Slewing Ring Bolt Fatigue Calculation: 3 Steps for Safety

For the slewing ring bolt fatigue calculation, we estimate the fatigue limit according to our handbook. We take 0.33 as the stress concentration factor ( k_f ).

Bolts present stress concentrations in the head and thread. This factor is usually 3 for rolled bolts and 3.8 for machined ones. However, this concentration does not decisively influence static loads. This is because the yield strength is usually not exceeded.

In contrast, in fatigue analysis, the situation changes. Since it is a physical rupture calculation, the yield strength is locally exceeded. Here is where stress concentrators are determinant.

For this slewing ring bolt fatigue calculation, we use a concentration value of 3. This is because most are produced by cold rolling. You can check our Mechanical Simulation Services for more info.

k_f = \Large \frac{1}{3} \normalsize = 0.33

Once the infinite life limits (> 10^6 cycles) are established, we extrapolate the value for fewer cycles under alternating loads.

To correctly execute the slewing ring bolt fatigue calculation, we have considered the following loads:

• Alternating Moment ( M ) on the ring. This causes mean and alternating traction due to cyclic forces.
• Constant Axial Compression Load ( R_a ). This derives from the self-weight supported by the bearing. It produces compression stresses lower than the traction of the moment.

Bolts only work in traction. Therefore, they only support mean ( \sigma'_m ) and alternating ( \sigma'_a ) stresses of this type.

For this state of loads, the traction stresses in the joint are defined as:

\sigma'_a = \sigma'_m = \Large \frac{\sigma_a - \sigma_c}{2} \normalsize,   for   \sigma_a > \sigma_c

Where:

• \sigma_a : alternating stress due to moment.
• \sigma_c : compression stress due to axial load.
  Although we study all combinations, this is the most relevant for Tecma Drive S.L.

There are several recognized criteria for the slewing ring bolt fatigue calculation:

1. Soderberg Criterio
2. Modified Goodman Criterion
3. Gerber Criterion
4. ASME-elliptic Criterion

The detailed equations are in our handbook on Fluctuating Stresses. For this project, we chose the Soderberg criterion. It is the most restrictive and places us on the safe side:

\Large \frac{\sigma'_a}{S_e} \normalsize + \Large \frac{\sigma'_m}{S_y} \normalsize = 1

Knowing that:

\sigma'_a = \sigma'_m = \Large \frac{\sigma_a - \sigma_c}{2}

\sigma_a  \Large \frac{4 M}{n \phi A_s}

\sigma_c  \Large \frac{R_a}{n A_s}

Substituting stresses for loads in the Soderberg equation:

\sigma_a = \Large \frac{2 S_e  S_y}{S_e + S_y} \normalsize + \sigma_c

\Large \frac{4M}{n \phi A_s} = \Large \frac{2 S_e  S_y}{S_e + S_y} \normalsize + \Large \frac{R_a}{n A_s}

Rearranging, we obtain the limit line for the hardware analysis:

M = M* + \Large \frac{\phi}{4} \normalsize R_a

Where:

M* = M_{Sod} = \Large \frac{n \phi A_s S_e  S_y}{2(S_e + S_y)}

This indicates the alternating failure moment at infinite life with zero axial load.

We can adapt this line to other criteria by replacing the moment M* :

M_{ASME-Elliptic} = \Large \frac{n \phi A_s S_e  S_y}{2 \sqrt{(S_e + S_y)}}

M_{Goodman} = \Large \frac{n \phi A_s S_e  S_{ut}}{2(S_e + S_{ut})}

M_{Gerber} = \Large \frac{1}{4} \normalsize n \phi A_s  S^2_{ut} \left(- \Large \frac{1}{S_e} \normalsize + \Large \sqrt( \frac{1}{S^2_e} \normalsize + \Large \frac{4}{S^2_{ut}}) \right)

Variables used:

• n : number of bolts.
• \phi : position diameter.
• A_s : resistant section.
• S_e : fatigue limit.
• S_{ut} : ultimate tensile strength.
  S_y : yield strength.