The mean torsion strength of the wire was calculated as σ_B = 1800 N/mm², with a standard deviation of 219501650. The torsion yield limit τ_s was determined as 0.4537 × σ_B = 816.66 N/mm². The variation coefficients were calculated as C1 = 0.17 and C2 = 0.28. The combined coefficient C_T was found to be 0.033. Using this, the standard deviation S_τs was calculated as 0.033 × 816.66 = 26.95 N/mm².
Next, the working torque of the spring wire was analyzed. The spring curvature coefficient C_k was calculated as 1.16 (with a rotation ratio C = D/d = 14/2.5 = 5.6). The variation coefficient C_k was found to be 0.037. The mean working torsional stress was calculated using the formula: τ = (F × D × C_k) / (π × d³) = 713.11 N/mm². Since the load deviation △F is zero, the standard deviation S_F was also zero, and the coefficient of variation CF was zero. With Cd = 0.004 and CD = 0.0033, the comprehensive coefficient was calculated as 0.039. Therefore, the standard deviation S_τ = 0.039 × 713.11 = 27.84 N/mm².
To estimate the reliability index, it was noted that both C_τ = 0.037 and C_τs = 0.033 are less than 0.07, indicating small variations and an approximate normal distribution. The reliability index Z_R was calculated as 2.65. Using a 95% confidence level, the lower limit of reliability was estimated to be RL = 0.995. This means that with 95% confidence, the spring’s reliability exceeds 0.995.
The sample sizes for strength and stress were nx = 16 and ny = 11, respectively. From previous calculations, the mean torsion strength was s = 816.66 N/mm², with a standard deviation of 25.31 N/mm². The average working torsional stress was 709.93 N/mm², with a standard deviation of 26.27 N/mm². The effective sample size n_C was calculated as 23.62, leading to a Zk value of 2.9113. This confirmed that the lower limit of reliability is 0.995 at a 95% confidence level.
In conclusion, the spring used in the torque tester meets the design requirements, ensuring that the wrench remains accurate even under pre-tightening static pressure. Through optimization of the experiment and reliability calculation, the spring's dimensions were refined, resulting in a more compact and aesthetically pleasing wrench design. Furthermore, this method can be applied to other types of springs for similar reliability and confidence analysis.
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