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##### Fatigue Analysis of the spring rack for Shredder

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Fatigue Assessment of the spring rack

Figure 1. Photo of the shredder with included spring rack

#### Introduction

Subject of the investigation was a spring rack for agricutural shredder. Photo of the shredder can be seen in Figure 1. Overall dimensions of the spring rack are shown in Figure 2.

In accordance with the Customer request two spring racks with different dimensions were analyzed for fatigue strength with a matter to check lifetime and improve existing design.

Finite element models (FEM) of spring racks were prepared and can be seen in Figure 3. FEM consists 3D hexa elements, 1D rigid and spring elements and 0D concentrated mass elements.

#### Loads and Constraints

In work condition alternating loads act on the structure.

The following max. load values were taken into account:

• longitudinal load: Fy = 200 kgf (approx. 2000 N);
• transverse load: Fz = -50 kgf / +200 kgf (appox. 500 N / 2000N);
• vertical load: Fx = 300 kgf (apporox. 3000 N).

Load schem can be seen in Figure 2.

Constraint scheme of the spring rack was the follow. Top and bottom faces of the model were fixed in vertical (DOF1=0) and horizontal (DOF3=0) directions. With CELAS2 elements small displacement of the structure was allowed in horizontal direction. Such approach was used for simulation of mounting gap (0.1 mm). Constraint scheme is shown in Figure 4.

Figure 7. Explanation of simplified "Tension-Compression" loading in time scale

#### Results Overview

1. Natural frequencies of both designs were analyzed on potential resonances. For the model №1 (diam. 145 mm) there are two natural frequencies (10.7 Hz and 11.8 Hz) which have offset from dangerous induced vibration of the equipment about 40%. For the model №2 (diam. 180 mm) which have two natural frequencies (9.5 Hz and 10.5 Hz) offset from dangerous induced vibration approx. is 47%. Based on sufficient safety factor dynamic solution was not taken into account.
2. The most critical section in the structure was analyzed using max. stress range in the cycle for load combinations. Envelope stress range results are shown in Figures 8 and 9. Detail values of the results are shown in Table 1.

Figure 2. General view of the spring rack with a schematic loads

Figure 3. Finite element model of spring rack with element type description

Figure 4. Constraints description

#### Fatigue Solution Approach

• Fatigue curve determination

The initial data for determining number of cycles maintained by the rack was the fatigue curve (SN curve).
Due to the fact that open sources have limited information on the test results of samples made of 50ХФА (GOST) steel or its analogues for endurance in the range from 10Е+07 to 10Е+09 of the number of cycles, therefore, the results of the study described in [1] were taken as the basis, where fatigue tests were described for samples made of 50CrV4 steel, which is an analogue of 50ХФА (GOST) steel. Samples were subjected to tensile-compression.

SN curve of 50CrV4 is shown in Figure 5.

• Determination of the stress range in the cycle

To determine the number of work cycles, the fatigue endurance chart shown in Figure 5 should be used. To simplify the comparative calculation of the number of cycles, instead of applying geometric / fatigue similarity coefficients (due to the difference in the physical and geometric parameters of the tested products), it was necessary to construct a geometrically similar part of the fatigue endurance curve within the limits necessary for calculation (Figure 6).

The distribution of the level of loads over time in the initial range is probably chaotic. Therefore, for a comparative calculation, the number of the worst cycles was determined. That is such cycles within which the stresses vary from the maximum possible compression value to the maximum possible tensile value, the sum of the values modulo such stresses will be considered the range of cycle stresses.

Figure 7 shows the conventional diagram of the cycle stress range (σsr):

• σmax - maximum principal tensile stress;
• σmin - minimum principal compressive stress.

Figure 5. Initial SN curve for analogue material 50CrV4

[1] International Journal of Fatigue. “Influence of inclusion size on fatigue behavior of high strength steels in the gigacycle fatigue regime.”

[2] "Gigacyclic fatigue", Levin D.M. and others, Tula, 2006. *** http://physics.tsu.tula.ru/bib/izv/6/2006-fiz-20.pdf ***

Figure 6. SN curve for used material 50ХФА (GOST)

Figure 8. Max. stress range distribution [MPa]
in the model №1 (diam. 145 mm) for load combinations

Figure 9. Max. stress range distribution [MPa]
in the model №2 (diam. 180 mm) for load combinations

Table 1. Max. stress and lifetime results.

#### Conclusions

1. It was determined that the resource of the existing rack construction (model # 1 Ø145 mm) was approximately 10Е+07 cycles before probable fatigue failures occur.
2. Based on the max. stress amplitudes in the cycle, 2 weak sections were determined (Figures 10).
3. According to the results of the calculations, the stress level for Model#2 (Ø180 mm) is 1% higher than for Model#1 (Ø145 mm), which can lead to a significant reduction in the likely number of work cycles. However, given the probabilistic nature of the phenomena of fatigue and a large effect of surface defects in metal for the cycle range (10E+07 to 10E+09) [2], it can be said that both spring racks will work approximately equally in terms of durability.

Figure 10. Max. stress range distribution [MPa] near dangerous section cut:
a) Model #1 (diam. 145 mm); b) Model #2 (diam. 180 mm)

a)

b)