Introduction. The transmission changes the driving wheel’s torque and speed by changing the transmission ratio, which plays a vital role in the vehicle transmission system. As an important component parts, the synchronizer effectively reduces the shift of shock, vibration, and noise, greatly improving the transmission shift quality. Therefore the performance of the synchronous directly influences the transmission control comfort and stability. According to the investigation, the failure rate in use of the gearbox synchronizer is high, while the maintenance department only restores synchronizer function by the repair and replacement method, without analyzing its failure mechanism [1, 2]. As a result, the high failure rate of the synchronizer reduces the reliability of the whole vehicle. As the synchronizer is a compact and complex system in the transmission, it is very difficult to obtain some data signals in the working process by traditional testing methods, and it is very difficult to analyze the working state of the synchronizer currently. At present, there are few references on relevant synchronizers at home and abroad, and the design theory of synchronizer is basically in the stage of experience design. The parameters of synchronizer are given on the premise of ensuring reliable gear shift and satisfying the requirements of life, without comprehensive research and analysis on the performance of synchronizer. With the wide application of multidisciplinary co-simulation technology in vehicles, the problem of low reliability caused by a high failure rate of the synchronizer is effectively solved [3, 4]. The MSC.Patran software applied in this paper is a professional finite element analysis software. The software integrates engineering design, engineering analysis, result evaluation, and other functions into one, which can realize mesh generation, CAD geometric transformation, and finite element solution analysis.

Authors [3] established a dynamic model and simulated for the shift process of planetary gear transmission [4], but did not analyze the synchronizer which playing a very key role in gear shift. In this paper, a virtual prototype model of the gearbox synchronizer is established, the finite element analysis and evaluation of the gearbox synchronizer is carried out by using the MSC.Patran software, and the fatigue life prediction and analysis model of the gearbox synchronizer pin is established, which provides an important theoretical basis for fault prediction and optimal design of the gearbox synchronizer.

1. Structure and Working Principle of Transmission Synchronizer. Synchronizer is an important part of vehicle transmission, which is divided into atmospheric, inertia, and inertia booster. In this paper, the study of transmission uses an inertial synchronizer, which main and driven parts are combined after reaching the same speed when shifted, reducing the impact and noise, enabling a smooth shift, and extending the transmission gear life [5, 6].

Figure 1 shows the working principle of a transmission synchronizer, the synchronizer is composed of connecting gear, sliding gear sleeve, locator, synchronizer body, fork ring, and pin. When in gear, the working process is as follows. In the first stage, the control device drives the fork ring, pin, and sliding gear sleeve, and drives the synchronizer body to move towards the gear hanging direction together through the locator. When the cone clearance between the synchronizer and the driving gear disappears, the synchronizer stops moving. In the second stage, because the synchronous speed is higher (lower) than the speed of the driving gear, the driving gear drives the synchronizer body to turn an angle slower (faster) than the pin by virtue of the friction effect on the cone surface, the front (back) wall of the special hole presses the pin, and sticks the pin, preventing the pin and the sliding gear sleeve moving towards the gear hanging direction, and avoiding the forced gear hanging under the circumstance of inconsistent speed of the gear ring. At the same time, the vehicle with large inertia forces synchronizer is decelerated or accelerated by friction. When the speed of the synchronizer drops (rises) to be consistent with the driving gear, the sliding friction is terminated, and the resistance of the special hole of the synchronizer body to the pin also disappears, allowing the pin and the sliding gear sleeve to move towards the gear. In the third stage, the gear ring meshing is completed [7, 8].

Fig. 1.
figure 1

The operating principle of the synchronizer: (1) connecting gear, (2) sliding gear sleeve, (3) positioner, (4) synchronizer body, (5) fork ring, and (6) pin.

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2. Reliability Data Collection and Analysis of Transmission Synchronizer. Transmission reliability data collection and analysis provides a decision basis for the reliability management, plays an important role in reliability engineering. The reliability data in the use stage of the transmission synchronizer reflects the use and environmental conditions of the transmission. The data is the final test of the reliability of the transmission synchronizer, and also provides useful data support for the reliability design of new products. The most common method of reliability data collection and analysis is failure mode, effects, and criticality analysis (FMECA), which is summarized in engineering practice. It is an analysis technique based on failure mode and aiming at the influence or consequence of failure. It analyzes the different failure of each component on the system work, the influence of the weak link in the design of comprehensive identification and key projects, and provides basic information for evaluating and improving the reliability of system design [9].

In this paper, the failure mode, effects and criticality analysis of a transmission synchronizer are analyzed, and the key important components of FMECA analysis table is established, as shown in Table 1 [10].

Table 1. FMECA of Transmission Synchronizer
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The synchronizer pin is an important part of the gear shifting mechanism in the transmission system. Its function is to transfer the friction torque to the A-axis system before in gear, in coordination with the synchronizer body. After in gear, it prevents the sliding gear sleeve from getting out of gear. Table 1 shows that the synchronizer pin failure level is high, the consequences are serious. The common failure mode is head fatigue fracture, as shown in Fig. 2. Figure 2a presents the fracture diagram, and Fig. 2b shows the microstructure of fracture. In this paper, the failure mechanism of the synchronizer pin is analyzed, and the fatigue life of the synchronizer pin is predicted by the co-simulation technology, which provides an important theoretical basis for further optimization design [10].

Fig. 2.
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The fracture of the synchronizer: (a) the fracture diagram; (b) microstructure of fracture.

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3. Research on Life Prediction of Transmission Synchronizer Based on Multi-Field Collaborative Technology. In this paper, the reliability data of the transmission synchronizer under different working conditions is collected and analyzed. According to the failure forms of the synchronizer in use, the weak links corresponding to the synchronizer are established, and dynamic analysis, life prediction, and structural optimization are studied by multidisciplinary co-simulation. The flow chart of fatigue life prediction of gearbox synchronizer is shown in Fig. 3 [6, 10].

Fig. 3.
figure 3

Co-simulation flow chart of gears’ fatigue life prediction based on interface.

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4. The Fatigue Life Prediction Research of Synchronizer Pin.

4.1. The Virtual Prototype Model of Synchronizer. The virtual prototype technology is an effective means of virtual prototype design and simulation analysis. MSC.ADAMS is a large simulation and analysis software of mechanical system, with powerful modeling and analysis function. The dynamics simulation software ADAMS of MSC and mechanical CAD software Pro/E of PTC are selected as modeling tools, and the interface between them adopts the special interface Mechanism/Pro of MSC. First, the models of main and passive gears and gear shafts are built and assembled in Pro/E. During assembly, the two tooth surfaces initially engaged should be as tangent as possible to reduce the error caused by the initial state of the model during simulation analysis. The virtual prototype model of a transmission synchronizer is shown in Fig. 4 [10, 11].

Fig. 4.
figure 4

Structural pattern of the synchronizer.

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4.2. The Constraints of Synchronizer Pins. As shown in Fig. 5, when in gear, the fork ring gives the axial thrust P of the synchronizer pin to enable it to be in gear, while the friction force F of the synchronizer pin prevents it from being in gear, and the friction force F by bevel of ring groove of synchronizer body. The ratio of P to F depends on the angle β at the point of contact between pin and groove, i.e., self-locking depends on the value of β.

Fig. 5.
figure 5

Schematic diagram of synchronizer locking angle calculation.

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The synchronizer body is a free body, and the forces and torques on it. It is assumed that the shift of axial thrust P through the pin, and the axial force transmitted by the positioner is omitted; N is the normal reaction of pin from synchronizer ring groove, F is friction of pin from synchronous ring groove, Mm is the moment passed between sliding gear sleeve and pin is the moment of friction of synchronizer [10]:

$$ {M}_m=\frac{F\upmu {R}_m}{\sin \upalpha}, $$
(1)

where α is half-angle of friction cone, μ is coefficient of friction between working cones, Rm is mean radius of friction cone, and F is the axial shifting force acting on the synchronizer.

To simplify the spatial force system to a plane force system, a synchronizer pin represents all the pins and the circular force Q instead of Mm at the radius Rx,

$$ Q=\frac{M_m}{R_x}=\frac{P\upmu {R}_c}{R_x\sin \upalpha}, $$
(2)

where Rc is average radius of the friction cone. Assuming Rx = Rc, we get

$$ Q=\frac{P\upmu}{\sin \upalpha}. $$
(3)

Now there are four forces on the pin, P, Q, N, and F, forming into a plane force system, as shown in Fig. 5.

Each force projection to the direction of N and F, then

$$ \left\{\begin{array}{l}P\sin \upbeta +Q\cos \upbeta =N,\\ {}P\sin \upbeta +Q\cos \upbeta =F\le fN,\end{array}\right. $$
(4)

N is eliminated from the two equations,

$$ f\left(P\sin \upbeta +Q\cos \upbeta \right)\ge P\cos \upbeta -Q\sin \upbeta, $$
(5)
$$ \frac{fp+Q}{P- fQ}\ge \cot \upbeta . $$
(6)

Substitute Eq. (3) in Eq. (6), and simplify

$$ \cot \upbeta \le f+\frac{\upmu}{\sin \upalpha}, $$
(7)
$$ \upbeta \ge \operatorname{arccot}\left(f+\frac{\upmu}{\sin \upalpha}\right). $$
(8)

That is, synchronize previous self-locking conditions.

After synchronization, the force is changed. At this time, the sliding stops and the friction torque is only used to drive the parts of the axis system to rotate, not reach the maximum value of Eq. (1):

$$ {M}_m<<\frac{P\upmu {R}_c}{\sin \upalpha}. $$
(9)

Equation (3) takes the following form:

$$ Q<<\frac{P\upmu}{\sin \upalpha}. $$
(10)

Omitting Q, we get a common problem of friction angle. The equilibrium equation of force is

$$ \left\{\begin{array}{l}P\sin \upbeta =N,\\ {}P\cos \upbeta >{F}_{\mathrm{max}}= fN.\end{array}\right. $$
(11)

This yields,

$$ \upbeta <\operatorname{arccot}f. $$
(12)

Finally, to achieve the conditions of self-locking before the synchronization and non-self-locking after synchronization, β must satisfy the following nonequality:

$$ \operatorname{arccot}\left(f+\frac{\upmu}{\sin \upalpha}\right)\le \upbeta <\operatorname{arccot}f. $$
(13)

4.3. Simulation Analysis of Fatigue Life of Synchronizer Pin.

4.3.1. Finite Element Analysis of Synchronizer. MSC/Patran is a pre- and post-processing software for finite element analysis. It can easily complete the work of the meshing and model description by a graphical interface, freeing engineering analysts from heavy data preparation work; and the calculated results can be provided to users in a variety of ways, so that users can easily obtain information and complete post-processing. At present, the software has been widely used in aerospace, automotive, shipbuilding, national defense, and other fields. According to the design specification of the synchronizer pin, the material data on a synchronizer pin is as follows: the material of the synchronizer pin is 20Cr2Ni4A, and its physical properties are σb = 1175 MPa, σs = 1080 MPa, E = 206 GPa, Poisson’s ratio is 0.29, and the density is 7.88·10–6 kg/mm3.

The material composition of 20Cr2Ni4A is consistent with that of SAE4340-350b-QT. The cyclic stress-strain relationship and S–N curve of 20Cr2Ni4A can be obtained by referring to the fatigue characteristics of SAE4340-350b-QT, as shown in Figs. 6 and 7 [10]. The fatigue characteristic data of the part can be created by means of correction coefficient, according to the fatigue characteristics of 20Cr2Ni4A material.

Fig. 6.
figure 6

The cycle stress–strain curve of 20Cr2Ni4A material.

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Fig. 7.
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The S–N curve of 20Cr2Ni4A material.

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The solid model established in Pro/E was imported into MSC.Patran through stp file, and the finite element mesh was divided. The finite element analysis model by MSC.Patran is shown in Fig. 8 [12, 13]. According to the stress analysis and the structure of the pin, the load of the pin can be simplified to the action of P, N, and F, and the lower end is fixed at the joint of the sliding gear sleeve, when calculating the stress and strain in the finite element software, as shown in Fig. 9.

Fig. 8.
figure 8

The pin mesh.

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Fig. 9.
figure 9

Boundary condition and load on the pin.

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Even so, the force on the pin is very difficult to impose in Patran. For example, the force F is a friction force with a small area of contact with the synchronizer body, Saint-Venant’s principle is adopted here to treat the force F and to apply it uniformly to the area of force P.

First, the geometric model, finite element meshing, material properties, loading, and boundary conditions are established for the synchronizer pin. Second. Then, finite element simulation analysis and calculation were carried out to generate the stress distribution cloud map of the synchronizer pin, as shown in Fig. 10 [10, 12].

Fig. 10.
figure 10

Stress distribution in the pin.

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The maximum stress value 52.8 MPa is far less than σb and σs of the material of the pin, which can obtain from the stress showed in Fig. 10. Therefore, the pin will not break from the static design, while the pin will have fatigue fracture in practical applicatio. It is of practical significance to study the fatigue life prediction of pins under working load [14, 15].

4.3.2. Calculation of Fatigue Life of Synchronizer Pin under Working Load. To determine the working load of the synchronizer pin, the maximum gear force is obtained by simulation when analyzing two- and three-gear of synchronizer body.

It is worth noting that:

(1) Gear is a dynamic impact process. According to the material mechanics, the stress and deformation of the component under the sudden impact load are twice higher than those under the static load, so the load should be multiplied by 2 times in processing.

(2) Although the interval between engaging and picking or shifting is short, the stress of the pin is basically in an alternating state for a long time. For this reason, the force of the pin is simplified to receive an alternating load, as shown in Fig. 11. Figure 12 shows the distributed contour of fatigue life of the synchronizer pin under the working load of Fig. 12 [13,14,15].

Fig. 11.
figure 11

The load suffered by the pin.

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Fig. 12.
figure 12

The distributed contour of fatigue life.

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According to the distributed contour of fatigue life of pins under working load, the fatigue life of the most dangerous part of pins is 59,591 working cycles. The fatigue life under working load is converted into the mileage of transmission by the Eq. (14):

$$ {L}_s= ntV, $$
(14)

where Ls is mileage (in km), n is the number of load cycles, t is load spectrum time in hours, and V is driving speed (in km/h).

It can be concluded that the life of the pin is 6788.1 km running in third gear on the three-level road surface, based on the time and speed (25.63 km/h) of the load spectrum.

Conclusions. In this paper, the force and motion of the gearbox synchronizer are analyzed, the finite element analysis and calculation of the synchronizer are carried out by using the fatigue simulation method, and the fatigue life of the gearbox synchronizer is analyzed. The research in this paper provides important theoretical support for the parameter optimization design and reliability design of synchronizer.