Numerical simulation and performance optimisation of in-cylinder friction of cylinder liner and piston ring in internal combustion engine based on deep neural network

In today’s society, science and technology are developing rapidly. The requirements for mechanical products in the working environment are more and more demanding, the product structure is also more and more complex, and the user of mechanical products reliability requirements are increasing day by day. This means that the performance of mechanical products must be reliable. Users put forward higher requirements for the power source of mechanical products [1-3]. So far, as far as thermal efficiency is concerned, the internal combustion engine is deservedly the best among all power machines. Construction machinery, automobiles, ships, agricultural machinery, etc., without exception, will use the internal combustion engine as its power source [4-5]. Frictional wear is unavoidable in the working process of the internal combustion engine, and excessive wear will inevitably deteriorate the performance of the internal combustion engine, reduce the reliability of the whole mechanical product and even make the machinery prematurely obsolete [6-8].

Piston ring-cylinder liner friction is the largest sliding friction in the internal combustion engine. Internal combustion engines, especially diesel engines, large loads, unstable force state and other problems often lead to poor lubrication, which in turn increases the friction power loss of piston ring-cylinder liner [9-11]. The frictional wear problem is more serious during cold start. The lack of oil film and the wear of the cylinder liner and piston ring can also lead to a sharp increase in the amount of outgassing of the diesel engine [12-14]. The quality of the tribological design between the piston ring and cylinder liner is related to the power, reliability, fuel economy and emission cleanliness of the internal combustion engine, which in turn is related to the life of the internal combustion engine [15-17]. In recent years, people have mainly carried out the surface processing technology of piston ring-cylinder liner, tribological test design, reasonable selection of friction materials, optimization of lubrication state and other aspects of the analysis and research [18-20].

The first step in establishing the cylinder liner-piston coupling dynamics model is to analyze the dynamics of the cylinder liner-piston system.Key dynamic performance indicators, such as the trend of cylinder liner-piston ring friction in internal combustion engines, are obtained. Then, a multi-scale combined recurrent neural network model is proposed, which integrates the multi-scale feature extraction technique with the combined recurrent neural network (RNN) architecture and is equipped with the capability of nonlinear wear amount regression by capturing and learning the time-series features and their dynamic relationships during the cylinder liner wear process. In the experimental validation part, the article simulates and analyzes the piston ring, studies the influence of its structural parameters on the lubrication performance between the contact surface of the piston ring and the cylinder liner, designs the orthogonal test to optimize the piston ring profile, and analyzes the in-cylinder friction of the piston ring of the cylinder liner of the combustion engine before and after the optimization using the constructed prediction model for the wear on the cylinder liner surface of the internal combustion engine, in order to verify the validity of the optimization scheme.

2

Dynamic modeling of the cylinder liner-piston system

2.1

Piston second-order motion - cylinder liner vibration response coupling analysis model

2.1.1

Piston second-order motion analysis

The cylinder liner-piston system and forces are shown in 1, the motion model of the cylinder liner-piston system is shown in Fig. 1(a), and the force analysis of the piston is shown in Fig. 1(b).

When the crank rotates at a constant angular velocity ω, the displacement, velocity, and acceleration of the piston center of mass and the piston pin center of mass along the y-axis can be expressed as:

Piston displacement: (1) $s_{p i s} = r_{c} \cos θ + l_{r} {[1 - k_{1}^{2} {(\sin θ - k_{2})}^{2}]}^{0.5}$

Piston Speed: (2) $v_{p i s} = - r_{c} ω {\sin θ + k_{1} {[1 - k_{1}^{2} {(\sin θ - k_{2})}^{2}]}^{- 0.5}} (\sin θ - k_{2}) \cos θ$

Piston acceleration: (3) $a_{p i s} = - r_{c} ω^{2} {\begin{cases} \cos θ + k_{1}^{3} {[1 - k_{1}^{2} {(\sin θ - k_{2})}^{2}]}^{- 1.5} {(\sin θ - k_{2})}^{2} \cos^{2} θ \\ + k_{1} {[1 - k_{1}^{2} {(\sin θ - k_{2})}^{2}]}^{- 0.5} (\cos 2 θ + k_{2} \sin θ) \end{cases}}$

During the operation of an internal combustion engine, the piston not only makes reciprocating linear motion along the cylinder axis, but also accompanies the second-order motion, i.e., transverse swing, knocking the cylinder liner and rotation around the piston pin [21]. To analyze the force on the piston, the dynamic equations of the piston can be obtained from the force balance and moment balance as shown below:

Force balance equation for piston x direction: (4) $F + F_{i n x} + F_{i s x} + F_{p r} \sin φ = 0$

Equilibrium equations for forces in the direction of piston y: (5) $F_{i n y} + F_{i s y} + F_{p r} \cos φ - F_{f} = 0$

Moment balance equation for the center of the piston pin: (6) $M + M_{f} + M_{i b} + F_{i x x} (s_{c} - s_{b}) - F_{i s y} s_{d} = 0$

Where: F_pr is the force acting on the piston by the connecting rod. F_isx, F_isy is the inertia force on the piston in the transverse and longitudinal directions. F_inx, F_iny for the piston pin along the transverse and longitudinal force of inertia. M_is is the moment of inertia of the piston center of mass around the piston pin. F, F_f, M, M_f are the lateral and frictional forces and moments on the piston generated by the mixed lubrication of the piston-cylinder liner friction pair, F=F_h+F_c, F_f=F_fh+F_fc, M=M_h+M_c, M_f=M_fh+M_fc, F_h, F_fh, M_h, and M_fh are generated by the hydrodynamic pressure action, and F_c, F_fc, M_c, and M_fc are generated by the microbump contact. φ is the connecting rod angle of rotation.

(7)

φ = \tan^{- 1} {\frac{k_{1} (\sin θ - k_{2})}{{[1 - k_{1}^{2} {(\sin θ - k_{2})}^{2}]}^{0.5}}}

Set the top and bottom of the piston skirt transverse displacement were e_t, e_b, according to the geometric relationship can be obtained from the piston pin center of mass and the piston center of mass transverse displacement and the piston swing angle:

Piston center of mass transverse motion displacement: (8) $x_{p i s} = e_{t} - \frac{s_{b}}{L_{s}} (e_{t} - e_{b})$

Displacement of the piston pin center of mass in transverse motion: (9) $x_{p i n} = e_{t} - \frac{s_{c}}{L_{s}} (e_{t} - e_{b})$

Piston swing angle: (10) $γ = \frac{1}{L_{s}} (e_{t} - e_{b})$

Set the piston second-order motion acceleration of ë_t, ë_b, according to the relationship between displacement, velocity. Acceleration can be obtained from the piston pin center of gravity, as well as the center of gravity of the piston transverse motion acceleration and the angular acceleration of the piston swing:

Piston center of mass transverse motion acceleration: (11) ${\ddot{x}}_{p t s} = {\ddot{e}}_{t} - \frac{s_{b}}{L_{s}} ({\ddot{e}}_{t} - {\ddot{e}}_{b})$

Acceleration of transverse motion of piston pin center of mass: (12) ${\ddot{x}}_{p i n} = {\ddot{e}}_{t} - \frac{a}{L_{s}} ({\ddot{e}}_{t} - {\ddot{e}}_{b})$

Piston swing angle angular acceleration: (13) $\ddot{γ} = \frac{1}{L_{s}} ({\ddot{e}}_{t} - {\ddot{e}}_{b})$

From Newton’s second law, the inertia force and moment of inertia acting on the center of mass of the piston as well as the center of mass of the piston pin are: transverse inertia force on the center of mass of the piston: (14) $F_{i s x} = - m_{p i s} {\ddot{x}}_{p i s}$

Piston pin center of mass transverse inertia force: (15) $F_{i n x} = - m_{p i n} {\ddot{x}}_{p i n}$

Piston center of mass longitudinal inertia force: (16) $F_{i s y} = - m_{p i s} a_{p i s}$

Piston pin center of mass longitudinal inertia force: (17) $F_{i n y} = - m_{p i n} a_{p i s}$

Piston center of mass moment of inertia: (18) $M_{i s} = - I_{p i s} \ddot{γ}$

Where m_pis is the piston mass. m_pin is the mass of the piston pin. I_pis is the piston moment of inertia.

The second-order motion model of the piston can be obtained by substituting Eqs. (11)-(18) into the piston dynamics equations (4)-(6) and eliminating the connecting rod force F_pr: (19) ${\begin{array}{l} \begin{array}{l} [m_{p i n} (1 - \frac{s_{c}}{L_{s}}) + m_{p i s} (1 - \frac{s_{b}}{L_{s}})] {\ddot{e}}_{t} + (m_{p i s} \frac{s_{c}}{L_{s}} + m_{p i s} \frac{s_{b}}{L_{s}}) {\ddot{e}}_{b} \\ = F + F_{a} + F_{f} \tan φ \end{array} \\ \begin{array}{l} [\frac{I_{p i s}}{L_{s}} + m_{p i s} (s_{c} - s_{b}) (1 - \frac{s_{b}}{L_{s}})] {\ddot{e}}_{t} + [m_{p i s} (s_{c} - s_{b}) \frac{s_{b}}{L_{s}} - \frac{I_{p i s}}{L_{s}}] {\ddot{e}}_{b} \\ = M + M_{a} + M_{f} \end{array} \end{array}$

Where F_a and M_a are intermediate variables with the expressions: (20) $F_{a} = - (F_{i n y} + F_{i s y}) \tan φ$ (21) $M_{a} = - F_{i s y} s_{d}$

2.1.2

Cylinder liner-piston coupling dynamic model

During the operation of the internal combustion engine, the piston will produce a second-order motion, affected by the side thrust of the piston knocking the cylinder liner to produce a strong vibration. The vibration model of the cylinder liner and its force analysis are shown in Figure 2.

Let the mass of the cylinder liner be m_ln, the stiffness coefficient of vibration be k_l, the damping coefficient be δ_i, its transverse displacement be s, its velocity be ṡ, and its acceleration be $\ddot{s}$ . Then, during the vibration of the cylinder liner, it is subjected to the elastic restoring force of –k_ls, the damping force of –δ_lṡ, and its own inertia force of $m_{l l n} \ddot{s}$ In addition, the cylinder liner is subjected to an external excitation force of F, which is generated by the lubrication of the liner-piston friction pair [22]. The differential equation of cylinder liner vibration established according to Newton’s second law and Hooke’s law is: (22) $m_{l i n} \ddot{s} + δ_{l} \dot{s} + k_{l} s = - F$

The vibration response model of the cylinder liner considering the second-order motion of the piston can be obtained by coupling Eq. (19) with Eq. (22): (23) $\begin{array}{l} ⌊ \begin{matrix} m_{p i n} (1 - \frac{s_{c}}{L_{s}}) + m_{p i s} (1 - \frac{s_{b}}{L_{s}}) & m_{p i s} \frac{s_{c}}{L_{s}} + m_{p i s} \frac{s_{b}}{L_{s}} & 0 \\ \frac{I_{p i s}}{L_{s}} + m_{p i s} (s_{c} - s_{b}) (1 - \frac{s_{b}}{L_{s}}) & m_{p i s} (s_{c} - s_{b}) \frac{s_{b}}{L_{s}} - \frac{I_{p i s}}{L_{s}} & 0 \\ 0 & 0 & m_{l i n} \end{matrix} ⌋ [\begin{matrix} {\ddot{e}}_{t} \\ {\ddot{e}}_{b} \\ \ddot{s} \end{matrix}] \\ = [\begin{matrix} F + F_{a} + F_{f} \tan φ \\ M + M_{a} + M_{f} \\ - F - δ_{l} \dot{s} - k_{l} s \end{matrix}] \end{array}$

2.2

Hybrid Fluid-Dynamic-Pressure Lubrication Model

2.2.1

Average flow Reynolds equation

Internal combustion engine piston skirt and cylinder liner lubrication between the typical fluid dynamic pressure lubrication and oil film bearing area shown in Figure 3.

For the cylinder liner-piston system, focusing on the lubrication between the piston skirt and the cylinder liner, the average Reynolds equation can be expressed as the cylinder liner is fixed to the body with a slip velocity of 0, and only the piston slides along the surface of the cylinder liner: (24) $\begin{matrix} \frac{\partial}{\partial x} (ϕ_{x} \frac{h^{3}}{12 μ} \frac{\partial p_{h}}{\partial x}) + \frac{\partial}{\partial y} (ϕ_{y} \frac{h^{3}}{12 μ} \frac{\partial p_{h}}{\partial y}) \\ = \frac{v_{p i s}}{2} \frac{\partial {\bar{h}}_{T}}{\partial y} + \frac{v_{p i s}}{2} σ \frac{\partial ϕ_{s}}{\partial y} + \frac{\partial {\bar{h}}_{T}}{\partial t} \end{matrix}$

If the effect of piston and cylinder liner surface roughness on lubricant film stability is neglected, the oil film thickness between the cylinder liner-piston is the nominal oil film thickness h, which can be expressed as: (25) $\begin{matrix} h = C + e_{t} (t) \cos ϕ + [e_{b} (t) - e_{t} (t)] \frac{y}{L_{s}} \cos ϕ \\ + f (ϕ, y) + s (t) \cos ϕ \end{matrix}$

When analyzing the lubrication characteristics between the cylinder liner and piston, it is necessary to fully consider the lubricant film by the cylinder liner and piston surface roughness, in order to describe this effect, it is necessary to use the actual oil film oil film thickness h_T description, the lubricant film microscopic schematic shown in Figure 4. The expression for h_T is: (26) $h_{T} = h + δ_{1} + δ_{2}$

Where δ₁ and δ₂ satisfy the normal Gaussian distribution with corresponding standard deviations of σ₁ and σ₂, respectively, so that the integrated height distribution function δ can be expressed as δ=δ₁+δ₂ and the integrated roughness variance σ can be expressed as $σ^{2} = σ_{1}^{2} + σ_{2}^{2}$ .

Due to the complexity of the representation of the actual oil film thickness, which makes the analysis process very cumbersome, in order to simplify the analysis process, the concept of the average value of the actual oil film thickness ${\bar{h}}_{T}$ is introduced, and the average oil film thickness ${\bar{h}}_{T}$ is used to represent the expected value of the actual oil film thickness h_T, ${\bar{h}}_{T} = E (h_{T})$ . Its calculation formula is as follows: (27) ${\bar{h}}_{T} = \int_{- h}^{+ \infty} (h + δ) f (δ) d δ$

where f(δ) is the probability density function of the surface roughness, obeying a Gaussian distribution, and f(x) can be written as: (28) $f (x) = \frac{1}{\sqrt{2 π} σ} e^{\frac{x^{2}}{2 σ^{2}}}$

Thus, the right end of the Reynolds equation can be written as: (29) $\frac{d {\bar{h}}_{T}}{d y} = \frac{d {\bar{h}}_{T}}{d h} \frac{d h}{d y} = ϕ_{c} \frac{d h}{d y}$ (30) $\frac{d {\bar{h}}_{T}}{d t} = \frac{d {\bar{h}}_{T}}{d h} \frac{d h}{d t} = ϕ_{c} \frac{d h}{d t}$

Introducing the dimensionless contact factor $ϕ_{c} = d {\bar{h}}_{T} / d h$ , the mean Reynolds equation can be rewritten as: (31) $\begin{matrix} \frac{\partial}{\partial x} (ϕ_{x} \frac{h^{3}}{12 μ} \frac{\partial p_{h}}{\partial x}) + \frac{\partial}{\partial y} (ϕ_{y} \frac{h^{3}}{12 μ} \frac{\partial p_{h}}{\partial y}) \\ = \frac{v_{p i s}}{2} ϕ_{c} \frac{\partial h}{\partial y} + \frac{v_{p i s}}{2} σ \frac{\partial ϕ_{s}}{\partial y} + ϕ_{c} \frac{\partial h}{\partial t} \end{matrix}$

The oil film pressure boundary conditions are as follows:

At the upper boundary y=0 and lower boundary y=L of the piston skirt, the oil film pressure is zero due to contact with the external gas.

(32)

p_{h} (ϕ, 0) = p_{h} (ϕ, L) = 0

The oil film pressure acts only in the oil film carrying area, outside the carrying area the oil film pressure is zero: (33) $p_{h} (ϕ, y) = 0, \frac{π}{6} \leq ϕ \leq π - \frac{π}{6}$

Considering the symmetry of the piston skirt, when calculating the oil film pressure, only half of its area (0≤ϕ<π) needs to be calculated: (34) ${\frac{\partial p_{h}}{\partial ϕ} |}_{ϕ = 0} = {\frac{\partial p_{h}}{\partial ϕ} |}_{ϕ = π} = 0$

By solving the average Reynolds equation, the distribution of the oil film pressure p_h can be obtained, and the total normal force caused by the dynamic pressure of the lubricant on the piston skirt and the resulting moment can be obtained by the following integral equation: (35) $F_{h} = R_{p} \iint_{A} p_{h} (ϕ, y) \cos ϕ d ϕ d y$ (36) $M_{h} = R_{p} \iint_{A} p_{h} (ϕ, y) (s_{c} - y) \cos ϕ d ϕ d y$

In analyzing the effect of cylinder liner-piston skirt surface roughness on the lubricant film, the shear stress induced by the action of fluid dynamic pressure can be expressed as: (37) $τ_{h} (ϕ, y) = - \frac{μ v_{p i s}}{h} (ϕ_{f} + ϕ_{f s}) + ϕ_{f p} \frac{h}{2} \frac{\partial p}{\partial y}$

Where ϕ_f, ϕ_fs and ϕ_fp are shear stress factors.

The friction force acting on the piston skirt produced by the action of the dynamic pressure of the lubricant and the resulting friction moment is calculated as: (38) $F_{f h} = R_{p} \iint_{A} τ_{h} (ϕ, y) d ϕ d y$ (39) $M_{f_{1}} = R_{p} \iint_{A} τ_{h} (ϕ, y) (R_{p} \cos ϕ - S_{a}) d ϕ d y$

2.2.2

Microconvex body contact modeling

The micro convex body contact model proposed by Greenwood and Tripp is used to calculate the contact pressure generated by the contact between the two, which is expressed as: (40) $p_{c} = \frac{16 \sqrt{2}}{15} π {(η β σ)}^{2} E \sqrt{\frac{σ}{β}} F_{s / 2} (H_{a})$

Where E is the integrated modulus of elasticity, $E = \frac{1}{\frac{1 - v_{1}^{2}}{E_{1}} + \frac{1 - v_{2}^{2}}{E_{2}}}$ . H_a is the film thickness ratio, $H_{a} = \frac{h}{σ}$ . ν is the peak element density on the rough surface. β is the radius of curvature of peak elements. According to the previous calculation experience, ηβσ=0.04 and σ/β=10^–3 are taken, where the expression of the F_5/2(H_a) function is as follows: (41) $F_{5 / 2} (H_{a}) = \int_{H_{a}}^{\infty} {(s - H_{a})}^{2.5} E (s) d s$

Where E(s) is the integrated standard probability density function of the piston skirt and cylinder liner, assuming both of them are Gaussian surfaces: (42) $E (s) = \frac{1}{\sqrt{2 π}} e^{\frac{- s^{2}}{2}}$

Solving the above equation yields: (43) $F_{5 / 2} (H_{a}) = {\begin{array}{l} \begin{array}{l} 2.1339 \times 10^{- 4} \exp (3.8045 \ln (4 - H_{a}) + 1.3415 {(\ln (4 - H_{a}))}^{2}) \\ H_{a} \leq 3.5 \end{array} \\ \begin{array}{l} 1.1201 \times 10^{- 4} {(4 - H_{a})}^{1.9447} \\ 3.5 < H_{a} \leq 4 \end{array} \\ 0, H_{a} > 5 \end{array}$

Simplified and obtained: (44) $F_{5 / 2} (H_{a}) = {\begin{array}{l} 4.4086 \times 10^{- 5} {(4 - H)}^{6.804}, (H_{a} \leq 4) \\ 0, (H_{a} > 4) \end{array}$

At the cylinder liner and piston skirt microscopic level, when solid-solid contact occurs between the two, the shear stress generated by the interaction between the cylinder liner and piston skirt micro convex body surface is: (45) $τ_{c} = - \frac{| v_{p i s} |}{v_{p i s}} μ_{f} p_{c}$

Where μ_f is the solid-solid contact friction coefficient, which takes the value of 0.15.

(46)

F_{c} = R_{p} \iint_{A} p_{c} (θ, y) \cos θ d θ d y

(47)

M_{c} = R_{p} \iint_{A} p_{c} (θ, y) (s_{c} - y) \cos θ d θ d y

(48)

F_{f c} = R_{p} \iint_{A} τ_{c} (θ, y) d θ d y

(49)

M_{f c} = R_{p} \iint_{A} τ_{c} (θ, y) (R_{p} \cos θ - s_{a}) d θ d y

After finding the friction force, the friction power consumption of the cylinder liner-piston system can be found according to the mechanical power calculation formula: (50) $W = F_{f} v_{p i s}$

2.2.3

Calculation of impact factors

In this paper, it is assumed that the height distribution of the micro-convex body on the inner wall surface of the piston skirt as well as the cylinder liner obeys the Gaussian distribution, and according to the characteristics of the Gaussian distribution, the calculation of each factor is based on its numerical fitting formula.

Calculation of flow factor

According to the literature, the fitting formula of the pressure flow factor is: (51) $ϕ_{x} = ϕ_{y} = {\begin{array}{l} 0; & H_{a} \leq 0.5 \\ 1 - 0.9 \exp (- 0.56 H_{a}); & H_{a} > 0.5 \end{array}$ The shear flow factor ϕ_s represents the additional flow impact between two rough surfaces due to the occurrence of relative sliding, reflecting the additional fluid dynamics due to relative sliding, and is expressed as: (52) $ϕ_{s} = {\begin{array}{l} 1.899 (V_{r 1} - V_{r 2}) H_{a}^{0.98} \exp (- 0.92 H_{a} + 0.05 H_{a}^{2}), H_{a} \leq 5 \\ 1.126 (V_{r 1} - V_{r 2}) \exp (- 0.25 H_{a}), H_{a} > 5 \end{array}$ Where $V_{r 1} = {(\frac{σ_{1}}{σ})}^{2}$ , $V_{r 2} = {(\frac{σ_{2}}{σ})}^{2}$ .

Contact factor calculation

The literature gives expressions for the contact factor for the four commonly used distribution types, and the contact factor fitting equation for the Gaussian distribution of the height of the microconvex body is: (53) $ϕ_{c} = {\begin{array}{l} \exp (- 0.6912 + 0.782 H_{a} - 0.304 H_{a}^{2} + 0.0401 H_{a}^{3}), H_{a} \leq 3 \\ 1, H_{a} > 3 \end{array}$

Shear stress factor: (54) $ϕ_{f} = {\begin{matrix} \begin{array}{l} \frac{35 z}{32} {(1 - z^{2})}^{3} \ln \frac{z + 1}{ε^{*}} \\ + \frac{7 z}{384} (- 55 + 132 z + 345 z^{2} - 160 z^{3} - 405 z^{5} + 60 z^{5} + 147 z^{6}) \\ H_{a} \leq 3 \end{array} \\ \begin{array}{l} \frac{35 z}{32} {(1 - z^{2})}^{3} \ln \frac{z + 1}{z - 1} + \frac{7 z^{2}}{96} (66 + 30 z^{4} - 80 z^{2}) \\ H_{a} > 3 \end{array} \end{matrix}$ (55) $ϕ_{c} = {\begin{array}{l} \exp (- 0.6912 + 0.782 H_{a} - 0.304 H_{a}^{2} + 0.0401 H_{a}^{3}), H_{a} \leq 3 \\ 1, H_{a} > 3 \end{array}$

3

Internal combustion engine cylinder liner surface wear prediction model

In this study, 1 model is proposed for predicting the amount of wear on the cylinder liner surface of an internal combustion engine. The input information to the model is the cylinder liner wear over time per unit time, which is used as the input to the main body of the network after min-max normalization for scaling the data interval. The main part of the network adopts a combined structure of 2-layer serial LSTM and 2-layer parallel GRU, in which the number of the three hidden layers is in the ratio of 1:2:4. The 2-layer LSTM at the front end extracts temporal features and long-term dependencies from the forward and backward directions, respectively, to provide comprehensive temporal information for the model, and the parallel GRU at the back end further deepens the model’s learning of complex features and relationships.

In order to preserve the original information, residual connectivity is used for both internal and head-to-tail features of the network. The residual connection enables cross-layer transfer of features by introducing jump connections between layers, which helps to alleviate the gradient vanishing problem and improve training efficiency.Finally, data prediction is performed using fully connected layers and regression layers. This design enables the model to learn the input sequence in an end-to-end form and predict the wear on the cylinder liner surface [23].

3.1

Min-max data normalization

Min-max normalization is 1 common method of data interval scaling, which transforms the value domain of the input data into a fixed interval: (56) $Y = \frac{[X - \min (X)] (\max_{n e w} - \min_{n e w})}{\max (X) - \min (X)} + \min_{n e w}$

Where: X is the original data, [max_new,min_new] is the normalized range, and the range of [0,1] is used in this paper.

3.2

Bidirectional LSTM layer

LSTM controls the flow of information by introducing a gating mechanism to effectively capture and memorize the long-term dependencies in a sequence. The basic unit of the long short-term memory network is shown in Fig. 5. The input state is x_t and the output hidden state is h_t. It mainly contains three core parts: input gate, forgetting gate and output gate.

The input gate is responsible for filtering the amount of information received: the input data and previously hidden states are processed through a Sigmoid activation function, which outputs a value between 0 and 1 to determine the amount of information allowed to pass through, the mathematical expression for the input gate is (57) $i_{t} = σ (W_{i i} x_{t} + b_{i i} + W_{h i} h_{t - 1} + b_{h i})$

Where: σ is the sigmoid activation function, x_t is the input at the current moment, h_t–1 is the hidden state at the previous moment, W_ii, b_ii and W_hi, b_hi are the weights and biases corresponding to the current input x_t and the previous hidden state h_t–1 in the input gate.

The forgetting gate is used to determine the amount of information discarded in the cell state. It employs a Sigmoid activation function, which determines the extent to which previous cell states are discarded. The mathematical representation of the forgetting gate is (58) $f_{t} = σ (W_{i f} x_{t} + b_{i f} + W_{h f} h_{t - 1} + b_{h f})$

Where: x_t is the input at the current moment, h_t–1 is the hidden state at the previous moment, W_if, b_if and W_hf, b_hf are the weights and biases corresponding to the current input x_t and the previous hidden state h_t–1 in the forgetting gate.

The cell update state step remembers or ignores the current input. Using the tanh activation function, 1 new cell state candidate is generated. Its update state candidate generation formula is expressed as (59) ${\tilde{C}}_{t} = \tanh (W_{i g} x_{t} + b_{i g} + W_{h g} h_{t - 1} + b_{h g})$

Where: x_t is the input at the current moment, h_t–1 is the hidden state at the previous moment, W_ig, b_ig and W_hg, b_hg are the weights and biases in the candidate states corresponding to the current input x_t and the previous hidden state h_t–1.

The formula for cell state update is expressed as (60) $C_{t} = f_{t} C_{t - 1} + i_{t} {\tilde{C}}_{t}$

Where: C_t–l is the cell state at the previous moment, and ⊙ is the Hadamard product, which represents the element-by-point multiplication.

The output gate determines which part of the cell state will be output based on the current input and hidden state, which uses the Sigmoid activation function and the tanh activation function, denoted by Eq: (61) $o_{t} = σ (W_{i o} x_{t} + b_{i o} + W_{h o} h_{t - 1} + b_{h o})$

Where: x_t is the input at the current moment, h_t–1 is the hidden state at the previous moment, W_io, b_io and W_ho, b_ho are the weights and biases in the candidate states corresponding to the current input x_t and the previous hidden state h_t–1.

The final hidden state and passes through the output gate o_t and the cell state C_t undergoes a combination of tanh activation functions: (62) $h_{t} = o_{t} ⊙ \tanh (C_{t})$

The bi-directional LSTM layer is based on LSTM, where past and future information is considered at each time step in chronological order and reverse chronological order, respectively. The hidden information states are connected to provide a more comprehensive contextual understanding through the flow of information in the 2 directions. It has a more powerful inverse evaluation capability to utilize past and future information to make more reliable model predictions. Its integrated hidden state is represented as: (63) $h_{t}^{(B L)} = [h_{t}^{(f)}; h_{t}^{(b)}]$

Where: $h_{t}^{(f)}$ is the forward hidden state and $h_{t}^{(b)}$ is the reverse hidden state.

The bidirectional LSTM layer learns the features of the input sequence more comprehensively than the two-layer stacked LSTM layer, which helps to save the design cost of the subsequent model architecture and reduce the number of parameters.

3.3

Combinatorial recurrent neural networks

Gated Recurrent Unit (GRU) is another RNN variant for processing sequential data. Similar to LSTM, GRU is designed to simplify the structure of LSTM by introducing update gates and reset gates while still being able to efficiently capture long-term dependencies.

The synthesized hidden state of the bidirectional LSTM is used as the input state of the GRU, denoted as: (64) $x_{t}^{(g r u)} = h_{t}^{(B L)}$

Updates the computation of gate vector z_t: (65) $z_{t} = σ (W_{z} x_{t}^{(g r u)} + U_{z} h_{t - 1}^{(g r u)} + b_{z})$

Where: W_z, U_z and b_z are the weights and biases corresponding to the current input $x_{t}^{(g r u)}$ and the previous hidden state $h_{t - 1}^{(g r u)}$ in the update gate computation, with the notation remaining consistent below.

Computation of the reset gate vector r_t: (66) $r_{t} = σ (W_{r} x_{t}^{(g r u)} + U_{r} h_{t - 1}^{(g r u)} + b_{r})$

Computation of new candidate hidden states: (67) $h_{t} = \tanh (W_{h} x_{t}^{(g r u)} + U_{h} (r_{t} □ h_{t - 1}^{(g r u)}) + b_{h})$

Updates the calculation of the hidden state: (68) $h_{t}^{(g r u)} = (1 - z_{t}) ⊙ h_{t - 1}^{(g r u)} + z_{t} ⊙ {h^{'}}_{t}$

3.4

Multiscale structures and residual connections

In this paper, we design a 1 multi-scale feature extraction architecture based on GRU units, and the number of bi-directional LSTM and GRU hidden layers set up in the paper are 100, 200 and 400, respectively, with the ratio of 1:2:4, which indicates that for each bi-directional LSTM layer, there are 2 GRU layers of different scales in parallel. For GRU layers operating on different scales s, they can correspond to different feature resolutions: (69) $h_{t, s}^{(g r u)} = G R U_{s} (X_{t}, h_{t - 1, s}^{(g r u)})$

Where: $h_{t, s}^{(g r u)}$ denotes the hidden state of the GRU layer at time step t and scale s, GRU_s denotes the GRU layer at scale s, and X_t denotes the input data at time step t.

Each of the different scale layers outputs 1 feature vector that encapsulates the information learned at a particular scale, and then the feature vectors are fused by a form of cascade operation: (70) $H_{t} = C o n c a t (h_{t, 1}^{(g r u)}, h_{t, 2}^{(g r u)})$

The multi-scale structure enables the extraction of features at different levels of abstraction. Bidirectional LSTM layers capture patterns in the data that are more detailed and smaller in granularity. The GRU layers are larger and focus on broader trends, and this hierarchical feature extraction is key to predicting the progression of wear dynamics.

Bidirectional LSTM units are good at understanding long-term dependencies but can be computationally expensive. By having a smaller number of bi-directional LSTM units, it can be ensured that these units focus on capturing the most important long-term trends. In contrast, GRUs efficiently process data at a higher temporal resolution, capturing short-term correlations that are also critical for accurate prediction. In contrast, a larger number of GRU units can increase network capacity without causing any complexity. Thus, increasing the number of GRU units by a factor of 1 can provide the network with more functionality for complex modeling without making training too difficult. The structure of the multiscale temporal network is shown in Figure 6.

In order to facilitate the direct propagation of gradients and thus alleviate the gradient magnitude decay often encountered in deeper network training, in this paper, pathways are established between multiple modules by means of residual connections, which enhances the ability of the network to be trained efficiently at a deeper level. The residual connections of the forward and reverse LSTM are denoted as: (71) $h_{t}^{(B L)} = h_{t}^{(f)} + h_{t}^{(b)}$

The residual connection between GRU and the original input data is denoted as: (72) $H_{t} = G R U (h_{t - 1}^{(g r u)}, X_{t}^{(b)}) + X_{t}^{(b)}$

Residual layer connectivity refines the feature representation propagated by the previous layers, thus preserving critical information in the depth of the network and enabling feature extraction to be enhanced without degrading the accuracy of the characterization.

4

Experimental analysis

4.1

Numerical simulation of cylinder liner-piston ring in-cylinder friction

This section of the experiment focuses on the impact of the coupled analytical model of piston second-order motion-cylinder liner vibration response and the fluid dynamic-pressure hybrid lubrication model established in this paper on the numerical simulation of friction and performance optimization of the friction in the cylinder liner-piston ring cylinder of an internal combustion engine.

4.1.1

Effect of Piston Ring Barrel Height on Friction Lubrication

The variation of oil film thickness with crankshaft rotation angle at different barrel heights is shown in Fig. 7. The relationship between the oil film thickness between the two lubricating surfaces of the piston ring and the cylinder liner varies with the crankshaft rotation angle. According to the image, it can be seen that the peak of the oil film thickness appears near the upper and lower stops of the piston stroke, which is because when the piston moves to the vicinity of the upper and lower stops, its running speed is the smallest, and due to the stroke process of scraping the oil, at this time, the lubricating oil between the surface of the piston ring and the surface of the cylinder liner has a large amount of agglomeration, and therefore the oil film thickness near the upper and lower stops is larger. When the upper and lower stops are reached, the piston speed becomes 0. At the instant of reverse motion, the oil film thickness decreases sharply, even to 0. After the start of reverse motion, the thickness of the oil film increases due to the scraping of oil by the piston ring. When the height of the barrel surface is 1.5μm, the thickness of the oil film is obviously smaller than the thickness of the oil film when the height of the barrel surface is 4μm, but with the increase of the barrel surface height, the thickness of the oil film is not getting bigger and bigger, and when the height of the barrel surface is increased to 12μm, the thickness of the oil film is smaller than the thickness of the oil film when the height of the barrel surface is 8μm. This is because the extrusion effect of the piston ring mainly determines the size of the oil film thickness. Too large and too small barrel heights are not conducive to the formation of the extrusion effect of the piston ring, so the barrel height should be more reasonable.

The influence of the barrel surface height of the piston ring on the friction force and friction loss of the piston ring-cylinder liner friction pair is shown in Figures 8 and 9. When the piston ring moves near the upper and lower stops, its speed is very low. At this time, the micro-convex body friction is the main force between the piston ring and the cylinder liner, and the larger the barrel surface height of the piston ring, the larger the micro-convex body friction is. In the process of piston movement, fluid friction is the main force between the piston ring and cylinder liner, and the thickness of oil film produced by smaller barrel height is larger, so the fluid friction is also larger. In the whole movement process, fluid friction accounts for the main part. When the barrel height of the piston ring is larger, the total friction between the piston ring and cylinder liner is smaller, and the total friction loss is also smaller, so the friction and friction loss between the piston ring and cylinder liner at the barrel height of 8 μm is smaller than that of the friction loss at the barrel height of 1.5 μm and 4 μm. However, when the barrel height is too large, the relative area between the piston ring and the cylinder liner decreases, resulting in increased friction loss throughout the stroke, and the friction force and friction loss between the piston ring and the cylinder liner increase to different degrees when the barrel height is 12μm.

4.1.2

Effect of Piston Ring Barrel Face Offset on Friction Lubrication

Depending on the actual situation, barrel-faced piston rings do not always take the form of a symmetrical barrel face, and the highest point of the barrel face the highest point of the barrel face is sometimes shifted toward the combustion chamber or the second gas ring, which is called barrel face offset. The highest point of the barrel face is moved towards the combustion chamber or the second gas ring.

The offset of the highest point of the barrel face toward the combustion chamber is called the positive barrel face offset, and the offset towards the second gas ring is called the negative barrel face offset.The variation of oil film thickness, friction, and friction loss power between the piston ring and cylinder liner with different barrel surface offsets as a function of the engine crankshaft angle is shown in Fig. 10, Fig. 11 and Fig. 12. From the figure, it can be seen that in the upward process of the piston, the oil film thickness of the piston ring barrel surface negative offset is slightly larger than the barrel surface positive offset and barrel surface symmetrical piston ring oil film thickness, while in the downward process of the piston, the oil film thickness of the barrel surface negative offset is relatively small, the oil film thickness of the barrel surface positive offset is the largest, and the oil film thickness of the larger barrel surface positive offset to be relatively large. For example, when the crankshaft rotation angle of 90 °, the barrel surface offset 30 μm, the oil film thickness of 0.52 μm, the barrel surface offset 60 μm, and the oil film thickness of 0.5 μm. Barrel surface positive offset friction and friction loss are smaller than the barrel surface negative offset and the barrel surface of the nominal piston ring. This is because, during the upward movement of the piston, the barrel faces a negative offset piston ring, and the wedge gap between the end face of the piston ring and the cylinder liner is more favorable to the formation of the lubricant film. In contrast, when the piston ring moves downward, the result is just the opposite.The barrel faces a positive offset of the oil film thickness, which is relatively the largest. The more barrels face positive offset, the longer the wedge inlet formed by the piston ring and the cylinder liner wall, the more conducive to the formation of the oil film, and therefore, the larger the barrel faces positive offset. Therefore, the oil film thickness formed by the larger barrel positive offset is larger. Overall, the positive offset of the barrel surface can effectively reduce the friction force and friction loss, so that the moving parts are in an ideal lubrication state.

4.1.3

Influence of piston ring closing gap on friction lubrication

Due to the piston ring installation process needs, a certain closed gap, closed gap for the piston installed to the piston ring groove and is in the working state of the piston ring between the distance between the cut end face. Due to the existence of the closed gap, the piston ring is allowed to have a certain expansion and contraction margin when the piston is working, which can effectively reduce the piston ring stuck in the piston, and reduce the seriousness of the piston ring will cause cylinder pulling, melting or even broken, so the piston ring closed gap plays a very critical role in the smooth operation of the piston. This paper establishes the closing gap for the piston ring in the cold state.When the engine is working, the piston ring expands at high temperatures, and the closing gap in the hot state is smaller than the setting value in the cold state.The relationship between oil film thickness, friction force, and friction loss power with crankshaft angle at different closing gaps is shown in Fig. 13, Fig. 14 and Fig. 15. The variation of oil film thickness, friction force and friction loss power between piston ring and cylinder liner with crankshaft rotation angle under different closing clearances are shown in Fig. 13, Fig. 14 and Fig. 15, respectively. From the figure, it can be seen that the oil film thickness between the piston ring and the cylinder liner is gradually smaller with the increase of the closure gap and decreases more obviously. For example, when the crankshaft rotation angle is 90°, the oil film thickness under the closure gap of 0.25 mm is 0.52 μm, and under the closure gap of 0.4 mm is 0.5 μm, and friction and friction loss increase slightly with the increase of the closure gap. The existence of the closing gap will make part of the lubricant between the piston and the cylinder liner flow away through the closing gap, and a larger closing gap will cause more lubricant loss so that the oil film thickness will decrease with the increase of the closing gap. However, due to the regulating effect of the closing gap, the closing gap does not cause a more obvious effect on the up and down operation of the piston ring, the friction force and friction loss changes are not obvious.

4.2

Optimization Performance Analysis

4.2.1

Orthogonal optimization scheme

Orthogonal testing is an efficient test design method that selects a representative part of the test program from all of them based on orthogonal design.The minimum oil film thickness and friction loss work of the piston ring are used as evaluation indexes for the orthogonal optimization test.The three structural parameters of the top ring, namely the mid-bump position, effective lubrication length, and barrel height, were used as optimization factors in the orthogonal optimization test. Table 1 displays the factor levels of the orthogonal optimization test for piston ring profile parameters for the three groups of levels designed for this orthogonal test.

Table 1.

Orthogonal optimization test factor level of piston ring type line parameter

Name	Medium convex point offset	Effective lubrication length (mm)	Barrel height(μm)
Level 1	10%	5	10
Level 2	20%	5.4	14
Level 3	30%	5.8	18

4.2.2

Analysis of orthogonal optimization results

The optimization test of piston ring profile parameters designed in this paper has three factors and three levels, and a total of 27 groups of tests need to be done if the method of full-scale test is used, while only 9 groups of tests need to be carried out if the method of orthogonal test is used. Therefore, the orthogonal optimization test has the potential to significantly enhance the test efficiency.The greater the extreme results of the three factors of center bump position, effective lubrication length, and barrel height, the greater the influence of the factor on the evaluation index. The results of the orthogonal optimization test of piston ring profile parameters are shown in Table 2. The height of the barrel surface has the greatest influence on the minimum oil film thickness, while the effective lubrication length has the least influence. In addition, the position of the center bump has the greatest influence on the work of friction loss. The lower the combined score of each level, the better its effect on the minimum oil film thickness and friction loss work of the top ring.

Table 2.

Orthogonal optimization test results of piston ring line parameters

Name	Medium convex point offset	Effective lubrication length (mm)	Barrel height(μm)	Minimum oil film thickness(μm)	Friction loss work(kW)
Solution 1	10%	5	10	1.912	0.331
Solution 2	10%	5.4	14	1.829	0.325
Solution 3	10%	5.8	18	1.762	0.332
Solution 4	20%	5	14	1.859	0.312
Solution 5	20%	5.4	18	1.785	0.309
Solution 6	20%	5.8	10	2.015	0.310
Solution 7	30%	5	18	1.811	0.280
Solution 8	30%	5.4	10	2.021	0.289
Solution 9	30%	5.8	14	1.965	0.284

The results of the extreme deviation of each factor and the comprehensive score of each level are shown in Table 3. From the table, it can be seen that in the analysis of the comprehensive score of each level of the top ring profile parameters, the 3rd level of the comprehensive score of the position of the center bump is the lowest, so the center bump should be designed to be shifted upward by 30%, and similarly, the optimal design of the effective lubrication length is 4.8 mm, and the optimal design of the barrel surface height is 10 μm.

Table 3.

The difference of each factor and the overall score of each level

Name	Medium convex point offset	Effective lubrication length (mm)	Barrel height(μm)
Minimum oil film thickness
First level(i=1)	1.833	1.849	1.989
Second level(i=2)	1.881	1.874	1.892
Third level(i=3)	1.934	1.917	1.78
Aberration R	0.102	0.064	0.189
The friction loss of the top ring
First level(i=1)	0.332	0.311	0.306
Second level(i=2)	0.312	0.324	0.311
Third level(i=3)	0.286	0.32	0.303
Aberration R	0.038	0.001	0.004
Minimum oil film thickness
First level(i=1)	4	3	1
Second level(i=2)	3	2	2
Third level(i=3)	2	1	3
The evaluation index of the friction loss
First level(i=1)	4	1	2
Second level(i=2)	3	3	3
Third level(i=3)	2	2	1
Top ring type line parameter
First level(i=1)	7	4	3
Second level(i=2)	5	5	5
Third level(i=3)	3	3	4

The best-optimized solution obtained through the orthogonal optimization test is compared with the original solution, and the results of minimum oil film thickness and friction loss work of the top ring are compared, as shown in Table 4. Compared with the original scheme, the minimum oil film thickness of the optimized scheme increases by 45.67%, and the work of friction loss decreases by 3.2%.

Table 4.

The original scheme is compared with the proposed scheme

Name	Medium convex point offset	Effective lubrication length (mm)	Barrel height(μm)	Minimum oil film thickness(μm)	Friction loss work(kW)
Original plan	Unbiased shift	2.6	18	1.431	0.295
After optimization	35%	4.6	10	2.051	0.282

4.3

Analysis of the effects of predictive modeling

The input variables of the prediction model were set to be the ratio of the four additives, and the output variables were the average friction coefficient and. The model prediction results were analyzed in comparison to the actual values.The prediction of the average friction coefficient is shown in Fig. 16. From the figure, the average coefficient of friction of the real value is 0.984, and the average coefficient of friction predicted by using the model of this paper is 0.994. The prediction results of the model designed in this paper are more consistent with the real value, and the deviation of predictions is smaller, which indicates that the model fitting effect is better.

In order to further verify the reliability of the optimization scheme above, this section uses the proposed model for predicting the wear on the surface of the cylinder liner of the internal combustion engine to predict the wear on the piston rings of the cylinder liner of the internal combustion engine, which uses the optimization scheme in the previous section. The friction of the piston ring set before and after optimization is shown in Fig. 17. The friction power consumption of the piston ring set before and after optimization is shown in Fig. 18. From the figure, it can be seen that the surface wear prediction model proposed in this paper has a good prediction effect for internal combustion engine cylinder liners. The friction power of the piston ring group at the upper and lower stops is significantly improved, while the improvement of friction power at other angles of the crank angle is relatively not as obvious as that at the upper and lower stops. The friction power consumption tends to decrease throughout the cycle, especially near the upper and lower stops.

5

Conclusion

The cylinder liner piston is one of the important friction factors in internal combustion engines. Its wear state directly affects the performance and life of the internal combustion engine. Therefore, this paper proposes a method for numerical simulation and performance optimization of in-cylinder friction of the cylinder liner piston ring of an internal combustion engine based on a deep neural network. Through experimental tests, this paper concludes:

In the analysis of the comprehensive score of each level of the top ring profile parameter, the 3rd level of the comprehensive score of the mid-bump position is the lowest, so the mid-bump should be shifted upward by 30%, the optimal design of the effective lubrication length is 4.8 mm, and the optimal design of the barrel surface height is 10 μm.

After analyzing the effect of the cylinder liner surface wear prediction model proposed in this paper on the internal combustion engine, it is found that the friction of the piston ring set at the upper and lower stops has a significant improvement.

Language:: English

Publication timeframe:: 1 times per year
Journal Subjects:: Life Sciences, Life Sciences, other, Mathematics, Applied Mathematics, General Mathematics, Physics, Physics, other

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Numerical simulation and performance optimisation of in-cylinder friction of cylinder liner and piston ring in internal combustion engine based on deep neural network

Yichao Qian

Yuxian Li

Published Online: Mar 17, 2025

Received: Oct 11, 2024

Accepted: Jan 31, 2025

DOI: https://doi.org/10.2478/amns-2025-0164

KeywordsKinetic modeling, Wear prediction model, Multi-scale features, Combined recurrent neural network

© 2025 Yichao Qian et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Keywords
Kinetic modeling, Wear prediction model, Multi-scale features, Combined recurrent neural network