Press brake is the most widely used bending forming equipment, which plays a very important role in the current sheet metal processing process.

The bending parts with different shapes can be made on the CNC press brake. They are lighter than rolled profiles and have a beautiful appearance.

Compared with the same kind of steel castings, the components welded by bending parts can be 30% – 50% lighter in quality, and the manufacturing is simple and the production efficiency is high.

However, when the press brake is used to bend the plate, the worktable will inevitably produce downward elastic deformation due to the lack of stiffness.

This results in the same deformation of the die installed on the upper end of the worktable, reducing the depth of the upper die into the lower die, and the uneven pressure distribution between the dies during bending.

The pressure at both ends of the die along the length direction is greater than the middle, the bending angle in the middle is greater than both ends, and the straightness in the middle is worse than both ends.

Therefore, in the design of the press brake, it is necessary to take corresponding measures to make up or reduce the bending deformation of the press brake.

Taking a CNC press brake as the research object, the finite element theory and experimental test are used to study it.

Table of Contents

## 1. Elastic analysis of worktable deformation

The machining accuracy of the press brake mainly depends on the bending deformation of the sliding block and the worktable.

In this section, the deformation of the worktable is analyzed by using the theory of elasticity.

It is supposed that the length of the worktable is l and the height is h, and the upper boundary of the worktable is subjected to the uniform load g;

The worktable is supported at both ends, and the supporting reaction acts on it in the form of shear force distributed in the sections at both ends;

Ignoring the small influence of self-weight, the semi inverse method is used to solve the deformation of the worktable.

The elastic model is shown in Figure 1.

Fig. 1 Uniform load on worktable

The calculation process is introduced in detail in the textbook of elastic mechanics.

The results are given directly and the deformation curve of the upper edge of the rectangular plate is obtained as follows:

It can be seen from the functional expression that the deformation occurring in the rectangular plate is a quadratic curve.

Such a deflection deformation is the main reason for the poor processing accuracy of the plate.

## 2. Deflection compensation principle of worktable

Due to the elastic deformation of the worktable, the bending quality is reduced.

At present, the CNC press brake is mostly the drive type, and the worktable remains static in the bending process.

The press brake studied in this paper is the top-drive type.

Limited to the structure and transmission mode of the machine tool, it is more convenient and easy to compensate for the hydraulic pressure of the worktable.

The compensation principle is as follows:

Several compensation hydraulic cylinders are arranged in the middle of the worktable.

During the bending process, the front and rear vertical plates support the compensation hydraulic cylinders.

The cylinders provide upward force to the neutral plate, which overcomes the bending deformation of the worktable.

The compensation amount can be easily adjusted through the proportional pressure reducing valve.

The compensation amount can be easily adjusted by the proportional reducing valve, and the convex device is controlled by the numerical control system, so that the pre convex amount can be determined according to the bending mode, plate thickness, die opening and material properties during bending, as shown in Figure 2.

Fig. 2 Schematic diagram of pressure compensation structure

The pressure compensation makes full use of the hydraulic principle, the amount of compensation increases with the increase of load, and users can easily adjust and use it.

Therefore, the pressure compensation is widely used in CNC press brake to improve the machining accuracy.

## 3. Finite element analysis and test of press brake

**3.1. Brief introduction of finite element analysis**

Based on the finite element analysis and optimization of the slider and side plate of the press brake, the structure of the press brake is partially optimized to eliminate the phenomenon of stress concentration, and the overall size of the machine remains unchanged.

In this section, the simplification of the finite element model, boundary condition constraints, load application and other contents will not be repeated.

For the press brake, there are two kinds of bending forms: with crowning and without crowning;

From the bending method, it can be divided into two forms: coining and air bending.

In general, the most commonly used is air bending with crowning.

Limited by the article length and workload, two typical working conditions are introduced here: working condition 1, full load 110 t, coining and bending without crowning; working condition 2, full load 110 t, air bending, with the maximum compensation pressure 25 MPa.

The pressure on the loading surface corresponding to the front and rear vertical plates is 43 MPa.

**3.2 Analysis results**

Some results of finite element stress calculation are shown in Table 1, and some results of finite element displacement calculation are shown in Table 2.

Table 1 Partial finite element stress calculation results MPa

Working condition | Max stress of upper throat | Max stress of circular arc on slider shoulder | Max stress at the joint of worktable and side plate |

Working condition 2 | 178 | 270 | 138 |

Table 2 Partial finite element displacement calculation results

Working condition | Upper end face of neutral plate Vertical relative displacement | Lower end face of slider Vertical relative displacement | ||

Maximum value /mm | Occur position | Maximum value /mm | Occur position | |

Working condition 1 | -0.521 | Middle of upper end face | 0.428 | Middle of lower end face |

Working condition 2 | 0.597 | Middle of upper end face | 0.439 | Middle of lower end face |

**3.3 Experimental test and result comparison**

In order to verify the accuracy of the finite element calculation, the structure of the press brake is tested on site.

The resistance strain gauge is used to test the stress of the key parts of the press brake, and the displacement sensor is used as the measuring tool to measure the deformation of the press brake.

Some experimental test sites are shown in Figure 3.

Fig. 3 Some photos of test site

From Table 3 and 4, it can be seen:

- The experimental results are basically consistent with the finite element calculation results.
- The partial error of stress measurement is less than 10%.
- The vertical deformation of the slider is similar to the calculation results.

Table 3 Comparison of partial stress results

Working condition 2 | Test stress / MPa | Finite element analysis stress / MPa | Relative error /% |

Upper throat of side plate | 183 | 178 | 2.8 |

Slider shoulder arc | 261 | 270 | 3.3 |

Connection between side plate and worktable | 126 | 138 | 8.7 |

Table 4 Comparison of partial displacement results mm

Working condition 2 | Maximum test displacement | Finite element analysis of displacement | |

The vertical relative deformation of the lower end of the slider | Full load length | 0.390 | 0.439 |

The upper end of the worktable is vertical and relatively deformed | Full load length | 0.236 | 0.597 |

In the actual test process, the compensation is automatically given and compensated by the CNC system.

Under working condition 2, the actual compensation is 0.34 mm, and the maximum compensation of the machine tool is 0.60 mm.

But in the finite element calculation, the actual compensation pressure can not be accurately known, so the maximum compensation pressure is applied in the calculation process.

This explains why there is a difference between the test results and the finite element calculation results of the upper end of the worktable.

Through the comparison, the accuracy of the finite element model is basically verified, which provides the basis for the subsequent use of finite element software to compensate and optimize the deflection of the worktable.

## 4. Research on hydraulic compensation technology

**4.1 Function analysis of compensation cylinder**

In order to improve the machining accuracy, a hydraulic compensation device is designed to make the worktable deform upward, so as to compensate the deformation of the slider.

But how to reasonably set the compensation pressure, the compensation position and the number of compensation cylinders is an important problem in optimization.

The optimization design module in ANSYS Workbench can describe the relationship between design variables and product performance, modify the parameters in the generated parameter workspace.

The design point table can quickly run multiple analysis schemes, and choose to input the range of design parameter values in the new row for new design points.

After all the design points are defined, the design points are updated, and the program will automatically generate enough design points.

After the program runs, the calculation results of the sample design points will be obtained.

In most cases, the whole length of the worktable is uniformly loaded.

Therefore, the optimization of worktable compensation is also based on the typical working condition of working condition 2.

When the slider is fully loaded, the maximum vertical deformation occurs in the middle of the lower end face, and the maximum vertical deformation of the upper-end face of the worktable also occurs in the middle.

The comparison of the press brake deflection curve is shown in Figure 4.

Through comparison, it is found that the maximum vertical deformation of the lower end of the slider is 0.39 mm, and the maximum vertical deformation of the upper end of the worktable is 0.236 mm.

The compensation of 0.34 mm in the field test is automatically given by the CNC system according to the bending parameters, which indicates that the compensation given by the CNC system is too small.

Through the finite element calculation, the maximum deformation of the lower end of the slider is 0.439 mm, and the maximum deformation of the upper end of the worktable is 0.597 mm, which indicates that the full load compensation is too large in the finite element calculation.

Thus, the compensation pressure should be reduced.

Fig. 4 Comparison of vertical deformation between slide block and worktable

According to the above analysis, the conclusion is as follows:

The original numerical control system calculation compensation is small, and the full load compensation in the finite element calculation is too large, so it is very necessary to optimize the calculation of compensation.

**4.2 Optimization analysis of compensation cylinder effect**

Some parametric model of the press brake is established in ANSYS Workbench. V is defined as the spacing of the compensation cylinder, and the original spacing is 500 mm;

H is the distance between the base of the oil cylinder and the bottom of the worktable, and the initial value is 336 mm.

The maximum compensation pressure of compensation cylinder is 25 MPa.

For the convenience of optimization calculation, the cylinder pressure is converted into the actual pressure on the loading surface for calculation.

When the vertical plate thickness is 60 mm, the conversion ratio is 1.955, that is, the compensation pressure P is equal to the actual loading surface pressure P_{1}/1.955.

The parameter setting is shown in Figure 5.

Fig. 5 Schematic diagram of parameter setting

Because the number of oil cylinders is 4, and the reasonable layout in the length direction needs to be considered, which does not affect the aesthetics.

The acceptance range of V in the design parameter attribute table is 400-600 mm.

The acceptance range of H is set to 236 – 436 mm, the maximum value of p does not exceed the maximum compensation pressure, and the acceptance range of p_{1} is 0 – 48.8 MPa.

The calculation results of the sample design point are obtained by running the program.

Through analysis and calculation, it is found that when v = 528 mm, H = 307 mm and p_{1} = 45.9 MPa, the deformation curve of the worktable is in good agreement with that of the slider, and the maximum vertical deformation of the worktable is 0.44 mm.

After rounding, v = 530 mm, H = 310 mm and p = 23.5 MPa were finally determined.

The comparison of the vertical deformation between the optimized slider and the worktable is shown in Figure 6.

Fig. 6 Comparison of vertical deformation of slide block and worktable after compensation optimization

The deformation of the slider in Figure 6 is the absolute deformation calculated by the finite element method, which includes the superimposed deformation caused by the insufficient rigidity of the fuselage, so there is a gap between the two curves in the figure.

However, the deformation of the middle part of the working end face of the slider and the worktable is basically consistent with the vertical relative deformation of the two ends, and the two deflection curves tend to be parallel, indicating that the compensation effect after optimization is better.

**4.3 Sensitivity of response parameters**

The sensitivity chart shows that the design point is sensitive to the output parameters.

By changing the design point value, it can observe how an output parameter changes with one or more input parameters.

As shown in Figure 7, according to the sensitivity diagram analysis, the biggest influence on the deflection curve is the vertical height of the compensation cylinder and the compensation pressure.

The horizontal distance between cylinders has little effect on the maximum value of deflection curve, but only has some effect on the smoothness of deflection curve.

The analysis results are in line with the actual situation.

Fig. 7 Parameter sensitivity results at response points

## 5. Conclusion

This article analyzes the causes of poor bending accuracy and the worktable of press brake by using finite element software, and tests and compares the stress and deformation of machine tool by combining with strain electric measurement technology, which provides the basis for using finite element to compensate the pressure of worktable.

The typical working conditions of the press brake are optimized, and the ideal compensation curve is obtained.