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This paper aims to comprehensively achieve the requirements of high assembly precision and low cost, a precision-cost model of assembly based on three-dimensional (3D) tolerance is established in this paper.

The assembly precision is related to the tolerance of parts and the deformation of matching surfaces under load. In this paper, the small displacement torsor (SDT) theory is first utilized to analyze the manufacturing tolerances of parts and the assembly deformation deviation of matching surface. In the meanwhile, the extracting method of SDT parameters is proposed and the assembly precision calculation model based on the 3D tolerance is established. Second, an integrated optimization model based on the machining cost, assembly cost (mapping the deviation domain to the SDT domain) and quality loss cost is built. Finally, the practicability of the precision-cost model is verified by optimizing the horizontal machining center.

The assembly deviation has a great influence on cost fluctuation. By setting the optimization objective to maximize the assembly precision, the optimal total cost is CNY 72.77, decreasing by 16.83 per cent from the initial value, which meets economical requirements. Meanwhile, the upper bound of each processing tolerance is close to the maximum value of 0.01 mm, indicating that the load deformation can be offset by appropriately increasing the upper bound of the tolerance, but it is necessary to strictly restrict the manufacturing tolerances of lower parts in a reasonable range.

In this paper, a 3D deviation precision-cost model of assembly is established, which can describe the assembly precision more accurately and achieve a lower cost compared with the assembly precision model based on rigid parts.

The optimal control on reassembly (remanufacturing assembly) error is one of the key technologies to guarantee the assembly precision of remanufactured product. However, because of the uncertainty existing in remanufactured parts, it is difficult to control assembly error during reassembly process. Based on the state space model, this paper aims to propose the optimal control method on reassembly precision to solve this problem.

Initially, to ensure the assembly precision of a remanufactured car engine, this paper puts forward an optimal control method on assembly precision for a remanufactured car engine based on the state space model. This method takes assembly workstation operation and remanufactured part attribute as the input vector reassembly status as the state vector and assembly precision as the output vector. Then, the compensation function of reassembly workstation operation input vector is calculated to direct the optimization of the reassembly process. Finally, a case study of a certain remanufactured car engine crankshaft is constructed to verify the feasibility and effectiveness of the method proposed.

The optimal control method on reassembly precision is an effective technology in improving the quality of the remanufactured crankshaft. The average qualified rate of the remanufactured crankshaft increased from 83.05 to 90.97 per cent as shown in the case study.

The optimal control method on the reassembly precision based on the state space model is available to control the assembly precision, thus enhancing the core competitiveness of the remanufacturing enterprises.

The assembly quality of complex products is pivotal to their lifecycle performance. Assembly precision analysis (APA) is an effective method used to check the feasibility and quality of assembly. However, there is still a need for a systematic approach to be developed for APA of kinematic mechanisms. To achieve more accurate analysis of kinematic assembly, this paper aims to propose a precision analysis method based on equivalence of the deviation source.

A unified deviation vector representation model is adopted by considering dimension deviation, geometric deviation, joint clearance and assembly deformation. Then, vector loops and vector equations are constructed, according to joint type and deviation propagation path. A combined method, using deviation accumulation and sensitivity modeling, is applied to solve the kinematic APA of complex products.

When using the presented method, geometric form deviation, joint clearance and assembly deformation are considered selectively during tolerance modeling. In particular, the proposed virtual link model and its orientation angle are developed to determine joint deviation. Finally, vector loops and vector equations are modeled to express deviation accumulation.

The proposed method provides a new means for the APA of complex products, considering joint clearance and assembly deformation while improving the accuracy of APA, as much as possible.

The traditional precision design only takes the influence of geometric tolerance of the parts and does not involve the load deformation in the assembly process. This paper aims to analyze the influence mechanism of flexible parts deformation on the geometric precision, and then to ensure the reliability and stability of the mechanical system.

Firstly, this paper adopts the N-GPS to analyze the influence mechanism of flexible parts deformation on the geometric precision and constructs a coupling 3D tolerance mathematical model of the geometric tolerance and the load deformation deviation based on the SDT theory, homogeneous coordinate transformation theory and surface authentication idea. Secondly, the least square method is used to fit the deformation surface of the mating surface under load so as to complete the conversion from the non-ideal element to the ideal element.

This paper takes the horizontal machining center as a case to obtain the deformation information of the mating surface under the self-weight load. The results show that the deformation deviation of the parts has the trend of transmission and accumulation under the load. The terminal deformation cumulative amount of the system is up to –0.0249 mm, which indicated that the influence of parts deformation on the mechanical system precision cannot be ignored.

This paper establishes a comprehensive 3D tolerance mathematical model, which comprehensively considers the effect of the dimensional tolerance, geometric tolerance and load deformation deviation. By this way, the assembly precision of mechanical system can be accurately predicted.

The coupling impact of hybrid uncertain errors on the machine precision is complex, as a result of which the designing method with multiple independent error sources under uncertainties remains a challenge. For the purpose of precision improvement, this paper focuses on the robot design and aims to present an assembly precision design method based on uncertain hybrid tolerance allocation (UHTA), to improve the positioning precision of the mechanized robot, as well as realize high precision positioning within the workspace.

The fundamentals of the parallel mechanism are introduced first to implement concept design of a 3-R(4S) &3-SS parallel robot. The kinematic modeling of the robot is carried out, and the performance indexes of the robot are calculated via Jacobian matrix, on the basis of which, the 3D spatial overall workspace can be quantified and visualized, under the constraints of limited rod, to avoid the singular position. The error of the robot is described, and a probabilistic error model is hereby developed to classify the hybrid error sensitivity of each independent uncertain error source by Monte Carlo stochastic method. Most innovatively, a methodology called UHTA is proposed to optimize the robot precision, and the tolerance allocation approach is conducted to reduce the overall error amplitude and improve the robotized positioning precision, on the premise of not increasing assembly cost.

The proposed approach is validated by digital simulation of medical puncture robot. The experiment highlights the mathematical findings that the horizontal plane positioning error of the parallel robotic mechanism can be effectively reduced after using UHTA, and the average precision can be improved by up to 39.54%.

The originality lies in UHTA-based precision design method for parallel robots. The proposed method has widely expanding application scenarios in industrial robots, biomedical robots and other assembly automation fields.

Coordination feature (CF) is the information carrier in dimension and shape transfer process in aircraft manufacturing. The change of its geometric size, shape, position or other attributes would affect the consistency of accumulated errors between two or more assemblies. To identify these “key characteristics” that have a close relationship with the assembly precision, a comprehensive method was developed under digital manufacturing environment, which was based on importance calculation. The multi-hierarchy and multi-station assembly process of aircraft products were also taken into consideration.

First, the interaction and evaluation relationship between components at different manufacturing stages was decomposed with a hierarchical net. Second, to meet coordination accuracy requirements, with the integrated application of Taguchi quality loss function, accuracy principal and error correction coefficient H, the quality loss between target features and candidate features at adjacent assembly hierarchies were calculated, which was based on their precision variation. Third, the influence degree and affected degree of the features were calculated with DEMATEL (decision-making trial and evaluation laboratory) method, and the concepts of centrality degree index and cause degree index were proposed for calculating the complete importance degree to eventually identify the CFs.

Based on the proposed methodology, CFs, affecting the skin profile and the flush coordination accuracy, were successfully identified at different assembly hierarchies to a certain type of wing flap component.

Benefit results for the engineering application showed that the deviation of skin profile was more accurate than before, and the tolerance was also closer to the centerline of required assembly precision range. Moreover, the stability in the assembly process was increased by 26.9 per cent, which could bring a higher assembly quality and an enhancement on aircraft’s flight performance.

The purpose of this paper is to design an automatic press-fit instrument to realize precision assembly and connection quality assessment of a small interference fitting parts, armature.

In this paper, an automatic press-fit instrument was developed for the technical problems of reliable clamping and positioning of the armature, automatic measurement and adjustment of the attitude and evaluation of the connection quality. To compensate for the installation error of the equipment, corresponding calibration method was proposed for each module of the instrument. Assembly strategies of axial displacement and perpendicularity were also proposed to ensure the assembly accuracy. A theoretical model was built to calculate the resistant force generated by the non-contact regions and then combined with the thick-walled cylinder theory to predict the press-fit curve.

The calibration method and assembly strategy proposed in this paper enable the press-fit instrument to achieve good alignment and assembly accuracy. A reasonable range of press-fit curve obtained from theoretical model can achieve the connection quality assessment.

This instrument has been used in an armature assembly project. The practical results show that this instrument can assemble the armature components with complex structures automatically, accurately, in high-efficiency and in high quality.

This paper provides a technical method to improve the assembly quality of small precision interference fitting parts and provides certain methodological guidelines for precision peg-in-hole assembly.

The purpose of this paper is to propose a novel method of coaxial optical precision alignment based on surface roughness and reflectiveness matching.

The micro-assembly experiment system set-up was constructed according to the principle of the coaxial optical alignment. The coaxial optical alignment error is theoretically analyzed and calculated. When the prism orthogonal alignment mechanism produces the error of 0.001°, the theoretical deviation was less than 0.87 μm and the actual experimental micro-assembly platform assembly accuracy exceeded 3 μm. A peg-in-hole precise assembly of punching pin micro-assembly experiment was done in order to validate feasibility of this method.

The results indicate that coaxial optical precision alignment could be used for the assembly of complex micro-heterogeneous system which is integrated by similar devices, such as 3D complex micro-structures, silicon micro-electro-mechanical system (MEMS) devices and non-silicon MEMS devices with flat structure.

The paper provides certain methodological guidelines for MEMS for high precision automatic assembly of complex 3D micro-structures.

The pivotal aspect of aircraft assembly lies in precise measurement accuracy. While a solitary digital measuring tool suffices for analytical and small surfaces, it falls short for extensive synthetic surfaces like aircraft fuselage panels and wing spars. The purpose of this study is to develop a “combined measurement method” (CMM) that enhances measurement quality and expands the evaluative scope, addressing the limitations posed by singular digital devices in meeting measurement requirements across various aircraft components.

The study illustrated the utilization of the CMM by combining a laser tracker and a portable arm-measuring machine. This innovative approach is tailored to address the intricate nature and substantial dimensions of aircraft fuselage panels. The portable arm-measuring machine performs precise scans of panel components, while common points recorded by the laser tracker undergo coordinate conversion to reconstruct the fuselage panel’s shape. The research outlines the CMM’s measurement procedure and scrutinizes the data processing technique. Ultimately, the investigation yields a deviation vector matrix and chromatogram deviation distribution, pivotal in achieving enhanced measurement precision for the novel CMM device.

The use of CMM noticeably enhances fuselage panel assembly accuracy, concurrently reducing assembly time and enhancing efficiency compared to conventional measurement systems.

The research’s practical implication lies in revolutionizing aircraft assembly by mitigating accuracy issues through the innovative digital CMM for aircraft synthetic structure type product (aircraft fuselage panel). This ensures safer flights, reduces rework and enhances overall efficiency in the aerospace industry.

Introducing a new aircraft assembly accuracy compensation method through digital combined measurement, pioneering improved assembly precision. Also, it enhances aerospace assembly quality, safety and efficiency, offering innovative insights for optimized aviation manufacturing processes.

This paper aims to illustrate the tolerance optimization method based on the assembly accuracy constrain, precession constrain and the cost of production of the assembly product.

A tolerance optimization method is an excellent way to perform product assembly performance. The tolerance optimization method is adapted to the process analysis of the hatch and skin of an aircraft. In this paper, the tolerance optimization techniques are applied to the tolerance allocation for step difference analysis (example: step difference between aircraft cabin door and fuselage outer skin). First, a mathematical model is described to understand the relationship between manufacturing cost and tolerance cost. Second, the penalty function method is applied to form a new equation for tolerance optimization. Finally, MATLAB software is used to calculate 170 loops iteration to understand the efficiency of the new equation for tolerance optimization.

The tolerance optimization method is based on the assembly accuracy constrain, machinery constrain and the cost of production of the assembly product. The main finding of this paper is the lowest assembly and lowest production costs that met the product tolerance specification.

This paper illustrated an efficient method of tolerance allocation for products assembly. After 170 loops iterations, it founds that the results very close to the original required tolerance. But it can easily say that the different number of loops iterations may have a different result. But optimization result must be approximate to the original tolerance requirements.

It is evident from Table 4 that the tolerance of the closed loop is 1.3999 after the tolerance distribution is completed, which is less than and very close to the original tolerance of 1.40; the machining precision constraint of the outer skin of the cabin door and the fuselage is satisfied, and the assembly precision constraint of the closed loop is satisfied.

The research may support further research studies to minimize cost tolerance allocation using tolerance cost optimization techniques, which must meet the given constrain accuracy for assembly products.