Variation Analysis Application Experience for Mechanical Assembly Accuracy Assessment

The manufacturing/assembly error of machine parts is a key factor that influences the performance and economy of mechanical systems. To achieve high assembly precision and performance on the basis of low manufacturing accuracy and cost, this study primarily optimizes the assembly error of machine parts. First, the small displacement torsor is used to characterize the small deformation between the mating surfaces of parts. Subsequently, to realize the combination of small displacement torsor and tolerance, the small displacement torsor with manufacturing error and assembly deformation is mapped to the tolerance domain. Second, based on the relationship between small displacement torsor and tolerance, an assembly error optimization model is established on the basis of the conventional tolerance-cost model, considering the emergence of manufacturing error and assembly deformation. Third, aiming at the high-pressure rotor for aeroengines, the error optimization design of assembly is carried out developed with the assembly accuracy requirement as the constraint condition, and the total costs of the manufacturing and assembly processes as the objective. The optimization results indicate that the manufacturing error range of each mating surface after optimization changes, from small to large, under the premise of ensuring the product’s performance, which verifies that the difficulty in processing parts is reduced, and that the efficiency of parts processing is also improved. Meanwhile, the relative manufacturing cost after optimization is reduced by 6.79%, which reflects the economic requirements to a certain extent. The content of this article provides the necessary design basis and reference for the realization of high assembly accuracy of mechanical systems, under low cost requirements from the design perspective.

Nowadays, assembly tolerance analysis has become a challenging problem to predict the accuracy of a final assembly and examine whether specified tolerances satisfy assembly functional requirements (AFRs) for ensuring product assembly performance. Skin model shapes can be addressed to represent part geometric tolerances with manufacturing defects, thereby providing high fidelity surfaces that can replace nominal or ideal surfaces and significantly improve the accuracy and reliability of assembly tolerance analysis. However, their application in easy-to-use assembly simulation is limited by the level of detail required for manufacturing defect simulation and the complicated calculation process for integrating these defects into the tolerance analysis. Therefore, to overcome these issues in predicting assembly deviations in the early design stage, we propose a generic integrated approach of assembly tolerance analysis based on skin model shapes. First, two methods are introduced for modelling and generating skin model shapes according to different mate types of assembly key features. Second, a calculation method of assembly deviation propagation is developed by the integration of skin model shapes and stream-of-variation theory with accuracy and efficiency guarantees. Besides, a slightly modified relative contact positioning method is presented, based on different surface and progressive contact method, to obtain deterministic contact points and contact positioning errors between key mating joint surfaces. And then, the deviation values of AFRs are calculated, considering the inevitable manufacturing and assembly process errors. Finally, a typical mechanical assembly on assembly tolerance analysis is used as a case study to demonstrate the effectiveness of the proposed approach.

When designing harmonic drives, it is important to address the issue of reducing the kinematic error of the drive occurring due to the deformation of the flexible gear, radial oscillations of the cam, manufacturing and installation errors of the gears. Conventionally, this problem is solved by increasing the accuracy class of the gears and the parts where manufacturing errors impact the accuracy of cam installation. A mathematical model is proposed that enables researchers to study the dependency of the kinematic error of the harmonic drive on various factors already at the design stage. Calculation techniques are developed that take into account elastic interaction between the main elements of the drive as well as manufacturing and installation errors. The results of theoretical studies of the influence of the angular position of the flexible and rigid gears on the kinematic error of a harmonic drive with a cam wave generator are presented. The possibility of reducing the kinematic error by turning the fixed gear is proven.

For any practical gear transmission, precise match� ing of the active tooth surfaces should be regarded as problematic. Unavoidable manufacturing errors and deformation under the action of forces and tempera� tures in the course of operation must be taken into account at the design stage and compensated in the manufacturing process. Therefore, in design, engage� ment must be regarded as an approximate component; accordingly, a parabolic error function is introduced in the angle of rotation of the driven component during the engagement of a single pair of teeth [1]. In prac� tice, this entails introducing longitudinal and profile modifications of one or both of the engaging tooth sur� faces; in other words, the surfaces will differ from the theoretically ideal form. This localizes the contact spot within a specified region of tooth surface. Strictly speaking, what matters in functional terms is not the direction of localization with respect to the tooth profile or length but with respect to the nominal instantaneous contact line [2]. Localization along this line does not change the instantaneous gear ratio and, at the same time, prevents departure of the contact spot from the edge of the tooth. In other words, it per� mits partial or complete compensation of the negative influence of assembly errors and subsequent deforma� tion of the housing. Localization normal to the instan� taneous contact line results in variation of the instan� taneous gear ratio in the engagement of a single pair of teeth. However, the corresponding composition of the pitch error in tooth cutting moderates the edge impacts in tooth engagement and sharply reduces the corresponding contact stress, strain, and tooth wear [2, 3]. In worm transmissions with a cylindrical (in partic� ular, Archimedes) worm, the instantaneous contact lines run along the gear teeth. Therefore, modification of the tooth surface along this longitudinal line com� pensates the installation error (the error in the mutual + ()

<div class="section abstract"><div class="htmlview paragraph">During mechanical assembly, individual parts are joined by different types of fasteners which are commonly to be installed into tightly tolerated holes. Drilling of widely used modern materials like CFRP and titanium leads to challenges in terms of tool and process development. A significant challenge is one step drilling in assemblies made from mixed material stacks. It results in deviating hole diameters making the additional reaming operation essential.”But also drilling of thick single material stacks imposes difficulties in terms of hole tolerance, chip extraction, heat accumulation and lubrication issues, leading to the necessity of drilling in several steps to achieve the required hole quality and integrity.</div><div class="htmlview paragraph">During orbital drilling the drive spindle rotates eccentrically in addition to tool rotation and feed movement, leading to a circular path of the cutting tool. Orbital drilling can offer advantages compared with conventional drilling and reaming. The eccentricity can be set steplessly even during the drilling process which allows to drill different hole diameters with one tool, tapered holes, change diameter within the hole or to perform a finishing cut during the tool return stroke. Tool diameter deviations also can be compensated, thus tool diameter tolerances can be enlarged and regrinding of worn tools can be applied more often, saving tool costs. The interrupted cut facilitates an extraction of the small chips, enabling drilling of closed structures without subsequent cleaning or deburring as well as one-way-assembly applications in case of blind fastener use. Damaged surfaces due to snarl chips can be avoided. Furthermore, dry drilling of aluminum material can be applied due to the reduced introduction of process heat.</div><div class="htmlview paragraph">Although already applied in several Airbus sites, the orbital drilling process still faces different challenges depending of the relevant application. In general, the radial loads on the cutting tool and machine present challenges in terms of hole tolerance when drilling high thickness / diameter ratio stacks or hole diameters below approximately ¼”. Bending of the cutting tool and vibration issues can lead to high tolerance widths and poor surface quality.</div><div class="htmlview paragraph">Due to the changed cutting kinematics compared with conventional drilling and depending of the cut material, tool and cutting parameters, the orbital drilling process introduces reduced compressive residual stresses into the hole wall, leading to a decrease of joint fatigue life. Strategies to produce orbitally drilled holes having at least the same fatigue life level compared to conventional drilling while optimizing the drilling parameters to meet engineering as well as economical requirements are going to be presented.</div></div>

Indirect inverse substructuring dynamic analysis has been developed recently by the author of this paper and provides a new simple approach to determine the coupling dynamic stiffness, which is one of important characteristics estimating dynamic quality of a mechanical product assembly. Based on a physical model consisting of “8-mass plus 16-spring and 8-damping” elements, this paper provides a set of validation on the completeness and effectiveness of the approach. Experimental verification is also carried out by use of eighty testing data of frequency response functions (FRFs).

Some new techniques are presented for experimentally determining the dynamical characteristics of linear systems. These techniques are based on analysis of random variations in the operating variables during the normal course of operation of the system. Particular attention is paid to the effects of uncorrelated variations (noise) on the methods. The use of the “delay-line synthesizer” as a device for discovering system characterizations is presented. Results obtained for the determination of a transfer operator for a human being engaged in tracking a target are presented as an example of the effectiveness of the random-data-analysis approach.

Abstract. Background: Significant economic growth in many countries of the world can contribute to an increase in the speed of movement of modern and fundamentally new vehicles. This will increase the turnover of goods during the transportation of goods, revive international trade, increase the comfort of passengers and reduce their travel time.
 Aim: The solution of this problem is the development and wide application of high-speed magnetic-levitation transport (HSMLT) with linear traction engines. It is promising to use linear induction motors (LIM) for the HSMLT drive, which can have various design versions. Linear induction motors come with a longitudinal, transverse and longitudinal-transverse closure of the magnetic flux. LIM inductors can be installed on both high-speed transport crews and in the HSMLT track structure, as it was done in the People’s Republic of China, where express trains on magnetic suspension connect Shanghai with the airport and reliably operate for more than 10 years. The main elements of the inductor of a linear induction motor are a magnetic core (ferromagnetic core) a multiphase (usually three-phase) winding. With the development of high-speed magnetic-levitation transport, the issues of improving the manufacturing technology of various HSMLT devices, including the methods for producing inductors of linear induction motors, will become increasingly relevant. Traditionally, LIM inductors are assembled from pre-manufactured individual parts.
 Methods: An integral technology for manufacturing inductors of linear induction motors for high-speed magnetic-levitation transport is proposed and considered by the method of spraying materials onto a substrate through replaceable stencils. The new technology eliminates the alternate manufacture of individual assemblies and parts and their subsequent assembly to obtain a finished product. A method for determining the size of stencils for manufacturing one of the inductor variants of a linear induction motor is proposed as an example.
 Conclusion: Integral manufacturing technology is promising for the creation of high-speed magnetic-levitation transport.

PurposeThree-dimensional computer-aided design (CAD) assembly model has become important resource for design reuse in enterprises, which implicates plenty of design intent, assembly intent, design experience knowledge and functional structures. To acquire quickly CAD assembly models associated with specific functions by using product function requirement information in the product conceptual design phase for model reuse, this paper aims to find an approach for structure-function correlations analysis and functional semantic annotation of mechanical CAD assembly model before functional semantic-based assembly retrieval.Design/methodology/approachAn approach for structure-function correlations analysis and functional semantic annotation of CAD assembly model is proposed. First, the product knowledge model is constructed based on ontology including design knowledge and function knowledge. Then, CAD assembly model is represented by part attributed adjacency graph and partitioned into multiple functional regions. Assembly region and flow-activity region are defined for structure-function correlations analysis of CAD assembly model. Meanwhile, the extraction process of assembly region and flow-activity region is given in detail. Furthermore, structure-function correlations analysis and functional semantic annotation are achieved by considering comprehensively assembly structure and assembled part shape structure in CAD assembly model. After that, a structure-function relation model is established based on polychromatic sets for expressing explicitly and formally relationships between functional structures, assembled parts and functional semantics.FindingsThe correlation between structure and function is analyzed effectively, and functional semantics corresponding to structures in CAD assembly model are labeled. Additionally, the relationships between functional structures, assembled parts and functional semantics can be described explicitly and formally.Practical implicationsThe approach can be used to help designers accomplish functional semantic annotation of CAD assembly models in model repository, which provides support for functional semantic-based CAD assembly retrieval in the product conceptual design phase. These assembly models can be reused for product structure design and assembly process design.Originality/valueThe paper proposes a novel approach for structure-function correlations analysis and functional semantic annotation of mechanical CAD assembly model. Functional structures in assembly model are extracted and analyzed from the point of view of assembly structure and function part structure. Furthermore, the correlation relation between structures, assembled parts and functional semantics is expressed explicitly and formally based on polychromatic sets.

The performance of a gear set is strongly influenced by the manufacturing and assembly quality. Therefore, detailed analyses at the design stage, where the effects of expected assembly and manufacturing errors can be simulated, are crucial. At an early design stage, when contact conditions are addressed, the widely used finite element method (FEM) may still result in unwanted computing time. The paper presents an Express model developed to serve as a fast design tool offering fine simulation and a high precision level. The model establishes load sharing, fillet stresses and pressure distribution along the contacting surfaces of meshing helical gear teeth. The calculations combine the finite strip method with a pseudo-three-dimensional (3D) model of the tooth base solved with finite differences to calculate tooth bending deflexion and fillet stresses. The accuracy of the procedure is demonstrated through 3D FEM models. A contact cell discretization completes the model. This very fast and accurate approach gives the contact pressure distributions resulting from the roll-slide motion of mating teeth. An analysis of a helical gear set in two different assembly positions reveals the effects of edge contact, and exhibits the influence of tooth stiffness reduction near tooth corners.

The article deals with the view of modern wheelset drive construction design in the first part. Next part deals with dynamics of the wheelset individual drive torsion system in electric traction vehicles, explained by the drive model in several variants. The basics of time simulation of the transition dynamics effects have been explained and the frequency analysis of the system has been shown. Identification of transition dynamics effects in the wheelset drive enables to evaluate precisely the loading on individual parts during the design stage, to apply the results in anti‐skid protection and probably also to disclose some effects due to wear in the wheel‐rail contact.

A methodology and a Monte Carlo simulation flow with integrated LSI Logic's OPC package, Molotof, was applied to the 65nm poly line sensitivity analysis. Strong phase shift mask (sPSM) manufacturing specifications were optimized to obtain image critical dimensions (CD) and image placement errors (IPE) complying with technology design rules. Reticle manufacturing statistical errors of phase depth, phase width, and phase intensity imbalance were used to generate a virtual sPSM for imaging poly lines. A criterion for qualifying reticle specification is to obtain all latent image CDs and IPEs within a design rule allowed range for a given mask specification. The approach allows for computing reticle and litho budgets into CD imaging performance. We present simulation and empirical results of statistical analysis of the 65nm poly line (clear field) printability, and a method for optimizing a strong phase shift reticle specification. Sensitivity to a single parameter variation and full statistical analysis of the 65nm poly line imaging performance affected by manufacturing errors is presented. The optimum reticle specification, yielded 100% of critical dimensions and image placement errors, was found in simulation and confirmed by empirical data.

In order to analyze the sharing mechanism of marine high-speed star gearing system, a static mechanical model is presented in the paper, in which manufacturing errors, assembly errors, bearing errors and tooth thickness error are all considered. In consideration of equivalent mesh error and static balance of floating components, the load sharing coefficient of the system in different kinds of errors was obtained. And the sensitivities of the load sharing coefficient on different types of errors are analyzed. The result shows that the effects of the eccentric error of sun and tooth thickness error of star gear upon load sharing coefficient are larger than those of the other errors. The influences on load sharing coefficient of each error have cumulative effects. The research has provided a useful reference for improving the load sharing capability of marine star gearing system.

The measurement and assembly of the aero-engine rotor are separated from each other, which makes it difficult to keep the assembly datum consistent with the measurement datum; the existence of the datum error will cause the characteristic matrix to fail to truly reflect the geometric state of the rotor itself and cause the assembly model to be inaccurate, then ultimately affect the assembly accuracy prediction. Combined with the fact that the geometric characteristics of parts/components are not related to the measurement datum, the datum error elimination method has been proposed which makes the rotor characteristic matrix and assembly model more accurate, thereby improving the prediction effect of assembly accuracy. At the same time, the proposed direct optimization strategy is more efficient than the traditional genetic algorithm. The assembly experiment of the aero-engine rotor shows that the model and method proposed in this paper can better reflect the geometric characteristics of the rotor itself and are beneficial to reduce the coaxiality of the front and rear fulcrum. The related research also has reference significance for other large-scale and high-precision mechanical product assemblies.

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