Involute CNC pipe bending based on Delta 20PM motion controller

Abstract: This paper mainly utilizes the circular interpolation function of the 20PM bending machine because, when bending short pipes on a bending machine, improper control can lead to the flattening of the copper pipe. Although PLCs also support circular interpolation, their use has many limitations. On this equipment, the 20PM controls the forward and backward, and up and down axes of the cantilever. The machine uses the cantilever to pull the copper pipe and perform circular interpolation to bend it into shape. Later, during debugging, based on actual requirements, the circular curve was changed to an involute curve for better pipe bending results.

Keywords: Involute coordinate calculation in circular interpolation bending mode

1 Introduction

Pipe plastic forming is a processing technology that uses pipes as blanks and manufactures pipe parts through plastic forming methods. Because it easily meets the requirements of lightweight, strong, tough, low-consumption, high-efficiency, and precision manufacturing of plastic-formed products, pipe plastic forming has become an important direction for the research and development of advanced plastic forming technology in the 21st century.

2. CNC pipe bending

2.1 Pipe bending process

There are many different pipe bending processes in practice, which can be classified in various ways from different perspectives. In engineering, bending is usually classified into cold bending and hot bending based on whether heating is used during bending, and into mandrel bending and mandrelless bending based on whether filler is used during bending. Dieless bending refers to bending where the pipe's deformation zone is not directly acted upon by a die; the final shape is determined by the relative movement of the tool and the workpiece, making it a highly flexible processing method. Die bending refers to bending the pipe by directly applying a rigid die to the deformation zone. This requires the size of the rigid die's acting portion to compensate for the bending springback that occurs after the workpiece is unloaded, making it a highly repeatable and fast processing method. Several new pipe bending processes include thermal stress bending; dieless bending based on tool motion control; superposition bending; and CNC machine tool bending, etc.

2.2 CNC pipe bending

CNC pipe bending clamps the pipe onto a bending die, which rotates with the die. When the pipe is pulled past a pressure block, the block bends the pipe around the bending die, a process known as forming die bending. Traditional bending processes are mostly manual, resulting in low efficiency and inconsistent quality. With the development of CNC machine tools, using advanced CNC pipe bending machines to achieve this bending process can significantly improve production efficiency and ensure product quality. Because process parameters can be easily adjusted, CNC pipe bending machines can accurately and stably complete bending, feeding, and turning actions, ensuring the bending accuracy of the pipe components. CNC pipe bending machines can automatically and continuously form spatial bent parts with different radii of curvature. Combined with corresponding database software systems, the control program can also pre-correct the bending springback. However, the die structure for this process (see Figure 7) is relatively complex, and the quality of the parts is sensitive to process parameters, requiring thorough preparation and trial production. Especially when bending thin-walled pipe components, improper selection of process parameters can easily lead to wrinkling, resulting in the scrapping of parts or even the die. How to efficiently and accurately obtain these process parameters and fully guarantee the quality of bent pipe products is a research hotspot in CNC bending technology.

3. CNC pipe bending system

3.1 System Composition

The CNC pipe bending machine based on the Delta mechatronics platform has six motion axes. The process requires two axes to perform linear interpolation, two axes to perform circular interpolation, and the other two axes have no special requirements. The PLC controllers selected are 32EH00T2 and 20PM00D, and the display is a 10.4-inch touch screen DOP-AE10THTD1, as shown in Table 1.

Table 1 Configuration of CNC Pipe Bending System

3.2 20PM Motion Controller

The core of the pipe bending control system is the Delta DVP-20PMMOOD motion controller. The Delta DVP-20PM00D is a programmable controller with dedicated motion control functions. The most significant feature of the DVP-20PM00D is that the PLC host directly provides electronic cam functionality; in other words, the DVP-20PM00D is a PLC with built-in electronic cam functionality. Therefore, in some applications, the DVP-20PM00D is simply referred to as the Delta 20PM motion controller. The 20PM has two 500kHz inputs and outputs. In the electronic cam function, the X-axis is defined as the slave axis, and the encoder input axis is the master axis. After the CAM table is defined, the slave axis follows the master axis according to the defined curve. It adopts a high-speed dual-CPU structure, utilizing an independent CPU to process motion control algorithms, which can effectively realize various motion trajectory control, logic action control, linear/circular interpolation control, etc. CNC pipe bending machines utilize the electronic cam function of the 20PM motion controller to solve complex motion trajectory control problems.

4. 20PM CNC Pipe Bending Programming Design

4.1 Bending die mode

Based on the requirements for pipe bending, two pipe bending process modes were developed, as shown in Figure 1.

Figure 1. Pipe bending mode

4.2 Process Flow

The equipment has manual and automatic modes. The manual mode mainly includes returning the equipment to the origin, moving the cantilever forward/backward at a fixed length, raising/lowering the cantilever at a fixed length, and manually bending the mold when bending short pipes.

The equipment's automated process is divided into Mode A and Mode B, corresponding to the A and B processes below, respectively. Switching between processes is accomplished through a human-machine interface. In practical implementation, the PLC is the main controller, used to control process selection and jumps, and also to send commands to the PM to complete the tasks assigned to the PM.

Figure 2 Flowchart of Bending Die A Mode

Figure 3 Flowchart of Bending Die Mode B

4.3 Involute Coordinate Calculation

Since the 20PM itself does not support involute interpolation, in practice, the involute curve is divided into multiple points according to the curvature angle. The coordinates of each point are calculated by a human-computer interface, and finally, the PM performs linear interpolation to achieve the user's required functionality. The specific involute equation given at the time was:

X = (R + H) * sinα + (L - α * R) * cosα

Y= R-(R+H)* cosα+(L-α*R)*sinα

L, R, and H are all constants that can be set via human-machine interface.

To prevent the macro commands written during calculations from affecting the execution speed of the human-computer interface, a screen cycle macro is used to calculate the coordinates. This way, it won't affect the operation speed of other pages on the human-computer interface. Below is the written macro command:

BMOV($88, (2@D664), 2)

BMOV($90, (2@D144), 2)

## X=(R+H)*SINθ+(LR*θ)COSθ

## Y=R-(R+H)*COSθ+(LR*θ)SINθ

# Initialization operations

IF $58 <= $M56 (Signed DW)

$112 = SIN($58) (Signed DW)

$116 = COS ($58) (Signed DW)

$66 = FCNV ($58) (Signed DW)

$60 = FCNV($M50) (Signed DW)

$62 = FCNV($M52) (Signed DW)

$64 = FCNV($M54) (Signed DW)

$120 = FDIV($66, 180.0) (Signed DW)

$124 = FMUL($120, 3.14) (Signed DW)

$128 = FMUL($124, $62) (Signed DW)

##R+H

$108 = FADD($62, $64) (Signed DW)

##LR*θ

$132 = FSUB($60, $128) (Signed DW)

##(R+H)*SINθ

$136 = FMUL($108, $112) (Signed DW)

##(LR*θ)COSθ

$140 = FMUL($132, $116) (Signed DW)

##(R+H)*COSθ

$144 = FMUL($108, $116) (Signed DW)

##(LR*θ)SINθ

$148 = FMUL($132, $112) (Signed DW)

##Start Calculation

## X

$152 = FADD($136, $140) (Signed DW)

## Y

$156 = FSUB($62, $144) (Signed DW)

$160 = FADD($156, $148) (Signed DW)

##The angle increases by one

$58 = $58 + 1 (Signed DW)

## Convert to integer and store

$164 = iCNV($152) (Signed DW)

$168 = iCNV($160) (Signed DW)

$170 = $88 - $164 (Signed DW)

$172 = $90 - $168 (Signed DW)

*$200 = $170 (Signed DW)

*$900 = $172 (Signed DW)

$200 = $200 + 2 (DW)

$900 = $900 + 2 (DW)

ELSEIF $58 < 120 (Signed DW)

$58 = $58 + 1 (Signed DW)

*$200 = 400 (Signed DW)

*$900 = 400 (Signed DW)

$200 = $200 + 2 (DW)

$900 = $900 + 2 (DW)

ELSE

## Assign the value to PM and reinitialize

BMOV((2@D3000), $500, 240)

BMOV((2@D3600), $1000, 240)

$58 = 0 (DW)

$200 = 500 (DW)

$900 = 1000 (DW)

SETB $50.0

endif

end

5. Conclusion

The Delta PM20 motion controller is closer to a professional CNC system in performing circular interpolation and continuous motion processes, and has advantages that PLCs cannot match. However, it still lags behind PLCs in terms of the flexibility of executing program processes.

Bending parts made from tubing, whether planar or spatial, are widely used not only in gas and liquid transport pipelines but also in metal structures. Therefore, tubing bending forming technology is a highly regarded and rapidly developing field, and conducting research in this area is of great significance.