The spring stiffness is calculated. The lever ratio of the tester is 1:10. The measuring object is a common cylindrical spiral compression spring. The weight of each load is 20g, and the load is evenly loaded in 10 times. The cumulative loading is 200g. Using the regression analysis method, according to the linear correspondence between spring force and spring deformation, the linear regression equation y=a+bx, one-dimensional linear regression model y=a+bx+EEN(0,R2)(1) Medium: a, b are regression coefficients. Using the ordinary least squares method, the above equation is denoted as Q(a,b)=Eni=11yi-(a+bxi)22(2) The a and b whose Q(a,b) take the minimum value are taken as a and b. The 1 point estimate is denoted by a and b, that is, minQ(a,b)=Q(a,b)(3) The partial derivative of equation (2) and the partial derivative are obtained, and it is equal to zero, which gives 5Q5a=- 2Eni=1(yi-a-bxi)=05Q5b=-2Eni=1(yi-a-bxi)xi=0(4) Simplify the above equations to obtain the binary linear equations na+bEni for a and b =1xi=Eni=1yiaEni=1xi+bEni=1xi2=Eni=1xiyi(5) The regression coefficient of the estimated regression linear equation between x and y can be solved by the equations bb=Eni=1xiyi-nxy)))Eni= 1xi2-n? In the formula x2: xi, yi are any set of sample values. Let Lxx=Eni=1xi2-nx2, Lxy=Eni=1xiyi-nxy))), that is, the spring stiffness k=1/b=Lxx/Lxy.
After the program runs, the screen displays: pleaseinputcountweightdata: (requires input of weight data) 20406080100120140160180200f (stroke from the keyboard) pleaseinputdeformationdata: (requires input spring deformation) 0.520.921.321.782.182.663.103.523.964.40f (typed from the keyboard). The spring stiffness value obtained from the program is: k = 4.51 N/mm. If the measured actual size of the large hole depth is 40.36, the actual deviation is +0.36, which is 0.17 larger than its maximum limit size, which is considered to be waste, but if the total length measured at this time is exactly its maximum limit Size 50, the true hole depth is guaranteed to be 50-40.36 = 9.64, which is the minimum limit size. It can be seen that when the indirect measurement method is adopted, the workpieces that are not qualified in form may be scrapped, that is, the fake waste products appear (these workpieces do not meet the process size requirements, but meet the design size requirements of the workpiece drawings).
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