SSHT Material Auto-Recommendation: Scoring Model Based on Temperature and Load

In high-temperature disc spring design, the most suitable material must be automatically screened based on the maximum operating temperature $T_{max}$ and load requirements (required yield strength $\sigma_{req}$). The recommendation algorithm comprehensively considers the material's high-temperature strength, thermal expansion coefficient, cost, and machinability, outputting the optimal choice through a weighted scoring method.

1. Material Suitability Scoring Formula

For each candidate material $i$, define its comprehensive suitability $S_i$:

• $S_i$: Comprehensive score for material $i$, higher is more recommended.
• $k_{T,i}$: Temperature feasibility factor, characterizing the material's temperature tolerance margin.
• $k_{\sigma,i}$: Strength availability factor, characterizing whether the strength at the operating temperature meets the requirement.
• $k_{\alpha,i}$: Thermal expansion matching factor, where lower thermal stress when mating with the connected part yields a higher score (set to 1 if not considered).
• $k_{cost,i}$: Cost factor, inversely proportional to the material's relative price.
• $k_{mfg,i}$: Machinability factor, reflecting the difficulty of stamping, heat treatment, and surface treatment.

Each factor is defined as follows:

1.1 Temperature Feasibility Factor $k_T$

If $T_{max}$ exceeds the material's allowable limit temperature $T_{allow}$, it is directly eliminated ($S_i=0$). Otherwise, the larger the temperature margin, the higher the score:

1.2 Strength Availability Factor $k_\sigma$

Calculate the yield strength $\sigma_{y,i}(T_{max})$ of material $i$ at the operating temperature $T_{max}$. If it is below $1.2 \times \sigma_{req}$ (lacking safety margin), the score is reduced:

1.3 Thermal Expansion Matching Factor $k_\alpha$

If the linear expansion coefficient $\alpha_{mate}$ of the connected part material is known, the smaller the thermal expansion difference, the better:

If no matching is required, then $k_{\alpha,i} = 1$.

1.4 Cost Factor $k_{cost}$

Using the most common 51CrV4 as the baseline (cost set to 1.0), the higher the cost of other materials, the lower the score:

1.5 Machinability Factor $k_{mfg}$

Assigned based on experience: spring steel (0.95), hot work tool steel (0.80), superalloy (0.60).

2. Typical Candidate Material Database

Note: $\sigma_y$ values are typical reference values for heat-treated states; actual values should be based on material certificates.

3. Calculation Example

Design Requirements: Maximum operating temperature $T_{max}=300°C$, required yield strength $\sigma_{req}=1000\ \text{MPa}$, connected part is stainless steel ($\alpha_{mate}=18.0\times10^{-6}$).

For 51CrV4: - $T_{max}=300 > 250$, $k_T = 0$ → Directly eliminated.

For H13: - $T_{allow}=500$, $k_T = 1 - (300/500)^2 = 0.64$ - $\sigma_y(300°C)=1300\ \text{MPa}$, $k_\sigma = \min(1, 1300/(1.2\times1000)) \approx \min(1, 1.083) = 1.0$ - $|\alpha - \alpha_{mate}| = |11.5 - 18.0| = 6.5\times10^{-6}$, $k_\alpha = 1/(1+6.5) \approx 0.133$ - $k_{cost} = 1/2.5 = 0.40$, $k_{mfg}=0.80$ - Comprehensive score $S_{H13} = 0.64 \times 1.0 \times 0.133 \times 0.40 \times 0.80 \approx 0.0272$

For Inconel 718: - $T_{allow}=700$, $k_T = 1 - (300/700)^2 \approx 0.816$ - $\sigma_y(300°C)=1150\ \text{MPa}$, $k_\sigma = \min(1, 1150/(1.2\times1000)) \approx 0.958$ - $|\alpha - \alpha_{mate}| = |14.2 - 18.0| = 3.8\times10^{-6}$, $k_\alpha = 1/(1+3.8) \approx 0.208$ - $k_{cost} = 1/8 = 0.125$, $k_{mfg}=0.60$ - Comprehensive score $S_{718} = 0.816 \times 0.958 \times 0.208 \times 0.125 \times 0.60 \approx 0.0117$

Conclusion: Although Inconel 718 has higher temperature resistance and sufficient strength, due to its high cost and slightly poorer thermal expansion matching, the comprehensive score H13 wins by a large margin. This result aligns with engineering intuition: at 300°C and without extreme corrosion, hot work tool steel is the most balanced choice.

4. Material Recommendation Quick Reference Table

5. Important Notes

• Strength data must be based on the actual heat treatment state: Room temperature properties from material handbooks cannot be directly used for high-temperature design; always obtain measured yield strength at the operating temperature.
• Tempering temperature limit: The long-term operating temperature of spring steel must be at least 50°C below its tempering temperature, otherwise hardness will irreversibly decrease.
• Thermal expansion matching: In dissimilar material connections, the weight of $k_\alpha$ should be increased, as thermally induced preload changes are often the primary cause of failure.
• Dynamic performance: When subjected to impact, the material's fracture toughness $K_{IC}$ must also be considered, especially avoiding brittle materials at high temperatures.

Summary: The material auto-recommendation algorithm based on the comprehensive score $S_i$ unifies temperature feasibility, strength margin, thermal expansion matching, cost, and machinability into quantifiable indicators, enabling rapid selection of the optimal material from candidates. H13 fills the gap between spring steel and superalloys, making it a highly competitive choice in the 250–500°C temperature range.