient for specific geometries such as cylinder and sphere, whereas the application to extend this method for describing complex shapes would be difficult. ...
Purpose
One major problem preventing further application and benefits from additive manufacturing (AM) nowadays is that AM build parts always end up with poor geometrical quality. To help improving geometrical quality for AM, this study aims to propose geometrical deviation identification and prediction method for AM, which could be used for identifying the factors, forms and values of geometrical deviation of AM parts.
Design/methodology/approach
This paper applied the skin model-based modal decomposition approach to describe the geometrical deviations of AM and decompose them into different defect modes. On that basis, the approach to propose and extend defect modes was developed. Identification and prediction of the geometrical deviations were then carried out with this method. Finally, a case study with cylinders manufactured by fused deposition modeling was introduced. Two coordinate measuring machine (CMM) machines with different measure methods were used to verify the effectiveness of the methods and modes proposed.
Findings
The case study results with two different CMM machines are very close, which shows that the method and modes proposed by this paper are very effective. Also, the results indicate that the main geometrical defects are caused by the shrinkage and machine inaccuracy-induced errors which have not been studied enough.
Originality/value
This work could be used for identifying and predicting the forms and values of AM geometrical deviation, which could help realize the improvement of AM part geometrical quality in design phase more purposefully.
... The Weiestrass-Mandelbrot fractal function, which contains trigonometric terms, is used to simulate manufactured surfaces [33,59,60]. There are also other models that are based on trigonometric functions [82][83][84][85][86]. In the following, we describe in detail the most used methods: Zernike polynomials and the discrete cosine transform (DCT). ...
... Homri et al. [82,94] extracted specific modes for cylindrical features. Qiao et al. [83,95] and Zhu et al. [37] modified the method Transactions of the ASME for cylindrical surfaces. The spherical harmonic based method can be considered as the extension of the method to 3D sphere [96]. ...
... The advantage of the DCT method is that the explicit form makes it easy to control the shape, and any shape of form error could be reconstructed. However, it is usually limited to plane features; to apply this method to other general shapes, a projection process may be required before simulation [32,[82][83][84]. ...
Computer-aided tolerancing (CAT) aims to predict and control geometrical and dimensional deviations in the early design stage. Former simulation models based on the translation and rotation of nominal features cannot fulfill engineering demands or cover the product lifecycle. Nonideal feature-based simulation methods are, therefore, drawing a great deal of research attention. Two general problems for non-ideal feature-based methods are how to simulate manufacturing defects and how to integrate these defects into tolerance analysis. In this paper, we focus on the first problem. There are already many manufacturing defect simulation methods. Although they are derived from different fields and have different names, they share common characteristics in application. In this study, we collected different simulation methods and classified them as random noise methods, mesh morphing methods, and mode-based methods. The theoretical backgrounds of these methods are introduced, and the simulation examples are conducted on a consistency model to show their differences. Criteria such as multiscale, surface complexity, measurement data integration, parametric control, and calculation complexity are proposed to compare these methods. Based on these analyses, the advantages and drawbacks of each method are pointed out, which may help researchers and engineers to choose suitable methods for their work.
... In Fig. 2, the curvilinear coordinate system (q 1 , q 2 ) consists of two curvilinear coordinates q 1 and q 2 , in which q 1 describes the position of cutting point along the feed movement direction, while q 2 describes the position of cutting point along the main movement direction. The curvilinear coordinate system facilitates the expression of nominal surfaces, so that the position of points on the nominal surface can be represented by two curvilinear coordinates [47,48]. In these two references, the non-ideal surface representation methods are proposed for cylindrical surfaces. ...
Assembly analysis, as an important step in the product design stage, provides verifications of product design with specific requirements. The manufactured surfaces that participate in the analysis result from different manufacturing methods and show inconsistency with the designed surfaces due to the effects of numerous manufacturing errors. These deviations have a vital impact on the assembly analysis results and make a big difference on the final product design process. Therefore, consideration of such manufactured surface deviations in assembly analysis is critical in order to achieve an effective product design. In this paper, a general surface deviation modeling and representation approach based on curvilinear coordinate system is proposed. Different curvilinear coordinate systems for various manufacturing methods are defined on nominal product surfaces. By introducing the deviation dimension in the orthogonal direction of the curvilinear coordinates, deviation coordinate systems are formed. The deviation coordinate system could be used to describe deviation surfaces resulting from numerous manufacturing errors with deviation functions. As an example, non-ideal planar surfaces in the face milling process are modelled with the proposed method. With the generated non-ideal planar surfaces, the sealing performance analysis of an assembly is implemented. The validity of the proposed method and its applicability in simulation are verified in the end.
... contains trigonometric terms, is used to simulate the manufactured surfaces [38,44,45]. There are also other models that are based on trigonometric functions [54][55][56]. In the following, we describe in detail the most used methods: Zernike polynomials and the Discrete Cosine Transform (DCT). ...
... As ( , ) indicates frequency along the , axes, the modes used are shown in The advantage of the DCT method is that the explicit form makes it easy to control the shape, and any shape of form error could be reconstructed. However, it is usually limited to plane features; to apply this method to other general shapes, a projection process may be required before simulation [37,[54][55][56]]. ...
The geometry of a real manufactured part differs from the virtual workpieces designed in Computer Aided Design (CAD) systems. This difference is due to the accumulation of unavoidable manufacturing deviations. The objective of this work is to implement virtual workpieces with form defects (Skin Model Shape) in engineering applications to meet the industry’s increasing demands in product geometry quality management. Various aspects are covered here, in particular form defect generation, assembly simulation and virtual metrology.Methods to generate form defects on simple surfaces are reviewed and classified. Due to form defects, the combination of simple surfaces to generate a whole part led to inconsistency on the edges. A global FEA-based method and a local mesh smoothing based method are used to overcome this issue.To predict the deviation of functional characteristics, assembly simulation is conducted using skin model shapes. An approach is developed based on the Linear Complementarity Condition and the Small Displacement Torsor to take into account assembly boundary conditions, such as displacements and loads.Methods to evaluate deviation values on skin model shapes are also studied. Product specifications are expressed with GeoSpelling, and evaluated using the Small Displacement Torsor method. The developed methods are integrated into an online Virtual Laboratory for e-learning.The above-mentioned studies complement and extend the tolerance management methods based on GeoSpelling and skin models.
... Efforts on surface deviation representations have been put forward as well. Qiao et al. [6] have presented a surface deviation representation method in which a deviation coordinate system is constructed on the nominal surface by adding a deviation dimension on curvilinear coordinate system. The method can facilitate the explicit and convenient representation of non-ideal surfaces, and make it more convenient for assembly simulation. ...
... According to the definition of the nominal surface in the CCS, a two-dimensional (2D) systemcylindrical surface curvilinear coordinate system (CSCCS) (z, u) is defined. 30 The entire nominal surface could be mapped onto this coordinate system. ...
Assembly process simulation has been recognized as an effective tool for design verification. The representation of actual part surfaces produced by manufacturing processes is an important issue for assembly simulation. Manufactured part surfaces can also be regarded as non-ideal surface morphologies caused by manufacturing errors. This article presents a new approach to describe non-ideal cylindrical surface morphologies. A deviation coordinate system is developed by adding a new deviation dimension along the normal direction of the nominal surface modeled in the cylindrical surface curvilinear coordinate system. Considering characteristics of the cylindrical surface machining process, a unified expression of combined Hermite polynomials and Fourier series is used to demonstrate deviations that commonly appear on manufactured non-ideal cylindrical surfaces. The Hermite–Fourier polynomials constitute multi-morphologies resulting from different manufacturing errors. In the proposed method, a parametric matrix is created from the expansion of the Hermite–Fourier polynomials. Each morphology can be represented by a corresponding matrix. The total deviation of a non-ideal part surface is the sum of deviations caused by each manufacturing error source through a linear combination of various matrices. The effectiveness of the proposed method is verified by a simulation of the sealing function of shaft-hole assemblies.
