Introduction

The reverse engineering was originally developed on the basis of analyzing existing products for the convenience of innovating existing products1. With the popularization of computer technology, the trend of using digital measurement technology, computer-aided design and manufacturing technology was becoming increasingly obvious. This kind of reverse research from entity to model had become a valuable and new research topic2. In the case of ensuring the three basic elements of cost, efficiency, and quality, it was possible to customize and improve production methods and products in a targeted manner to meet the needs of different groups of people, improve the speed and intensity of the enterprise’s response to the market, and promote the competitiveness of the enterprise3.

Gear is one of the important parts of mechanical products, and it undertakes the important task of transmitting torque4. The surface structure of gear parts is quite complex, which is easy to wear and tear during the continuous meshing process5, and then step into its failure. It is quite difficult to establish a high-precision gear model. Using reverse engineering technology can restore the three-dimensional model of the gear more accurately and maintain the continuous operation of the gear system. The reverse design system, Geomagic Studio, has powerful point processing functions and can flexibly design and edit polygonal mesh models. Geomagic DesignX is a CAD modeling software based on the history tree of building a product, which can conveniently realize the parametric modeling of point cloud data, and achieve flexible compatibility with other common CAD softwares.

This paper adopts the hybrid modelling technology based on the Geomagic platform to build and analyze gear parts’ structure and service features. A scientific forward and reverse modelling process is established, and the chromatographic analysis is conducted to evaluate the precision based on the solid model. In addition, the process parameters are formulated to complete the rapid prototyping of gear parts, providing a practical and feasible reference model for the design and development of products for enterprises.

Gear parts analysis

As one of the most widely used transmission structures in mechanical transmission, gears have the advantages of high working efficiency, long working hours, compact structure, and precise transmission6. This kind of component, however, can also cause noise, vibration and gear fracture etc. due to poor manufacturing accuracy, harsh service environment, deterioration of sealing or lubrication7,8.

Gears are generally made of forged steel, cast steel, ductile iron, and other materials9, and different heat treatment methods are used according to various working environments to obtain tooth surfaces with different hardness10. The main failure modes, as shown in Fig. 1, are tooth fracture, tooth surface pitting, tooth surface wear, tooth surface gluing, and tooth surface plastic deformation. Among these failures, tooth surface wear is the most common one11,12,13. Therefore, for gear parts, especially some key gear parts with special shapes, there is an urgent need for rapid prototyping technology to quickly design and reproduce gear parts14, improve the quality of gear remanufacturing, and reduce the downtime of enterprise production.

Fig. 1
figure 1

Typical failures of gears.(adapted from11. (a) Dents and notches, (b) Grooves, (c) Scratches, (d) Deformation, (e) Chipped parts,, (f) Surface pitting, (g) Progressive pitting, (h) micro-pitting, (i) Flake pitting, (j) Spalling, (k) Fatigue cracks and, (l) Fatigue fracture.

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Data acquisition and reduction

The first step of reverse engineering is to digitize the surface of the physical sample, obtain the scattered point cloud coordinate data of the physical surface through professional measuring equipment, and then further complete the reconstruction, modification, innovation and remanufacturing of the physical model. The data measurement method can be divided into contact measurement and non-contact measurement according to the distance between the data detection probe and the real object. After a comprehensive comparison of the two detection methods15 and the field conditions of the laboratory, the point cloud data of the gear parts was obtained by using the non-contact flexible 3D laser scanner daisyPH10T16, as the subsequent input for the reverse design. This article only uses spur gears as an example to introduce the basic process of obtaining point cloud data, the same process of the data acquisition and reduction is conducted on the spiral bevel gear.

In order to obtain a better display effect, a layer of imaging agent is sprayed on the physical parts. To facilitate the post-scanning and splicing of the point cloud fragments of the parts, it is necessary to paste marker points on the object coated with an imaging agent, as shown in Fig. 2. Considering that the peripheral features of the gear are relatively complex, ignoring the details of the internal keyway, and adopting the strategy of rotating the turntable to scan the outer circumference of the gear, it can not only reduce the data scanning time, but also reduce the number of marked points, which is conducive to the integrity of the model features.

Fig. 2
figure 2

Gear model with developer spray (including encoded points).

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Data processing

Case 1: spur gear

In Geomagic Studio software, the collected point cloud data of spur gears in different orientations are merged, integrated into a complete part point cloud data, and colored subsequently, as shown in Fig. 3. It can be seen that there are many redundant noise points in the model, which still need to be optimized.

Fig. 3
figure 3

Point cloud model of spur gear model.

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The irrelevant point cloud data far away from the main model are first deleted by disconnecting the component connection option. The isolated points outside the main body are further removed using disconnect in vitro isolated point option. Systematic errors and random errors in the scan can be eliminated by using the noise reduction option again, to increase the smoothness level of the model. The optimized point cloud model is shown in Fig. 4. The yellow indication in the figure refers to the paste marker points on the object which are used to merge to the collected point cloud data. There is no point cloud data at the paste marker points. Since this kind of hollow area is a plane in the gear, it can be easily re-constructed in the following process without affecting the geometry of the part.

Fig. 4
figure 4

Point cloud model of gear model after optimization.

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Then the optimized point cloud model is imported into Geomagic DesignX software. The reference plane 1 is created by selecting three points at different positions on the outermost edge of the side of the spur gear. Take reference plane 1 as the datum plane, the section multi-line segments are added, the spline curve is selected and then the gear profile is projected to the datum plane. The tooth hole and side circle of the gear are measured and drawn, sketch 1 and sketch 2 of the gear outline are then completed as shown in Fig. 5.

Fig. 5
figure 5

Gear outline: (a) sketch 1, (b) sketch 2.

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The tooth width and outer grove depth of the gear is measured as 6 mm and 2 mm, respectively. Then sketches 1 and 2 can be stretched and trimmed accordingly. The chamfering of the inner hole is performed as distance of this feature is measured as 0.6 mm, completing the creation of the gear solid model, as shown in Fig. 6.

Fig. 6
figure 6

Spur gear design model.

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Case 2: spiral bevel gear

The spiral bevel gear model is more complex than the spur gear, but the modeling process is basically the same. In Geomagic DesignX, the domain identification of the point cloud digital model (Fig. 7(a)) can be performed first, so as to identify the type of surface to which the model belongs. Through parameters such as sensitivity and surface roughness, operations such as segmentation and merging of the model are performed to complete the identification of the model domain, as shown in Fig. 7(b).

Fig. 7
figure 7

(a) Point cloud model, (b) Domain segmentation.

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Plane 1 (Fig. 8a) is selected as the reference plane to draw the outline sketch 1 of the spiral bevel gear (Fig. 8b). The rotation operation of sketch 1 is carried out to complete the drawing of the basic part of the gear (Fig. 8c).

Fig. 8
figure 8

(a) Plane 1, (b) Sketch 1, (c) Gear base.

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The mesh fitting operation is performed on the gear teeth of the spiral bevel gear. According to the domain identification in Fig. 7(b), a Certain gear tooth in the model is selected and allowable deviation, smoothness and controllable network density etc. are set to generate the side and top surface patches of single helical gear (Fig. 9a). The fitted patches are trimmed to retain the tooth-shaped surface patches, which is shown in Fig. 9(b).

Fig. 9
figure 9

(a) Fitting patch on a single tooth, (b) Surface of tooth profile.

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The corresponding surface on the gear base is extended to form a closed surface ring with the tooth profile surface (Fig. 10a). The surface is then trimmed to retain a single tooth-shaped surface (Fig. 10b). All surfaces are stitched to form the single-tooth surface body (Fig. 10c) to complete the solid construction of the single-tooth spiral bevel gear.

Fig. 10
figure 10

(a) Surrounding surface, (b) Surface of a single tooth, (c) Surface body of a single tooth.

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The number of gears is counted and the helical angle β in the digital model of the point cloud is measured. A circular array operation is then performed on the single-tooth surface body. The Boolean summation with the gear matrix is finally conducted to obtain a complete solid model of the spiral bevel gear, as shown in Fig. 11.

Fig. 11
figure 11

Spiral bevel gear design model.

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Precision analysis

The volume deviation in the view tool is selected, and the created entity is compared with the original scan data. The system can automatically display the deviation chromatogram of the two selected models.

Case 1: spur gear

The body deviation analysis of the spur gear is shown in Fig. 12. It can be seen that the deviation of the solid model is within ± 0.1 mm, and the average deviation is 2e-4 mm. Through the creation of annotations, it is found that except for the position deviation of the outer groove of the gear exceeding ± 0.05 mm, the rest positions (root, top, Tooth profile, etc.) are all controlled within ± 0.05 mm. It is expected that the larger deviation at the outer groove is caused by an un-even imaging agent layer on the part of interest. A more even layer of imaging agent is needed to mitigate this issue. The 2D deviation analysis of the tooth profile is carried out, and the statistical results are shown in Fig. 13, which shows that the created solid model is accurate enough to fully meet the production requirements.

Fig. 12
figure 12

Body deviation chromatography of spur gear.

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Fig. 13
figure 13

2D deviation statistics.

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Case 2: spiral bevel gear

The body deviation analysis of the spiral bevel gear is shown in Fig. 14. The deviation of the physical model is within ± 0.1 mm. Since there is only a part of the comparable model, the colour spectrum of the physical deviation beyond the model is dark blue and red, and the deviation is relatively large, which should not be included in the deviation data.

Fig. 14
figure 14

Body deviation chromatography of spiral bevel gear.

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The part of the model that needs to be compared can be directly extracted from the digital model. Annotation marks with relatively obvious colour difference between the inner and outer sides and tooth surface of the bevel gear are added, which is shown in Fig. 15. The deviation tolerance is set as ± 0.1 mm, as shown in Table 1. It can be seen that the deviation between the solid model and the point cloud data does not exceed ± 0.05 mm, and most of them do not exceed ± 0.02 mm. The created solid model has a high degree of restoration and fully meets the production needs.

Fig. 15
figure 15

(a) Inner-side of gear and tooth surface, (b) Outer-side of gear and tooth surface.

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Table 1 Distribution of local deviations.
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3D printing

According to the equipment conditions in the laboratory, an industrial-grade 3D printer (HORI Z600) produced by a certain company was selected, and the spiral bevel gear was taken as an example for 3D printing to verify the completion of the reverse modelling of the product. The 3D printing equipment adopts the Fused Deposition Modeling (FDM) working principle, which heats and melts the filamentous hot-melt material, then puts it into a container, and sprays it out through a nozzle with a fine nozzle. The nozzle can move along the X-axis direction of the coordinate axis, and the table can move up and down along the Y-axis direction. During the printing process, it is necessary to ensure that the hot-melt profile can be thermally fused with the previous material immediately after spraying. The curing temperature should always be lower than the temperature of the hot-melt profile, and the curing temperature should be slightly higher than the moulding temperature. Then the workbench is lowered by a thickness, completing one circle of the printing sub-process. The above deposition process is repeated until the ultimate product is finished17.

The relatively environmentally friendly polylactic acid (PLA) wire (diameter d: 1.75 mm) is selected as the 3D printing consumable, which is only used to quickly characterize the completion of the reverse modeling of the product. After the collision check of the part model, appropriate initial size parameters of the platform are set. Technical parameters of the spiral bevel gear in the 3D printing process are shown in Table 2.

Table 2 Technical parameters of 3D printing the spiral Bevel gear.
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The final printed product is shown in Fig. 16, where a small number of burrs on the inner ring at the bottom of the product are the bottom support structure. It can be seen that the structural integrity of the product is relatively good, indicating the feasibility of the product reverse modeling + rapid prototyping solution. It should be noted that the final manufacturing tolerance of the product is comparable with the scanning tolerance and these two tolerances affect and stack up each other due to the accuracy of the 3D printer and the variation of process parameters using the PLA material. For further validation like fitment tests, dimensional checks of the sample of interest, a 3D printer with higher accuracy and stable manufacturing process is needed.

Fig. 16
figure 16

Product of the spiral bevel gear.

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Conclusions

Based on the Geomagic system, this paper uses a hybrid modeling and rapid prototyping technology to carry out rapid reverse design and physical prototyping of spur gear and spiral bevel gear parts. It is known that the non-contact laser measurement technology can better capture all features of the physical object. This kind of operation is simple and convenient, and the operating environment of this kind of measuring method is relatively friendly. The forward and reverse hybrid modelling technology of Geomagic system can efficiently complete the construction of point cloud data to CAD solid model, and realize the rapid reconstruction of the model. The subsequent accuracy analysis verifies its high degree of product restoration. The application of 3D printing technology can realize the rapid reproduction of the actual product. This can effectively realize rapid replacement of failed products or update iterations of products in a short period of time, which has a promising prospect.