# Fault Diagnosis of Double Pitch Time-Sharing Meshing Toothed Conveyor Chain Transmission System Based on Neural Network

Authors: Song Ding; Donglin Jiang; Hongyan Zhou
Journal: Mathematical Problems in Engineering
 (2022)

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## Abstract

With the rapid development of industry, the production and demand of automobiles have increased significantly. The generation of cars often requires tens of thousands of processes, consisting of hundreds of assembly lines to complete. Chain conveyors are widely used in the transportation of automobile assembly lines. The existing conveyor chains are roller chains. With the improvement of the requirements for conveyor reliability, synchronization, and environmental friendliness, the characteristics of roller conveyor chains restrict the further development of chain conveyors. It is urgent to study a new conveyor chain system to improve the synchronization, reliability, and environmental friendliness of chain conveyors on hundreds of assembly lines. In this paper, the mathematical modeling, meshing analysis, reliability, and environmental friendliness of the parameters of the components of the double pitch time-sharing meshing toothed conveyor chain system are studied. In addition, a novel fault diagnosis method of double pitch time-sharing meshing toothed conveyor chain transmission system based on neural network model is proposed in this paper.


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## Body

## 1. Introduction

A car consists of more than 5000 parts, excluding interchangeable and universal standard parts (such as bolts, nuts, and gaskets). For the automobile assembly process is complex, the output of a car often requires a lot of labor, which is completed through hundreds of assembly lines composed of tens of thousands of processes. The integrity, reliability, and service life of the automobile require a high degree of specialization, strong continuity, and coordinated flow production.At present, the conveyor system of automobile assembly line mainly adopts roller conveyor chain transmission and belt transmission. Due to the polygon effect in the transmission process of roller conveyor chain, there will be a large instantaneous impact in the meshing process of chain and sprocket. This impact process will produce large noise and serious wear, resulting in large wear elongation. In serious cases, tooth skipping and fracture will occur, which will seriously affect the continuity and rhythm coordination of the assembly line. Under heavy load and variable load, the belt transmission has low transmission efficiency and service life, and slip will occur. When the tension is too large, the joint or weak link of the belt will be broken. The most important thing is that the belt will deviate during the transmission process, which will seriously affect the normal operation of the assembly line. It is found that the noise of toothed chain is almost the same as that of belt drive. The toothed chain is limited by the guide plate, so there will be no deviation in the transmission process. At the same time, the toothed chain is meshed transmission and has a constant average transmission ratio. It can be seen that the toothed chain can better ensure the continuity and rhythm coordination of the automobile assembly line. However, the toothed chain with the same pitch is heavier than the roller chain, and the weight of the conveyor itself will affect the conveying performance. Therefore, it is difficult for the traditional toothed chain to meet the increasing requirements of the conveyor. With the rapid development of automobile manufacturing industry, there is an urgent need to study a new chain conveyor system with better conveying performance and higher transmission efficiency, which is suitable for conveyor applications.As one of the basic parts of mechanical transmission [1–5], toothed chain has stronger bearing capacity and lower noise. For the working conditions of large center distance and variable speed and load, its transmission performance is better than that of toothed belt transmission, gear transmission, and roller chain transmission. Toothed chains are divided into external meshing toothed chains, internal meshing toothed chains, internal and external meshing toothed chains, and other toothed chains. The existing standards are the design standards of transmission toothed chain, which are not suitable for the conveyor chain on the assembly line, and there is little research on the conveyor toothed chain. In this paper, the multibody dynamics model of the double pitch time-sharing meshing toothed conveyor chain system is established, and the kinematics and dynamics characteristics of the double pitch time-sharing meshing toothed conveyor chain system are studied. When conveying and transmitting the same force, the chain transmission system has stable meshing and meshing, low impact vibration and noise, less consumables, high motion accuracy, and good reliability. The new double pitch time-sharing meshing toothed transmission chain system has a very broad application prospect in various assembly lines, especially in automobile assembly lines. Finally, a novel fault diagnosis method of double pitch time-sharing meshing toothed conveyor chain transmission system based on neural network model is constructed in this paper.


## 2. Related Work

### 2.1. Research on Toothed Chain Transmission System

Because the meshing mode of toothed chain transmission system is different from that of roller chain transmission, the structural parameters are more complex. There is relatively little research on toothed chain transmission system. Because of its great manufacturing difficulty and high production technology content, only a few manufacturers can produce toothed chain internationally. Bucknor N.K makes static and dynamic analysis of Hy-VO toothed chain with external meshing mechanism, adds the influence of link clearance, establishes the quasi-static equation of roll pin toothed chain on the basis of analyzing the influence of the parameters of chain plate and pin shaft on the transmission performance of toothed chain, and calculates the maximum torque value under the condition of static balance. It is concluded that the extreme torque is related to the corresponding center distance and the design parameters of the chain drive system [6, 7]. Based on the finite element method, Adnan et al. analyzed the fatigue strength of the toothed chain plate of the external meshing mechanism under cyclic load, and proposed corresponding improvement methods according to the research conclusions. Weber, Stephenson, and others used telemetry to continuously observe a series of parameters such as wear, noise, and dynamic characteristics of timing chain system under different engine working conditions [8, 9]. Heinz Heisler put forward a relatively complete design scheme for V-type engine, in which the design layout of camshaft, installation position of chain tensioner, and oil pump drive chain were studied in detail [10]. Masakazu Wada, Shouchiro IDE, and others proposed a toothed chain product with a pitch of 6.35 mm, which was successfully applied to a single camshaft timing transmission system. Based on the dynamic analysis of external meshing circular pin toothed chain by using Adams/engine module, some researchers obtained the characteristic equivalence of tight edge tension and contact force between driving and driven sprocket and chain plate in the process of chain transmission and simulated and analyzed the calculation results. In order to solve the wear problem of toothed chain sprocket, Jeffrey et al. started with the material and processing technology of toothed chain and used powder metallurgy technology to manufacture the timing round pin toothed chain sprocket of engine. In addition, some scholars improved the wear resistance of toothed chain by coating the surface of toothed chain plate and pin shaft.


### 2.2. Application of Chain Drive System in Conveyor

The chain is the bearing and traction component of the chain conveyor. The bearing capacity and running length of the conveyor mainly depend on the conveyor chain system. Therefore, whether the design of the conveyor chain system is reasonable not only is related to the productivity, reliability, and service life of the conveyor, but also affects the driving power of the conveyor and the consumption of steel for manufacturing the conveyor chain. Industrial developed countries attach great importance to the design and standardization of the conveyor chain system. For example, Germany, France, Finland, Sweden, and other countries have developed their own national standards din8167, nfe26-106, sfs2380, and sms2083 based on iso/r1977 recommended by international standards. Through these standards, the conveyor chain systems of the same model produced by these countries can be used universally, and there will be no obstacles in technology, trade, or academic exchanges. Compared with other types of conveyors, the chain conveyor has low energy consumption and high efficiency, and the energy consumption of the same conveying length and volume is 50% lower than that of the screw conveyor. With simple structure and light weight, it can ensure stable transmission ratio, convenient maintenance, and low operation cost and can work normally in various environments, including corrosive, flammable, and explosive working conditions, as well as transporting hot materials. It is commonly used in building materials, chemical industry, mechanical assembly, metallurgy, grain, hydropower, light industry, ports, mines, transportation, and other departments and is suitable for transportation density of 0.2 ∼ l.8 t/m³ and powdery, granular, or small loose materials with temperature ≤80°C. At present, the commonly used chain conveyors mainly include KS double chain scraper conveyor, DTS chain conveyor, Fu chain conveyor, and SFC chain conveyor.


### 2.3. Problems in the Application of Toothed Chain in Conveyor

With the development of industrial automation, the performance requirements of conveyors are becoming higher and higher. In addition to ensuring transmission accuracy, service life, and reliability, environmental friendliness has also been put on the agenda. Therefore, it has been difficult for the chain conveyor of roller chain drive system to meet the demand. We need to have the environmental friendliness of belt transmission system and the reliability of roller chain transmission system at the same time. Only the toothed chain transmission system has the common advantages of belt transmission and roller chain transmission system at the same time. Due to the complexity of toothed chain transmission system, there is no international standard at this stage. The research on toothed chain mainly focuses on the tooth profile and tooth profile design method of round pin toothed chain and roller pin toothed chain used in high-speed transmission methods of reducing polygon effect, establishment of kinematic model, establishment of dynamic model, transverse and longitudinal vibration of chain, noise source, software simulation, development of test equipment, etc. Through the research, it is found that the toothed chain has many advantages, but it is not used in the conveyor, because the self-weight of the chain drive system affects the working performance of the conveyor. Based on the development needs of mechanical automation and the advantages of toothed chain transmission system, this paper proposes a double pitch time-sharing meshing toothed conveyor chain system. It is hoped that, through the establishment and research of this project, some theoretical and methodological problems of the application of toothed chain in conveyors, that is, the double pitch time-sharing meshing toothed conveyor chain system, can be effectively solved.


## 2.1. Research on Toothed Chain Transmission System

Because the meshing mode of toothed chain transmission system is different from that of roller chain transmission, the structural parameters are more complex. There is relatively little research on toothed chain transmission system. Because of its great manufacturing difficulty and high production technology content, only a few manufacturers can produce toothed chain internationally. Bucknor N.K makes static and dynamic analysis of Hy-VO toothed chain with external meshing mechanism, adds the influence of link clearance, establishes the quasi-static equation of roll pin toothed chain on the basis of analyzing the influence of the parameters of chain plate and pin shaft on the transmission performance of toothed chain, and calculates the maximum torque value under the condition of static balance. It is concluded that the extreme torque is related to the corresponding center distance and the design parameters of the chain drive system [6, 7]. Based on the finite element method, Adnan et al. analyzed the fatigue strength of the toothed chain plate of the external meshing mechanism under cyclic load, and proposed corresponding improvement methods according to the research conclusions. Weber, Stephenson, and others used telemetry to continuously observe a series of parameters such as wear, noise, and dynamic characteristics of timing chain system under different engine working conditions [8, 9]. Heinz Heisler put forward a relatively complete design scheme for V-type engine, in which the design layout of camshaft, installation position of chain tensioner, and oil pump drive chain were studied in detail [10]. Masakazu Wada, Shouchiro IDE, and others proposed a toothed chain product with a pitch of 6.35 mm, which was successfully applied to a single camshaft timing transmission system. Based on the dynamic analysis of external meshing circular pin toothed chain by using Adams/engine module, some researchers obtained the characteristic equivalence of tight edge tension and contact force between driving and driven sprocket and chain plate in the process of chain transmission and simulated and analyzed the calculation results. In order to solve the wear problem of toothed chain sprocket, Jeffrey et al. started with the material and processing technology of toothed chain and used powder metallurgy technology to manufacture the timing round pin toothed chain sprocket of engine. In addition, some scholars improved the wear resistance of toothed chain by coating the surface of toothed chain plate and pin shaft.


## 2.2. Application of Chain Drive System in Conveyor

The chain is the bearing and traction component of the chain conveyor. The bearing capacity and running length of the conveyor mainly depend on the conveyor chain system. Therefore, whether the design of the conveyor chain system is reasonable not only is related to the productivity, reliability, and service life of the conveyor, but also affects the driving power of the conveyor and the consumption of steel for manufacturing the conveyor chain. Industrial developed countries attach great importance to the design and standardization of the conveyor chain system. For example, Germany, France, Finland, Sweden, and other countries have developed their own national standards din8167, nfe26-106, sfs2380, and sms2083 based on iso/r1977 recommended by international standards. Through these standards, the conveyor chain systems of the same model produced by these countries can be used universally, and there will be no obstacles in technology, trade, or academic exchanges. Compared with other types of conveyors, the chain conveyor has low energy consumption and high efficiency, and the energy consumption of the same conveying length and volume is 50% lower than that of the screw conveyor. With simple structure and light weight, it can ensure stable transmission ratio, convenient maintenance, and low operation cost and can work normally in various environments, including corrosive, flammable, and explosive working conditions, as well as transporting hot materials. It is commonly used in building materials, chemical industry, mechanical assembly, metallurgy, grain, hydropower, light industry, ports, mines, transportation, and other departments and is suitable for transportation density of 0.2 ∼ l.8 t/m³ and powdery, granular, or small loose materials with temperature ≤80°C. At present, the commonly used chain conveyors mainly include KS double chain scraper conveyor, DTS chain conveyor, Fu chain conveyor, and SFC chain conveyor.


## 2.3. Problems in the Application of Toothed Chain in Conveyor

With the development of industrial automation, the performance requirements of conveyors are becoming higher and higher. In addition to ensuring transmission accuracy, service life, and reliability, environmental friendliness has also been put on the agenda. Therefore, it has been difficult for the chain conveyor of roller chain drive system to meet the demand. We need to have the environmental friendliness of belt transmission system and the reliability of roller chain transmission system at the same time. Only the toothed chain transmission system has the common advantages of belt transmission and roller chain transmission system at the same time. Due to the complexity of toothed chain transmission system, there is no international standard at this stage. The research on toothed chain mainly focuses on the tooth profile and tooth profile design method of round pin toothed chain and roller pin toothed chain used in high-speed transmission methods of reducing polygon effect, establishment of kinematic model, establishment of dynamic model, transverse and longitudinal vibration of chain, noise source, software simulation, development of test equipment, etc. Through the research, it is found that the toothed chain has many advantages, but it is not used in the conveyor, because the self-weight of the chain drive system affects the working performance of the conveyor. Based on the development needs of mechanical automation and the advantages of toothed chain transmission system, this paper proposes a double pitch time-sharing meshing toothed conveyor chain system. It is hoped that, through the establishment and research of this project, some theoretical and methodological problems of the application of toothed chain in conveyors, that is, the double pitch time-sharing meshing toothed conveyor chain system, can be effectively solved.


## 3. Simulation Analysis of Double Pitch Time-Sharing Meshing Toothed Conveyor Chain System

In the process of double pitch time-sharing meshing toothed conveying chain, polygon effect is an inherent attribute in the process of chain transmission, and it is also the main factor causing the horizontal and vertical fluctuations of the chain. Therefore, to evaluate the advantages and disadvantages of the new double pitch time-sharing meshing toothed conveyor chain, it is necessary to carry out dynamic simulation analysis in kinematics. In order to analyze the influence of the characteristic parameters of the new double pitch time-sharing meshing toothed conveyor chain on the polygon effect, the kinematic simulation analysis of the chain and sprocket of the double pitch time-sharing meshing toothed conveyor chain is carried out based on the multibody dynamics simulation software Adams [11–13] without considering the chain plate hole and pin shaft clearance. The vibration generated by the meshing impact excitation between the chain and the sprocket is the main source of noise. In order to evaluate the noise reduction characteristics of the double pitch time-sharing meshing toothed conveyor chain, a dynamic model is established on the premise of considering the chain plate hole and the pin shaft clearance, and the multibody dynamics technology is used to study the contact meshing impact force between the double pitch time-sharing meshing toothed conveyor chain and the sprocket teeth.


### 3.1. Theoretical Basis of Multibody Dynamics

In multibody dynamics, three rectangular coordinates and rotational coordinates in the inertial coordinate system of the center of mass of each rigid body are selected as Cartesian generalized coordinates, and the multibody system equation is derived by using the first kind of Lagrange equation with Lagrange multiplier. The multibody system includes the inertial coordinate system and the follow-up coordinate system. The follow-up coordinate system is fixed on the component and moves with it. In the process of establishing and solving the dynamics of the multibody system, the motion of the rigid body in the inertial coordinate system can be determined by establishing the position of the center of mass of the rigid body in the follow-up coordinate system and then establishing the position relationship between the follow-up coordinate system and the inertial coordinate system with the azimuth angle.


#### 3.1.1. Establishment of Kinematic Equation

In a multirigid body system, rigid bodies are connected in the form of kinematic pairs. These kinematic pairs are expressed as algebraic equations through generalized coordinates, which can be holonomic constraints, steady constraints, and unsteady constraints.(1)Φkq⟶=Φ1kq⟶,Φ2kq⟶,…,Φkq⟶T=0.In the above formula, the constraint equation is a time function, which is called unsteady constraint; if the constraint equation contains an integrable velocity term, it is called incomplete constraint. The motion constraint equation and the driving constraint equation together form the position equation of the system:(2)Φq⟶,t=Φkq⟶ΦDq⟶,t=0.By differentiating the above formula, the velocity constraint equation can be obtained:(3)Φ˙q⟶,q⟶˙,t=Φqq⟶,tq⟶+Φtq⟶,t=0.Continue to differentiate the above formula to obtain the acceleration constraint equation:(4)Φ¨q⟶,q⟶˙,q⟶¨,t=Φqq⟶,tq⟶¨+Φqq⟶,tq⟶˙qq⟶˙+2Φqtq⟶,tq⟶˙+Φttq⟶,t=0.The above equation is solved by Calahan method:(5)q⟶˙=−Φq−1Φt,q⟶¨=−Φq−1Φqq⟶˙q⟶˙+2Φqtq⟶˙+Φtt.


#### 3.1.2. Establishment of Dynamic Equation

The coordinate transformation matrix of the follow-up coordinate system and inertial coordinate system of the component centroid is(6)cosψcosφ−sinψcosθsinφ−cosψsinφ−sinψcosθcosφsinψcosθsinψcosφ+cosψcosθsinφ−sinθsinφ+cosψcosθcosφ−cosψsinθsinθsinφsinθcosφcosθ.Then define an Euler axis coordinate system. The coordinate transformation matrix from this coordinate system to the component centroid follow-up coordinate system is(7)B⟶=sinθsinφ0cosθsinθcosφ0−sinθcosθ10.Then the kinetic energy of the multirigid body system is(8)T⟶=12R⟶˙TM⟶R⟶R˙+12B⟶r⟶˙TJ⟶B⟶r⟶˙.The Euler Lagrange equation of the multirigid body system is(9)M⟶Φ⟶qTΦ⟶q0q⟶¨λ⟶=Q⟶Aη⟶.


### 3.2. 3D Model Establishment

The multibody kinematics and dynamics of the double pitch time-sharing meshing toothed conveyor chain system are analyzed in Adams simulation software. First, carry out geometric modeling. The double pitch time-sharing meshing toothed conveyor chain system is a newly designed structure, which cannot be directly obtained in the Adams Geometric Modeling Toolbox, and there are many structural parameters of the chain plate. Therefore, the three-dimensional modeling and virtual assembly of chain and sprocket are carried out in pro/e first.The design parameters of the chain and sprocket of the double pitch time-sharing meshing toothed conveyor chain are designed. Taking the single pitch of the chain as 15.875 mm, the number of sprocket teeth as 45, and the sprocket pitch as 15.875 mm, the component models of the linear tooth profile double pitch time-sharing meshing toothed chain sprocket and the corresponding double pitch time-sharing meshing toothed conveyor chain are established in pro/e, respectively. We designed the negative modification involute tooth profile sprocket and modified the parameters of the double pitch time-sharing meshing tooth profile conveyor chain plate. Similarly, we established the component model of the double pitch involute tooth profile sprocket and the corresponding modified double pitch time-sharing meshing tooth profile conveyor chain in pro/e.In the process of simulation and analysis, the double pitch roller conveyor chain should have the same pitch as the new double pitch time-sharing meshing toothed conveyor chain. Therefore, when the double pitch time-sharing meshing toothed conveyor chain has a single pitch of 15.875 mm and the number of sprocket teeth is 45, the model parameters of the double pitch roller conveyor chain and sprocket are based on the standard. The model of the chain is 210a, and the number of sprocket teeth is 45, and the pitch is 15.875 mm standard roller chain sprocket.


### 3.3. Kinematic Simulation Analysis of Double Pitch Time-Sharing Meshing Toothed Conveyor Chain System

#### 3.3.1. Initial Condition Analysis

After entering the 3D model and establishing constraints, Adams will analyze the initialization conditions to ensure that the simulation model meets all constraints. The initial condition analysis is achieved by solving the minimum value of the corresponding position, velocity, and acceleration objective function.


#### 3.3.2. Meshing Simulation Model

When the double pitch time-sharing meshing toothed conveyor chain is meshed with the sprocket, the tooth shape parameters of the chain plate and the number of teeth of the sprocket have a great impact on the conveying characteristics of the double pitch time-sharing meshing toothed conveyor chain system. The more the number of teeth of the sprocket is, the more stable the transmission of the chain drive system is. In order to analyze the influence of the extension of the internal tooth profile of the chain plate on the meshing polygon effect of the double pitch time-sharing meshing toothed transmission chain, when the number of sprocket teeth is certain, the influence of the extension of the internal tooth profile on the tight side wave momentum of the double pitch time-sharing meshing toothed transmission chain system is established, respectively. Without considering the chain plate hole and pin shaft clearance, a three-dimensional parametric simulation model of the double pitch time-sharing meshing toothed conveyor chain system and the double pitch roller conveyor chain system is established by using Adams simulation software.


#### 3.3.3. Influence of Tooth Profile Extension in Chain Plate on Tight Side Wave Momentum of Chain Drive System

The single pitch of the chain is 15.875 mm, the number of driving and driven sprocket teeth is 45, the pitch of the sprocket is 15.875 mm, and the protrusions are 0.05 mm, 0.10 mm, 0.15 mm, 0.20 mm, 0.25 mm, 0.30 mm, 0.35 mm, and 0.40 mm, respectively. The simulation model of the double pitch time-sharing meshing toothed conveyor chain system is analyzed. In the initial setting, the driving wheel speed is 4π/Z per second, and the simulation runs for 1s. In a meshing cycle, the fluctuation of the tight side center of the double pitch time-sharing meshing toothed conveyor chain is within a certain range. The larger the extension, the smaller the fluctuation of the tight side of the chain center, which is in line with the function of the extension of the inner tooth profile. The extension of the inner tooth profile can reduce the polygon effect. However, when the extension value is too large, the whole meshing is completely double pitch time-sharing meshing, and the inner tooth profile of the toothed conveyor chain is meshed. During meshing rotation, the inner tooth profile cannot shrink into the outer tooth profile of the adjacent chain link, and the meshing impact is large when meshing with the intermediate tooth. When the extension is very small, in the meshing process, the internal tooth profile meshing is transformed into the external tooth profile meshing of adjacent links in a very short time, so the effect of reducing the polygon is not obvious. Therefore, for the calculation example, the best internal tooth profile elongation is δ = 0.25 mm.


#### 3.3.4. Comparative Analysis of Tight Edge Fluctuation between Double Pitch Roller Conveyor Chain System and Double Pitch Roller Conveyor Chain System

For the double pitch time-sharing meshing toothed conveyor chain system with a single pitch of 15.875 mm and double pitch of 31.67 mm and the double pitch roller conveyor chain system with a single pitch of 15.875 mm and double pitch of 31.75 mm, the number of teeth of the driving and driven wheels of the two conveyor chain systems is 45. In order to show generality, the extension is 0.15 mm. The simulation models of the two conveyor chain systems are analyzed. In the initial setting, the driving wheel speed is 4π/Z per second, and the simulation runs for 1s. In a cycle, two conveyor chains fluctuate around the center. The simulation analysis shows that the transverse wave momentum of the double pitch time-sharing meshing toothed conveyor chain is 113.19–113.53 mm, and the fluctuation range is 0.34 mm. The transverse wave momentum of the double pitch roller conveyor chain is 113.08–113.91 mm, and the fluctuation range is 0.83 mM. It can be concluded that the transverse fluctuation of the tight side of the double pitch time-sharing meshing toothed conveyor chain is 59% lower than that of the double pitch roller conveyor chain.


### 3.4. Dynamic Simulation Analysis of Double Pitch Time-Sharing Meshing Toothed Conveyor Chain System

Dynamics is to study that the vibration and noise of the double pitch time-sharing meshing toothed conveyor chain system change with the evolution of time under the action of meshing impact force, and the polygon effect of the double pitch time-sharing meshing toothed conveyor chain is the main cause of meshing impact. By studying the meshing impact force, Newton’s law of motion is used to study the influence on the double pitch time-sharing meshing toothed conveyor chain system.


#### 3.4.1. Contact Force Model

The double pitch time-sharing meshing toothed conveyor chain system is composed of a driving and driven sprocket, a chain, and a tensioning device. The chain extends due to wear, and the tensioning device compensates for the wear elongation. Therefore, in the process of simulation, it is only necessary to establish a double pitch time-sharing meshing toothed conveyor chain system composed of driving and driven sprocket and chain. The driving and driven wheels in the simulation model carry out the predetermined relative motion through the contact force and friction between the chain and sprocket teeth, and the driving wheel sets the driving constraint of constant speed. Each section of the double pitch time-sharing meshing toothed conveyor chain is connected by multiple rows of chain pieces through pin shafts, and there is a guide plate in the middle of every other section. The guide plate plays a role in horizontal positioning and adjusting the strength between chain links and does not play a major role in the meshing process. Without affecting the calculation results, simplify the contact force simulation model and establish 5 × Model 6 double pitch time-sharing meshing toothed conveyor chain link simulation model. In the practical application of toothed chain for inner guide conveying, the outer chain plate and the pin shaft are interference fit, while all the other chain plates and guide plates are clearance fit with the pin shaft. Therefore, in order to make the simulation results true, we establish the geometric model of the link. The pin shaft of 6 chain links and two outer chain plates form one part, and the clearance between the inner chain plate and the pin shaft is considered, with a unilateral clearance of 0.01 mm.The meshing contact force of the double pitch time-sharing meshing toothed conveyor chain system is mainly considered in the simulation model, using the search algorithm. The search process is as follows: define a boundary circle whose center coincides with the center of the sprocket, then search the chain for the starting link and the ending link that may contact the sprocket, and then search the starting link and the ending link in the boundary circle in detail to observe the direct contact of the chain link. For the double pitch time-sharing meshing toothed conveyor chain and the linear tooth profile, there are three possible contacts between the sprockets of the double pitch time-sharing meshing toothed conveyor chain, namely, the circular arc linear contact between the inner tooth profile of the chain plate and the linear tooth profile of the sprocket, the linear point contact between the outer tooth profile of the chain plate (middle tooth profile) and the linear tooth profile of the sprocket, and the circular arc circular arc contact between the hole of the chain plate and the pin shaft. The double pitch roller conveyor chain conveying system is mainly arc-arc contact.


#### 3.4.2. Contact Impact Analysis

In order to verify the rationality of the structure of the double pitch time-sharing meshing toothed conveyor chain and the reduction of the meshing impact by the tooth profile structure, the double pitch time-sharing meshing toothed conveyor chain with a single pitch of 15.875 mm and a sprocket tooth number of 45 and the double pitch roller conveyor chain are compared and analyzed. To analyze the meshing contact impact, only one meshing cycle needs to be analyzed, so the simulation model can be simplified.In the process of establishing the simulation model, the unilateral clearance between the chain plate hole and the pin shaft is considered to be 0.01 mm. The sprocket is the driving wheel, which rotates counterclockwise and rotates at a speed of 4π/Z degrees per second. In order to obtain the meshing impact between the chain plate and the sprocket and the tension of the tight chain during the operation of the chain drive system, it is necessary to establish contact pairs between the chain plate and the sprocket, and between the chain plate and the pin shaft In addition, in order to make the simulation process close to the running state of the conveyor chain system in reality, that is, to realize the horizontal movement state of the tight side chain, a 2Kn fixed tension is applied to the center of the chain plate pin to simulate the tension of the tight side chain. The extension of the tooth profile in the chain plate is 0.15 mm, 0.20 mm, 0.25 mm, and 0.30 mm, respectively. When the sprocket rotates at a constant speed of 4π/Z degrees, the contact force between the chain plates 2 and 3 of the double pitch time-sharing meshing toothed conveyor chain and the sprocket can be seen. When the extension of the tooth profile in the chain plate increases within a certain range, the meshing impact contact force decreases, but when it reaches a certain value, contact is found with the increase of the extension_ 3. There is no meshing impact force, and the meshing impact force is all in contact_ 2. At this point, explain contact_ 3. It does not participate in meshing. According to the simulation results, it conforms to the role of the inner tooth profile of the chain plate. When the extension is very small, the meshing of the inner tooth profile will soon be transformed into the meshing of the outer tooth profile, and the contact impact force will soon be changed from contact_ 2 convert to contact_ 3. As the extension increases, the conversion time increases, and it is consistent when the extension is 0.15–0.25 mm. However, when the extension reaches a certain value, the internal engagement cannot be converted to the external engagement. There is no contact impact on contact 3.The contact force of the double pitch time-sharing meshing tooth profile transmission link can show that, at the beginning of operation, the impact force of the contact between the inner tooth profile of link 2 and the sprocket is large, and link 1 and the sprocket do not contact without impact force. When the operation is 0.13s, link 1 and link 2 participate in the meshing at the same time and gradually transition to the meshing of the outer tooth profile of link 1. The impact force of link 1 is slightly greater than that of link 2. However, they are much smaller than the impact force of link 2 when it just runs. When it runs to about 0.5s, the external tooth profile meshing of link 1 is transformed into the internal tooth profile meshing of adjacent link 2. Link 1 disengages without impact force, while the impact force of link 2 in contact with the sprocket is instantaneous large, and link 2 gradually engages and locates to complete one-time meshing. The meshing impact force of the roller and sprocket of the double pitch roller chain is instantaneous contact meshing, and the initial meshing impact is large. The simulation results show that the maximum meshing impact force of the double pitch time-sharing meshing toothed conveyor chain is 4542.6 n, and the maximum meshing impact force of the double pitch roller conveyor chain is 8726.5 n. The meshing of the double pitch time-sharing meshing toothed conveyor chain system is stable, and the maximum impact force is 51.9% of the double pitch roller chain. Considering the influence of the internal tooth profile extension on the tight side wave momentum and the meshing impact force of the double pitch time-sharing meshing toothed conveyor chain system, the internal tooth profile extension of the double pitch time-sharing meshing toothed conveyor chain system with a single pitch of 15.875 mm and a sprocket tooth number of 45 is taken as 0.25 mm.


## 3.1. Theoretical Basis of Multibody Dynamics

In multibody dynamics, three rectangular coordinates and rotational coordinates in the inertial coordinate system of the center of mass of each rigid body are selected as Cartesian generalized coordinates, and the multibody system equation is derived by using the first kind of Lagrange equation with Lagrange multiplier. The multibody system includes the inertial coordinate system and the follow-up coordinate system. The follow-up coordinate system is fixed on the component and moves with it. In the process of establishing and solving the dynamics of the multibody system, the motion of the rigid body in the inertial coordinate system can be determined by establishing the position of the center of mass of the rigid body in the follow-up coordinate system and then establishing the position relationship between the follow-up coordinate system and the inertial coordinate system with the azimuth angle.


### 3.1.1. Establishment of Kinematic Equation

In a multirigid body system, rigid bodies are connected in the form of kinematic pairs. These kinematic pairs are expressed as algebraic equations through generalized coordinates, which can be holonomic constraints, steady constraints, and unsteady constraints.(1)Φkq⟶=Φ1kq⟶,Φ2kq⟶,…,Φkq⟶T=0.In the above formula, the constraint equation is a time function, which is called unsteady constraint; if the constraint equation contains an integrable velocity term, it is called incomplete constraint. The motion constraint equation and the driving constraint equation together form the position equation of the system:(2)Φq⟶,t=Φkq⟶ΦDq⟶,t=0.By differentiating the above formula, the velocity constraint equation can be obtained:(3)Φ˙q⟶,q⟶˙,t=Φqq⟶,tq⟶+Φtq⟶,t=0.Continue to differentiate the above formula to obtain the acceleration constraint equation:(4)Φ¨q⟶,q⟶˙,q⟶¨,t=Φqq⟶,tq⟶¨+Φqq⟶,tq⟶˙qq⟶˙+2Φqtq⟶,tq⟶˙+Φttq⟶,t=0.The above equation is solved by Calahan method:(5)q⟶˙=−Φq−1Φt,q⟶¨=−Φq−1Φqq⟶˙q⟶˙+2Φqtq⟶˙+Φtt.


### 3.1.2. Establishment of Dynamic Equation

The coordinate transformation matrix of the follow-up coordinate system and inertial coordinate system of the component centroid is(6)cosψcosφ−sinψcosθsinφ−cosψsinφ−sinψcosθcosφsinψcosθsinψcosφ+cosψcosθsinφ−sinθsinφ+cosψcosθcosφ−cosψsinθsinθsinφsinθcosφcosθ.Then define an Euler axis coordinate system. The coordinate transformation matrix from this coordinate system to the component centroid follow-up coordinate system is(7)B⟶=sinθsinφ0cosθsinθcosφ0−sinθcosθ10.Then the kinetic energy of the multirigid body system is(8)T⟶=12R⟶˙TM⟶R⟶R˙+12B⟶r⟶˙TJ⟶B⟶r⟶˙.The Euler Lagrange equation of the multirigid body system is(9)M⟶Φ⟶qTΦ⟶q0q⟶¨λ⟶=Q⟶Aη⟶.


## 3.1.1. Establishment of Kinematic Equation

In a multirigid body system, rigid bodies are connected in the form of kinematic pairs. These kinematic pairs are expressed as algebraic equations through generalized coordinates, which can be holonomic constraints, steady constraints, and unsteady constraints.(1)Φkq⟶=Φ1kq⟶,Φ2kq⟶,…,Φkq⟶T=0.In the above formula, the constraint equation is a time function, which is called unsteady constraint; if the constraint equation contains an integrable velocity term, it is called incomplete constraint. The motion constraint equation and the driving constraint equation together form the position equation of the system:(2)Φq⟶,t=Φkq⟶ΦDq⟶,t=0.By differentiating the above formula, the velocity constraint equation can be obtained:(3)Φ˙q⟶,q⟶˙,t=Φqq⟶,tq⟶+Φtq⟶,t=0.Continue to differentiate the above formula to obtain the acceleration constraint equation:(4)Φ¨q⟶,q⟶˙,q⟶¨,t=Φqq⟶,tq⟶¨+Φqq⟶,tq⟶˙qq⟶˙+2Φqtq⟶,tq⟶˙+Φttq⟶,t=0.The above equation is solved by Calahan method:(5)q⟶˙=−Φq−1Φt,q⟶¨=−Φq−1Φqq⟶˙q⟶˙+2Φqtq⟶˙+Φtt.


## 3.1.2. Establishment of Dynamic Equation

The coordinate transformation matrix of the follow-up coordinate system and inertial coordinate system of the component centroid is(6)cosψcosφ−sinψcosθsinφ−cosψsinφ−sinψcosθcosφsinψcosθsinψcosφ+cosψcosθsinφ−sinθsinφ+cosψcosθcosφ−cosψsinθsinθsinφsinθcosφcosθ.Then define an Euler axis coordinate system. The coordinate transformation matrix from this coordinate system to the component centroid follow-up coordinate system is(7)B⟶=sinθsinφ0cosθsinθcosφ0−sinθcosθ10.Then the kinetic energy of the multirigid body system is(8)T⟶=12R⟶˙TM⟶R⟶R˙+12B⟶r⟶˙TJ⟶B⟶r⟶˙.The Euler Lagrange equation of the multirigid body system is(9)M⟶Φ⟶qTΦ⟶q0q⟶¨λ⟶=Q⟶Aη⟶.


## 3.2. 3D Model Establishment

The multibody kinematics and dynamics of the double pitch time-sharing meshing toothed conveyor chain system are analyzed in Adams simulation software. First, carry out geometric modeling. The double pitch time-sharing meshing toothed conveyor chain system is a newly designed structure, which cannot be directly obtained in the Adams Geometric Modeling Toolbox, and there are many structural parameters of the chain plate. Therefore, the three-dimensional modeling and virtual assembly of chain and sprocket are carried out in pro/e first.The design parameters of the chain and sprocket of the double pitch time-sharing meshing toothed conveyor chain are designed. Taking the single pitch of the chain as 15.875 mm, the number of sprocket teeth as 45, and the sprocket pitch as 15.875 mm, the component models of the linear tooth profile double pitch time-sharing meshing toothed chain sprocket and the corresponding double pitch time-sharing meshing toothed conveyor chain are established in pro/e, respectively. We designed the negative modification involute tooth profile sprocket and modified the parameters of the double pitch time-sharing meshing tooth profile conveyor chain plate. Similarly, we established the component model of the double pitch involute tooth profile sprocket and the corresponding modified double pitch time-sharing meshing tooth profile conveyor chain in pro/e.In the process of simulation and analysis, the double pitch roller conveyor chain should have the same pitch as the new double pitch time-sharing meshing toothed conveyor chain. Therefore, when the double pitch time-sharing meshing toothed conveyor chain has a single pitch of 15.875 mm and the number of sprocket teeth is 45, the model parameters of the double pitch roller conveyor chain and sprocket are based on the standard. The model of the chain is 210a, and the number of sprocket teeth is 45, and the pitch is 15.875 mm standard roller chain sprocket.


## 3.3. Kinematic Simulation Analysis of Double Pitch Time-Sharing Meshing Toothed Conveyor Chain System

### 3.3.1. Initial Condition Analysis

After entering the 3D model and establishing constraints, Adams will analyze the initialization conditions to ensure that the simulation model meets all constraints. The initial condition analysis is achieved by solving the minimum value of the corresponding position, velocity, and acceleration objective function.


### 3.3.2. Meshing Simulation Model

When the double pitch time-sharing meshing toothed conveyor chain is meshed with the sprocket, the tooth shape parameters of the chain plate and the number of teeth of the sprocket have a great impact on the conveying characteristics of the double pitch time-sharing meshing toothed conveyor chain system. The more the number of teeth of the sprocket is, the more stable the transmission of the chain drive system is. In order to analyze the influence of the extension of the internal tooth profile of the chain plate on the meshing polygon effect of the double pitch time-sharing meshing toothed transmission chain, when the number of sprocket teeth is certain, the influence of the extension of the internal tooth profile on the tight side wave momentum of the double pitch time-sharing meshing toothed transmission chain system is established, respectively. Without considering the chain plate hole and pin shaft clearance, a three-dimensional parametric simulation model of the double pitch time-sharing meshing toothed conveyor chain system and the double pitch roller conveyor chain system is established by using Adams simulation software.


### 3.3.3. Influence of Tooth Profile Extension in Chain Plate on Tight Side Wave Momentum of Chain Drive System

The single pitch of the chain is 15.875 mm, the number of driving and driven sprocket teeth is 45, the pitch of the sprocket is 15.875 mm, and the protrusions are 0.05 mm, 0.10 mm, 0.15 mm, 0.20 mm, 0.25 mm, 0.30 mm, 0.35 mm, and 0.40 mm, respectively. The simulation model of the double pitch time-sharing meshing toothed conveyor chain system is analyzed. In the initial setting, the driving wheel speed is 4π/Z per second, and the simulation runs for 1s. In a meshing cycle, the fluctuation of the tight side center of the double pitch time-sharing meshing toothed conveyor chain is within a certain range. The larger the extension, the smaller the fluctuation of the tight side of the chain center, which is in line with the function of the extension of the inner tooth profile. The extension of the inner tooth profile can reduce the polygon effect. However, when the extension value is too large, the whole meshing is completely double pitch time-sharing meshing, and the inner tooth profile of the toothed conveyor chain is meshed. During meshing rotation, the inner tooth profile cannot shrink into the outer tooth profile of the adjacent chain link, and the meshing impact is large when meshing with the intermediate tooth. When the extension is very small, in the meshing process, the internal tooth profile meshing is transformed into the external tooth profile meshing of adjacent links in a very short time, so the effect of reducing the polygon is not obvious. Therefore, for the calculation example, the best internal tooth profile elongation is δ = 0.25 mm.


### 3.3.4. Comparative Analysis of Tight Edge Fluctuation between Double Pitch Roller Conveyor Chain System and Double Pitch Roller Conveyor Chain System

For the double pitch time-sharing meshing toothed conveyor chain system with a single pitch of 15.875 mm and double pitch of 31.67 mm and the double pitch roller conveyor chain system with a single pitch of 15.875 mm and double pitch of 31.75 mm, the number of teeth of the driving and driven wheels of the two conveyor chain systems is 45. In order to show generality, the extension is 0.15 mm. The simulation models of the two conveyor chain systems are analyzed. In the initial setting, the driving wheel speed is 4π/Z per second, and the simulation runs for 1s. In a cycle, two conveyor chains fluctuate around the center. The simulation analysis shows that the transverse wave momentum of the double pitch time-sharing meshing toothed conveyor chain is 113.19–113.53 mm, and the fluctuation range is 0.34 mm. The transverse wave momentum of the double pitch roller conveyor chain is 113.08–113.91 mm, and the fluctuation range is 0.83 mM. It can be concluded that the transverse fluctuation of the tight side of the double pitch time-sharing meshing toothed conveyor chain is 59% lower than that of the double pitch roller conveyor chain.


## 3.3.1. Initial Condition Analysis

After entering the 3D model and establishing constraints, Adams will analyze the initialization conditions to ensure that the simulation model meets all constraints. The initial condition analysis is achieved by solving the minimum value of the corresponding position, velocity, and acceleration objective function.


## 3.3.2. Meshing Simulation Model

When the double pitch time-sharing meshing toothed conveyor chain is meshed with the sprocket, the tooth shape parameters of the chain plate and the number of teeth of the sprocket have a great impact on the conveying characteristics of the double pitch time-sharing meshing toothed conveyor chain system. The more the number of teeth of the sprocket is, the more stable the transmission of the chain drive system is. In order to analyze the influence of the extension of the internal tooth profile of the chain plate on the meshing polygon effect of the double pitch time-sharing meshing toothed transmission chain, when the number of sprocket teeth is certain, the influence of the extension of the internal tooth profile on the tight side wave momentum of the double pitch time-sharing meshing toothed transmission chain system is established, respectively. Without considering the chain plate hole and pin shaft clearance, a three-dimensional parametric simulation model of the double pitch time-sharing meshing toothed conveyor chain system and the double pitch roller conveyor chain system is established by using Adams simulation software.


## 3.3.3. Influence of Tooth Profile Extension in Chain Plate on Tight Side Wave Momentum of Chain Drive System

The single pitch of the chain is 15.875 mm, the number of driving and driven sprocket teeth is 45, the pitch of the sprocket is 15.875 mm, and the protrusions are 0.05 mm, 0.10 mm, 0.15 mm, 0.20 mm, 0.25 mm, 0.30 mm, 0.35 mm, and 0.40 mm, respectively. The simulation model of the double pitch time-sharing meshing toothed conveyor chain system is analyzed. In the initial setting, the driving wheel speed is 4π/Z per second, and the simulation runs for 1s. In a meshing cycle, the fluctuation of the tight side center of the double pitch time-sharing meshing toothed conveyor chain is within a certain range. The larger the extension, the smaller the fluctuation of the tight side of the chain center, which is in line with the function of the extension of the inner tooth profile. The extension of the inner tooth profile can reduce the polygon effect. However, when the extension value is too large, the whole meshing is completely double pitch time-sharing meshing, and the inner tooth profile of the toothed conveyor chain is meshed. During meshing rotation, the inner tooth profile cannot shrink into the outer tooth profile of the adjacent chain link, and the meshing impact is large when meshing with the intermediate tooth. When the extension is very small, in the meshing process, the internal tooth profile meshing is transformed into the external tooth profile meshing of adjacent links in a very short time, so the effect of reducing the polygon is not obvious. Therefore, for the calculation example, the best internal tooth profile elongation is δ = 0.25 mm.


## 3.3.4. Comparative Analysis of Tight Edge Fluctuation between Double Pitch Roller Conveyor Chain System and Double Pitch Roller Conveyor Chain System

For the double pitch time-sharing meshing toothed conveyor chain system with a single pitch of 15.875 mm and double pitch of 31.67 mm and the double pitch roller conveyor chain system with a single pitch of 15.875 mm and double pitch of 31.75 mm, the number of teeth of the driving and driven wheels of the two conveyor chain systems is 45. In order to show generality, the extension is 0.15 mm. The simulation models of the two conveyor chain systems are analyzed. In the initial setting, the driving wheel speed is 4π/Z per second, and the simulation runs for 1s. In a cycle, two conveyor chains fluctuate around the center. The simulation analysis shows that the transverse wave momentum of the double pitch time-sharing meshing toothed conveyor chain is 113.19–113.53 mm, and the fluctuation range is 0.34 mm. The transverse wave momentum of the double pitch roller conveyor chain is 113.08–113.91 mm, and the fluctuation range is 0.83 mM. It can be concluded that the transverse fluctuation of the tight side of the double pitch time-sharing meshing toothed conveyor chain is 59% lower than that of the double pitch roller conveyor chain.


## 3.4. Dynamic Simulation Analysis of Double Pitch Time-Sharing Meshing Toothed Conveyor Chain System

Dynamics is to study that the vibration and noise of the double pitch time-sharing meshing toothed conveyor chain system change with the evolution of time under the action of meshing impact force, and the polygon effect of the double pitch time-sharing meshing toothed conveyor chain is the main cause of meshing impact. By studying the meshing impact force, Newton’s law of motion is used to study the influence on the double pitch time-sharing meshing toothed conveyor chain system.


### 3.4.1. Contact Force Model

The double pitch time-sharing meshing toothed conveyor chain system is composed of a driving and driven sprocket, a chain, and a tensioning device. The chain extends due to wear, and the tensioning device compensates for the wear elongation. Therefore, in the process of simulation, it is only necessary to establish a double pitch time-sharing meshing toothed conveyor chain system composed of driving and driven sprocket and chain. The driving and driven wheels in the simulation model carry out the predetermined relative motion through the contact force and friction between the chain and sprocket teeth, and the driving wheel sets the driving constraint of constant speed. Each section of the double pitch time-sharing meshing toothed conveyor chain is connected by multiple rows of chain pieces through pin shafts, and there is a guide plate in the middle of every other section. The guide plate plays a role in horizontal positioning and adjusting the strength between chain links and does not play a major role in the meshing process. Without affecting the calculation results, simplify the contact force simulation model and establish 5 × Model 6 double pitch time-sharing meshing toothed conveyor chain link simulation model. In the practical application of toothed chain for inner guide conveying, the outer chain plate and the pin shaft are interference fit, while all the other chain plates and guide plates are clearance fit with the pin shaft. Therefore, in order to make the simulation results true, we establish the geometric model of the link. The pin shaft of 6 chain links and two outer chain plates form one part, and the clearance between the inner chain plate and the pin shaft is considered, with a unilateral clearance of 0.01 mm.The meshing contact force of the double pitch time-sharing meshing toothed conveyor chain system is mainly considered in the simulation model, using the search algorithm. The search process is as follows: define a boundary circle whose center coincides with the center of the sprocket, then search the chain for the starting link and the ending link that may contact the sprocket, and then search the starting link and the ending link in the boundary circle in detail to observe the direct contact of the chain link. For the double pitch time-sharing meshing toothed conveyor chain and the linear tooth profile, there are three possible contacts between the sprockets of the double pitch time-sharing meshing toothed conveyor chain, namely, the circular arc linear contact between the inner tooth profile of the chain plate and the linear tooth profile of the sprocket, the linear point contact between the outer tooth profile of the chain plate (middle tooth profile) and the linear tooth profile of the sprocket, and the circular arc circular arc contact between the hole of the chain plate and the pin shaft. The double pitch roller conveyor chain conveying system is mainly arc-arc contact.


### 3.4.2. Contact Impact Analysis

In order to verify the rationality of the structure of the double pitch time-sharing meshing toothed conveyor chain and the reduction of the meshing impact by the tooth profile structure, the double pitch time-sharing meshing toothed conveyor chain with a single pitch of 15.875 mm and a sprocket tooth number of 45 and the double pitch roller conveyor chain are compared and analyzed. To analyze the meshing contact impact, only one meshing cycle needs to be analyzed, so the simulation model can be simplified.In the process of establishing the simulation model, the unilateral clearance between the chain plate hole and the pin shaft is considered to be 0.01 mm. The sprocket is the driving wheel, which rotates counterclockwise and rotates at a speed of 4π/Z degrees per second. In order to obtain the meshing impact between the chain plate and the sprocket and the tension of the tight chain during the operation of the chain drive system, it is necessary to establish contact pairs between the chain plate and the sprocket, and between the chain plate and the pin shaft In addition, in order to make the simulation process close to the running state of the conveyor chain system in reality, that is, to realize the horizontal movement state of the tight side chain, a 2Kn fixed tension is applied to the center of the chain plate pin to simulate the tension of the tight side chain. The extension of the tooth profile in the chain plate is 0.15 mm, 0.20 mm, 0.25 mm, and 0.30 mm, respectively. When the sprocket rotates at a constant speed of 4π/Z degrees, the contact force between the chain plates 2 and 3 of the double pitch time-sharing meshing toothed conveyor chain and the sprocket can be seen. When the extension of the tooth profile in the chain plate increases within a certain range, the meshing impact contact force decreases, but when it reaches a certain value, contact is found with the increase of the extension_ 3. There is no meshing impact force, and the meshing impact force is all in contact_ 2. At this point, explain contact_ 3. It does not participate in meshing. According to the simulation results, it conforms to the role of the inner tooth profile of the chain plate. When the extension is very small, the meshing of the inner tooth profile will soon be transformed into the meshing of the outer tooth profile, and the contact impact force will soon be changed from contact_ 2 convert to contact_ 3. As the extension increases, the conversion time increases, and it is consistent when the extension is 0.15–0.25 mm. However, when the extension reaches a certain value, the internal engagement cannot be converted to the external engagement. There is no contact impact on contact 3.The contact force of the double pitch time-sharing meshing tooth profile transmission link can show that, at the beginning of operation, the impact force of the contact between the inner tooth profile of link 2 and the sprocket is large, and link 1 and the sprocket do not contact without impact force. When the operation is 0.13s, link 1 and link 2 participate in the meshing at the same time and gradually transition to the meshing of the outer tooth profile of link 1. The impact force of link 1 is slightly greater than that of link 2. However, they are much smaller than the impact force of link 2 when it just runs. When it runs to about 0.5s, the external tooth profile meshing of link 1 is transformed into the internal tooth profile meshing of adjacent link 2. Link 1 disengages without impact force, while the impact force of link 2 in contact with the sprocket is instantaneous large, and link 2 gradually engages and locates to complete one-time meshing. The meshing impact force of the roller and sprocket of the double pitch roller chain is instantaneous contact meshing, and the initial meshing impact is large. The simulation results show that the maximum meshing impact force of the double pitch time-sharing meshing toothed conveyor chain is 4542.6 n, and the maximum meshing impact force of the double pitch roller conveyor chain is 8726.5 n. The meshing of the double pitch time-sharing meshing toothed conveyor chain system is stable, and the maximum impact force is 51.9% of the double pitch roller chain. Considering the influence of the internal tooth profile extension on the tight side wave momentum and the meshing impact force of the double pitch time-sharing meshing toothed conveyor chain system, the internal tooth profile extension of the double pitch time-sharing meshing toothed conveyor chain system with a single pitch of 15.875 mm and a sprocket tooth number of 45 is taken as 0.25 mm.


## 3.4.1. Contact Force Model

The double pitch time-sharing meshing toothed conveyor chain system is composed of a driving and driven sprocket, a chain, and a tensioning device. The chain extends due to wear, and the tensioning device compensates for the wear elongation. Therefore, in the process of simulation, it is only necessary to establish a double pitch time-sharing meshing toothed conveyor chain system composed of driving and driven sprocket and chain. The driving and driven wheels in the simulation model carry out the predetermined relative motion through the contact force and friction between the chain and sprocket teeth, and the driving wheel sets the driving constraint of constant speed. Each section of the double pitch time-sharing meshing toothed conveyor chain is connected by multiple rows of chain pieces through pin shafts, and there is a guide plate in the middle of every other section. The guide plate plays a role in horizontal positioning and adjusting the strength between chain links and does not play a major role in the meshing process. Without affecting the calculation results, simplify the contact force simulation model and establish 5 × Model 6 double pitch time-sharing meshing toothed conveyor chain link simulation model. In the practical application of toothed chain for inner guide conveying, the outer chain plate and the pin shaft are interference fit, while all the other chain plates and guide plates are clearance fit with the pin shaft. Therefore, in order to make the simulation results true, we establish the geometric model of the link. The pin shaft of 6 chain links and two outer chain plates form one part, and the clearance between the inner chain plate and the pin shaft is considered, with a unilateral clearance of 0.01 mm.The meshing contact force of the double pitch time-sharing meshing toothed conveyor chain system is mainly considered in the simulation model, using the search algorithm. The search process is as follows: define a boundary circle whose center coincides with the center of the sprocket, then search the chain for the starting link and the ending link that may contact the sprocket, and then search the starting link and the ending link in the boundary circle in detail to observe the direct contact of the chain link. For the double pitch time-sharing meshing toothed conveyor chain and the linear tooth profile, there are three possible contacts between the sprockets of the double pitch time-sharing meshing toothed conveyor chain, namely, the circular arc linear contact between the inner tooth profile of the chain plate and the linear tooth profile of the sprocket, the linear point contact between the outer tooth profile of the chain plate (middle tooth profile) and the linear tooth profile of the sprocket, and the circular arc circular arc contact between the hole of the chain plate and the pin shaft. The double pitch roller conveyor chain conveying system is mainly arc-arc contact.


## 3.4.2. Contact Impact Analysis

In order to verify the rationality of the structure of the double pitch time-sharing meshing toothed conveyor chain and the reduction of the meshing impact by the tooth profile structure, the double pitch time-sharing meshing toothed conveyor chain with a single pitch of 15.875 mm and a sprocket tooth number of 45 and the double pitch roller conveyor chain are compared and analyzed. To analyze the meshing contact impact, only one meshing cycle needs to be analyzed, so the simulation model can be simplified.In the process of establishing the simulation model, the unilateral clearance between the chain plate hole and the pin shaft is considered to be 0.01 mm. The sprocket is the driving wheel, which rotates counterclockwise and rotates at a speed of 4π/Z degrees per second. In order to obtain the meshing impact between the chain plate and the sprocket and the tension of the tight chain during the operation of the chain drive system, it is necessary to establish contact pairs between the chain plate and the sprocket, and between the chain plate and the pin shaft In addition, in order to make the simulation process close to the running state of the conveyor chain system in reality, that is, to realize the horizontal movement state of the tight side chain, a 2Kn fixed tension is applied to the center of the chain plate pin to simulate the tension of the tight side chain. The extension of the tooth profile in the chain plate is 0.15 mm, 0.20 mm, 0.25 mm, and 0.30 mm, respectively. When the sprocket rotates at a constant speed of 4π/Z degrees, the contact force between the chain plates 2 and 3 of the double pitch time-sharing meshing toothed conveyor chain and the sprocket can be seen. When the extension of the tooth profile in the chain plate increases within a certain range, the meshing impact contact force decreases, but when it reaches a certain value, contact is found with the increase of the extension_ 3. There is no meshing impact force, and the meshing impact force is all in contact_ 2. At this point, explain contact_ 3. It does not participate in meshing. According to the simulation results, it conforms to the role of the inner tooth profile of the chain plate. When the extension is very small, the meshing of the inner tooth profile will soon be transformed into the meshing of the outer tooth profile, and the contact impact force will soon be changed from contact_ 2 convert to contact_ 3. As the extension increases, the conversion time increases, and it is consistent when the extension is 0.15–0.25 mm. However, when the extension reaches a certain value, the internal engagement cannot be converted to the external engagement. There is no contact impact on contact 3.The contact force of the double pitch time-sharing meshing tooth profile transmission link can show that, at the beginning of operation, the impact force of the contact between the inner tooth profile of link 2 and the sprocket is large, and link 1 and the sprocket do not contact without impact force. When the operation is 0.13s, link 1 and link 2 participate in the meshing at the same time and gradually transition to the meshing of the outer tooth profile of link 1. The impact force of link 1 is slightly greater than that of link 2. However, they are much smaller than the impact force of link 2 when it just runs. When it runs to about 0.5s, the external tooth profile meshing of link 1 is transformed into the internal tooth profile meshing of adjacent link 2. Link 1 disengages without impact force, while the impact force of link 2 in contact with the sprocket is instantaneous large, and link 2 gradually engages and locates to complete one-time meshing. The meshing impact force of the roller and sprocket of the double pitch roller chain is instantaneous contact meshing, and the initial meshing impact is large. The simulation results show that the maximum meshing impact force of the double pitch time-sharing meshing toothed conveyor chain is 4542.6 n, and the maximum meshing impact force of the double pitch roller conveyor chain is 8726.5 n. The meshing of the double pitch time-sharing meshing toothed conveyor chain system is stable, and the maximum impact force is 51.9% of the double pitch roller chain. Considering the influence of the internal tooth profile extension on the tight side wave momentum and the meshing impact force of the double pitch time-sharing meshing toothed conveyor chain system, the internal tooth profile extension of the double pitch time-sharing meshing toothed conveyor chain system with a single pitch of 15.875 mm and a sprocket tooth number of 45 is taken as 0.25 mm.


## 4. Construction of Diagnosis Model Based on Deep Neural Network

With the continuous improvement of the complexity of data processing, artificial neural network has natural advantages in signal processing. Its excellent nonlinear characteristics, adaptive characteristics, the ability to learn from the environment in a supervised or unsupervised manner, and extensive global approximation ability make it a natural tool to solve adaptive and nonlinear signal processing problems. It has good fault tolerance, strong parallel computing capability, and distributed information storage capability. It has a wide range of applications, such as smart medicine [14–16], smart finance [17, 18], and smart transportation [19, 20]. At present, there are many neural network models, and RBF neural network is a popular application in fault diagnosis and prediction. This paper is based on RBF neural network for fault diagnosis.


### 4.1. Neural Network

#### 4.1.1. Artificial Neural Network

Artificial neural network belongs to one of the application branches of artificial intelligence. Artificial neuron is an important component of artificial neural network. Its function is to sum the input signals of neurons through the connection weight and then compare them with the fixed threshold through the activation function. If the value after the sum is less than the threshold, it will output 0; otherwise it will output 1. The common neural network is a forward network structure, and the training value is transferred to the hidden layer through the network. In the network, the input vector and output vector are in one-to-one correspondence. When the state of the network is updated, the output vector is obtained from the output layer.


#### 4.1.2. RBF Neural Network

RBF neural network belongs to local approximation network, which has strong pattern classification and self-learning ability. For local areas, the selection of the number of nodes and connection weights of only hidden layers affects the output of the network. In terms of structure, RBF neural network is a three-layer feedforward network with a hidden layer. The essence of its learning process is to find the best fitting hyperplane with the training data set in the weight space. RBF neural network is more suitable for online monitoring and diagnosis because of its shorter time to achieve the best fitting and higher real-time performance when training data sets.


#### 4.1.3. Construction of RBF Neural Network

The training process of the network first takes the number of extracted feature vectors as the number of nodes in the input layer and transmits them to the RBF neural network for training through the input layer. Secondly, by adjusting the relevant parameters between the hidden layer unit and the output unit to realize the corresponding relationship between input and output, the information of the network can be fully reflected. Figure1 shows the network training steps:(1)
Build RBF neural network. The numbers of input layers, output layers, and hidden layers are selected according to the vector dimension of the extracted feature vector and the number of selected fault types.(2)
Initialize the RBF neural network.(3)
Calculate the output value of hidden layer neurons.(4)
Calculate the output of neurons in the output layer.(5)
terative calculation of weight parameters.(6)
Calculate the result of network output.Figure 1
Method flowchart.


#### 4.1.4. Experimental Result

RBF neural network is used to train the data to achieve the purpose of fault diagnosis and state trend prediction. First, we construct samples according to the signal data obtained after feature extraction. Then we will divide the constructed data samples into training data set and test data set. After the division, we can start to create RBF neural network and set the parameters of RBF neural network. Before we input the data samples into the RBF neural network, we also need to normalize the training data and test data with the same parameters. Then the output value of our data samples after RBF neural network training should also be denormalized with the same parameters as the input. After completing the above series of operations, we can get the prediction value we need based on RBF neural network. We calculate the error index of RMSE and Mae to measure the prediction accuracy and compare the prediction accuracy of fault diagnosis and prediction combined with other intelligent control algorithms. Table1 shows that the proposed method achieves the best classification performance.Table 1
Comparison of results.
MAERMSESVM0.160.32RF0.100.24RBF0.040.10


## 4.1. Neural Network

### 4.1.1. Artificial Neural Network

Artificial neural network belongs to one of the application branches of artificial intelligence. Artificial neuron is an important component of artificial neural network. Its function is to sum the input signals of neurons through the connection weight and then compare them with the fixed threshold through the activation function. If the value after the sum is less than the threshold, it will output 0; otherwise it will output 1. The common neural network is a forward network structure, and the training value is transferred to the hidden layer through the network. In the network, the input vector and output vector are in one-to-one correspondence. When the state of the network is updated, the output vector is obtained from the output layer.


### 4.1.2. RBF Neural Network

RBF neural network belongs to local approximation network, which has strong pattern classification and self-learning ability. For local areas, the selection of the number of nodes and connection weights of only hidden layers affects the output of the network. In terms of structure, RBF neural network is a three-layer feedforward network with a hidden layer. The essence of its learning process is to find the best fitting hyperplane with the training data set in the weight space. RBF neural network is more suitable for online monitoring and diagnosis because of its shorter time to achieve the best fitting and higher real-time performance when training data sets.


### 4.1.3. Construction of RBF Neural Network

The training process of the network first takes the number of extracted feature vectors as the number of nodes in the input layer and transmits them to the RBF neural network for training through the input layer. Secondly, by adjusting the relevant parameters between the hidden layer unit and the output unit to realize the corresponding relationship between input and output, the information of the network can be fully reflected. Figure1 shows the network training steps:(1)
Build RBF neural network. The numbers of input layers, output layers, and hidden layers are selected according to the vector dimension of the extracted feature vector and the number of selected fault types.(2)
Initialize the RBF neural network.(3)
Calculate the output value of hidden layer neurons.(4)
Calculate the output of neurons in the output layer.(5)
terative calculation of weight parameters.(6)
Calculate the result of network output.Figure 1
Method flowchart.


### 4.1.4. Experimental Result

RBF neural network is used to train the data to achieve the purpose of fault diagnosis and state trend prediction. First, we construct samples according to the signal data obtained after feature extraction. Then we will divide the constructed data samples into training data set and test data set. After the division, we can start to create RBF neural network and set the parameters of RBF neural network. Before we input the data samples into the RBF neural network, we also need to normalize the training data and test data with the same parameters. Then the output value of our data samples after RBF neural network training should also be denormalized with the same parameters as the input. After completing the above series of operations, we can get the prediction value we need based on RBF neural network. We calculate the error index of RMSE and Mae to measure the prediction accuracy and compare the prediction accuracy of fault diagnosis and prediction combined with other intelligent control algorithms. Table1 shows that the proposed method achieves the best classification performance.Table 1
Comparison of results.
MAERMSESVM0.160.32RF0.100.24RBF0.040.10


## 4.1.1. Artificial Neural Network

Artificial neural network belongs to one of the application branches of artificial intelligence. Artificial neuron is an important component of artificial neural network. Its function is to sum the input signals of neurons through the connection weight and then compare them with the fixed threshold through the activation function. If the value after the sum is less than the threshold, it will output 0; otherwise it will output 1. The common neural network is a forward network structure, and the training value is transferred to the hidden layer through the network. In the network, the input vector and output vector are in one-to-one correspondence. When the state of the network is updated, the output vector is obtained from the output layer.


## 4.1.2. RBF Neural Network

RBF neural network belongs to local approximation network, which has strong pattern classification and self-learning ability. For local areas, the selection of the number of nodes and connection weights of only hidden layers affects the output of the network. In terms of structure, RBF neural network is a three-layer feedforward network with a hidden layer. The essence of its learning process is to find the best fitting hyperplane with the training data set in the weight space. RBF neural network is more suitable for online monitoring and diagnosis because of its shorter time to achieve the best fitting and higher real-time performance when training data sets.


## 4.1.3. Construction of RBF Neural Network

The training process of the network first takes the number of extracted feature vectors as the number of nodes in the input layer and transmits them to the RBF neural network for training through the input layer. Secondly, by adjusting the relevant parameters between the hidden layer unit and the output unit to realize the corresponding relationship between input and output, the information of the network can be fully reflected. Figure1 shows the network training steps:(1)
Build RBF neural network. The numbers of input layers, output layers, and hidden layers are selected according to the vector dimension of the extracted feature vector and the number of selected fault types.(2)
Initialize the RBF neural network.(3)
Calculate the output value of hidden layer neurons.(4)
Calculate the output of neurons in the output layer.(5)
terative calculation of weight parameters.(6)
Calculate the result of network output.Figure 1
Method flowchart.


## 4.1.4. Experimental Result

RBF neural network is used to train the data to achieve the purpose of fault diagnosis and state trend prediction. First, we construct samples according to the signal data obtained after feature extraction. Then we will divide the constructed data samples into training data set and test data set. After the division, we can start to create RBF neural network and set the parameters of RBF neural network. Before we input the data samples into the RBF neural network, we also need to normalize the training data and test data with the same parameters. Then the output value of our data samples after RBF neural network training should also be denormalized with the same parameters as the input. After completing the above series of operations, we can get the prediction value we need based on RBF neural network. We calculate the error index of RMSE and Mae to measure the prediction accuracy and compare the prediction accuracy of fault diagnosis and prediction combined with other intelligent control algorithms. Table1 shows that the proposed method achieves the best classification performance.Table 1
Comparison of results.
MAERMSESVM0.160.32RF0.100.24RBF0.040.10


## 5. Conclusion

In this paper, three-dimensional modeling of the newly designed double pitch time-sharing meshing toothed conveyor chain and linear tooth profile sprocket is carried out by using three-dimensional software. Through the interface between Adams and pro/e, the assembled double pitch time-sharing meshing toothed conveyor chain, linear tooth profile sprocket system, and double pitch roller conveyor chain system are introduced into Adams, respectively. The kinematic model and meshing impact dynamic model of the two chain transmission systems are established by using multibody dynamics technology, and the influence of internal tooth profile elongation parameters on the system and the superior performance of the new conveyor chain system and the traditional conveyor chain system are analyzed. In addition, a novel fault diagnosis method of double pitch time-sharing meshing toothed conveyor chain transmission system based on neural network model is proposed in this paper.Some achievements have been made in the parameter design, meshing theory, simulation analysis, and bench test of the double pitch time-sharing meshing toothed conveyor chain system, and the laboratory research stage has been completed. The double pitch time-sharing meshing toothed conveyor chain system can be further studied in the following aspects, so that the toothed chain system can be more perfectly applied to the chain conveyor. In the process of structural design of double pitch time-sharing meshing toothed chain, the pin shaft of variable pitch time-sharing meshing toothed chain is further designed, so that the excellent characteristics of toothed chain are widely used in conveyors. The test of the double pitch time-sharing meshing toothed conveyor chain system made in this paper is carried out on the closed force flow chain test-bed. By increasing the load to simulate the self-weight and the friction generated by the load, the actual working conditions can be simulated. However, if conditions permit in the future, the noise test and durability wear test of the double pitch time-sharing meshing toothed conveyor chain system will be further carried out on the workshop conveyor [21–23].



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*Source: 8159609-2022-09-19.xml*