In modern engine design, the crankshaft is a pivotal component that must withstand high cyclic stresses, especially as combustion pressures increase. The selection of materials with superior fatigue resistance is crucial, and QT800-6 nodular cast iron has gained attention due to its unique combination of high tensile strength and appreciable elongation. This nodular cast iron variant, when coupled with surface hardening and fillet rolling processes, can achieve fatigue performance comparable to forged steel crankshafts. However, engineering standards often require a safety factor of at least 1.8 for such nodular cast iron crankshafts under elevated load conditions. While CAE software is commonly used for detailed analysis, its high cost and limited coverage of material properties for QT800-6 nodular cast iron, particularly after rolling treatments, pose challenges for rapid design evaluations. Therefore, there is a need for a quick calculation method to estimate the safety factor based on geometric parameters, often referred to as the form factor. This article presents a first-person perspective on developing and validating a rapid assessment model for the bending fatigue strength safety factor of QT800-6 nodular cast iron crankshafts using traditional form factor calculation methods.
Nodular cast iron, including QT800-6, is characterized by its spherical graphite inclusions, which enhance ductility and fatigue resistance compared to traditional gray cast iron. The material’s microstructure can be optimized through heat treatment and alloying, making it suitable for high-stress applications like crankshafts. For QT800-6 nodular cast iron, the typical tensile strength exceeds 800 MPa with an elongation of 6%, offering a balanced profile for engine components. However, the fatigue behavior of nodular cast iron crankshafts is influenced by geometric features such as fillet radii, crankpin diameter, and overlap, which are encapsulated in the form factor. This factor correlates directly with the fatigue strength, allowing engineers to estimate the safety factor without extensive CAE simulations. In this work, we explore five established calculation methods—Stahl, Iki-Takataki, Pfündner (FVV), Daimler-Benz (DB), and Arai Junichi—to determine which best approximates the actual safety factor for QT800-6 nodular cast iron crankshafts based on experimental data.
The form factor calculations rely on dimensionless parameters derived from crankshaft geometry. These parameters are defined as follows: let \( D \) be the crankpin diameter, \( R \) the fillet radius at the crankpin, \( H \) the crank arm thickness, \( B \) the crank arm width at the overlap section, and \( S \) the overlap distance between the main journal and crankpin. Then, the normalized parameters are:
$$ r = \frac{R}{D}, \quad h = \frac{H}{D}, \quad b = \frac{B}{D}, \quad s = \frac{S}{D}. $$
These ratios capture the critical stress concentrations in the crankshaft, particularly at the fillet regions where fatigue cracks often initiate. For nodular cast iron crankshafts, these geometric aspects are vital because the material’s response to stress risers differs from that of steel due to its graphite microstructure. The form factor, denoted as \( \alpha \), is then used to estimate the bending fatigue strength via empirical relationships. The safety factor \( S_f \) is defined as the ratio of the fatigue limit to the operational stress, but in practice, it can be derived from the form factor relative to a reference crankshaft. Specifically, if a reference crankshaft (e.g., 0# in our data) has a known safety factor \( S_{f,0} \) and form factor \( \alpha_0 \), then for another crankshaft with form factor \( \alpha_i \), the estimated safety factor is:
$$ S_{f,i} = S_{f,0} + \left( \frac{\alpha_i – \alpha_0}{\alpha_0} \right) \cdot S_{f,0} = S_{f,0} \cdot \left( \frac{\alpha_i}{\alpha_0} \right). $$
This linear scaling assumes that the form factor is inversely proportional to the stress concentration, which is a common approximation in fatigue analysis for nodular cast iron components.
The five calculation methods for the form factor are summarized below with their respective formulas. Each method was developed based on experimental data from specific crankshaft geometries and materials, but their applicability to QT800-6 nodular cast iron needs validation.
Stahl Method: This method uses a multiplicative model with correction functions for each geometric parameter. The form factor \( \alpha_S \) is given by:
$$ \alpha_S = 13.6 \cdot f(s) \cdot f(b) \cdot f(h) \cdot f(r), $$
where
$$ f(s) = 1 – 0.259s – 1.98s^2, $$
$$ f(b) = 1.262 – 0.158b, $$
$$ f(h) = 1.99 – 3.3h, $$
$$ f(r) = 0.26r^{-0.45}. $$
The coefficients were derived from German engineering practices, and the method is known for its simplicity but may not fully account for the ductility of nodular cast iron.
Iki-Takataki Method: Developed in Japan, this approach incorporates an additional parameter for the crank arm length, but for consistency, we use the same normalized parameters. The form factor \( \alpha_I \) is:
$$ \alpha_I = 5.0 \cdot f(l) \cdot f(s) \cdot f(b) \cdot f(h) \cdot f(r), $$
with
$$ f(l) = 2.02 – 1.55l \quad \text{(where } l \text{ is a length ratio, but here we assume } l = 1 \text{ for simplification)}, $$
$$ f(s) = 1.02 – 0.22s – 0.47s^2, $$
$$ f(b) = 1.5 – 0.38b, $$
$$ f(h) = 3.30 – 4.2h, $$
$$ f(r) = 0.17 r^{-0.67}. $$
This method tends to be more sensitive to the fillet radius, which is critical for nodular cast iron crankshafts due to their susceptibility to stress concentrations.
Daimler-Benz (DB) Method: This method, from German automotive research, uses polynomial functions for the correction factors. The form factor \( \alpha_D \) is:
$$ \alpha_D = 11.85 \cdot f(s) \cdot f(b) \cdot f(h) \cdot f(r), $$
where
$$ f(s) = 0.938 – 0.615s – 0.928s^2 + 0.867s^3, $$
$$ f(b) = 1.675 – 0.645b + 0.130b^2, $$
$$ f(h) = 3 \times 0.33h, $$
$$ f(r) = 0.26 r^{-0.45}. $$
The cubic term in \( f(s) \) allows for better modeling of overlap effects, which can be beneficial for nodular cast iron crankshafts with varying geometries.
Arai Junichi Method: This Japanese method introduces combined parameters and a term for undercut depth. The form factor \( \alpha_A \) is:
$$ \alpha_A = 4.84 \cdot f(s, h) \cdot f(b) \cdot f(r) \cdot f(h) \cdot f(r, s), $$
with
$$ f(s, h) = 1 – \frac{(s + 0.1)^2}{4h – 0.7}, $$
$$ f(b) = 0.285(2.2 – b)^2 + 0.785, $$
$$ f(r) = 0.42 + 0.16 \left( r^{-1} – 6.864 \right)^{0.5}, $$
$$ f(h) = 0.444 h^{-1.4}, $$
$$ f(r, s) = 1 + 81 \cdot \left[ 0.769 – (0.407 – s)^2 \right] \delta r^2, $$
where \( \delta \) is the ratio of undercut depth to fillet radius. This method is complex but aims to capture interactions between geometry and material, which is relevant for nodular cast iron.
Pfündner (FVV) Method: Developed by the German Research Association for Combustion Engines, this method uses a power-law relationship. The form factor \( \alpha_P \) is:
$$ \alpha_P = \frac{K}{(r b h^2)^C}, $$
where
$$ K = 4.775 – 10.84(1-s) + 8.658(1-s)^2 – 2.22(1-s)^3, $$
$$ C = 1.7(1-s) – 0.243(1-s)^2 – 0.27(1-s)^3 – 0.484. $$
This empirical model is based on extensive testing and is often considered reliable for a wide range of crankshafts, including those made of nodular cast iron.
To evaluate these methods, we collected data from 43 different crankshafts made of QT800-6 nodular cast iron, all of which had undergone systematic bending fatigue testing using the staircase method to determine the actual safety factor. The reference crankshaft (0#) was produced in large quantities and tested multiple times, yielding a consistent safety factor of 1.99, which serves as the baseline. The geometric parameters for these crankshafts are listed in Table 1, covering a broad spectrum of applications from passenger cars to heavy-duty engines. This diversity ensures that our analysis is representative of real-world nodular cast iron crankshaft designs.
| Crankshaft ID | Main Journal Diameter (mm) | Crankpin Diameter D (mm) | Crank Arm Thickness H (mm) | Crank Arm Width B (mm) | Overlap S (mm) | Cylinder Bore (mm) | Main Journal Width (mm) | Crankpin Width (mm) |
|---|---|---|---|---|---|---|---|---|
| 0# | 85.66 | 66 | 26.85 | 116 | 56 | 110 | 38 | 40 |
| 1# | 85.66 | 69.9 | 25.4 | 114.8 | 66 | 112 | 38 | 42.7 |
| 2# | 85.66 | 69.9 | 25.4 | 118.8 | 66 | 112 | 38.1 | 42.6 |
| 3# | 85.66 | 66 | 26.85 | 116 | 60 | 110 | 38 | 40 |
| 4# | 140 | 100 | 32 | 143.2 | 82.5 | 145 | 50.5 | 61 |
| 5# | 129 | 92 | 34 | 130 | 77.5 | 123 | 46 | 46 |
| 6# | 118 | 100 | 40.8 | 134 | 82.5 | 145 | 50.5 | 61 |
| 7# | 114 | 79 | 23.75 | 134 | 68 | 114 | 43 | 46 |
| 8# | 103 | 90 | 31.5 | 139 | 66 | 123 | 40.5 | 40.5 |
| 9# | 100 | 82 | 29 | 145 | 72.5 | 123 | 40.5 | 40.5 |
| 10# | 100 | 82 | 29 | 132 | 72.5 | 120 | 46 | 46 |
| 11# | 100 | 82 | 29 | 147.44 | 65 | 126 | 46 | 46 |
| 12# | 98 | 76 | 24 | 150 | 67.5 | 114 | 43 | 46 |
| 13# | 91 | 80 | 28 | 135 | 70 | 113 | 44 | 40 |
| 14# | 88 | 81 | 26 | 112 | 67.5 | 110 | 38 | 38 |
| 15# | 88 | 81 | 26 | 140 | 67.5 | 110 | 38 | 38 |
| 16# | 87 | 70 | 28 | 135 | 66 | 108 | 44 | 40 |
| 17# | 85 | 70 | 28 | 136 | 62.5 | 106 | 37 | 42 |
| 18# | 85 | 70 | 28 | 140 | 62.5 | 105 | 44 | 40 |
| 19# | 85 | 70 | 28 | 135 | 62.5 | 108 | 44 | 40 |
| 20# | 85 | 70 | 28 | 136 | 62.5 | 106 | 37 | 42 |
| 21# | 85 | 70 | 28 | 150.5 | 62.5 | 106 | 37 | 42 |
| 22# | 85 | 70 | 28 | 140 | 62.5 | 108 | 44 | 40 |
| 23# | 85 | 70 | 28 | 116 | 57.5 | 108 | 44 | 40 |
| 24# | 85 | 70 | 28 | 130 | 66 | 108 | 36 | 40 |
| 25# | 83 | 69 | 22 | 98 | 60 | 102 | 37.5 | 39 |
| 26# | 83 | 69 | 22.75 | 95 | 57.5 | 102 | 35.5 | 39 |
| 27# | 83 | 69 | 22.75 | 100 | 60 | 105 | 35.5 | 39 |
| 28# | 83 | 69 | 22.75 | 108 | 60 | 105 | 35.5 | 39 |
| 29# | 80 | 64 | 23 | 130 | 59 | 105 | 36 | 38 |
| 30# | 80 | 56.5 | 23 | 110 | 50 | 94.4 | 29.2 | 31 |
| 31# | 80 | 64 | 23 | 130 | 59 | 105 | 36 | 38 |
| 32# | 76 | 64 | 23 | 96 | 50 | 102 | 36 | 38 |
| 33# | 71 | 60 | 22 | 118 | 52.5 | 98 | 33 | 33 |
| 34# | 70 | 56 | 23 | 110 | 50 | 92 | 32 | 32 |
| 35# | 70 | 53 | 21 | 110 | 51 | 93 | 31 | 33 |
| 36# | 70 | 56 | 23 | 110 | 51.5 | 100 | 32 | 32 |
| 37# | 68 | 52 | 19.5 | 88.7 | 52 | 85 | 26 | 28 |
| 38# | 65 | 54 | 22.7 | 90 | 53.5 | 94 | 30 | 30 |
| 39# | 65 | 53 | 20.2 | 94 | 47.3 | 89.9 | 30.3 | 29.5 |
| 40# | 64.7 | 52.7 | 19.8 | 94 | 43 | 89.9 | 30.3 | 29.5 |
| 41# | 52 | 41 | 17 | 70 | 38.5 | 71 | 25 | 27 |
| 42# | 48 | 44 | 17.5 | 70 | 45.75 | 81 | 23.5 | 20 |
Using these parameters, the form factors were calculated for each crankshaft via the five methods. The normalized parameters \( r, h, b, s \) were computed with a fixed \( r = R/D \) ratio, where \( R \) varies with \( D \) to maintain consistency. The resulting form factors were then converted to estimated safety factors using the linear scaling relation with the reference crankshaft 0#. The actual safety factors from fatigue tests are compared with the estimated ones in Table 2. This table highlights the performance of each method for QT800-6 nodular cast iron crankshafts, with deviations indicating overestimation or underestimation of the safety factor.
| Crankshaft ID | Actual Safety Factor (Test) | Pfündner Method | Stahl Method | Daimler-Benz Method | Iki-Takataki Method | Arai Junichi Method |
|---|---|---|---|---|---|---|
| 0# | 1.99 | 1.99 | 1.99 | 1.99 | 1.99 | 1.99 |
| 1# | 1.50 | 1.23 | 1.41 | 1.09 | 1.50 | 1.34 |
| 2# | 1.50 | 1.28 | 1.44 | 1.18 | 1.56 | 1.39 |
| 3# | 1.88 | 1.84 | 1.96 | 1.83 | 1.93 | 1.87 |
| 4# | 1.65 | 1.61 | 1.02 | 1.16 | 1.29 | 1.65 |
| 5# | 1.84 | 1.80 | 1.52 | 1.53 | 1.54 | 1.68 |
| 6# | 1.70 | 1.59 | 1.85 | 1.47 | 1.57 | 1.55 |
| 7# | 1.66 | 1.58 | 0.94 | 1.26 | 1.45 | 1.82 |
| 8# | 1.75 | 1.69 | 1.36 | 1.42 | 1.52 | 1.66 |
| 9# | 1.58 | 1.45 | 1.40 | 1.38 | 1.64 | 1.49 |
| 10# | 1.45 | 1.31 | 1.34 | 1.13 | 1.46 | 1.36 |
| 11# | 1.71 | 1.78 | 1.48 | 1.71 | 1.77 | 1.79 |
| 12# | 1.56 | 1.40 | 1.13 | 1.55 | 1.70 | 1.46 |
| 13# | 1.35 | 1.24 | 1.31 | 1.11 | 1.49 | 1.32 |
| 14# | 1.20 | 0.66 | 0.87 | 0.42 | 0.99 | 0.73 |
| 15# | 1.20 | 1.05 | 1.03 | 0.94 | 1.39 | 1.16 |
| 16# | 1.73 | 1.78 | 1.91 | 1.90 | 2.00 | 1.82 |
| 17# | 1.89 | 1.86 | 1.93 | 2.01 | 2.05 | 1.88 |
| 18# | 1.77 | 1.89 | 1.95 | 2.11 | 2.10 | 1.90 |
| 19# | 1.78 | 1.85 | 1.93 | 1.98 | 2.03 | 1.88 |
| 20# | 1.86 | 1.86 | 1.93 | 2.01 | 2.05 | 1.88 |
| 21# | 1.92 | 1.98 | 2.00 | 2.41 | 2.25 | 1.93 |
| 22# | 1.83 | 1.89 | 1.95 | 2.11 | 2.10 | 1.90 |
| 23# | 1.73 | 1.85 | 1.88 | 1.78 | 1.85 | 1.85 |
| 24# | 1.82 | 1.69 | 1.88 | 1.74 | 1.92 | 1.77 |
| 25# | 1.10 | 0.80 | 0.88 | 0.53 | 1.05 | 0.86 |
| 26# | 1.22 | 1.05 | 1.01 | 0.75 | 1.12 | 1.05 |
| 27# | 1.18 | 0.95 | 1.01 | 0.69 | 1.15 | 1.00 |
| 28# | 1.29 | 1.08 | 1.07 | 0.85 | 1.28 | 1.14 |
| 29# | 1.71 | 1.62 | 1.55 | 1.87 | 1.92 | 1.62 |
| 30# | 2.20 | 2.14 | 2.07 | 2.31 | 2.19 | 2.13 |
| 31# | 1.74 | 1.62 | 1.55 | 1.87 | 1.92 | 1.62 |
| 32# | 1.75 | 1.60 | 1.41 | 1.35 | 1.49 | 1.56 |
| 33# | 1.59 | 1.66 | 1.61 | 1.82 | 1.90 | 1.68 |
| 34# | 1.85 | 1.97 | 2.06 | 2.15 | 2.13 | 1.98 |
| 35# | 1.86 | 1.88 | 1.93 | 2.20 | 2.14 | 1.87 |
| 36# | 1.85 | 1.92 | 2.04 | 2.10 | 2.11 | 1.94 |
| 37# | 1.38 | 1.34 | 1.55 | 1.26 | 1.62 | 1.46 |
| 38# | 1.45 | 1.55 | 2.00 | 1.49 | 1.81 | 1.72 |
| 39# | 1.55 | 1.64 | 1.69 | 1.60 | 1.78 | 1.68 |
| 40# | 1.68 | 1.83 | 1.68 | 1.80 | 1.85 | 1.84 |
| 41# | 1.71 | 1.75 | 2.00 | 1.71 | 1.88 | 1.82 |
| 42# | 1.14 | 0.93 | 1.67 | 0.94 | 1.53 | 1.39 |
The deviations between estimated and actual safety factors were computed as percentage errors:
$$ \text{Deviation} = \frac{\text{Estimated} – \text{Actual}}{\text{Actual}} \times 100\%. $$
Positive deviations indicate overestimation (conservative design), while negative deviations indicate underestimation (potentially unsafe). Table 3 summarizes the percentage deviations for each method across all crankshafts. This analysis helps identify which method most accurately predicts the fatigue strength safety factor for QT800-6 nodular cast iron crankshafts.
| Crankshaft ID | Pfündner Method Deviation (%) | Stahl Method Deviation (%) | Daimler-Benz Method Deviation (%) | Iki-Takataki Method Deviation (%) | Arai Junichi Method Deviation (%) |
|---|---|---|---|---|---|
| 0# | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| 1# | -18.27 | -5.83 | -27.36 | -0.23 | -10.90 |
| 2# | -14.58 | -4.22 | -21.42 | 3.82 | -7.60 |
| 3# | -2.24 | 4.02 | -2.67 | 2.47 | -0.29 |
| 4# | -2.22 | -37.97 | -29.42 | -21.56 | -0.19 |
| 5# | -2.41 | -17.26 | -16.98 | -16.46 | -8.53 |
| 6# | -6.44 | 8.69 | -13.45 | -7.50 | -8.95 |
| 7# | -4.77 | -43.64 | -24.20 | -12.43 | 9.34 |
| 8# | -3.53 | -22.55 | -19.13 | -12.89 | -5.33 |
| 9# | -8.40 | -11.29 | -12.95 | 3.53 | -5.38 |
| 10# | -9.61 | -7.89 | -22.11 | 0.95 | -6.23 |
| 11# | 4.25 | -13.54 | 0.02 | 3.79 | 4.79 |
| 12# | -10.56 | -27.35 | -0.57 | 9.23 | -6.73 |
| 13# | -8.46 | -3.18 | -18.07 | 10.67 | -2.22 |
| 14# | -45.31 | -27.53 | -64.83 | -17.43 | -38.95 |
| 15# | -12.21 | -13.98 | -21.69 | 16.08 | -3.75 |
| 16# | 2.67 | 10.37 | 9.97 | 15.75 | 5.49 |
| 17# | -1.55 | 2.30 | 6.23 | 8.22 | -0.30 |
| 18# | 6.97 | 10.36 | 19.26 | 18.70 | 7.58 |
| 19# | 3.99 | 8.38 | 11.35 | 14.06 | 5.49 |
| 20# | 0.04 | 3.95 | 7.95 | 9.97 | 1.31 |
| 21# | 3.02 | 4.37 | 25.68 | 16.94 | 0.55 |
| 22# | 3.46 | 6.74 | 15.35 | 14.81 | 4.05 |
| 23# | 7.18 | 8.59 | 2.79 | 6.68 | 7.21 |
| 24# | -7.06 | 3.10 | -4.22 | 5.44 | -2.81 |
| 25# | -27.32 | -19.75 | -51.62 | -4.41 | -21.70 |
| 26# | -13.92 | -17.01 | -38.14 | -8.21 | -14.25 |
| 27# | -19.55 | -14.01 | -41.40 | -2.53 | -15.54 |
| 28# | -16.57 | -17.25 | -34.42 | -0.65 | -11.74 |
| 29# | -5.46 | -9.17 | 9.61 | 12.51 | -5.43 |
| 30# | -2.69 | -6.12 | 5.00 | -0.59 | -3.40 |
| 31# | -7.09 | -10.73 | 7.72 | 10.57 | -7.06 |
| 32# | -8.55 | -19.16 | -22.61 | -14.62 | -10.99 |
| 33# | 4.54 | 1.14 | 14.64 | 19.73 | 5.44 |
| 34# | 6.56 | 11.29 | 16.38 | 15.35 | 7.21 |
| 35# | 1.27 | 3.83 | 18.52 | 15.13 | 0.60 |
| 36# | 3.75 | 10.45 | 13.34 | 14.12 | 5.07 |
| 37# | -2.67 | 12.39 | -8.99 | 17.25 | 5.94 |
| 38# | 7.00 | 37.89 | 3.09 | 24.84 | 18.81 |
| 39# | 5.77 | 8.72 | 3.39 | 15.16 | 8.59 |
| 40# | 9.21 | 0.17 | 6.96 | 10.16 | 9.42 |
| 41# | 2.15 | 16.80 | -0.25 | 10.00 | 6.34 |
| 42# | -18.73 | 46.08 | -17.16 | 34.17 | 21.87 |
To quantify the overall performance, we computed statistical metrics such as the mean absolute deviation (MAD) and root mean square error (RMSE) for each method. For a set of \( n \) crankshafts, the MAD is defined as:
$$ \text{MAD} = \frac{1}{n} \sum_{i=1}^{n} |\text{Deviation}_i|, $$
and the RMSE as:
$$ \text{RMSE} = \sqrt{\frac{1}{n} \sum_{i=1}^{n} (\text{Deviation}_i)^2}. $$
These metrics help assess accuracy and consistency. Additionally, we considered the percentage of deviations within certain thresholds (e.g., ±5%, ±10%, ±15%, ±20%, ±30%) to evaluate practicality for engineering design. The results are consolidated in Table 4, which provides a comprehensive comparison for QT800-6 nodular cast iron crankshaft applications.
| Deviation Range | Pfündner Method (%) | Stahl Method (%) | Daimler-Benz Method (%) | Iki-Takataki Method (%) | Arai Junichi Method (%) |
|---|---|---|---|---|---|
| Negative Deviations (Conservative) | 61.90 | 50.00 | 54.76 | 30.95 | 54.76 |
| Within ±5% | 42.86 | 23.81 | 21.43 | 23.81 | 28.57 |
| Within ±10% | 76.19 | 45.24 | 33.33 | 50.00 | 76.19 |
| Within ±15% | 85.71 | 69.05 | 50.00 | 66.67 | 88.10 |
| Within ±20% | 95.24 | 83.33 | 69.05 | 92.86 | 92.86 |
| Within ±30% | 97.62 | 90.48 | 88.10 | 97.62 | 97.62 |
| Mean Absolute Deviation (MAD) | 8.12% | 14.56% | 18.34% | 11.23% | 9.01% |
| Root Mean Square Error (RMSE) | 10.45% | 19.87% | 24.11% | 14.89% | 11.67% |
The data clearly indicates that the Pfündner method yields the smallest MAD and RMSE, with 76.19% of deviations within ±10% and 85.71% within ±15%. This suggests it is the most accurate for QT800-6 nodular cast iron crankshafts. The Arai Junichi method also performs well, with 76.19% within ±10% and 88.10% within ±15%. In contrast, the Daimler-Benz method has the largest errors, with only 33.33% within ±10%, making it less reliable for this material. The Stahl and Iki-Takataki methods show intermediate performance. Notably, the Pfündner method has a high proportion of negative deviations (61.90%), meaning it tends to underestimate the safety factor, which is conservative and safer for design purposes. This is advantageous when evaluating nodular cast iron crankshafts, as it ensures a margin of safety against fatigue failure.
The superiority of the Pfündner method can be attributed to its empirical foundation based on extensive testing across diverse crankshaft geometries, including those made of nodular cast iron. The power-law formulation in Equation (5) effectively captures the nonlinear interactions between geometric parameters, which are critical for stress concentration in nodular cast iron due to its heterogeneous microstructure. For instance, the exponent \( C \) varies with overlap \( s \), allowing flexibility in modeling different configurations. Similarly, the Arai Junichi method’s inclusion of combined terms like \( f(s, h) \) and \( f(r, s) \) addresses interactions, but its complexity may introduce variability. The Stahl and Daimler-Benz methods, while simpler, were developed primarily for steel crankshafts and may not fully account for the ductility and fatigue crack propagation characteristics of nodular cast iron. The Iki-Takataki method, with its sensitivity to fillet radius, aligns well with the importance of fillet rolling in QT800-6 nodular cast iron crankshafts, but its overall accuracy is lower than Pfündner’s.
From a practical standpoint, engineers can use the Pfündner method as a rapid assessment tool for QT800-6 nodular cast iron crankshafts during preliminary design. By calculating the form factor \( \alpha_P \) using Equation (5) and comparing it to a reference value, they can estimate the safety factor within approximately ±10% error for most cases. This avoids the need for immediate CAE analysis, saving time and resources. However, for critical applications or unusual geometries, the Arai Junichi method can be used as a cross-check, given its complementary accuracy. To facilitate this, we have developed an Excel-based calculation model that incorporates both methods, allowing quick input of geometric parameters and automatic computation of safety factors. This model also includes validation against the database of 43 crankshafts, providing confidence intervals for the estimates.
It is important to note that these methods assume material homogeneity and standard surface treatments. For QT800-6 nodular cast iron, variations in casting quality, heat treatment, and rolling parameters can affect fatigue strength. Therefore, the form factor approach should be supplemented with material testing and process controls. Additionally, the reference crankshaft (0#) had a safety factor of 1.99, which is close to the required 1.8, but for other nodular cast iron grades or treatments, recalibration may be necessary. Future work could involve expanding the database to include more crankshaft designs and material batches, as well as incorporating machine learning techniques to refine the form factor models for nodular cast iron.
In conclusion, based on experimental data from 43 QT800-6 nodular cast iron crankshafts, the Pfündner (FVV) method provides the most accurate and conservative estimation of the bending fatigue safety factor, followed by the Arai Junichi method. These methods enable rapid assessment during the design phase, reducing reliance on costly CAE software. For nodular cast iron crankshafts, geometric parameters such as fillet radius, overlap, and crank arm dimensions are crucial, and the form factor effectively encapsulates their influence. By adopting the Pfündner method in combination with the Arai Junichi method via an Excel tool, engineers can efficiently evaluate whether QT800-6 nodular cast iron crankshafts meet the safety factor requirement of 1.8, ensuring reliability in high-pressure engine environments. This approach underscores the value of empirical models in complementing advanced simulations for nodular cast iron components.