V/P switching means that during injection process, when mold cavity is about to be filled with melt, screw movement of injection molding machine is changed from speed control to pressure control, so that melt can fill cavity more smoothly. There are many ways to control V/P switching, such as pressure control, speed control, time control, and position control. Among them, position control has the best stability and reliability and is the most widely used.
Realization of V/P switching position control requires operator to pre-set a screw position parameter. During injection stage, when screw position sensor in injection system detects that screw moves to set position, a feedback signal is sent to injection molding machine. Control system, control system executes V/P switching command to change movement mode of screw from constant speed drive to constant voltage drive. During this process, due to factors such as mechanical inertia of screw movement, electromagnetic inertia of transmission motor, signal feedback delay, corresponding screw position when V/P switch is actually completed will be greater than value set by operator. This feature of injection molding machine makes operator always face problem of repeated debugging when determining appropriate V/P switching position. For example, during mold trial process, injection samples with same V/P switching setting parameters often have different filling states, that is, appropriate V/P switching position at a certain injection speed is not applicable at another speed.

In order to study influence of material viscosity and injection speed on control stability of V/P switching position of injection molding machine, three groups of variables, material type, injection speed and melt temperature, were set up for experiments, V/P switch position and injection end point data of each group of experiments were collected, stability of V/P switch position control of injection molding machine was described by difference between set V/P switch position and injection end point. The smaller difference, the better stability. 
Using test mold (see Figure 1) to test with 5 different materials (see Table 1) on a 1 200 kN electric injection molding machine, maximum injection speed of injection molding machine is 200 mm/s, and injection speed of test is limited to 10 ~180 mm/s. At the same time, purpose of test is to study fluctuation of V/P switching position. There is no need to carry out pressure-holding process, and pressure-holding time of test is set to 0.

 

Figure 1 Test mold

Table 1 Test materials

Inject 5 injections under each test condition, collect V/P switching setting position S of the fifth injection and minimum value of screw position curve S' of current injection, S' is actual injection end point, then calculate difference between set position and actual injection end point △S=S-S', define △S as fluctuation of V/P switching position at current injection speed, △S reflects transition inertia of injection drive system of injection molding machine to V/P switching position control impact. Data according to injection test are shown in Table 2.
Table 2 V/P switching position fluctuation △S data table

Test data shows that V/P switching position fluctuation ΔS is same for various materials at same injection speed, and melt temperature has no effect on ΔS, indicating that ΔS has nothing to do with viscosity of material. Test data also show that △S increases with increase of injection speed, as shown in Figure 2.
 
Fig.2 Scatter diagram of V/P switching position fluctuation amplitude and injection speed
In statistics, Pearson product-moment correlation coefficient is commonly used to measure relationship between two variables. Pearson product-moment correlation coefficient is defined as quotient of covariance of two variables and product of standard deviations of two variables, generally represented by R . Suppose sample is marked as (Xi,Yi), its Pearson coefficient
 
is 0.975 by calculating Pearson coefficient of △S and V array, reflecting strong correlation between the two.

In original data set of △S and V, value of velocity V is distributed in the range of 0-200 mm/s, and value range of △S is 0-5 mm. In order to make values of the two groups of variables as close as possible, it is necessary to carry out data analysis on variable V transform. Any injection molding machine has a calibrated maximum injection speed, so any speed V can represent percentage of maximum speed of injection molding machine, and map it to interval from 0 to 1 to get a new variable V', define V' as injection speed coefficient. Maximum injection speed of injection molding machine of test object is 200 mm/s, and transformation of original data set is shown in Table 3.
Table 3 Test data transformation

Because any function can be approximated by polynomials, polynomial regression has a wide range of applications, especially in the field of error compensation, there have been a lot of research reports. Du Xiliang used polynomials to fit nonlinear compensation equation of intelligent sensors, and Wang Zhiming established a thermal error compensation model for machine tools based on polynomial regression theory. The two variables of injection speed and V/P switching position error involved in experimental data can also be fitted by constructing a polynomial.
Polynomial regression formula is:
 
To construct a polynomial function needs to solve a0, a1, a2...am, where m is number of items of polynomial, taking arrays x[1,2,3] and y[1,3,9] as an example, calculate its fitting binomial when calculating various coefficients of formula , it is first necessary to construct a data matrix X with three rows and three columns according to normal equation matrix.

 

In matrix of normal equations, n is sum  of all items in x array to power of 0, and its value is equal to number of items in x array.
Then, according to partial derivative matrix, calculate product of 0~2 power of each item in x array and corresponding item in y array and then sum to construct a data matrix Y with three rows and one column.
 
Finally substitute X and Y into matrix formula for polynomial:
 
Transform to obtain a ternary linear equation system about a0, a1, a2:
 
Solving above equations shows that a0=3, a1=-4, a2=2, quadratic fitting equation of array x[1,2,3] and array y[1,3,9] is obtained as:
 
In actual operation, polynomial fitting equation of a set of data can be quickly fitted by software such as Matlab, CurveFitter, etc. Figure 3 shows 2~6 fitting polynomials of test variation data set using regression analysis tool of Excel .
 
Fig.3 Polynomial fitting equation of experimental data
According to above five fitting equations, △S' under each V' were calculated respectively, and fitting effect was evaluated by comparing difference between actual value of position deviation △S and value of △S' calculated by fitting equation, as shown in Table 4.
Table 4 Polynomial fitting error
 
Error comparison method shows that the higher number of items in polynomial equation, the smaller fitting error, but on the other hand, as number of items increases, equation becomes more inclined to fit obtained data points, resulting in a sharp increase in overfitting. Since variable V' represents injection speed of injection molding machine, its size is limited, equation curve shown in Figure 3 can be pushed forward by one cycle, and the most suitable fitting equation for experimental data can be determined by observing respective monotonicity number of items.
It shows that after variable V' is pushed forward by one cycle, equation curves of 4, 5, and 6 terms have obvious deformations, as shown in Figure 4. It can be predicted that within a limited range, after V' increases to a certain extent, prediction results will have obvious deviations, so 4, 5, and 6-term equations have obvious over-fitting problems for the experimental data studied.
 
Figure 4 Curve of polynomial fitting equation is pushed forward by one cycle

Based on above analysis, it is determined that functional relational equation between V/P switching position control deviation and injection speed of experimental injection molding machine is that average deviation predicted by this equation is only 0.02 mm, which is suitable for any speed within 2 times maximum injection speed calibrated by injection molding machine, has high precision and stability.