To explore the relationship between cutting force

vibration and surface roughness is of great significance to predict surface roughness. In this paper

the 64 all-factor experiments of milling 45 steel were conducted with the control variable method of three factors and four levels of cutting speed v

feed per tooth f

z

and cutting depth a

p

. The main cutting force

axial force

radial force and vibration were measured on line

and the corresponding average value

standard deviation and RMS values of cutting force w

ere obtained. At the same time

the two-dimensional surface roughness R

a

three-dimensional roughness average S

a

and RMS S

q

were measured off-line. Then five distribution functions such as Normal distribution

Exponential distribution

Gamma distribution

Weibull distribution and Cauchy distribution were used to fit the sample data. The optimal distribution function was determined by AIC criteria

and the unknown parameters were estimated by maximum likelihood method. The five Copula functions such as Gaussian Copula

t-Copula

Frank Copula

Gumbel Copula

and Clayton Copula were used to fit the related structural forms between milling force

vibration

and roughness

and the optimal Copula function was selected according to the AIC criteria and the parameters are determined. Deriving from the optimal Copula function

the Kendall rank correlation coefficient τ was chosen as the evaluation index to analyze and compared the overall relativity between milling force and surface roughness. A mixed Copula function was constructed to analyze the tail correlation between milling force and surface roughness.