Design of the Spur Gear with Honeycomb Lattice Structure and PBF Printing

Abstract

In this study, the spur gear with honeycomb lattice structures are designed. The pitch diameter and body length of the spur gear are Ø93 mm and 104.0 mm, respectively. The designed gear was printed using Powder bed fusion (PBF) 3D printer. The gear is 3D printed perfectly. Even the teeth and honeycombs of the gear were output in the same way as the design shape. The printed gear with honeycomb lattice structure has a 24% smaller cross-sectional area and 29% smaller volume and weight than conventional solid structure gears. The surface roughness is approximately 4.5㎛, and the hardness is 345 HV.

1. Introduction

The traditional manufacturing method of gears creates rough shapes from forming processes such as plastic working, casting, powder compression molding, and extrusion. Then, manufacturing is completed through cutting (roughing, finishing) of machining [1-5]. The gear shape is composed of hub, body (or boss), and teeth. The part that occupies the largest volume (or weight) of the gear is the body. The gear body manufactured through the traditional manufacturing method has a solid structure [6-9]. Conventional manufacturing methods cannot design and manufacture gear bodies in a lattice structure. Therefore, it is not possible to reduce material cost through weight reduction, and it is difficult to reduce the size of stress, vibration, and noise generated during operation. Metal additive manufacturing technology can produce a lattice structure rather than a solid structure filled inside the product[10-12]. Therefore, if metal additive manufacturing technology is used, the body of the gear can also be designed and manufactured in a lattice structure. In this study, the body structure of the spur gear was designed as a honeycomb structure, which is a type of lattice structure. This gear was printed using Powder bed fusion (PBF) 3D printer in additive manufacturing technology. The printed gear was analyzed for shape, surface roughness, and hardness.

2. Design of the Spur Gear with the Honeycomb Lattice Structure

2.1 Design of the Basic Shape

Table 1 is the shape dimension data of the spur gear for printing with PBF. The body length is 104.0 mm, and the face width is 34.2 mm. Dedendum circle and clearance circle are Ø85.5 mm and Ø87.0 mm, respectively. Addendum circle is Ø99.0 mm. And the inner diameter connected to the shaft is Ø55.0 mm. The number of gear teeth is 31, and the pitch diameter is Ø93.0 mm. The module is 3 and the pressure angle is 20°. By applying the values of Used standard tooth systems applied to spur gears, detailed dimensional information of the gear teeth section can be calculated. Addendum is 3.0 mm, and dedendum is 3.75 mm. The clearance is 0.75 mm and the working depth is 6.0 mm. Therefore, the whole depth is 6.75 mm and the tooth thickness is 4.713 mm. The designed spur gear has a volume of 355,420 mm3 and a weight of 2.78 kg with the density of steel applied.

Table 1. Dimension of the spur gear

When the pinion and the gear are engaged with each other, the flank of the pinion teeth and the face of the gear teeth come into contact with each other. The gear is subjected to normal force and bending forced. The pinion also receives the same load due to the reaction. Due to the maximum compressive stress according to the size of the bending moment and the size of the moment of inertia, the clearance circle of the gear becomes the most vulnerable position for breakage[3-6].

Fig. 1 shows the state of stress received by gear teeth. The acting force F (686.6 N) is assumed to act at the tip of the teeth along the pressure line. The radial force Fr (234.8 N) generates a uniform compressive stress in the cross-section of the teeth. The tangential force Ft (645.2 N) is both a shear force and a bending force on the teeth. The bending force generates tensile stress and compressive stress that increase linearly around the cross section of the tooth. And the maximum shear stress is generated at the center of the tooth section by the shear force. The compressive stress due to the radial force Fr is 1.15 MPa.

The maximum bending stress (tension and compression)  due to the tangential force Ft is 22.38 MPa, and the shear stress  due to Ft is 4.76 MPa. The maximum compressive stress generated on the teeth is 23.54 MPa, which is the sum of the normal stress (compression) due to the radial force Fr and the maximum bending stress (compression) due to the bending force. The maximum tensile stress max generated in the teeth is 21.23 MPa offset by the magnitude of the normal stress (compression)  due to the radial force Fr in the maximum bending stress (tension)  .

Fig. 1 Stress generated in tooth of spur gear

2.2 Design of the Honeycomb Lattice Structure

The PBF 3D printing method can print freely regardless of the shape. Therefore, the body of an object can be output as a lattice structure rather than a solid structure filled inside. The area of the body that occupies the largest volume of the spur gear was designed as a Honeycomb structure, one of the lattice structures.

Fig. 2 shows the 3D modeling with the honeycomb structure applied to the body of the spur gear. A plurality of honeycombs are arranged in a rotational direction on the body of the gear. The spacing at which the honeycombs are arranged depends on the size of the radius. The stress is relatively large at the root of the teeth, and the stress is relatively small at the location far from the teeth. Therefore, the gap between the honeycombs arranged in the direction of increasing radius was designed to be wide. The honeycomb array spacing near the hole where the shaft is coupled is 0.28 mm, and the honeycomb array spacing near the teeth is 0.72 mm. The honeycombs are penetrated in the longitudinal direction of the gear. The honeycombs are not inserted in the tooth area of the gear because it is the location where deformation and stress occur the most. The length of one side of the honeycomb is 0.5 mm. In the radial direction, honeycombs are arranged in 10 rows. The body of the gear, designed in a honeycomb lattice structure, has a volume of 252,477 mm3 and weighs 1.97 kg with the density of steel applied. 29% weight reduction was achieved by designing the body with a honeycomb lattice structure compared to the body with a solid structure.

Fig. 2 Design of the spur gear with honeycomb structure

3. Experiment

3.1 Experimental Method

Using the DMP Flex 350 equipment of 3D SYSTEMS, USA, the printing work of the gear with honeycomb lattice structure was carried out. Output conditions were set to 215 W for laser power, 900 mm/s for scan speed, and 15,000 mm/s for jump speed. The surface state of the printed gear with honeycomb lattice structure was analyzed with a digital microscope. 3D surface profile and surface roughness were measured using optical surface roughness equipment. And the surface hardness was measured using the Vickers hardness.

3.2 Experimental Results

Fig. 3 is a spur gear with a honeycomb lattice structure printed by a PBF 3D printer. No additional post-processing was performed on the printed gears. It can be confirmed that the manufactured gear was printed in the same design shape.

Fig. 4 is an enlarged image of the teeth of the honeycomb lattice structure gear printed by PBF 3D printer with a digital microscope. The shape of the teeth was printed the same

Fig. 3 The spur gear with honeycomb structure printed by PBF

Fig. 4 Teeth of PBF printed spur gear with honeycomb structure

as the design shape. However, it can be seen that the surface of the gear teeth is somewhat rough.

Fig. 5 is an enlarged image of the honeycomb area with a digital microscope. It can be seen that the honeycomb arrangement spacing and honeycomb shape are the same as the design.

Fig. 5 Honeycombs of PBF printed spur gear

The tooth surface of the honeycomb structure gear printed by the PBF 3D printer was enlarged at a higher magnification with a digital microscope. Fig. 6 is an enlarged image of four positions on the surface of the printed gear teeth. The plane of the teeth looks bumpy, and the edges look rougher than the plane. It can be seen that the surface of ⓓ, which is close to the top land of the teeth, is relatively rough compared to other locations (ⓐ, ⓑ and ⓒ).

Vickers hardness was measured at four positions (ⓐ~ⓓ) of the gear teeth. Fig. 7 is a Vickers hardness graph of four positions of gear teeth. Position ⓐ is 340 HV, Position ⓑ

Fig. 6. Tooth surface of PBF printed spur gear with honeycomb structure.

Fig. 7 Vicker’s hardness in tooth of PBF printed spur gear with honeycomb structure

is 337 HV, Position ⓒ is 335 HV and Position ⓓ is 334 HV. There are some differences by location, but the differences

Fig. 8 3D surface profile in tooth of PBF printed spur gear with honeycomb structure

are very insignificant. The location with the highest hardness is the location ⓐ close to the tooth root, and the location with the lowest hardness is the location ⓓ close to the peak.

The 3D surface profile and surface roughness of the tooth surface of the honeycomb gear printed in PBF were measured using an optical surface roughness equipment. Fig. 8 shows the 3D surface profile for the four positions. The surface roughness (Ra) in the radial direction is 4.721 μm for position ⓐ, 4.529 μm for position ⓑ, 4.663 μm for position ⓒ, and 4.991 μm for position ⓓ. The surface roughness in the tangential direction is 3.919 μm for position

ⓐ, 4.170 μm for position ⓑ, 4.316 μm for position ⓒ, and 4.132 μm for position ⓓ. The surface roughness is smaller in the tangential direction than in the radial direction.

4. Conclusions

In this study, the spur gear with a pitch diameter of Ø93 mm and a body length of 104.0 mm was designed for weight reduction by applying the honeycomb lattice structure. The gear with the honeycomb lattice structure was printed using a PBF 3D printer. The results obtained are as follows.

(1) Gears with honeycomb lattice structure are 29% lighter than gears with solid structure.

(2) The gears of honeycomb lattice structure printed in PBF were identical to the design shape, and all honeycomb shapes were perfect. The hardness of the printed honeycomb lattice structure spur gear was 334~340 HV, and the surface roughness was 3.92~4.72 μm.

(3) Gear teeth printed with PBF have a rougher surface than gear teeth manufactured by the conventional method. There is a concern about wear or fatigue failure due to long-term use. Therefore, a post-processing process of polishing the surface of the gear teeth is required.