# Influence of Nonstationary Processes in Drill Rigs on the Durability of Structural Elements
## 6 Endurance Research of the Drill Rig Crown Block Axis  
To illustrate the influence of nonstationary loads on the durability of structural elements, endurance research on the crown block axis in the UKB-4P drilling rig was conducted. Prediction of the crack growth rate in the crown block axis was accomplished by NASGRO equation developed by NASA:  
\[\frac{da}{dN}=C\left[\frac{1-f}{1-R}\Delta K\right]^{n}\frac{\left(1-\frac{ \Delta K_{th}}{\Delta R}\right)^{p}}{\left(1-\frac{K_{max}}{K_{c}}\right)^{q}},\]  
where \(a\)--crack length; \(N\)--number of load cycles; \(C\), \(n\), \(p\), \(q\)--experimentally determined coefficients;\(f\)--Newman function; \(R\)--cycle asymmetry coefficient; \(\Delta K\)--diapason of stress intensity factor (SIF) for a specific load, \(\Delta K=K_{max}\)--\(K_{min}\); \(\Delta K_{th}\)--minimal limit value in SIF diapason; \(K_{max}\)--maximal value of SIF; \(K_{c}\)--critical value of SIF. The minimal limit value of SIF diapason for an individual cycle that ensures crack growth is determined by the question:  
\[\Delta K_{th}=\Delta K_{0}\left(\frac{a}{a+a_{0}}\right)^{\frac{1}{2}}/\left( \frac{1-f}{(1-A_{0})(1-R)}\right)^{1+C_{th}R},\]  
where \(\Delta K_{0}\)--value of \(\Delta K\) at \(R=0\); \(a_{0}\)--constructive crack length determined by the grain size in material (for steel \(a_{0}=3.81\cdot 10^{-6}\)); \(C_{th}\)--coefficient required to correct the crack growth curve at different values \(R\): for negative \(R\), this coefficient makes 0.1; for \(R\geq 0\), this coefficient can be found in NASGRO materials database; \(A_{0}\)--constant. The critical value of SIF can be defined from the following equation:  
\[\frac{K_{c}}{K_{lc}}=1+B_{K}e^{-(A_{K}\frac{t}{t_{0}^{2}})^{2}},\]  
where \(K_{lc}\)--SIF of destruction; \(A_{k}\), \(B_{k}\)--correction factors; \(t\)--sample thickness; \(t_{0}\)--nominal thickness of the sample for a plane stress condition. Nominal thickness of sample \(t_{0}\) is defined as  
\[t_{0}=2.5\left(\frac{K_{lc}}{\sigma_{T}}\right)^{2},\]  
where \(\sigma_{T}\)--material yield strength. The Newman function describing the closing part of the crack has the following form:  
\[f=max\Big{(}R,\ A_{0}+A_{1}R+A_{2}R^{2}+A_{3}R^{3}\Big{)},\ \text{if}\ R\geq 0; \tag{28}\]  
\[f=A_{0}+A_{1}R,\ \text{if}\ -2\leq R<\!0;\ f=A_{0}-2A_{1}\ \text{if}\ R<-2. \tag{29}\]  
Coefficients in Equations (28) and (29) are defined by the following formulas:  
\[A_{0}=\big{(}0.825-0.3\alpha+0.05\alpha^{2}\big{)}cos^{1/\alpha}\Big{(}\frac{ \pi S_{max}}{2\sigma_{T}}\Big{)};\ A_{1}=(0.415-0.07\alpha)\frac{S_{max}}{ \sigma_{T}};\]  
\[A_{2}=1-A_{0}-A_{1}-A_{3};\ A_{3}=2A_{0}+A_{1}-1,\]  
where \(\alpha\)--empirical coefficient. The lifecycle duration for the drill rig crown block axis is determined by using geometric parameters of the axis, stress spectrum, and crack growth prediction algorithm inbuilt in AFGROW. Since the greatest dynamic loads on the crown block occur during the technological operation of lifting the drill pipe string from a borehole, the effect of these loads on crownblock axis endurance is considered. For this purpose, time dependences of force in the wireline are determined for all cases of lifting pipe string with a number of stands that ranges from maximal to one. The obtained results were used to attain the stress spectrum in the material of the crown block axis and assess its endurance using AFGROW software, version 5.04.05.25, finding the final number of lifts for the string until the destruction of the axis. The axis is assumed to be made of X46 steel. The crack grows from the perimeter of the circular cross-section towards the center of the axis; the initial length of the crack is set to 1.5 mm. Figure 6 shows the graphic dependence of the crack growth rate on the diapason of the stress intensity factor for the full load cycles. The values of the stress cycle asymmetry coefficient were set equal to 0, 0.2, 0.4, 0.6, and 0.75. Durability research of the axis with consideration of load mode represents certain practical interest.