TWI912161B - Simulation method for multi-axis milling - Google Patents

Abstract

This invention relates to a simulation method for multi-axis milling. First, a workpiece model is established using a three-dimensional ray model, which accelerates calculations. Next, a tool model is established using a symbolic distance function, which quickly simulates the outline of the workpiece model. Finally, a path stepping algorithm is used to obtain a tool-workpiece contact area, and based on this contact area, it is calculated whether a cutting path of the tool model will cause improper collisions between the tool and workpiece models. Therefore, this simulation method effectively improves simulation efficiency and can quickly calculate the cutting path and instantaneous cutting force to optimize the tool path and feed rate in the actual machining process.

Description

Simulation method for multi-axis milling

This invention relates to multi-axis machining technology, and in particular to a simulation method for multi-axis milling.

CNC milling is a very common product manufacturing method in the industry. Before actual machining, operators usually use simulation software (such as B-rep Model or Voxel Model) to simulate the machining process to ensure the accuracy of the manufacturing process. Taking the Boundary-Representation Model (B-rep Model) as an example, when calculating the contact area between the tool model and the workpiece model, the complex intersecting surfaces require extremely high computational power, leading to low efficiency. As for the Voxel Model, which uses multiple cubic blocks to assemble the outlines of the tool and workpiece models, the large number of cubic blocks results in a significant amount of memory usage during calculations, also causing low computational efficiency.

As can be seen from the above, in the process of simulating actual machining, since the contour of the workpiece model needs to be continuously calculated and updated, choosing any of the aforementioned simulation software will inevitably have a significant impact on the simulation results and efficiency. Moreover, if further analysis of the machining process is desired (such as calculating instantaneous cutting forces), the problem of insufficient hardware computing power is usually encountered. In addition to improving the hardware, finding a more suitable workpiece model and tool model, along with a suitable algorithm, is currently a challenge.

The main objective of this invention is to provide a simulation method for multi-axis milling, which can improve simulation efficiency and quickly calculate cutting path and instantaneous cutting force to optimize tool path and feed rate in actual machining process.

To achieve the above-mentioned main objectives, the multi-axis milling simulation method provided by the present invention includes the following steps: (a) establishing a workpiece model using a three-dimensional ray model; (b) establishing a tool model using a symbolic distance function; and (c) obtaining a tool-workpiece contact area using a ray stepping algorithm, and calculating whether a cutting path of the tool model will cause improper collision between the tool model and the workpiece model based on the tool-workpiece contact area.

As described above, the simulation method of this invention uses the three-dimensional ray model to establish the workpiece model, which can speed up the calculation compared to the traditional B-rep Model, and reduce the amount of memory used compared to the Voxel Model. Secondly, the simulation method of this invention uses the symbolic distance function combined with the light path stepping algorithm to quickly find the tool-workpiece contact area and update the contour of the workpiece model. While updating the contour of the workpiece model, the data of the tool-workpiece contact area can be obtained. The aforementioned data is an important condition for calculating the cutting path. If an improper collision is anticipated, the cutting path needs to be adjusted to ensure that the two sides do not collide with each other, thereby achieving the effect of optimizing the actual machining process.

Preferably, in addition to obtaining the cutting path, in step (c), an instantaneous cutting force can also be calculated based on the tool-workpiece contact area. This allows the tool model to be machined on the workpiece model when it is close to the critical value of the instantaneous cutting force, thereby optimizing the feed efficiency of the actual machining.

Preferably, in step (c), the light trail stepping algorithm is used in conjunction with a graphics processor to perform parallel calculations to obtain data on the tool-workpiece contact area, which can further improve the calculation efficiency.

The detailed structure, features, assembly, or usage of the simulation method for multi-axis milling provided by this invention will be described in the subsequent detailed description of the embodiments. However, those skilled in the art should understand that such detailed descriptions and the specific embodiments listed in this invention are for illustrative purposes only and are not intended to limit the scope of the patent application of this invention.

The applicant hereby clarifies that throughout this specification, including the embodiments described below and the claims within the scope of this patent application, all directional terms are based on the directions shown in the drawings. Secondly, in the embodiments and drawings described below, identical component designations represent identical or similar components or their structural features.

The simulation method of this invention mainly simulates the process of multi-axis milling of a workpiece by a cutting tool before actual machining to ensure the accuracy and correctness of the machining process. The "multi-axis" can be dual-axis, three-axis, four-axis, or five-axis, and is not limited here. Referring to Figure 1, the simulation method of this invention includes the following steps:

(a) As shown in Figure 1, step S1, a workpiece model 10 is created using a three-dimensional ray model (Tri-Dexel Model).

The three-dimensional ray model used in this step emits rays from three ray planes in different directions to establish the outline of the workpiece model 10. In this embodiment, as shown in Figure 2, the workpiece model 10 is a tooth model, but it is not limited to this. In other embodiments, it can also be applied to different industry categories such as: manufacturing (aerospace, automotive, electronics, energy equipment, tools, molds or machine tools), medical industry (dental, orthopedics, plastic surgery, medical equipment, surgical planning or guides), academia (mechanical engineering, manufacturing engineering, industrial design, aerospace engineering or materials engineering)... etc. The advantages of the Tri-Dexel Model are that it is very suitable for parallel algorithms, which can significantly shorten the time required for machining simulation compared to the B-rep Model. Moreover, the Tri-Dexel Model consumes very little memory compared to the Voxel Model. Each ray's endpoint can carry the physical phenomenon values generated at each instant (such as the cutting area), thus possessing excellent scalability.

(b) As shown in step S2 of Figure 1, a tool model 20 is created using a Signed Distance Function (SDF).

The Signed Distance Function (SDF) used in this step is a directly defined mathematical model that calculates the distance from a given coordinate point to the target object in the form of an implicit function. Positive and negative signs indicate whether the point is inside or outside the object, thereby establishing the outline of the tool model 20 and quickly understanding its positional relationship with the workpiece model 10 (as shown in Figure 2).

(c) As shown in step S3 of Figure 1, a Cutter-Workpiece Engagement (CWE) region 30 is obtained using a Ray Marching algorithm, and an instantaneous cutting force is calculated based on the CWE region 30, and it is calculated whether the cutting path of the tool model 20 will cause improper collision between the tool model 20 and the workpiece model 10.

The ray Marching algorithm used in this step, after knowing the origin and direction of the light ray, can begin searching for the closest distance to the object. Then, it moves this distance from the origin of the light ray towards the direction of the light ray, updates the origin position, and repeats this process until the object is touched or the light ray is confirmed to be diverging. Since the workpiece model 10, built using the Tri-Dexel Model, is composed of multiple line segments, it can be considered as numerous light rays. Therefore, the Ray Marching algorithm quickly searches the boundary of the tool model 20 using the original outline of the workpiece model 10 to update the outline of the workpiece model 10. Simultaneously, it obtains data on the cutter-workpiece engagement (CWE) area 30 (as shown in Figure 2). This data is crucial for calculating the cutting path and instantaneous cutting force. The instantaneous cutting force refers to the instantaneous resistance experienced by the tool during machining of the workpiece. Excessive instantaneous cutting force can damage the tool and/or the workpiece. This allows the simulation of the tool model 20 machining the workpiece model 10 under conditions close to the critical value of the instantaneous cutting force, maximizing the feed efficiency of the actual machining process. Please refer to Figure 3, which shows the relationship between the travel distance of the tool model 20 and the three-axis cutting force in the machining simulation. However, in practice, time can also be used instead of travel distance, that is, to show the magnitude of the three-axis cutting force corresponding to the tool model 20 machining for a specific time (e.g., 10 seconds).

It is worth mentioning that the Ray Marching algorithm can also be used in parallel with a Graphics Processing Unit (GPU) to obtain the starting point and direction of multiple rays instead of obtaining the starting point and direction of a single ray. This further improves the calculation speed of the workpiece model 10 when updating the contour.

Table 1 below compares the efficiency differences of cutting paths designed using the Tri-Dexel Model in combination with the traditional Splits Bounding Volume Hierarchies (SBVH) and the combination of the Signed Distance Function and Ray Marching algorithm used in this invention.

Table 1 Number of times SBVH (unit: seconds) SDF+Ray Marching (Unit: seconds) 1 15.5336 9.30046 2 15.6123 9.27029 3 15.5674 9.26721 4 15.6874 9.26484 5 15.6036 9.29699 6 15.7078 9.30935 7 15.665 9.29641 8 15.8078 9.32197 9 15.6415 9.29707 10 15.8343 9.28962 11 15.5664 9.31953 12 15.6826 9.2958 13 15.9124 9.29946 14 15.5686 9.30116 15 15.5628 9.30366 Average time 15.6636 9.29559

As can be seen from the table above, the average computation time of the traditional simulation method is approximately 15.6636 seconds, and it can find approximately 702.329 cutter location points per second. The average computation time of the simulation method of this invention is approximately 9.29559 seconds, and it can find approximately 1183.464 cutter location points per second. In comparison, the computation time of the simulation method of this invention is significantly shortened, and the computation speed can be greatly improved by approximately 68.51%.

In summary, the simulation method of this invention can significantly improve the calculation speed by combining the three-dimensional ray model, the signed distance function, and the ray Marching algorithm. The saved calculation time can be used not only to analyze the magnitude of the instantaneous cutting force, but also to calculate whether the cutting path of the tool model 20 will cause improper collision between the tool model 20 and the workpiece model 10. If improper collision is expected, the cutting path needs to be adjusted to ensure that the two do not collide with each other.

S1: Step S2: Step S3: Step 10: Workpiece Model 20: Tool Model 30: Tool-Workpiece Contact Area

Figure 1 is a flowchart of the simulation method of the present invention. Figure 2 is a three-dimensional view of the workpiece model and tool model provided by the simulation method of the present invention. Figure 3 is a graph of the movement distance and cutting force provided by the simulation method of the present invention.

S1: Steps

S2: Steps

S3: Steps

Claims (3)

A simulation method for multi-axis milling includes the following steps: (a) establishing a workpiece model using a three-dimensional ray model; (b) establishing a tool model using a symbolic distance function; and (c) obtaining a tool-workpiece contact area using a ray stepping algorithm, and calculating whether a cutting path of the tool model would cause an improper collision between the tool model and the workpiece model based on the tool-workpiece contact area. In the simulation method for multi-axis milling as described in claim 1, in step (c), an instantaneous cutting force is calculated based on the tool-workpiece contact area. In the simulation method of multi-axis milling as described in claim 1 or 2, in step (c), the trace stepping algorithm is used in conjunction with a graphics processor to perform parallel calculations to obtain the tool-workpiece contact area.