**3.3 Verification of simulation method**

The purpose of this study is to quantitatively predict the residual stresses that are necessary before actual cylinder block for use. Therefore, it is important to set up an appropriate method of simulation, which is an economic evaluation method, before production. For this purpose, this study compares the surface pressure distribution of the simulation with the surface pressure prediction calculated as (**Figure 13** and Eq. 3) [6].

$$\mathbf{p} = \frac{\delta}{\frac{b}{E\_k} \left(\frac{b^2 + c^2}{c^2 - b^2} + \nu\_h\right) + \frac{b}{E\_\iota} \left(\frac{a^2 + b^2}{b^2 - a^2} - \nu\_\iota\right)}\text{ Face Pressure}\tag{3}$$

*Eh* ¼ modulus of elasticity for hole material,

*ν<sup>h</sup>* ¼ Poisson<sup>0</sup> s ratio for hole material,

*Es* ¼ modulus of elasticity for shrink material,

*ν<sup>s</sup>* ¼ Poisson<sup>0</sup> s ratio for shrink material

which is obtained by setting the following stress conditions (**Figure 14** and Eqs. (4) and (5)).

$$\frac{d\sigma\_r}{dr} + \frac{\sigma\_r - \sigma\_\theta}{r} = 0 \text{ Equilibrium Equation} \tag{4}$$

$$
\varepsilon\_r = \frac{du}{dr}, \varepsilon\_\theta = \frac{u}{r} \text{ Strain} \tag{5}
$$

*σ<sup>r</sup>* ¼ radial stress,

*σ<sup>θ</sup>* ¼ tangential stress,

*ε<sup>r</sup>* ¼ radial strain,

*εθ* ¼ tangential strain,

*u* ¼ displacement of radial direction

Point 9: The left limit of the Haigh diagram is given by the ultimate stress limit

*Fatigue lines to various fracture theories. (a) Fracture theory, and (b) Yield theory.*

*New Challenges in Residual Stress Measurements and Evaluation*

However, the S-N curve and the S-S curve can be changed by the size effect, the relative stress gradient, and the temperature effect, which are exactly the values of

under compression of the material.

*Drawing method of Haigh diagram.*

**Figure 10.**

**Figure 11.**

**132**

**Figure 16.**

**Figure 17.**

**135**

*Relationship between rates of shrink fit and residual stress.*

*State of contact pressure and residual stress.*

*Durability Assessment Considering Residual Stress DOI: http://dx.doi.org/10.5772/intechopen.90298*

**Figure 13.** *State of shrink fit.*

**Figure 14.** *Stress state.*

**Figure 15.** *Check of surface pressure.*

*Durability Assessment Considering Residual Stress DOI: http://dx.doi.org/10.5772/intechopen.90298*

**Figure 16.**

*State of contact pressure and residual stress.*

**Figure 17.** *Relationship between rates of shrink fit and residual stress.*

**Figure 14.** *Stress state.*

**Figure 15.**

**134**

*Check of surface pressure.*

**Figure 13.** *State of shrink fit.*

*New Challenges in Residual Stress Measurements and Evaluation*

The resulting equation assumes axial symmetry and does not take into account shear stress inherently. In addition, the constant surface pressure in the longitudinal direction is calculated, so it is not suitable for the shape of the cylinder block which is the object of this study, but it is judged to be suitable as the relative standard of the surface pressure to be derived from the structure simulation.

a high residual stress value. Therefore, in this study, the durability assessment was performed considering the residual stress. In addition, in this section, realistic load and boundary conditions considering the use environment are examined to improve

The cylinder block is fixed from the shoe plate of the main pump and rotates about the rotation axis. At this time, the shoe plate has a certain angle, and the stroke of the piston is generated through this. As a result, during one revolution of the cylinder block, the working fluid flows into the piston through the top dead center and the bottom dead center, and the high-pressure operating fluid what the user wants is discharged [9]. At this time, the cylinder block can be divided into a low-pressure suction portion and a high-pressure discharge portion, which is a main working load condition acting on the cylinder block. In order to quantitatively confirm the magnitude of this high pressure, this study uses the swash plate angle of the main pump, the position of the piston end when the cylinder block is rotated and the AMESim program. As a result, realistic loads such as **Figures 19** and **20** were obtained.

In addition, the boundary condition as shown in **Figure 21** was set in consideration of the operating condition of the cylinder block. The boundary conditions were fixed in the axial direction where the stopper was located, and the angle of the spline portion was fixed to prevent rigid body motion of the cylinder block. In this case, the accuracy of the simulation is ensured by applying the centrifugal force to the influence of the rotational speed of the cylinder block while rotating the cylinder block.

the reliability of the structural simulation results.

**4.1 Simulation condition of cylinder block**

*Durability Assessment Considering Residual Stress DOI: http://dx.doi.org/10.5772/intechopen.90298*

**Figure 19.**

**137**

*Piston end position from bottom for simulation.*

#### **3.4 Estimate residual stress using simulation**

The residual stress of the derived cylinder block using the structural simulation is shown in **Figure 15**. In order to determine the suitability of the simulation results, the surface pressure of the bushing was confirmed by angle. The surface pressure distribution of the simulation results follows the general shape [7] of the Hertz contact theory and most of the length of the surface pressure is higher than the constant value derived from the numerical formula (Eq. 5). The reason is that the shape of the cylinder block is not perfectly symmetrical and shear stress is generated almost everywhere (**Figures 16** and **23**).

In addition, the shape and numerical value of the residual stresses were checked within the range of possible shrink fit to confirm the aspect of the change in the residual stress with respect to the rate of shrink fit [8]. As a result, as shown in **Figure 17**, the shape of the residual stress was less dependent on the rate of shrink fit, and the numerical value of the residual stress was almost linearly related to the rate of shrink fit. Therefore, it was possible to set the rate of shrink fit and the residual stress in a linear relationship within the range of the producible shrink fit. In this study, it was possible to select the rate of shrink fit optimized for the use environment by using this relationship. If the relationship between the rate of shrink fit and the residual stress was nonlinear, then the simulation was additionally performed to find out the sections having linear relationship to find the optimal design.
