**4. Improving the reliability of the most thermally stressed parts of highly accelerated engines, based on the operating conditions**

Modernization of existing and creation of new engines of high specific power causes significant difficulties since it is necessary to minimize costs during the life cycle of a structure while ensuring a set of quality indicators during given service life. At the same time, for the most thermally stressed engine parts, the provision of their physical and parametric reliability must be taken into account. The practice of operating engines testifies to cases of failure of the combustion chamber parts due to their cracking during the declared resource and the appearance of chafes and scuffs on the lateral surface of the piston [11]. A substantiated increase in the reliability of heatstressed parts of an internal combustion engine requires the use at the design stage of mathematical models that take into account a complex of factors affecting the physical and parametric reliability.

Let us consider the process of loss of structural reliability based on the model of material damage accumulation in time *d*(*τ*). At the initial moment of operation, it is usually assumed that there is no damage to the material, the reliability factor is *d* (0) = 1. Then the values *d*(*τ*\*) = 0 correspond to the limiting state of the material. The dependence of the criterion *d*(*τ*) on the level of the engine-specific power is shown in **Figure 6**. Zone I corresponds to the absence of damage accumulation during the assigned resource P, zone II—to extensive accumulation of damage, zone III—to intensive accumulation of damage, and zone IV—to the loss of reliability during

**Figure 6.** *Typical zones of change in the reliability factor of the ICE heat-stressed part.*

operation, i.e. *d*(*P*) < 0. The main factors affecting the accumulation of damage are design features of the concerned part; properties of the part material(s); ICE operating conditions and features of the working process, cooling and lubrication systems. The influence of these factors is associated with the heat-stressed state of structures due to the material creep and fatigue over time.

**Figure 7a** shows a diagram of the part critical zone deformation for the case of possible instantaneous plastic deformations and creep deformations under the conditions of deformations structural limitation. Typical examples of such zones are the edges of the pistons combustion chamber and the cylinder head cross-sections between the valve orifice and the injector bore. Here, sections 1–2–3–4 denote the initial engine load, 4–5—work in a stationary heavy operating mode, 5–6–7–8—load reduction to a certain partial mode, 8–9—work in a stationary partial mode, 9–10—subsequent engine load to previous heavy-duty level. In this case, sections 1–2 and 5–6 correspond to the material elastic deformation, sections 2–3 and 6–7: creep deformation and stress relaxation, in sections 3–4 and 7–8 the creep process is accompanied by instant plastic deformations, and in Section 4–5 and 8–9 are characterized by stress relaxation.

In this case, the common condition for ensuring physical reliability during the work of the part material in such zones on the verge of strength are:

$$d\_1(\Xi, P) = \wp\_{\mathcal{f}}(\Xi, t(\tau), \sigma(\tau)) = \mathbf{1} - \sum\_{k=1}^{N\_P} \frac{\mathbf{1}}{N\_{sk}} - \sum\_{k=1}^{N\_P} \frac{\mathbf{1}}{N\_{fk}} > \mathbf{0},\tag{13}$$

where Ξ is the operating model of an engine for a specific purpose, Ξ ¼ *ζ*1, *ζ*<sup>2</sup> f g , … , *ζ<sup>n</sup>* ; *k* ¼ 1, *Np* � �<sup>Ξ</sup> <sup>¼</sup> <sup>ξ</sup>1, <sup>ξ</sup><sup>2</sup> f g , … , <sup>ξ</sup><sup>N</sup> —single-engine load cycle; *Np*—total number of engine load cycles during a given resource *P*; *t*—current temperature state of the part in the investigated area; σ—current tension value; *N*sk—number of cycles until material failure due to creep under the conditions of the *k*-th cycle of loads; *N*fk—number of cycles until material failure due to fatigue under the conditions of the *k*-th load cycle.

In practice, the choice of technical solutions to improve the physical reliability of the high specific power ICE heat-stressed parts corresponds to the solution of the

**Figure 7**. *Typical variants of deformation of the critical zone of ICE heat-stressed part.*

problem of transition of the calculated result in Eq. (13), in accordance with **Figure 1**, from zone IV to zone III.

**Figure 7b** presents a variant of the part critical zone deformation with practically no limitation of creep deformations. Side surface of the piston is a typical example of such a zone. Here sections 1–2–3 denote the initial engine load, 3–4—work on the stationary heavy operation mode, 4–5—load reduction to a certain partial mode and work on the stationary partial mode, 5–6-7—subsequent engine load to the level of the previous heavy-duty and 7–8—subsequent work on the stationary mode. In this case, sections 1–2 and 5–6 correspond to the material elastic deformation, and 2–3–4 and 6– 7–8 correspond to creep deformation *εs*, which increases with time.

Methods for determining the profile of the piston lateral surface are known. They consist in determining the clearance Δ*R*set(*hi*, *θi*) when installing a piston in a cylinder that is variable in height *hi* in piston circumferential direction *θi*. Subsequently, in the process of friction pair surfaces wear, the real gap increases to the permissible value [Δ*R*set]. Accordingly, the structure parametric reliability criterion is represented by the expression [12]:

$$0 < \Delta R\_{\text{set}}(h\_i, \theta\_i, \tau) \le \left[\Delta R\_{\text{set}}(P)\right] \tag{14}$$

With an increase in the level of engine boost due to the appearance of creep deformation, in accordance with **Figure 7b**, the size of the gap along with some coordinates hi, θ*<sup>i</sup>* may not increase, but decrease until chafing and scuffing occur, that is, the theoretical mutual penetration of the piston and cylinder materials, Δ*R*set (*hi*, *θi*, *τ*) < 0. Therefore, to the condition for ensuring parametric reliability in Eq. (14), it is necessary to add the condition for parametric reliability not to exceed the material creep limit:

$$d\_2(\Xi) = \begin{cases} 1, & \wp\_\iota(t,\sigma) \ge 1 \\ \wp\_\iota(t,\sigma), \wp\_\iota(t,\sigma) < 1 \end{cases},\tag{15}$$

where ϕ*<sup>s</sup>* is the function of bringing the creep threshold to the criterion *d*2.

Thus, the choice of technical solutions to improve the parametric reliability of the ICE piston side surface corresponds to the solution of the problem of transition of the calculated result from zone II to zone I (**Figure 6**).

To obtain a reliable result of the part guaranteed reliability, it is necessary to have input information about the non-stationary low-frequency and high-frequency temperature state of the structure in accordance with the adopted operating model:

$$t\_k(\tau) = \tilde{t}\_k(\tau) + \tilde{t}\_k(\tau) \tag{16}$$

$$
\sigma\_k(\mathfrak{r}) = \overline{\sigma}\_k(\mathfrak{r}) + \widetilde{\sigma}\_k(\mathfrak{r}) \tag{17}
$$

where the values *tk*ð Þ*τ* and *σk*ð Þ*τ* correspond to the instantaneous averaged values of the low-frequency change in temperatures and thermal stresses in the investigated area of the part under the conditions of a single load cycle of the type *<sup>k</sup>*, and~*tk*ð Þ*<sup>τ</sup>* <sup>і</sup>*σ*~*k*ð Þ*<sup>τ</sup>* correspond to the instantaneous deviation of temperatures and thermal stresses from the average value.

Formulation of the problem in the form Eqs. (16) and (17) with the subsequent use of model Eq. (13) significantly increases the design time. Therefore, a simplification of problem Eqs. (16) and (17) is proposed, which does not contradict the principle of

guaranteed ensuring the strength of a part during design [13]. With a load surge and engine operation in a heavy stationary mode, we take:

$$t\_k^{ab}(\tau) = \overline{t}\_k(\tau) + \widetilde{t}\_k^{b\max} \tag{18}$$

$$
\sigma\_k^{ab}(\mathfrak{r}) = \overline{\sigma}\_k(\mathfrak{r}) + \tilde{\sigma}\_k^{b \text{ min}} \tag{19}
$$

With a load drop and engine operation in a less heavy stationary mode, we take:

$$t\_k^{cd}(\tau) = \overline{t}\_k(\tau) + \widetilde{t}\_k^{d\max} \tag{20}$$

$$
\sigma\_k^{cd}(\tau) = \overline{\sigma}\_k(\tau) + \tilde{\sigma}\_k^{d \max} \tag{21}
$$

A graphical explanation of the values used is shown in **Figure 8**.

On the basis of the proposed approaches, we determined the reliability criteria *d*1(*Ξ*, *P*) and *d*2(*Ξ*) relative to the piston of a tractor diesel engine of the SMD type (the engine cylinder diameter is 120 mm, the piston stroke is 140 mm, and the number of cylinders is 4), the boundary conditions of heat transfer for which are well known. The main piston material is the AK12M2MgN alloy. A piston of traditional design and with a heat-insulating layer on the surface of the combustion chamber is considered. Layer material—Al2O3. Layer thickness—0.25 mm. For a piston with a surface layer, the analysis was carried out according to the parameters under the thermal insulation layer. The calculation of the value *d*1(Ξ, *P*) was carried out for the edge of the piston combustion chamber with a liter diesel power of 25 and 29 kW/l using the RESURS program (Pylyov, V.О., Prokopenko, M.V., Shekhovtsov, A.F.: Resurs. UA Computer Software 5915, 16 July 2002). The value of *Nsk* in Eq. (13) was determined by the energy criterion of Sosnin, the value of Nfk—on the basis of the generalized Neuber principle [14]. The calculated base is taken as *P* = 10,000 hours. The engine operation model is adopted for an agricultural tractor [14]. The number of calculation cycles

#### **Figure 8.**

*Local temperature (left) and thermal stress (right) in a single loading cycle of the studied zone of the piston: a temperature and b—stress state of the studied area of the part: a—load surge; b—heavily loaded stationary mode; c —load drop; d—less loaded stationary mode.*

**Figure 9.**

*Control points on the piston: a—Location of control points on the piston for levels a—D; b—Change in the thermally stressed state for control points.*

*N* = 80,800. The main calculation results are given in **Table 2**. It can be seen from the Table that for a given uncoated piston with a liter engine power of 25 kW/l, there is no cracking of the combustion chamber edge during a given resource, *d*1(Ξ, *P*) **=** 0.552. But with a liter power of 29 kW/l, the resource is not guaranteed, *d*1(Ξ, *P*) < 0. This means that at a power level of 25 kW/l, the piston is practically working on the verge of physical reliability. But with a thermal barrier layer with a liter engine power of 29 kW/l, the parameter of the physical reliability of the piston is 0.574, i.e. the reliability of the structure has been restored.

The calculated data on the structure thermal stress are also sufficient to determine the parametric reliability of the piston lateral surface *d*2(Ξ). The piston control points to be analyzed are shown in **Figure 9a**. The arrangement of the calculation array results for a piston with a thermal barrier layer at a liter engine power level of 29 kW/l is shown in **Figure 9b**. The data on the reduction of the creep threshold of the alloy to the criterio*n* d2(Ξ) in Eq. (15) were taken on the basis of work [14], *φ<sup>s</sup>* ¼ ð Þ 2, 5*σ* þ *t =*225. The figure shows that the parametric reliability of the structure is ensured.

The proposed approach to the analysis of the reliability of structures of heatstressed parts of highly accelerated engines takes into account the operating model and allows you to search for technical solutions while ensuring the operation of materials of structures on the verge of strength.

For monitoring and predicting the residual life of the most thermally stressed parts under engine operating conditions, the proposed methodology allows using modern 4.0 technologies.
