Introduction

High-speed trains are a crucial component of contemporary railroad transportation, and their dependability and safety directly affect the security of the lives and property of their passengers1. High-speed trains depend heavily on their braking system, and the braking effect and general operational safety are significantly impacted by the functionality and service behavior of the brake pads that link to the rivets2,3. The braking effect and overall operating safety are significantly impacted by the performance and service behavior of the brake pads connecting rivets, which are an essential component of the high-speed train’s braking system. As the speed of the train continues to increase, the working environment of the braking system becomes increasingly demanding. During its long-term service, the rivets may experience problems such as fracture, fatigue and corrosion4,as shown in Fig. 1. Consequently, a thorough investigation of the service behavior of the rivets attached to the brake pads of high-speed trains can serve as a crucial foundation for enhancing the braking system’s dependability, extending the equipment’s service life, and offering scientific backing for the creation of appropriate maintenance protocols and standards.

Fig. 1
figure 1

Failure of high-speed trains and connectors failure.

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Types of rivet failure

Accidents induced by riveting failures are widespread. Connection failure results from rivet breaking, which is typically brought on by overloading, poor design, or material flaws. The cyclic loads rivets experience in high-strength applications like high-speed railroads, aircraft, and automobiles raise the possibility of fatigue failure5. Many researchers have studied rivets failure and its causes in great detail. In order to identify the three primary causes of riveted assembly failure tension on the plate, shear on the rivet, and pressure on the rivet hole. Sire S6 et al. performed tensile tests on rigid riveted assemblies. They came to the conclusion that the friction strength of the component parts also affects riveted assembly failure. Jasinski J J7 et al. used material testing and finite element analysis to examine the fracture mechanism of E215 mild steel tube rivets in vehicles. The findings demonstrated that, in addition to structural flaws in the material brought on by incorrect final heat treatment parameter selection, the rivet cracking was caused by excessive critical stresses in the rivet flange during tube machining, final riveting, and molding. After conducting fatigue experiments on rivets at three distinct stress levels 90, 120, and 160 MPa. Armani E8 et al. examined the fatigue life and critical fracture size of each specimen and came to the conclusion that through-hole cracking rises as applied stress increases. To examine the mechanical characteristics of riveted street joints with varying interference fit sizes. Xingxing Wang et al. created a transverse ultrasonic vibration-assisted riveting technique9. The findings indicated that the ideal riveting process parameters could be accurately predicted by the quantitative optimization method, and that the tensile strength of the riveted parts rose as the interference fit riveting dimensions increased. Using a combination of experiments and finite element analysis techniques, Korbel Adam10 et al. examined how riveting process parameters affected the clamping stress, residual stress, and clamping force of rivets. They came to the conclusion that the site of fatigue crack initiation is influenced by the clamping force and residual stress in riveted joints. In order to determine the parameter combination and effective parameters for the greatest residual stress field. Pedram Z11. et al. used finite element simulation and analysis to compare and assess the combination of multiple sets of riveting process parameters. Both theoretical calculations and finite element analysis were used to calculate the stress intensity factor, and the results of both approaches were ultimately found to be consistent. The optimal model of the cost function and parameter definition level was obtained by Nejad, R. M12,13. et al. using the Taguchi method and the finite element method. The finite element method was used to examine the effects of pertinent rivet geometrical parameters, such as rivet material, distribution location, and rivet geometry, on the fatigue life. The findings indicate that the connection’s fatigue failure is significantly influenced by the service load, residual stress, and design arrangement.

Effect of the service environment on fatigue failure of rivets

However, the coupling of the residual stresses created by the riveting process with external multiphysical fields also plays a major role in the fatigue failure of rivets. The fatigue life of rivets will be significantly impacted by various service occasions, including temperature fluctuations, vibration environments, humidity, and other variations14. Therefore, Natascha Z. Borba15 et al. conducted a study on the microstructure and mechanical properties of the rivets during the friction process of Ti-6Al-4 V (rivets) and glass fiber reinforced polyester (GF-P) through two levels of energy input. When the temperature was changed from 460 ± 130 °C to 758 ± 56 °C, it was discovered that the grain boundaries in the heat-affected zone of the rivets with β-phase precipitation of equiaxial α-crystals produced a 24% increase in microhardness over the base material. In addition to studying the failure and fracture microscopic mechanisms of single lap joints of composite laminates under quasi-static and cyclic stress, N. Z. Borba16 et al. experimentally examined the mechanical behavior of riveted joints under various loading situations. Detachment of rivets from the composite material’s holes is the primary cause of joint failure. Adhesion/cohesion failure of the extruded material and rivet penetration failure follow. Using numerical analysis, Vijayamohanan M. M17. et al. examined interference fit rivets of glass laminated aluminum reinforced epoxy numerical (GLARE) composites and discovered that the interference fit greatly enhances the composite rivets’ tensile and impact characteristics under challenging loading circumstances. Qu Junsheng18,19 et al. developed a three-dimensional thermal-mechanical coupling model of high-speed wheel-mounted brake discs with bolt connections and contact relationships in order to identify the causes of fatigue cracking on the edge of bolt holes on the surface of brake discs of high-speed trains. They also tested the axial load of bolts connected to brake discs under various emergency braking initial speeds and thoroughly examined the evolution of the bolts’ axial load during the braking process. The findings demonstrate that as the initial speed of emergency braking increases, the combination of impact loads and working conditions causes the disk body to thermally deform. This, in turn, raises the axial tensile load on the connecting bolts, causing the bolts to loosen and fracture. For thermally driven riveted joints, Axel L20. et al. developed a modeling technique for static strength and failure mode. A nonlinear finite element analysis modeling framework was used to examine the rivet structure, geometry, material characteristics, and preload of thermally driven rivets. It was examined how rivet preload affected the rivets’ mechanical reaction. The findings demonstrated that as the rivets’ preload increased, so did the joint’s strength. Jan G21 et al. applied varying loads to fasteners of various materials and utilized numerical analysis to examine the impact of partially cracked bonded rivets on fastener loads. According to the analysis’s findings, hybrid rivets with partially fractured bonded rivets do not affect the fastener load or the rivets’ fatigue life.

Tools for monitoring and enhancement initiatives

Based on the above problems some scholars have also proposed monitoring and improvement programs. A numerical prediction technique for evaluating the fatigue life of intricate riveted aluminum alloy structures under variable amplitude loading was presented by Francis Corriveau22 et al. The suggested approach can be used to predict the life of rivets and structures subjected to variable amplitude loads in a satisfactory manner without the need for intricate finite element models of the riveted joints. It is based on the combination of fatigue testing and structural stress methods to generate S-N curves. Haoguang Wang23 et al. presented a Gaussian weighted correction post-processing approach and suggested a decentralized target center and low overlap rate marking method using segmentation as an example for autonomous rivet fracture identification. The experimental results show that this method outperforms the existing cutting-edge algorithms. The recall rate and mAP0.5 have reached 86.4% and 90.3% respectively, and this method is highly versatile. In order to achieve non-contact monitoring of the quality of self-punching riveting forming, Sen Lin24 et al. combined deep learning algorithms. They created a lightweight convolutional neural network with greater precision and less computation, and they demonstrated through comparative experiments that Su Shang’s monitoring improved by 4.5% in accuracy and 1.4% in recall rate, offering a more efficient way to monitor the quality of riveting forming. The effects of factors pertaining to the design and manufacturing of riveted joints attached to longitudinal plates in the fuselage of a pressurized transport aircraft were experimentally examined by A. Skorupa25 et al. The findings demonstrated that the kind of rivet and the amount of squeezing force were connected to the crack initiation location and fracture path, whereas increasing the squeezing force improved the rivets’ fatigue characteristics. The fatigue life of 2024 aluminum alloy single and double-head riveted bus rivets was experimentally studied by Hadi Moslemi26 et al., who also used numerical methods to forecast the rivets’ fatigue life. Three primary failure modes were identified by the experiments: mixed-mode fracture, fracture at the rivet hole’s edge, and fracture in the folded region. The finite element analysis results matched the experiments, and the rivets’ stress concentration coefficient increased longitudinally, lowering their service life. In order to optimize the number and spacing of locking bolts and prevent tensile, shear, and other static failures under the specified load conditions, Dailin Zhang27 et al. proposed a new locking bolt structure layout optimization scheme based on the sub-model, parametric model, and multi-strategy integration. This method also increases the safety margin of the optimized bolt structure by 59.81%. Rośkowicz M. R28. et al. computed the stress distribution of rivets numerically and used static and fatigue testing to confirm the viability of blind rivets and hybrid rivets. It was discovered that the fatigue life of aluminum alloy components was increased by using titanium-driven blind bolts with pins rather than standard hammer rivets. The fatigue life of repaired wing structures can be tripled by using customized hybrid rivets (rivets and adhesive) in place of regular rivets.

Nonetheless, riveting parameters, rivet service life under single operating conditions, and their improvement programs have been the subject of further in-depth research by both domestic and international experts. Actually, cyclic loading, high temperatures, vibration, and other multi-physical field coupling are the most common problems that riveted components encounter in engineering applications, particularly in the fields of high-speed trains, airplanes, cars, and so forth. High-speed train brake pads connecting rivets are the subject of this paper. First, the riveting process for high-speed train connecting pads has complex characteristics and high quality requirements. Secondly, there are residual stress, temperature, and relative motion of the components between complex factors like the rivets’ joint role during the braking process. It is also challenging to monitor rivets in real-time through the state of service test, and the rivets for the fatigue failure of the study have brought significant challenges. Few researchers have thoroughly examined the service behavior of connecting rivets in the braking process of high-speed train connecting brake pads because it is challenging to create a simulation model of the high-speed train braking process and it is computationally expensive.

In order to ascertain the time-varying law of each physical field and the causes of the riveting service process, this paper uses the finite element simulation analysis method to simulate the riveting process of brake pads and the service behavior of rivets under various braking conditions. In order to determine the residual compressive stresses following riveting, a finite element model of riveting brake pads is first created based on the theory of interference fit riveting, which analyzes the link between geometric characteristics and stresses in the riveting process. Second, create a simplified mechanical model of rivets used in train braking, theoretically examine the loads placed on them during service, add the riveted rivets to the brake pads’ heat-force coupling finite element model for braking simulation, and examine the patterns of physical fields that change over time, including displacement, temperature field, rivet contact stresses, etc. And the causes of these variations in the various starting braking speeds. The investigation of this issue may yield fresh concepts for the subsequent stage of structural optimization and the failure analysis of high-speed train brake pads.

Theoretical analysis of riveting process

Interference matching riveting theory

By creating an interference fit between the rivet and the workpiece, interference fit riveting can increase mechanical stiffness and strength. Interference fit riveting can be used to fix and fasten brake pads on high-speed trains and increase the stability and dependability of brake pads. The four stages of the interference fit riveting process are the rebound deformation stage, the cap forming stage, the rivet static stage, and the rivet elastic-plastic deformation stage. As illustrated in Fig. 2, consider the riveted sections of a rivet in the brake pads of a high-speed train.

Fig. 2
figure 2

The riveting procedure for interference fit.

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The rivet in the riveting punch can be thought of as a cylinder force under the action of local upsetting, which is related to the symmetry problem, when the riveting force is applied to cause its deformation process. A cylindrical coordinate system is established in the riveting bar on the upper surface of the arbitrary position of a point M(r, θ, z), as illustrated in Fig. 3a. The rivet assembly is placed before the center axis of the rivet bar and the upper riveting hole location of the center of the circle for the origin, the direction of the nail bar’s diameter for the y-axis, and the direction of the nail bar’s axis for the z-axis. Any point M after riveting has the coordinate M‘(r’,θ’,z’), and Fig. 3b displays the coordinate system following riveting assembly.

Fig. 3
figure 3

An analytical calculation of riveting force using a schematic picture of the coordinate system.

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The equilibrium differential Eq. in the cylindrical coordinate system are established for the point M:

$$\frac{{\partial \sigma_{r^{\prime}} }}{{\partial_{r^{\prime}} }} + \frac{{\partial \tau_{z^{\prime}r^{\prime}} }}{{\partial_{r^{\prime}} }} + \frac{1}{r^{\prime}}\frac{{\partial \tau_{\theta ^{\prime}r^{\prime}}^{{}} }}{{\partial \theta{\prime} }} + \frac{{\sigma_{r^{\prime}} - \sigma_{\theta ^{\prime}} }}{r^{\prime}} = 0$$
(1)

Where,σr’ is the radial force on the rivet; σθ’ is the annular stress on the rivet; r’ is in the radial position coordinate; θ’ is in the annular position coordinate; z’ is in the axial position coordinate; τz’r’ and τθ’r’are the shear stresses.

The annular positional stress state is axisymmetric and the distributed stresses cancel each other out there:

$$\tau_{{\theta{\prime} r{\prime} }} = \tau_{{\theta{\prime} z^{\prime}}} = 0$$
(2)

The stress component is independent of the value of θ’ coordinates. Therefore, the partial derivatives of θ’ are all zero. Assuming that the nail rod is uniformly deformed in the process of rivet upsetting, there is σr’=σθ’, so the simplified Eq. (1) can be obtained:

$$\frac{{\partial \sigma_{r^{\prime}} }}{{\partial_{r^{\prime}} }} + \frac{{\partial \tau_{z^{\prime}r^{\prime}} }}{\partial z^{\prime}} = 0$$
(3)

The yield strength is calculated from the Mises yield condition as:

$$(\sigma_{r^{\prime}} - \sigma_{z^{\prime}} )^{2} + 3\tau_{z^{\prime}r^{\prime}}^{2} = \sigma_{s}^{2}$$
(4)

Where σz’ is the axial stress on the rivet stem; σs is the yield strength of the rivet material.

Let the contact friction stress between the rivet and the die be τk, assuming that the shear stress τz’r’ is linearly distributed along the direction of the height of the rivet stem:

$$\tau_{{z^{\prime}r{\prime} }} = \frac{{2\tau_{k} }}{h} \cdot z^{\prime}$$
(5)

where h is the height of the rivet cap formed by riveting.

As it is known from the relevant study of Onkosov on frictional shear stresses on contact surfaces29during riveting, the only regions of friction that exist on the end face of the nailed bar are the region of constant friction coefficients and the region of decreasing frictional stresses.

In the region of constant friction coefficient, the friction stress conforms to Hooke’s law, τk=µσz’, then

$$\tau_{z^{\prime}r^{\prime}} = \frac{{2\mu \sigma_{z^{\prime}} }}{h} \cdot z^{\prime}$$
(6)

Where µ is the friction coefficient of contact between the die and the rivet; h is the height of the rivet cap. Associative Eqs. (3) and (6) can be obtained:

$$\frac{{\partial \sigma_{r^{\prime}} }}{{\partial_{r^{\prime}} }} + \frac{{2\mu \sigma_{z^{\prime}} }}{h} = 0$$
(7)

Taking the partial derivative of the Mises yield condition with respect to r’ and bringing it to the shear stress condition at the end face τz’r’=τk=µσz’, one obtains:

$$\frac{{\partial \sigma_{r^{\prime}} }}{\partial r^{\prime}}(\sigma_{r^{\prime}} - \sigma_{z^{\prime}} ) - \frac{{\partial \sigma_{z^{\prime}} }}{\partial r^{\prime}}(\sigma_{r^{\prime}} - \sigma_{z^{\prime}} - 3\mu^{2} \sigma_{z^{\prime}} ) = 0$$
(8)

Associative Eq.s (7) and (8) can be obtained:

$$\frac{{2\mu \sigma_{z^{\prime}} }}{h}(\sigma_{{r{\prime} }} - \sigma_{z^{\prime}} ) + \frac{{\partial \sigma_{z^{\prime}} }}{{\partial_{r^{\prime}} }}(\sigma_{{r{\prime} }} - \sigma_{z^{\prime}} - 3\mu^{2} \sigma_{z^{\prime}} ) = 0$$
(9)

Also the contact end faces are satisfied by the Mises yield condition:

$$\frac{{\partial \sigma_{z^{\prime}} }}{{\partial_{{r{\prime} }} }} = - \frac{{\frac{{2\mu \sigma_{z^{\prime}} }}{h}\sqrt {\sigma_{s}^{2} - 3\mu \sigma_{z^{\prime}}^{2} } }}{{\sqrt {\sigma_{s}^{2} - 3\mu^{2} \sigma_{z^{\prime}}^{2} } - 3\mu^{2} \sigma_{z^{\prime}} }}$$
(10)

Since σz’ is independent of θ’, then, for the stress state on the contact surface between the riveting die and the rivet head at z’= h/2, the above equation can be written as:

$$\frac{{\sqrt {\sigma_{s}^{2} - 3\mu^{2} \sigma {}_{z^{\prime}}^{2} } - 3\mu^{2} \sigma_{z^{\prime}} }}{{\frac{{2\mu \sigma_{z^{\prime}} }}{h}\sqrt {\sigma_{s}^{2} - 3\mu^{2} \sigma_{z^{\prime}}^{2} } }}d\sigma_{z^{\prime}} = - dr^{\prime}$$
(11)

Let the radius of the rivet cap be R. Integrate the above equation in the constant friction coefficient region:

$$\int_{{\sigma_{z^{\prime}} }}^{{\sigma_{z^{\prime}R} }} {\frac{{d\sigma_{z^{\prime}} }}{{\frac{2}{\sqrt 3 h}\sqrt {(\frac{{\sigma_{s} }}{\sqrt 3 \mu })^{2} - \sigma_{z^{\prime}}^{2} } }} - } \int_{{\sigma_{z^{\prime}} }}^{{\sigma_{z^{\prime}R} }} {\frac{{d\sigma_{z^{\prime}} }}{{\frac{{2\mu \sigma_{z^{\prime}} }}{h}}}} = \int_{r}^{R} d r^{\prime}$$
(12)

Where, σz’R is the axial stress on the outside of the rivet cap end face.

Integrating Eq. (12) yields:

$$\frac{2}{\sqrt 3 }(\arcsin \frac{{\sqrt 3 \mu \sigma_{z^{\prime}R} }}{{\sigma_{s} }} - \arcsin \frac{{\sqrt 3 \mu \sigma_{z^{\prime}} }}{{\sigma_{s} }}) - \frac{1}{2\mu }\ln \frac{{\sigma_{z^{\prime}R} }}{{\sigma_{z^{\prime}} }} = \frac{R - r^{\prime}}{h}$$
(13)

Because the side of the rivet cap is a free surface, there is no external force, so σR=0, σz’R=–σs, substituting into the above equation to get:

$$\frac{2}{\sqrt 3 }(\arcsin \frac{{\sqrt 3 \mu \sigma_{z^{\prime}} }}{{\sigma_{s} }} - \arcsin \sqrt 3 \mu ) - \frac{1}{2\mu }\ln \frac{{ - \sigma_{z^{\prime}} }}{{\sigma_{s} }} = \frac{R - r^{\prime}}{h}$$
(14)

The friction stress decreasing zone ranges from r’=0 to h, \(\tau _{k} = \sigma _{s} r^{\prime}/\sqrt {3h}\), then:

$$\tau_{k} = \frac{{2\sigma_{s} }}{{\sqrt 3 h^{2} }}r^{\prime}z^{\prime}$$
(15)

Substituting into Eq. (3) yields;

$$\frac{{\partial \sigma_{r^{\prime}} }}{\partial r^{\prime}} + \frac{{2\sigma_{s} }}{{\sqrt 3 h^{2} }}r^{\prime} = 0$$
(16)

The contact end face is satisfied at this point by the Mises yield condition:

$$\sigma_{r^{\prime}} - \sigma_{z^{\prime}} = \sqrt {\sigma_{s}^{2} - \frac{{r^{{\prime}{2}} \sigma_{s}^{2} }}{{h^{2} }}}$$
(17)

Associative Eqs. (16) and (17) can be obtained:

$$\sigma_{z^{\prime}} = - \frac{{\sigma_{s} }}{{\sqrt 3 h^{2} }}r^{{\prime}{2}} - \frac{{\sigma_{s} }}{h}\sqrt {h^{2} - r^{{\prime}{2}} }$$
(18)

For the Eq. (14) in r’=h ~ R for the integral, for the Eq. (18) in r = 0 ~ h for the integral, after the integration of the results of the summation of the rivet cap molding required to get the pressure riveting force calculation Eqation.:

$$\begin{gathered} F = - \frac{{\pi h^{2} \sigma_{s} }}{{2\mu^{2} }}(\frac{13 + \sqrt 3 }{3}\mu^{2} - \ln \frac{{1 + \sqrt {1 - 3\mu^{2} } }}{\sqrt 3 \mu } + 2\sqrt {1 - 3\mu^{2} } \hfill \\ - \sqrt 3 \mu + \frac{1}{\sqrt 3 \mu } + \frac{2 - \sqrt 3 }{{\sqrt 3 }}) + \frac{{\pi Rh\sigma_{s} }}{\mu }(1 - \sqrt {1 - 3\mu^{2} } ) \hfill \\ \end{gathered}$$
(19)

It is evident from the preceding equation that the size of the rivet cap, the rivet material, and the coefficient of friction between the rivet and the connecting portion all affect the pressure riveting force.

When riveting is actually done, the rivet material flows through the riveting punch and fills the riveting punch cavity gradually to produce the rivet cap. This procedure completes the rivet formation process while leaving residual compressive stress. The aforementioned parameters serve as a crucial reference for the residual stress of the rivets created by compression riveting, and they can be utilized to choose the proper riveting punch and riveting force based on the anticipated geometry of the rivet cap.

Modeling of the riveting process

Brake pads riveted process simulation finite element model was established in order to acquire the riveted brake pads for rivets to finish the study of service behavior, using a model of high-speed rail dovetail brake pads as the topic of study. The steel backing, friction blocks, rivets, and other components make up the majority of the brake pads. Figure 4 depicts the riveted brake pads structure. In order to link the friction block and steel backing, rivets, a non-standard fastener made up of a rivet head and rivet rod, primarily rely on the riveting force applied by the riveting die to rivet the rivet rod for the creation of a rivet cap.

Fig. 4
figure 4

The riveted gate plate’s structure.

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This study examines how rivets perform under various braking circumstances. The real riveted brake pads are made up of steel backing, friction blocks, rivets, elastic components, etc. The role of the elastic element, which can greatly increase computational efficiency and mesh quality, is disregarded in the modeling and subsequent calculations if the geometric model is entirely created in accordance with the actual, as this may result in irregular mesh delineation and non-convergence of the results of the subsequent calculations.

Considering the precision and economy of the model calculation, the brake pads components are meshed using a mesh module. The steel backing and riveting molds are meshed with a tetrahedral structure mesh, which has a mesh attribute of C3D4T, and the rivets and friction blocks are meshed with a hexahedral structure mesh, which has a mesh cell type of C3D8T and a number of 143,461.

In the riveting process, the rivet material deforms, which is a common nonlinear problem. The riveting punch mold and top mold deform in relation to the rivet and other small pieces, which are regarded as a rigid body in this case, while the remaining components are set as a flexible body. Taking into consideration the aforementioned reasons, the results of the smaller impact factors will be disregarded. During the riveting process, rivets will be in the riveting mold under the action of expansion and the surrounding connected parts to produce frictional contact. Additionally, during the process of parts and molds between the frictional contact will occur to produce wear. The following presumptions are made: material wear is disregarded; the steel backing, friction block, and rivet contact surfaces are perfect interfaces with a friction coefficient of 0.2.

The material properties of the components are set in accordance with the “Interim Technical Conditions for Brake Pads of EMU” (standard technical document number: TJ/CL307-2019)30, the steel backing is QT600-3 ductile cast iron, the friction block is powder metallurgy material, and the rivet is Q235b. The material of riveted brake pads is isotropic material, and the material parameters are shown in Table 1.

Table 1 Material properties of each component.
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Based on the riveting procedure in Sect. 2.1, which can be completed in two analysis steps, the time incremental algorithm in the Standard analysis module is used to simulate the riveting assembly of the brake pads. Step 1: riveting mold pressure riveting, where the steel back only maintains its degree of freedom along the x direction, the upper riveting die and the upper surface of the rivet rod contact and are set to fully fixed constraints, and finally the rivet rod along the x-axis of the downward pressure’s negative direction. When the top riveting die surface and the upper surface make contact with the steel’s back to stop the pressure, the top die will stop the pressure, and the rivet rod will be in the free upsetting and riveting holes with the steel’s back and friction block contact when the upper riveting die surface and the upper surface make contact with the steel’s back to stop the pressure. The rivets will be fixed by the punching die and top die to prevent considerable elastic recovery when the lower surface of the higher riveting die makes contact with the upper surface of the steel back and stops the downward pressure. Step 2: Following rivet formation, the top and punch molds are separated along the x-axis to obtain riveted rivets that form the rivet cap. The rivet mold is then separated following ten seconds of holding pressure and stagnation to obtain rivets with residual stress. Figure 5 displays the brake pads riveting finite element model.

Fig. 5
figure 5

Model of riveted brake pads using finite elements.

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Analysis of riveting results

Using the isovolumetric method as a basis, the rivet rod will fill the space between the steel backing and friction block, forming a rivet cap in the steel backing’s riveting holes to complete the connection. This is because the rivet rod material will flow laterally due to the connected parts. Following rivet rod upsetting and the formation of a hemispherical rivet cap in the upper part, the rivet rod and rivet cap used in the riveting process are free upsetting first, followed by a small elastic recovery that tends to stabilize with riveting mold separation. As seen in Fig. 6, The height of the rivet cap ranges from 3.2 to 4.4 mm, and the diameter ranges from 10.8 to 12.4 mm. Both meet the size requirements stipulated in the (QJ782A-2005) standard31.

Fig. 6
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Trend of rivet rod/cap dimensions.

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The riveting process of the stress changes as depicted in Fig. 7, which shows the first rise, then decrease, and finally tend to stabilize. The highest participation in the size of the compressive stress stabilized at approximately 200 MPa, in accordance with engineering reality, following numerical simulation solving to obtain the rivets Mises stress results after compression riveting. The final Mises stress of the rivets is the residual stress result after unloading. The maximum residual compressive stress value is approximately 313.1 MPa, located at the stress concentration point on the upper surface of the rivet cap. Apart from the local stress concentration at the rivet position, the riveting results are deemed to meet the requirements if the total residual stress of the rivet size is between 70 and 200 MPa, which is less than the yield limit of the rivet material, which is 235 MPa.

Fig. 7
figure 7

Distribution of residual compressive stress in rivets.

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Thermal-force coupling modeling and validation in the braking process

Analysis of the rivet service process mechanically

Brake pads connecting rivets in service play a role in connecting the steel backing and friction block to ensure that the brake pads can function properly. The brake service process can be simplified as illustrated in Fig. 8 mechanical model. Disc brakes primarily rely on the brake pads and brake disc contact friction to provide braking force.

Fig. 8
figure 8

Simplified mechanical model of rivet service process.

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The friction contact force between the braking components produces the braking torque during the braking process as follows:

$$M_{t} = F \cdot D_{t} \cdot \mu$$
(20)

where F is the braking pressure, Dt is the friction radius, and µ is the coefficient of friction between the brake pads and the brake disk.

The connecting rivets experience radial shear stresses as a result of braking torque:

$$F_{s} = \frac{{M_{t} }}{{n \cdot h_{i} }}$$
(21)

Where n is the number of rivets and hi is the distance from the shear force to the point of action.

From Eq. (21), the magnitude of the stress on the rivet during braking can be calculated as:

$$\sigma = \frac{{F_{s} }}{A} = \frac{{4F_{{\text{s}}} }}{{\pi D^{2} }}$$
(22)

Where D is the diameter of the rivet stem.

From the above Eqs., the shear force on the rivet at different locations during braking can be calculated. In the braking speed constant value of the braking bending moment is unchanged, from Fig. 8 can be intuitively seen, due to the h1 < h2 so by the Eq. (21) calculated rivets in the h1 part of the shear force borne by the larger, the same reason can be calculated from the Eq. (22) part of the rivets in the h1 part of the stress value is greater than that in the h2 part of the rivets to bear the value of the stress. The above theoretical analysis can provide a theoretical reference for the contact stress distribution trend of rivets in the subsequent braking simulation process.

Thermal-force coupling modeling in the braking process

The focus of this paper is a particular kind of high-speed train brake pads. These pads are mostly made of rivets, steel backing, and friction blocks. Figure 9 shows the structure of the brake pads. In order to accomplish the goal of joining the friction block and steel back together, rivets, a non-standard fastener made up of a rivet head and rivet rod, primarily rely on the riveting force applied by the riveting die to rivet the rivet rod to form a rivet cap. According to structural theory, the connection structure is a stiff connection, the rivets are entirely responsible for the degree of firmness of the steel back connection, and the brake pads in the friction block. The rivets must endure the corresponding shear action during the train’s braking process. Because of the train’s high inertia, the rivets experienced a great deal of shear and friction between the friction sub-block formation of the high temperature region during the braking process, which affected the mechanical properties of the riveting material. It is simple for the friction block to come loose from the steel backing during the service procedure if one of the fixed points fails, which could compromise the train’s operational safety. Analyzing the service behavior of the rivets holding the brake pads together is therefore essential.

Fig. 9
figure 9

Brake pads structure diagram.

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The braking system’s actuating device is primarily made up of brake discs, brake pads, brake cylinders, etc. The brake pads are made up of steel backing and friction blocks that are riveted together using pressure riveting and deformation. Each friction block is a friction component. Each friction component is numbered from left to right, and the brake pads are separated into three groups based on the different braking radius from the outside to the inside. The first group has eight irregular hexagonal friction components with the tip pointing inward, the second group has six positive hexagonal friction components, and the third group has four irregular hexagonal friction components with the tip pointing outward, for a total of 18 friction materials. In order to complete the initial assembly with the brake discs, the braking force of the braking system is derived from the braking cylinders. To make the calculation of the subsequent model easier, the braking cylinder for the braking piston will be simplified. Prior to braking, the rivets must be connected with the friction block and steel back to form the friction components. Therefore, the riveted rivets ODB file is imported into the CAE file of the braking model. Each component’s dimensional parameters are as follows: The brake disc’s outer diameter is 640 mm, its inner diameter is 350 mm, its thickness is 20 mm, the brake pads’ outer and inner diameters are 630 mm and 380 mm, respectively, and the brake piston’s diameter is 45 mm. The components’ material properties are established in accordance with the Standardized Technical Document No. TJ/CL307-201930, which contains the Provisional Technical Conditions for Brake Pads for Moving Trains. The steel backing is made of QT600-3 ductile cast iron, the friction block is made of powder metallurgy, and the rivets are made of Q235b. High-speed train brake pads are made of an isotropic material; Tables 2 and 3 lists the material properties.

Table 2 Brake disc material properties.
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Table 3 Properties of rivets and connecting components materials.
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The interface in the friction contact process will enlarge to create wear during the actual braking process because of the friction effect, which causes the contact state of the friction partner surface to change in real time. Taking into account the aforementioned elements, the following presumptions are formed and some elements that don’t significantly affect the outcomes will be disregarded: The ideal contact interface between the brake disk and brake pads has a constant friction coefficient; the braking process is a uniform deceleration motion; material wear and vibration influence are disregarded; the brake disk does not axially expand. Rivet initial state and residual stress data imported into CAE via predefined Field module. and every part-aside from the brake piston-is thought of as a flexible body. Using the ABAQUS Standard simulation analysis module, the effects of heat radiation, heat conduction, and heat convection between the friction pairs were considered. The environmental temperature was set at 20℃, and the convergence criterion was defined as a tolerance value of 0.5% of the structural average force. In order to replicate train travel, the brake disc is given a starting angular velocity. Its backside is subjected to symmetrical limitations, the piston surface is subjected to similar pressure, and the steel backside of the brake pads retains axial movement. Other components in the braking process are not subjected to any limits in order to better accurately represent their service behavior. Table 4 displays the braking settings.

Table 4 Braking parameters.
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The rivets, friction blocks, and brake discs are all set as hexahedral structural meshes with the grid cell type of C3D8T and the number of 118,490, while the other components are set as tetrahedral meshes with the grid attribute of C3D10MT and the number of 20,088 in consideration of the computational model’s accuracy and economy. Figure 10 displays the comprehensive riveted brake pads/disc brake finite element model.

Fig. 10
figure 10

Finite element model of brake pads/discs.

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Model validation

To validate the simulation model, a specific model 1:1 high-speed train braking test rig performs braking tests under identical operating conditions. The maximum brake torque is 15,000 N·m, the maximum inertia is 3000 kg·m2the maximum measurement temperature is 1000 ℃, the maximum test rig speed is 2500r/min, and the highest train running speed can be simulated as 450 km/h, as illustrated in Fig. 11. The thermocouple measurement method is used, the central friction region of the brake disc serves as the monitoring point, the train’s starting speed is 120 km/h, the braking pressure is 32 kN, and the braking time is 26 s as the test condition.

Fig. 11
figure 11

High-speed train braking test rig.

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Figure 12 displays the comparison curves of the braking disk’s test and simulation findings. The overall trend of the brake disk’s test and simulation temperature results is rising and then falling, as the figure illustrates. Because the simulation model doesn’t account for the material wear between the friction pair, the simulation temperature rises more quickly during braking and reaches a maximum temperature that is higher than the test maximum temperature. At the start of braking, the initial temperature is the same as the simulation initial temperature. Additionally, there is a discrepancy of 8.69 ℃ and an inaccuracy of 6.78% between the simulated value of 136.8 ℃ and the actual observed value of 128.11 ℃ for thermocouples. There is a 6.86 ℃ discrepancy and an inaccuracy of 6.36% between the test value of 107.93 ℃ and the simulated temperature of 114.79 ℃ at the end of braking. The heat build up phenomena is evident at the late stage of braking because no abrasion chip is produced during the simulation. This causes the gap between the test and simulated temperatures to gradually widen. The model’s logic is confirmed by the greatest error of 12.61%, minimum error of 5.83%, and average error of 9.22% between the simulation temperature results and the test results during the braking process.

Fig. 12
figure 12

Comparison curve of brake disk temperature results.

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Analysis of rivet service results

Analysis of rivet contact stress results

Figure 13 displays the rivet contact stress data during braking service conditions and starting speeds of 120 km/h and 160 km/h. The neck, middle, and bottom below the rivet cap are where the contact stresses of the rivets in service are primarily distributed under various conditions, and this distribution trend is consistent with the findings of the theoretical study in subsection 3.1 above. The maximum contact stress values, 604.9 MPa and 620.8 MPa, respectively, are found in the rivet cap at the point of stress concentration, which is negligible, while the overall average contact stress size of the rivets under 120 km/h and 160 km/h conditions is around 150 MPa.

Fig. 13
figure 13

Rivet contacts stressed cloud.

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Figure 14 illustrates the trend of decreasing and then increasing contact stress on the rivets from the speed intake to the speed outlet. The highest contact stress value is found in the rivets at the speed inlet, and as the initial braking speed increases, the maximum contact stress of the I-1 rivet increases from 223.5 MPa to 243.7 MPa. The rivets’ contact stress from the center section to the speed outlet exhibits a rising trend when the braking radius is constant, and it increases from 71.04 MPa to 85.07 MPa as the initial braking speed increases. Due to the fact that the outermost friction component of the I group first makes friction contact with the brake disc in the early stages of braking, and the I-1 rivet located in the friction component of the I group is the first friction component that has friction with the disc, the I-1 rivet at the speed entrance has the highest contact stress in both groups of conditions. This contact stress is primarily distributed in the neck under the rivet cap and the middle of the rivet stem. As a result, the I-1 rivet exhibits a higher amount of contact stress. In the middle stage of braking, the friction components of groups II and III make contact with the brake disc. In the late stage of braking, all of the friction components are involved in the braking and tend to stabilize.

Fig. 14
figure 14

Rivet contact stress cloud for different regions.

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The braking radius was generated for braking the initial speed of 120 km/h and 160 km/h of the time-varying curve of the contact stress, as shown in Fig. 15, in order to investigate the contact stress of rivets at different distribution locations in different service conditions and the reasons for the change rule. The contact stress results were extracted from the rivet neck nodes in the service process and its average value was calculated.

Fig. 15
figure 15

Time-varying curves of contact stress at rivet neck under different working conditions.

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The friction components in the various braking radius zones all show greater values of contact stresses for rivets I-1, II-1, and III-1 at the speed inlet, as shown in Fig. 15. The amount of friction components dispersed throughout the brake pads gradually diminishes as the braking radius steadily shrinks, which leads to an increase in the contact stress produced between the rivets and the connectors. The contact stress from the speed inlet to the speed outlet shows a distribution trend of first decreasing and then increasing when the braking radius is the same. As the initial braking speed increases, the contact stress time-varying curve fluctuates more intensely, ranging from 76.5 MPa to 128.9 MPa.

Analysis of the rivet temperature field

As seen in Fig. 16, the temperature cloud diagram of rivets operating under various braking situations displays the distribution trend of high temperatures at both ends and low temperatures in the center. Since the head of the rivets is near the side of the brake disc and the friction components on both sides of the brake pads make initial contact with the brake disc, the temperature rise area during the early stages of braking is primarily concentrated in the friction inlet and friction outlet rivets. As a result, when the rivets brake, the temperature rise area shows a trend from the bottom of the rivet head to the direction The comparison of the rivet temperature mapping results under the same braking pressure and varying braking speed conditions revealed that the overall trend of the rivet temperature rise is constant and that the temperature rise phenomenon is substantially higher on both sides of the rivets of the brake plate than it is in the center. When the starting braking speed is 120 km/h, as illustrated in Fig. 16a, the rivets’ maximum temperature is 28.2 ℃. The rivet’s maximum temperature is 37.71 ℃ when the starting braking speed is 160 km/h, as seen in Fig. 16b. The rivet’s temperature rises as the braking speed increases.

Fig. 16
figure 16

Rivets temperature results for different working conditions.

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Analysis of rivet displacement results

The displacement of each rivet neck node during braking was extracted separately, and the average value was calculated. The time-varying curves of the displacement at the braking initial rotational speeds of 120 km/h and 160 km/h were generated according to the different braking radius, respectively, as illustrated in Fig. 17. This is because the relative motion between the rivets and the connecting parts during the braking process has a significant impact on the temperature field and stress field of the rivets.

Fig. 17
figure 17

Rivet displacement results under different working conditions.

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Figure 17 illustrates how the trend of the rivet displacement’s time-varying curve and the trend of its related contact stress are extremely comparable when the braking radius is the same. The accompanying contact stress will cause a substantial variation and the corresponding rivet temperature field will also cause a significant temperature rise when the rivet’s displacement curve’s peak and trough are significantly different. Under the same braking radius conditions, the rivet displacement fluctuates between − 50 and 25 μm when the initial braking speed is 120 km/h. During the braking process, the fluctuation trend is more intense in the early stage, while it becomes relatively stable in the later stage. When the initial braking speed is 160 km/h, the fluctuation range of rivet displacement fluctuates between − 120 and 40 μm during the middle of the braking period, and the fluctuation tendency is more noticeable. oscillation while braking. Due to the high initial speed during the pre-braking phase, the friction components in the middle of the brake disc and on each side of the brake pads dominate the friction braking.The rivet’s displacement curve gradually tends to flatten as all of the brake pads’ components are used in the later stages of braking. It is evident that the wear degree of the friction component increases with increasing braking speed, as does the trend of rivet displacement change over the service operation.

Conclusions

A high-speed train brake pads heat-force coupling analysis model is developed in this paper to investigate the service behavior of the brake pads connecting rivets of high-speed trains during the braking process and the causes of this. The 1:1 high-speed train test rig is used to confirm the model’s accuracy. The specific findings from the service behavior analysis of brake pads connecting rivets under the braking initial speed conditions of 120 km/h and 160 km/h, respectively, are as follows:

  1. 1.

    The thermal coupling model of brake disc for high-speed train is constructed, taking into account the coupling effect between the residual stress, temperature field, and mechanical stress field following riveting and molding. The model’s reasonableness is demonstrated by the 1:1 high-speed train test rig brake disc temperature results and simulation comparison verification, which show an average temperature inaccuracy of 9.22% and a brake disc temperature distribution trend that is in line with the test findings.

  2. 2.

    The overall rivet contact stress distribution exhibits a tendency of initially reducing and then increasing when the braking radius remains constant. The maximum value of the rivet contact stress of I-1 rivet increases from 223.5 MPa to 243.7 MPa, with the highest value occurring at the speed entrance and increasing as the initial braking speed increases. The rivet contact stress’s time-varying curve exhibits a more violent fluctuating pattern as the initial braking speed increases, and the contact stress differential increases from 76.5 MPa to 128.9 MPa.

  3. 3.

    The total rivet temperature rise trend is constant under various braking circumstances, indicating that the rivets on each side of the brake pads have a higher temperature rise than the rivets in the middle. The rivets’ maximum temperature increased from 28.2 ℃ to 37.71 ℃ with a temperature increase of 9.5 ℃ from the initial braking speed of 120 km/h to 160 km/h. The rivets’ displacement has a significant impact on their temperature, and as the braking speed increased, the range of fluctuation in the rivets’ displacement expanded from − 50 to 25 μm to -120 μm to 40 μm, as well as the pre-braking period. The rivet with the rivet displacement fluctuations increases the degree of the more extreme fluctuation trend.