A multilevel multiobjective coordination matching design technique for the main bearing assembly structure of a diesel engine

The main bearing assembly structure is one of the most important main load‐bearing structures of a diesel engine. The working loads of this structure increases dramatically with the increase of the power density of diesel engines, resulting in the problem of unsatisfactory reliability coordination design in restricted design space, while the mechanisms for coordinated design are still at the blank stage. Aiming at the problem, a multilevel multiobjective coordination matching design technique is innovatively proposed in this paper. This technique is characterized by a multilevel multiobjective coordination evaluation system for the assembly structure and its components based on the improved analytic hierarchy process. The finite element model and mathematical model of the main bearing assembly structure are established to realize the joint of finite element technology and optimization technology for coordination matching design. By carrying out verification experiments, the strength coordination, deformation coordination and contact strength coordination of the assembly structure increase by 13.91%, 14.96%, and 2.63%, respectively, after matching design, while the mass coordination remains almost constant meeting the lightweight design requirements. The overall coordination of the main bearing assembly structure is improved by 11.10%, achieving the goal of matching design of the main bearing assembly structure. The results show that the coordination evaluation system can quantitatively characterize the coordination relationship of the assembly structure and the multi‐reliability of components, and it is a feasible coordination evaluation method. The demonstrated coordination evaluation system and coordination matching design modeling approach provide important theoretical guidance for the matching design of complex assembly structures.


| INTRODUCTION
With the advantages of high thermal efficiency, good adaptability and a wide power range, diesel engines have always been the main power source in socioeconomic and military technology fields. 1,2Power density refers to the ratio of diesel engine power to the mass of the engine.It is one of the most important performance indicators of diesel engines.A high power density (HPD) diesel engine can be defined as a diesel engine with a highly compact structural design based on a high power per unit displacement.HPD diesel engines are characterized by high compactness, 3,4 high combustion pressure, 5,6 high speed, 7,8 and a wide range of applications [9][10][11][12] compared with conventional diesel engines.The application of HPD diesel engines is very promising in vehicles with strict space dimension limitations, especially in the field of military armored vehicles.
As the representative of the highest level of HPD diesel engine, the MT890 series diesel engine produced by MTU in Germany has been applied to a variety of armored equipment with its excellent performance. 13hile the power per liter, average effective pressure and maximum combustion pressure of the HPD diesel engine have been improved, the mass and volume of the whole engine have been reduced by nearly 50%.5][16][17] The main technical problem is that as the power density of diesel engines increases, the speed and average effective pressure will increase significantly resulting in serious reliability challenges of key components.
9][20] It mainly consisted of the engine block, main bearing cover, main bearing shell, crankshaft, connecting bolts, and others.Jiao et al. investigated the strength reliability of the KL crankshaft by carrying out the physicochemical analysis, numerical simulation analysis and experimental research. 21The specific location of crankshaft fatigue failure, analyzed the causes of fatigue failure, and proposed improvement measures for crankshaft strength in the research.Vrublevskyi et al. researched the friction performance of crankshaft and main bearing shell, and revealed the influence law of design parameters on frictional reliability. 22An optimized design scheme to reduce friction and lubrication costs of the main bearing by optimizing the design parameters.Zhao et al. took the stiffness of the main bearing shell as the main objective and demonstrated a design scheme to significantly improve the stiffness of the main bearing by optimizing the parameters of the main bearing assembly structure. 23A theoretical reference is provided for the reliable design for the stiffness of the main bearing.
Summarizing the above research progress, it can be found that the current research on the reliability of main bearing assembly structure mainly focuses on the unilateral reliability of individual component.However, the main bearing assembly structure is an assembly containing multiple components.Each component has multiple reliabilities to be evaluated.][26] This could lead to the unsatisfactory coordination of the overall reliability of the main bearing assembly structure. 27][30][31][32][33][34] Osama et al. performed the research in diesel engine fueled with blends of biodiesel coupled with cerium oxide nanoparticles and hydrogen content to optimize the performance, vibration and emission by employing multiobjective optimization theories. 35The research demonstrated that blends of Water Hyacinth can be successfully applied in diesel engine with lower environmental impact and enhanced cost effectiveness.Although authors of this paper initially explored the coordinated matching design method in their previous studies, there are still problems of incomplete mechanisms and unclear methods for the coordination design. 36o address the above problem, the theory of the coordinated matching design is explored in this paper.A multilevel multiobjective coordination matching design technique that is characterized by a multilevel multiobjective coordination evaluation system for the assembly structure and its components based on the improved analytic hierarchy process (AHP) is innovatively proposed.A mathematical model for coordination matching design of the main bearing assembly structure is established by introducing multiobjective optimization theory.By solving the mathematical model, the final coordination matching design scheme is determined.The feasibility of the coordination matching design technique is verified by reliability experiments.The technical route for the coordinated matching design of the main bearing assembly structure is shown in Figure 1.

MULTIOBJECTIVE COORDINATION EVALUATION SYSTEM FOR MAIN BEARING ASSEMBLY STRUCTURE
The investigated elements of the coordination matching design of the main bearing assembly structure focus on the strength, deformation, contact strength and mass, respectively.For the coordination matching design, "coordination" indicates the design goal, which means that under the external load, the main bearing assembly structure presents a comprehensive optimal harmony of strength coordination (strength safety factors of the engine block and the main bearing cover are increased), deformation coordination (deformation of the main bearing shell is reduced), contact strength coordination (contact strength safety factor of the contact surface between the engine block and the main bearing cover is increased), and mass coordination (the mass is control)."Matching" reveals the design method, which refers to the process of optimizing all aspects of the performance of the main bearing assembly structure to achieve a comprehensive optimum by constructing the coordination evaluation system and introducing the multiobjective optimization theory.Therefore, the primary task of the coordination matching design is to establish the coordination evaluation system of the main bearing assembly structure.
F I G U R E 1 Technical route for the coordinated matching design.

| Evaluation criteria for strength coordination
Strength coordination refers to the coordinated degree of strength reliability between the components of the main bearing assembly structure.The focused components for the strength reliability are the engine block and the main bearing cover.The evaluation criteria for strength coordination are: (1) The strength safety factor of each component is higher than the minimum permissible value, that is, the strength reliability of each component meets the design requirements.(2) Under the premise (1), the higher the strength safety factors of the focused components the better the strength coordination of the assembly structure.(3) While the strength safety factors of the focused components are improved, the strength safety factors of the other components also need to be within the allowed range.The strength coordination coefficient is employed as the index to evaluate the strength coordination of the assembly structure.The strength coordination coefficient is reflected by the strength coordination factors of components.

| Strength coordination factor
The strength coordination factor is defined as the logarithm of the ratio of the minimum safety factor of a component to the limit value of the safety factor.The strength coordination factor can be used to quantitatively characterize whether the strength reliability of a component meets the design requirements based on the properties of the logarithmic function.The strength coordination factor of the ith component ξ i is greater than 0, which indicates that the strength reliability of this component meets the design requirements.On the other hand, the strength coordination factor is an evaluation index to measure the strength margin of a component.The larger the strength coordination factor of a component, the better the strength margin of the component.The strength coordination factor ξ i can be expressed as where S min( ) i is the minimum safety factor of the ith component.S i ref, is the limit of the safety factor of the ith component.The strength coordination factors are influenced by structure, load and material properties from a view of structural design.

| Strength coordination coefficient
The strength coordination coefficient is an evaluation index of the strength coordination of the main bearing assembly structure, which is defined as the weighted sum of the strength coordination factors of components.Using the weighting method is mainly to reflect the priority of the focused components in the strength coordination design.The larger the strength coordination coefficient, the better the strength coordination of the assembly structure.The strength coordination coefficient ξ ∆ can be expressed as where n indicates the number of components within the assembly structure.ξ i and w s i , denote the strength coordination factor of the ith component and its weight.For the weight .

| Evaluation criteria for deformation coordination
Deformation coordination refers to the degree of coordination of the stiffness reliability between the components among the main bearing assembly structure.The static stiffness is mainly concerned with the radial deformation of the main bearing shell.The evaluation criteria for deformation coordination are: (1) The maximum deformation of each component is lower than the limit of the maximum deformation, that is, the stiffness reliability of the component meets the design requirements.
(2) In the premise (1), the smaller the maximum deformations of the mainly concerned components, the better the deformation coordination of the assembly structure.(3) The maximum deformations of the mainly concerned components are reduced while the deformations of the other components should be within the permitted range.The deformation coordination coefficient is used as the index to evaluate the deformation coordination of the assembly structure.The deformation coordination coefficient can be reflected by the deformation coordination factors of components.

| Deformation coordination factor
The deformation coordination factor is characterized by the logarithm of the ratio of the maximum deformation limit to the maximum deformation of a component.The deformation coordination factor can be used to judge whether the stiffness reliability of the component meets the design requirements.The deformation coordination factor of the ith component φ i is greater than 0, which indicates that the stiffness reliability of the component meets the design requirements.Besides, the deformation coordination factor is an evaluation index to measure the margin of stiffness of a component.The larger the deformation coordination factor of a component, the better its stiffness margin.The deformation coordination factor φ i can be expressed as where δ i presents the maximum deformation of the ith component.δ i ref, is the limit of the maximum deformation of the ith component.Deformation coordination factors are related to structure, load and material properties.

| Deformation coordination coefficient
The deformation coordination coefficient is an evaluation index of the deformation coordination of the main bearing assembly structure, which is defined as the weighted sum of the deformation coordination factors of components.The larger the deformation coordination coefficient, the better the deformation coordination of the assembly structure.The deformation coordination coefficient φ ∆ can be expressed as where n indicates the number of components among the assembly structure.φ i and w r i , present the deformation coordination factor of the ith component and its weight, and .

| Evaluation criteria for contact strength coordination
Contact strength coordination refers to the degree of coordination of the contact strength reliability between the contact surfaces of the main bearing assembly structure.The contact strength reliability focuses on the contact surface between the engine block and the main bearing cover.The evaluation criteria of contact strength coordination are: (1) The maximum contact pressure of each contact surface is lower than the permissible maximum contact pressure of the material of the contact component, that is, the contact strength reliability meets the design requirements.(2) Under the premise (1), the higher the contact strength safety factor of the focused contact surfaces, the better the contact strength coordination of the assembly structure.(3) While the contact strength safety factor of the focused contact surfaces increases, the maximum contact pressure of the other contact surfaces should be in the permissible range.The contact strength coordination can be evaluated using the contact strength coordination coefficient.The contact strength coordination coefficient can be calculated by the contact strength coordination factors of contact surfaces.

| Contact strength coordination factor
The contact strength coordination factor is defined as the logarithm of the ratio of the permissible maximum contact pressure of the contact material to the maximum contact pressure of the contact surface.The contact strength coordination factor can be used to judge whether the contact strength reliability of the contact surface meets the design requirements.The contact strength coordination factor of the jth contact surface γ j is greater than 0, which indicates that the contact strength reliability of the contact surface meets the design requirements.Furthermore, the larger the contact strength coordination factor, the better the contact strength margin for the contact surface.The mathematical expression of the contact strength coordination factor where P j denotes the maximum contact pressure of the jth contact surface.P j ref, presents the maximum permissible contact pressure of the material of the jth contact surface.The contact strength coordination factors are determined by structure, load, and material properties.

| Contact strength coordination coefficient
The contact strength coordination coefficient is an evaluation index of the contact strength coordination of the main bearing assembly structure, which is defined as the weighted sum of the contact strength coordination factors of contact surfaces.The larger the contact strength coordination coefficient, the better the contact strength coordination of the assembly structure.The contact strength coordination coefficient γ ∆ can be mathematically expressed as where m indicates the number of contact surfaces among the assembly structure.γ j and w c j , are the contact strength coordination factor of the jth contact surface and its weight.For the weight w c j , ,  w = 1 .

| Evaluation criteria for mass coordination
Mass coordination refers to the degree of coordination of lightweight design performance of the components among the main bearing assembly structure.The engine block is the key component in lightweight design.
The evaluation criteria for mass coordination are: (1) The optimized mass is lower than the mass limit of the main bearing assembly structure.(2) In the premise of (1), the lower the masses of the key components after optimization, the better the mass coordination of the assembly structure.(3) The masses of the other components are within the permissible range while the masses of the key components are reduced.Mass coordination can be evaluated using the mass coordination coefficient.
It can be calculated by the mass coordination factors of components.

| Mass coordination factor
The mass coordination factor is defined as the logarithm of the ratio of the limit value of the mass of the assembly structure or its components to their actual mass.The mass coordination factor of a component can determine whether the mass of this component meets the design requirements.The mass coordination factor of the ith component ψ i is greater than 0, which indicates that the mass of the component meets the design requirements.
In addition, the larger the mass coordination factor, the better the mass margin of the component.The mathematical expression of the mass coordination factor where m′ i presents the mass of the ith component.m i ref, denotes the limit value of the mass of the component.
The mass coordination factor is the function of the structure and material properties.

| Mass coordination coefficient
The mass coordination coefficient is an evaluation index of the lightweight design performance of the main bearing assembly structure.It can be defined as the weighted sum of the mass coordination factors of components.The larger the mass coordination coefficient, the better the lightweight design performance of the assembly structure.The mass coordination coefficient ψ ∆ can be mathematically expressed as where n indicates the number of components within the assembly structure.ψ i and w m i , are the mass coordination factor of the ith component and its weight, and .

| Evaluation criteria for overall coordination
Overall coordination of the main bearing assembly structure refers to the coordination degree among the four investigated elements of strength coordination, deformation coordination, contact strength coordination and mass coordination.The first three are the elements to be focused in the coordination matching design.The overall coordination can be judged by the overall coordination coefficient of the assembly structure.The evaluation criteria for overall coordination are: (1) The coordination coefficient of each investigated element is greater than zero, that is, the design of each investigated element is coordinated.(2) On the basis of (1), the larger the overall coordination coefficient of the assembly structure, the better the overall coordination among the investigated elements.The overall coordination coefficient can be calculated by the weighted sum of the coordination coefficients of the investigated elements.It can be expressed as ZHAO ET AL.
| 4525 where ∆ is the overall coordination coefficient of the assembly structure.κ 1 , κ 2 , κ 3 , and κ 4 are the weights of the strength coordination coefficient, deformation coordination coefficient, contact strength coordination coefficient, mass coordination coefficient, and 2.6 | Establishment of coordination evaluation system based on improved AHP

| Hierarchical structure model establishment
The main bearing assembly structure coordination evaluation system can be divided into three hierarchies, including the target layer, the investigated elements layer and the evaluation indexes layer as shown in Figure 2. The target layer refers to the overall coordination of the assembly structure.The investigated element layer includes strength coordination, deformation coordination, contact strength coordination and mass coordination.The evaluation indexes layer consists of the evaluation indexes for the various reliability of the components or contact surfaces.

| Construction of judgment matrix based on improved scale determination method
8][39] In this method, if factor i is equally important to factor j, the scale of factor i to factor j is specified as one.The higher the importance of factor i to factor j, the greater the scale.The maximum scale is nine.The scale of factor i to factor j is reciprocal to the scale of factor j to factor i.However, the subjective consciousness of the designer has a strong influence on the scale determined by this method.In this paper, a scale determination method based on the margin of reliability evaluation indexes is proposed to avoid the subjective influence on the design results.

| Scales of the judgment matrix of the evaluation indexes layer to the investigated element layer
The scales of the judgment matrix of the evaluation indexes layer to the investigated elements layer are calculated by the coordination factors of components or contact surfaces.Taking the deformation coordination as F I G U R E 2 Coordination evaluation system of the main bearing assembly structure.
an example, the smaller the deformation coordination factor of a component, the higher the scale of this component, that is, the worse the stiffness margin, the higher the importance of the component.Following this principle, the scale of component i to component j can be defined as the rounded integer of the ratio of the inverse of the deformation coordination factor of component i to that of component j multiplied by focused target scale factor.It can be expressed as where β ij is the scale of component i to component j.A Round( ) denotes the rounded integer of A. φ i and φ j present the deformation coordination factors of component i and component j. k s indicates the focused target scale factor, which is a constant value, and its value range is [5, 10].Based on the calculation experience in this study, it is appropriate to set k = 7 s .The purpose of introducing the focused target scale factor is that when the difference between the coordination factors of the focused component and the non-focused component is very small, the focused target scale factor can be used to adjust the scale of the focused component to better highlight the importance of the focused component.
Taking the scale of the main bearing shell to the horizontal tension bolt as an example, the deformation coordination factors of the main bearing shell and the horizontal tension bolt are 0.169 and 0.235.The main bearing shell is the focused component for deformation coordination.Set k = 7 s .Conversely, set k = 1 s .The scale of the main bearing shell to the horizontal tension bolt β WH can be expressed as where φ W and φ H are the deformation coordination factors of the main bearing shell and horizontal tension bolt.The value of β WH is greater than the maximum scale of nine.So, the final scale is taken as nine, that is, β = 9

WH
. The scales between the other components in the deformation coordination can be calculated according to the above method as shown in Table 1.
In Table 1, φ 1 , φ 2 , φ 3 , φ 4 , and φ 5 present the deformation coordination factors of the horizontal tension bolt, vertical tension bolt, engine block, main bearing cover, and main bearing shell, respectively.Similarly, other judgment matrixes of reliability evaluation indexes to coordination can be obtained.The judgment matrixes of strength evaluation indexes, contact strength evaluation indexes and mass evaluation indexes to their coordination are shown in Tables 2-4, respectively.
T A B L E 1 The judgment matrix T 1 of deformation evaluation indexes to deformation coordination.

Deformation coordination
The judgment matrix T 2 of strength evaluation indexes to strength coordination.

Strength coordination
The judgment matrix T 3 contact strength evaluation indexes to contact strength coordination.

Contact strength coordination
The judgment matrix T 4 of mass evaluation indexes to mass coordination.
In Table 3, γ 1 γ 2 , γ 3 , and γ 4 indicate the contact strength coordination factors of the contact surface between the vertical tension bolt and the main bearing cover, the contact surface between the engine block and the main bearing shell, the contact surface between the engine block and the horizontal tension bolt, and the contact surface between the engine block and the main bearing cover, respectively.

| Scales of the judgment matrix of the investigated elements layer to the target layer
The scales of the judgment matrix of the investigated elements layer to the target layer are calculated by the coordination coefficients of investigated elements.The smaller the coordination coefficient of an investigated element, the larger its corresponding scale, that is, the poorer the coordination of an investigated element, the higher the importance of this investigated element.Following this principle, the scale of investigated element i to investigated element j can be defined as the rounded integer of the ratio of the inverse of the coordination coefficient of investigated element i to that of investigated element j multiplied by the focused target scale factor.It can be mathematically expressed as where β ij , ∆ presents the scale of investigated element i to investigated element j.Δ i and Δ j are the coordination coefficients of investigated element i and investigated element j.Taking the scale of the deformation coordination to the mass coordination as an example, the coordination coefficients of the deformation coordination and mass coordination are 0.152 and 0.221.The deformation coordination is the focused investigated element.Set k = 7 s .The scale can be calculated as is the scale of the deformation coordination to the mass coordination.Its value is greater than the maximum scale of nine.The final scale is taken as nine, that is, ∆ and ψ ∆ are the coordination coefficients of deformation and mass coordination.Similarly, the scales among the other investigated elements can be calculated as shown in Table 5.

| Calculation of weights
By solving the feature vector and carrying out the consistency test based on the original AHP, the weights of items in the coordination evaluation system of the main bearing assembly structure are solved as shown in Figure 3.In the figure, the separated sectors are present the focused components or contact surfaces of the corresponding investigated elements.

| MATCHING DESIGN FOR THE MAIN BEARING ASSEMBLY STRUCTURE
Matching design refers to the design process based on the multiobjective optimization theory, which takes the strength coordination factors, deformation coordination factors, contact coordination factors and mass coordination factors of the key components or contact surfaces of the main bearing assembly structure as the optimization objective to achieve the comprehensive optimum of four coordination.Therefore, the construction of the finite element model and the multiobjective optimization mathematical model of the main bearing assembly structure is the basis of matching design.
T A B L E 5 The judgment matrix T 5 of the investigated elements layer to the target layer.

Overall coordination
Weights in the coordination evaluation system of the main bearing assembly structure.
ZHAO ET AL.

| Establishment of the finite element model
The finite element analysis is carried out by software Abaqus.The main bearing assembly structure mainly consists of the engine block, the main bearing cover, the main bearing shell, the horizontal tension bolts, the vertical tension bolts and the crankshaft as shown in Figure 4. Symmetric displacement constraints are applied to the symmetric surfaces on both sides of the single partition board model of the main bearing assembly structure.The contact surfaces between the engine block, the main bearing cover, the main bearing shell and the crankshaft are employed "face-to-face" contact mode.The side walls of the engine block and the main bearing cover are assembled with clearance, and the initial clearance is 0.1 mm.The main bearing shell and main bearing hole are assembled with interference, and the initial interference is 0.16 mm.The main bearing assembly structure is mainly subjected to three loads, which are bolt load (98 kN for each horizontal tension bolt, 200 kN for each vertical tension bolt), interference load and main bearing load from the crankshaft (−78,370 N in Y-direction, −195,770 N in Zdirection).The model is discretized with tetrahedral meshes.Mesh refinement is performed for the contact surfaces and the danger areas where stress may concentrate.After the mesh irrelevance verification, the mesh number of the model is determined to be 202,538.

| Determination of design variables
According to the previous research results on the reliability of the main bearing assembly structure, 25 the typical structural size parameters, assembly parameters and bolt load parameters are taken as the design variables as shown in Table 6.The design variable vector X can be expressed as , , , , , ) .

| Determination of objective functions
The objective functions of the strength coordination The strength coordination factors of the engine block and the main bearing cover are taken as the strength coordination objective functions according to the strength coordination evaluation criteria.The high stress areas of the engine block and the main bearing cover are shown in Figures 5 and 6.The material of the engine block is cast aluminum with a tensile limit of 250 MPa.The material of the main bearing cover is steel with a tensile limit of 980 MPa.The minimum safety factor S i where σ J and σ Z are the stresses in the high stress area of the engine block and main bearing cover.

The objective function of the deformation coordination
The deformation coordination factor of the main bearing shell is taken as the deformation coordination objective function.According to the definition of the deformation coordination factor, δ i ref, denotes the limit value of the maximum deformation of the ith component among the assembly structure, that is, the minimum assembly clearance between the main bearing shell and the crankshaft, which is 0.11 mm.δ i indicates the maximum radial deformation of the main bearing shell. 18The objective function of the deformation coordination can be expressed as where φ W presents the maximum radial deformation of the main bearing shell.

The objective function of the contact strength coordination
The contact strength coordination factor of the contact surface between the engine block and the main bearing cover is taken as the objective function of the contact strength coordination.The contact surface between the engine block and the main bearing cover is shown in Figure 7.The ultimate contact pressure of the engine block material is 380 MPa.According to the definition of the contact strength coordination factor, the objective function can be expressed as where P JZ indicates the maximum contact pressure on the contact surface between the engine block and the main bearing cover.

The objective function of the mass coordination
The mass coordination factor of the assembly structure is taken as the objective function of the mass coordination.
The high stress area of the engine block.
The high stress area of the main bearing cover.
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| 4531 The contact surface between the engine block and the main bearing cover.
The limit for the mass of the single partition board model of the main bearing assembly structure is 78.76 kg.The objective function can be expressed as where m′ reveals the mass of the single partition model of the assembly structure.

Strength constraints
The design requirement of the strength for the main bearing assembly structure is that the strength safety factor for each component is higher than 1.2.The tensile stress limits that the engine block, main bearing cover, main bearing shell and horizontal and vertical tension bolts can withstand are 250, 980, 430, and 1200 MPa, respectively.According to the strength coordination evaluation criteria, extracting the stress in the high stress area of each component, the strength constraints can be defined as where g X i ( ), = 1, 2, …, 5 i are the strength constraints of the engine block, the main bearing cover, the main bearing shell and the horizontal and vertical tension bolts.σ J , σ Z , σ W , σ H , and σ V are the stresses in the high stress area of the corresponding components.

Stiffness constraints
The stiffness design of the main bearing assembly structure requires that the maximum deformation of each component is less than the limit of the maximum deformation of that component.The maximum deformation limit of the main bearing shell, the engine block, the main bearing cover, horizontal tension bolt and the vertical tension bolt are 0.11, 0.48, 0.30, 0.78, and 1.00 mm, respectively.Extracting the maximum deformation of each component in the poor stiffness area, the stiffness constraints can be expressed as where g X j ( ), = 6, 7, …, 10 j are the stiffness constraints of the engine block, the main bearing cover, the main bearing shell and the horizontal and vertical tension bolts.φ W , φ J , φ Z , φ H , and φ V are the maximum deformation of the corresponding components.

Contact strength constraints
The design requirement for the contact strength of the main bearing assembly structure is that the maximum contact pressure at each contact surface is less than the maximum permissible contact pressure of the contact component material.The maximum allowable contact pressures of the engine block and the main bearing cover are 380 and 2000 MPa, respectively.According to the definition of the contact coordination evaluation criteria, extracting the maximum contact pressure of each contact surface, the contact strength constraints can be expressed as where g X k ( ), = 11, 12, …, 14 k are the contact strength constraints of the contact surfaces between the engine block and the main bearing cover, the engine block and the main bearing shell, the engine block and the horizontal tension bolts, the main bearing cover and the vertical tension bolts.P JZ , P JW , P JH , and P VZ present the maximum contact pressure of the corresponding contact surfaces.

Mass constraints
The lightweight design requires that the mass of each component should be less than the maximum permissible mass of the component and that the rise in mass of the optimized assembly structure should not exceed 5% of the original model mass, that is, 78.76 kg.According to the details of the lightweight design requirements of this type of diesel engine, the maximum allowable masses of the engine block, the main bearing cover, the main bearing shell, the horizontal tension bolt, the vertical tension bolt and the crankshaft (simplified as a cylinder) are 70.0,25.0, 1.4, 1.5, 5.0, and 10.0 kg, respectively.The mass constraints can be expressed as where g X l ( ), = 15, 12, …, 21 l are the mass constraints of the assembly structure, the engine block, the main bearing cover, the main bearing shell, the horizontal tension bolt, the vertical tension bolt and the crankshaft.m′, m J , m Z , m W , m H , m V , and m Q present the mass of the corresponding assembly structure and its components.
In summary, with the typical design parameters as the design variables, taking the coordination factors of the focused components or contact surfaces as the objective functions, setting each component or contact surface satisfying the design requirements of strength, stiffness, contact strength and mass as the constraints, the mathematical model for the coordination matching design of the main bearing assembly structure could be defined as follows., , , , , ) ,

| Solution of the mathematical model for matching design
The mathematical model is solved by a joint simulation of I-sight and Abaqus.Based on the secondary development function of Abaqus, the finite element model of the main bearing assembly structure is parametrized.The automatic process of "modeling-setting boundary conditions-meshing-submitting calculation-post processing results" is implemented.The Python script for finite element model is imported through the Simcode module of I-sight.NSGA-II is selected as the solution algorithm.The population size is set to 12.The evolution generation is set to 50.The initial crossover probability and mutation probability are set to 0.9 and 0.1, respectively.

| RESULTS AND DISCUSSIONS
The Pareto optimal solution for the coordination matching design of the main bearing assembly structure is a solution set containing 10 sets of optimal solutions, as shown in Table 7.Based on the weights of investigated elements, the deformation coordination is determined as the first optimization objective, and the strength coordination, the contact strength coordination and the mass coordination are the second, third and fourth optimization objectives, respectively.It can be seen from the table that the schemes with the optimal deformation coordination objective function are Schemes 5 and 6.However, the difference between the two is so small that it is basically negligible in practical engineering.Comparing the other optimization objectives of the two, it can be found that the strength coordination, contact strength coordination and mass objective coordination functions of Scheme 6 are better than that of Scheme 5. Scheme 6 is taken as the final solution for the coordination matching design of the main bearing assembly structure.The design variables before and after optimization are shown in Table 8.
According to the matching design scheme and coordination evaluation criteria of the main bearing assembly structure, the coordination factor of each component and the contact surface and the coordination coefficient of each investigated element before and after optimization are calculated as shown in Table 9.After optimization, the strength coordination coefficient, deformation coordination coefficient, contact strength coordination coefficient and overall coordination coefficient of the main bearing assembly structure are improved by 13.91%, 14.96%, 2.63%, and 11.10%, respectively, and the mass coordination coefficient remains almost constant.It indicates that the overall coordination of the assembly structure and the coordination of the investigated elements have been improved.At the component level, the coordination factors of the focused components and contact surfaces have increased, indicating that the reliabilities of these components and contact surfaces have become better.Although the coordination factors of the nonfocused components and contact surfaces fluctuate, the design requirements for the main bearing assembly structure are still met.

| EXPERIMENTAL VERIFICATION
To verify the final matching design scheme, the improved structures of the main bearing cover and main bearing shell are produced.Considering the machining T A B L E 7 Multiobjective optimization results of coordination matching design. No.

| Strength verification
Strain measurement method is employed for strength verification.When the engine block is loaded, strain occurs at the measurement point and the sensitive grid on the strain gauge is deformed, which causes a change in its resistance.According to the current output, the corresponding stress value is obtained.It is inconvenient to place strain gauges at the high stress area of the main bearing cover after assembly.Therefore, the stress in the high stress area of the engine block is taken as the strength verification objective.Two BX 4 × 4 mm 2 resistance strain gauges are selected and attached to the measurement points on both sides of the rib as shown in Figure 9.
The measured and simulation results of the stresses in the high stress area of the engine block are compared as shown in Figure 10.Taking measurement Location 1 as an example, the difference between the test results and simulation results of the improved structure is large, while the difference between the test results of the improved structure and the original structure is small.This is because the stresses in this area are most sensitive to the thicknesses of the partition board and rib on the side wall.But the improved structure did not consider the two.The strength comparison at Location 2 is similar to that of Location 1.

| Contact strength verification
The maximum contact pressure of the contact surface between the engine block and the main bearing cover is measured using pressure-sensitive paper.When a pressuresensitive paper is pressed, the micro-particle color spheres break and interact with the chromogenic agent to produce color on the paper.The amount of contact pressure is obtained by the color differences produced by the pressuresensitive paper.HHS type pressure-sensitive paper is used for this experiment.The paper is cut so that it can be placed on the contact surface to be tested.The contact surfaces on the left and right side of the main bearing hole are taken as measurement Locations 1 and 2. Measurement Location 1 is shown in Figure 11.The results of the maximum contact pressure experimental measurement are shown in Figure 12.It can be seen from the figure that the test results of the maximum contact pressure at measurement Location 1 and measurement Location 2 are slightly lower than the simulation results, and the error between the two is about 5%, indicating the accuracy of the finite element model for the improved structure.The maximum contact pressures at the two measurement locations of the improved structure are significantly lower than that of the original structure, decreasing by 19.97% on average, revealing that the improved scheme of the main bearing assembly structure is effective in improving the reliability of the contact strength.

| Principle of the experiment
The radial deformation of the main bearing shell is calculated by measuring the circumferential strain of a section of the main bearing shell.The peak point ε max of the circumferential strain wave in the load state is extracted.The coordinate corresponding to this peak point before the deformation occurs is defined as ε 0 .The circumferential strain value at this point ε θ can be expressed as Assuming that the main bearing shell is an elastomer, according to the theory of elastic mechanics, the circumferential strain and radial deformation of the main bearing shell can be expressed as where ε r indicates the radial normal strain of the main bearing shell.u r is the radial deformation of the main bearing shell.r presents the radius of the main bearing shell before deformation.ε θ presents the circumferential normal strain of the main bearing shell.u r / r denotes the circumferential normal strain caused by the radial deformation of the main bearing shell.  v r θ /( × ) θ denotes the circumferential normal strain caused by the circumferential displacement of the main bearing shell.The main bearing shell and main bearing hole can be considered symmetrical.Therefore,   v r θ /( × ) θ is infinitesimal of higher order compared to the previous term, and its value is almost zero.This term can be ignored.The circumferential normal strain of the main bearing shell ε θ can be simplified as The data measured in the experiment is the circumferential normal strain of the main bearing shell under load, that is, ε θ .The radial deformation of the outer wall of the main bearing shell can be expressed as If the circumferential normal strain is 8.0 × 10 −5 , the diameter before deformation is 75 mm and the sensitivity factor of the instrument is set to 0.2, then the radial deformation of the outer wall of the main bearing shell can be calculated as u = 8.0 × 10 × 75/0.2 = 300 mm.

| Protocol of the experiment
The phenolic substrate strain gauges with the specification BX120-3AA are selected for the experiment.The strain gauge has a sensitivity factor of 2.08 and a resistance value of 120 Ω, allowing for temperature self-compensation.DH3840 strain amplifier and DH5932 data acquisition instrument are applied to the experiment.The center of the axial section in the middle of the main bearing shell is taken as the origin.The axial sections with coordinates of −13 and 13 mm are selected as the two investigated sections for the circumferential strain test.Taking the vertical diameter as the reference, and the position after 45°o f clockwise and counterclockwise rotation of this diameter is taken as the measurement points as shown in Figure 13.
To eliminate the effect of temperature variations on circumferential strain, a half-bridge measurement circuit is employed.Each measurement point is arranged with a combination, including a working strain gauge and a temperature compensated strain gauge as shown in Figure 14.
According to the design parameters of the improved structure, the main bearing shell with strain gauges and the other components are assembled.The loads of the bolts are applied.Four shallow traces are ground in the corresponding positions of the strain gauges on the main bearing hole to facilitate the assembly of the strain gauges inside.The crankshaft is replaced with a substitute crankshaft with the same diameter as its journal.The substitute crankshaft is loaded with −78,370 N in the Y-direction and −195,770 N in the Z-direction.The resultant force of the crankshaft is 210,870 N and its direction is 22°from the Z-axis as shown in Figure 15.After completing the loading, the strain data is collected.

| Results of the experiment
The circumferential strains are collected at four points in the axial section with coordinates of 13 and −13 mm of the original and improved main bearing shell.The radial deformations of the corresponding measurement points are calculated as shown in Table 10.It can be seen from the table that the circumferential strain measured at each measurement point of the improved structure is smaller than that of the original structure.The radial deformations on measurement points of the improved structure decrease by about 15.08% on average compared to that of the original structure.The measurement result verifies the effectiveness of the matching design method for the stiffness optimization of the main bearing shell.In addition, the measured radial deformations of the main bearing shell of the improved structure are slightly smaller than the simulation analysis results.This is because the variation of the thickness of the partition board is not considered in the improved structure, resulting in a slightly lower local stiffness of the main bearing hole.

| CONCLUSION
The research on the coordination evaluation system, matching design method and reliability verification method of the main bearing assembly structure are carried out in this paper.The main conclusions are as follows.
1.The multilevel multiobjective coordination evaluation system characterized by quantitatively expressing the coordination relationship between the multireliability of the assembly structure and its components based on AHP is feasible.2. After the coordination matching design, the strength coordination, deformation coordination and contact strength coordination of the main bearing assembly structure increase by 13.91%, 14.96%, and 2.63%, respectively, while the mass coordination remains almost constant.The overall coordination of the main bearing assembly structure is improved by 11.10%, demonstrating the effectiveness of the proposed coordination matching design method.3. The maximum contact pressures and the radial deformations on measurement points of the improved structure decrease by 19.97% and 15.08% on average by conducting verification experiments.The strength experiment results of the improved structure are not satisfactory due to the fact that two sensitive parameters (the thicknesses of the partition board and the rib on the side wall) for the strength of the engine block are not considered in the improved structure.
The research provides a new idea for the coordination design of the main bearing assembly structure, and enriches the multidisciplinary coordination optimization design theory of complex mechanical structures.The main limitation of this study is that the construction of the framework of the coordination evaluation system and the demonstration of the matching design method are mainly focused on in this paper.Only the strength, stiffness, contact strength and mass performance of the main bearing assembly structure are considered, and further consideration should be given to other reliabilities such as friction and wear.
ref, is set to 1.2.The objective functions of the strength coordination can be expressed as F I G U R E 4 Schematic diagram of the main bearing assembly structure.

T A B L E 6
Design variables and their value ranges.on the side wall of the engine block x 1 each horizontal tension bolt x 7 /kN 50 150

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I G U R E 9 Strain gauge measurement locations.F I G U R E 10 Test results and simulation results of strength.F I G U R E 11 Measurement Location 1 of the contact surface.F I G U R E 12 Test results and simulation results of contact strength.

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I G U R E 13 Distributions of measurement points.F I G U R E 14 Locations of strain gauges.F I G U R E 15 Schematic diagram of circumferential strain measurement.T A B L E 10 Comparison of circumferential strains and radial deformations between the original structure and the improved structure.
Design variables before and after optimization.Coordination of main bearing assembly structure before and after optimization.
F I G U R E 8 The original and improved main bearing covers.ZHAO ET AL.