Solution to the Jack Calibration Equation

During the calibration process of the jack, the calibration points are provided according to the calibration procedures for calibration. However, in practical work, force values outside the calibration points are often used. However, due to these points not being calibrated, it is often necessary to perform curve fitting on the jack during use due to the force value exceeding the tolerance. The purpose is to make the fitted value closer to the true value after fitting. The calibration equation can be obtained from two aspects:

1. Jack regression equation based on * small two multiplication

* small two multiplication is to find a "* good" function in the functional relationship for a given set of data (xi, yi) (i=1, 2,..., n)? Stain (x), make? Can the stain (x) ≈ f (x) meet the deviation? The condition that the sum of squares of peck i is * small. So,? Stain (x) can reflect the basic trend of data changes as a whole

In theory, the linear correlation R of the jack is 1, and the equation is

y=xS+f (1)

y - the actual force value

x - the displayed value on the pressure gauge

s - the effective area of the piston

f - the force value introduced by friction, piston pressure, etc.

In practical work, the linearity of the jack is better, and a linear regression equation is used.

y=a+bx (2)

to determine the unknown parameters a and b by * small multiplication. When we have the sum of squares of deviations

S=■ (yi-a bxi) 2 (3)

To make S take a small value, we take the partial derivatives of a and b, respectively, And make them equal to zero

■ (yi-a-bxi)=0 (4)

and ■ (yi-a-bxi) xi=0 (5)

Now we substitute the following measured data into formulas (4) and (5) above.

The solution is a=0.5885 b=0.0488. Substitute them into formula (2)

y=0.5885+0.0488x

2. Use Excel software to directly solve the linear equation

If the above formula is used step by step, The workload is large and prone to errors. Using Excel software is easy to operate and error free

Step 1

Write the above data in the Excel table according to Table 1.

Step 2

Insert the chart and select [XY Scatter Chart] in [Standard Type]. Click [Next], select the data area, and click [Finish]. After completion, Figure 1 appears

Step 3

Right click on any point, select [Add Trend Line], select [Options], check √ before displaying formulas and displayed values, and click [OK]. Appears as shown in Figure 2

y - pressure indication value

x - standard dynamometer indication value

The final results of these two methods are consistent, but using Excel tools will greatly reduce workload, and the drawing is convenient, which can intuitively understand whether there are gross errors in the data, making it suitable for grassroots calibration workers