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Estimation of the efficiency of the appliance of the bolting machine
The Machine Capability Index Calculation Method involves two key parameters: Cm and Cmk. The machine repeatability index, Cm, is calculated using the formula: Cm = T / (6s), where T represents the tolerance range—the difference between the maximum and minimum tolerances—and s is the standard deviation of the measurements. The standard deviation, s, is computed as follows: s = √[1/(n-1) × Σ(xi - x)²], where n is the number of measurements (typically 50), xi is the ith measurement, and x is the average of all measurements.
The tolerance range T is determined by subtracting the minimum tolerance value (Tmin) from the maximum tolerance value (Tmax): T = Tmax - Tmin. This defines the acceptable variation in the process.
For the machine accuracy capability index, Cmk, the formula is: Cmk = (1 - k) × T / (6s). Here, k is the offset coefficient, which is calculated as k = 2Bi / T. Bi represents the absolute deviation between the measured data (x) and the nominal value (x0) of the process: Bi = |x - x0|. This accounts for any shift in the process mean relative to the target.
According to international standards, new bolt assembly machines must meet a machine capability index of E1167 for both Cm and Cmk, while repaired machines should meet E1133. These calculations are based on 50 sampling measurements. If the number of samples is reduced to 10, the Cm and Cmk values may increase by approximately 5%, but the sample size must not fall below 20, as smaller samples can lead to inaccurate results.
As an example, consider a single-head bolt assembly machine purchased from Atlas with a stated accuracy of 3%. It is intended for high-strength bolt assembly of M10@50, specifically for a torque requirement of 55 Nm ± 5 Nm. To determine if this machine meets the required process specifications, a detailed testing procedure was conducted.
The machine was installed according to the manufacturer’s manual, and a high-precision HBM standard torque sensor (with 0.12% accuracy) was connected in series at the joint sleeve. The machine was then tested 50 times consecutively, and the test data was recorded.
From the test results, the average working sensor reading (x_work) was calculated as (55.31 + ... + 55.25) / 50 = 55.23 Nm. The standard deviation (s_work) was found to be 0.10 Nm. Meanwhile, the standard sensor's average (x_standard) was 55.20 Nm, with a standard deviation (s_standard) of 0.29 Nm.
It is evident that the standard sensor had a much higher standard deviation than the working sensor. This discrepancy highlights the lower accuracy of the working sensor. A low-accuracy sensor tends to show more variability in readings due to random errors. When the signal changes by 3%, the sensor might display values slightly above or below the set nominal value, resulting in a smaller calculated standard deviation. However, when the power is cut off, the actual reading may deviate further, increasing the standard deviation.
This is why a high-precision standard sensor is used during testing. In this case, the machine capability index measured by the Atlas sensor was nearly three times higher than that of the HBM sensor. This is because the Atlas sensor has a lower accuracy (3%), leading to greater variability in its readings. Conversely, the HBM sensor, with a much higher precision (0.12%), produces more consistent results, leading to a smaller machine capability index.
Therefore, when evaluating the machine capability of a bolt assembly machine, it is crucial to use a high-precision sensor to ensure accurate assessment. Lower-precision sensors may give misleadingly high capability indices, which could result in incorrect conclusions about the machine's performance.
Jiangsu XC Intelligent Technology Co., Ltd. is a pioneer in the field of industrial segmentation, a comprehensive solution provider that integrates software and hardware development, industrial digital intelligence, and industrial cost reduction and efficiency improvement.Jiangsu XC Intelligent Technology Co., Ltd. is a pioneer in the field of industrial segmentation, a comprehensive solution provider that integrates software and hardware development, industrial digital intelligence, and industrial cost reduction and efficiency improvement.Fork SLAM Navigation AGV
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