1. Introduction
In the CNC gantry machining centre, the horizontal spindle head design involves the straight bevel gear pair (as shown in Figure 1). And the number of gear teeth meshing, the position of the meshing point, and the instantaneous transmission ratio are constantly changing so that the rigidity of the gear teeth is continually evolving, and the gear teeth are constantly impacting each other during the meshing process, thereby exciting the gear vibration. These internal factors become the main cause of the noise. The machining accuracy of CNC gantry machining center machine tools and the high standard requirements for noise make the straight bevel gear pair with high noise at high noise speed. The main factor of vibration and noise. To reduce the intrinsic noise of such gears, the change in stiffness between the gear teeth should be as soft as possible, and the coincidence of the gears should be improved. The impact and noise will be weakened and decreased with the increase of the coincidence degree of the bevel gear pair, and the reduction of the stress of the bevel gear teeth also significantly reduces the impact phenomenon and noise intensity. Secondly, when the primary and passive gears enter meshing outside the meshing line, the immediate difference in speed causes a collision at the tooth top of the passive gear. The degree of noise generated by gear transmission under different loads is different because the amount of deformation of the gear teeth under other loads is different, and the resulting impact is different. The paper proposes using the spiral bevel gear pair to replace the straight bevel gear pair. Comparing the coincidence degree, bending stress of the tooth heel, and contact stress of the tooth surface, the bending pressure of the tooth heel and the contact stress of the tooth surface are compared between the straight tooth bevel gear and the spiral bevel gear. The comparison of the size reflects the comprehensive deformation of the gear teeth. It indirectly obtains the influence of the bending stress of the tooth heel and the contact stress of the tooth surface on the noise—the corresponding gear tooth performance of a straight bevel gear pair.
As shown in Figure 1, the internal structure of the rotatable horizontal spindle head has the function of four-station rotation on the horizontal plane, which broadens the processing range of the CNC gantry machining centre. The power transmission of the rotatable flat spindle head is driven by 2. BT50 transmission rod to go 4. Straight bevel gear 1, 4. Straight bevel gear 1, and the key connected to the 6 principal axes 5. Straight bevel gear 2 meshings to realize the transformation of the vertical rotation power of the 2.BT50 transmission rod into the horizontal rotation power of the 6 spindles and to drive the tool through the spindle to complete the task of cutting.
2. Coincidence Analysis of Straight Bevel Gear and Spiral Bevel Gear
A pair of straight bevel gears and spiral bevel gear gears in the rotatable horizontal spindle head of a CNC gantry machining center in a machine tool factory is selected for contact analysis to preliminarily analyze the stress distribution and deformation of the gear teeth. Except for the different types of gears, the other parameter settings are the same. According to the data in the column of coincidence degree in the parameters of the straight bevel gear in Table 1 and the parameters of the spiral bevel gear in Table 2 are 2.0411 and 3.4908 respectively, it can be easily obtained that the coincidence degree of the helical bevel gear is 71% larger than that of the straight bevel gear. and coincidence is an important indicator to reduce noise, it can be seen that under the same working conditions, the noise generated by the spiral bevel gear is much less than that of the straight bevel gear.
3. Gear Force Analysis
Both pairs of bevel gears are made of alloy structural steel, rated at 10 kW at 3000 rpm in operation.
Force Analysis of Straight Bevel Gear Teeth
Figure 2 shows the force of the driving gear when the gears are engaged in the transmission. When the friction force is not considered, the total force Fn on the gear teeth will be along the direction of the meshing line, and Fn is called the normal force. Fn can be decomposed on the index circle into a tangential force Ft tangent to the index circle and a tangential force Ft along the radial direction and pointing to the wheel center diameter Fr.
The force of periphery Fmt=2000T/dmN
Radial force Fr=FmttanαcosδN
Axial force Fx=FmttanαsinδN
The pitch diameter of the teeth midpoint dm(mm), dm=d(1-0.5b*R);
T — The nominal torque(N.m), T=9550P/n;
P — Nominal power(kW);
n — Rotate speed(r/min)
| Pinion gear | Bevel gear | |
| Large end modulus m | 4 | 4 |
| Number of teeth z | 41 | 41 |
| Face width | 36 | 36 |
| Face width factor | 0.31 | 0.31 |
| Contact ratio | 2.0411 | 2.0411 |
| Cone angle δ | 45° | 45° |
| Reference cone distance R | 115.97 | 115.97 |
| Pitch diameter d | 164 | 164 |
| Teeth space P | 12.57 | 12.57 |
| Mean spiral angle βb | 0 | 0 |
| Press angle α | 20° | 20° |
| Addendum | 3.4 | 3.4 |
| Whole depth | 7.552 | 7.552 |
| Accuracy class | 6-D6 | 6-D6 |
| Left hand | Right hand | |
| Large end modulus m | 4 | 4 |
| Number of teeth z | 41 | 41 |
| Press angle α | 20° | 20° |
| Face width | 36 | 36 |
| Face width factor | 0.31 | 0.31 |
| Contact ratio | 3.4908 | 3.4908 |
| Helical angle β | 35° | 35° |
| Cone angle δ | 45° | 45° |
| Reference cone distance R | 115.97 | 115.97 |
| Pitch diameter d | 164 | 164 |
| Center cone distance Rm | 97.97 | 97.97 |
| Teeth space P | 12.57 | 12.57 |
| Mean spiral angle βb | 42.793° | 42.793° |
| Hand of spiral | Left hand | Right hand |
| Addendum | 3.4 | 3.4 |
| Whole depth | 7.552 | 7.552 |
| Accuracy class | 6-D6 |
By the formula：
The force of the periphery Fmt=459.492N.
Radial force Fr=118.258N
Axial force Fx=118.258N.
T=9550P/n=31834N.mm
Force Analysis of Spiral Bevel Gear Teeth
The force of the periphery Fmt=2000T/dmN
Radial force Fr=Fmt/cosβm(tanαncosδ+sinβmsinδ)N
Axial force Fx=Fmt/cosβm(tanαnsinδ+sinβmcosδ)N
The pitch diameter of the teeth midpoint dm(mm), dm=d(1-0.5b*R);
T — The nominal torque(N.m), T=9550P/n;
P — Nominal power(kW);
n — Rotate speed(r/min);
The force of the periphery Fmt=459.492N;
Radial force Fr=-139.402N;
Axial force Fx=461.555N
T=9550P/n=31834N.mm
4. ANSYS Workbench Linear Statics Structural Analysis
In this paper, the basic parameters such as tooth number and modulus are kept consistent when the models generated by straight bevel gears and spiral bevel gears are analyzed, and the models are diagnosed with the same load and constraints. Under the condition that the structure size and material are the same, the same magnitude and direction of torque are applied to the straight bevel gear and the spiral bevel gear at the same time. The contact stress and strain of the straight bevel gear, the spiral bevel gear, and the bending stress and anxiety of the tooth heel, respectively.
1) Mesh, division of straight bevel gears and spiral bevel gears (Fig. 3),
2) Through the analysis of the contact stress and contact strain of the straight bevel gear and the spiral bevel gear, it can be easily known from the four figures (a), (b), (c), and (d) in the contact analysis of the bevel gear in Fig. 4: The equivalent stress program and equivalent strain program of the bevel gear are 62.185 MPa and 0.41 μm, respectively, and the equivalent stress and strain program of the spiral bevel gear is 33.96 Mpa and 0.19 μm, respectively. Under the same torque of 31834 N∙mm, the contact stress of the spiral bevel gear only accounts for 54.6% of the contact stress of the straight bevel gear, and the equivalent strain also accounts for only 46.3%. Based on the above data, the mechanical properties of spiral bevel gears are indeed superior to those of straight bevel gears. Take an average of 10 nodes from the small end to the big end of the nodes on the tooth contact line of the straight bevel gear and the spiral bevel gear in the figure, list their equivalent stresses in Table 1 and Table 2, and generate a stress comparison diagram. From Table 3, Table 4 and Figure 5, it can be seen that under the same constraint and load, the contact stress on the contact line of the straight bevel gear is more significant than that of the spiral bevel gear. It can be seen that the spiral bevel gear is stronger than the straight bevel gear. The contact strength of bevel gears is greater than that of straight bevel gears.
3) Through the analysis of the bending equivalent stress and strain of the straight bevel gear and the spiral bevel gear:
From the four graphs (a), (b), (c), and (d) in the bending stress analysis of the bevel gear tooth heel in Fig. 6, it can be easily known that: The programs are 32.248 MPa and 0.22 μm, respectively, and the equivalent stress program and the equivalent strain program of the tooth heel of the spiral bevel gear are 19.963 Mpa and 0.12 μm, respectively. Under the same torque of 31834 N∙mm, the equivalent bending stress at the heel of the spiral bevel gear only accounts for 61.9% of the match bending stress at the heel of the straight bevel gear, and the equivalent bending strain at the heel also only accounts for 54.5%. . Based on the above data, the bending capacity of the teeth of the spiral bevel gear is superior to the mechanical properties of the teeth of the straight bevel gear.
| Node number | 1 | 2 | 3 | 4 | 5 |
| Equivalent stress/Mpa | 39.709 | 43.351 | 48.803 | 49.03 | 45.283 |
| Node number | 6 | 7 | 8 | 9 | 10 |
| Equivalent stress/Mpa | 46.724 | 45.568 | 34.632 | 36.263 | 36.506 |
| Node number | 1 | 2 | 3 | 4 | 5 |
| Equivalent stress/Mpa | 8.308 | 1.1093 | 0.80781 | 7.2612 | 0.723 |
| Node number | 6 | 7 | 8 | 9 | 10 |
| Equivalent stress/Mpa | 4.7664 | 7.1391 | 24.878 | 6.713 | 2.8121 |
Take an average of 10 nodes from the small end to the big end of the nodes on the tooth heel line of the spur bevel gear and the spiral bevel gear in the figure, and list the equivalent stress in Table 5 and Table 6 and generate the tooth heel Bending stress comparison chart. It can be seen from Tables 5, 6, and Figure 7 that under the same restraint and load, the distribution of the equivalent bending stress value on the tooth heel of the spur bevel gear is higher than that of the spiral bevel gear. It can be seen that the spiral bevel tooth heel bearing capacity of the gear is higher than that of the straight bevel gear.
5. Conclusion
It can be seen from the above analysis that under the same conditions, the coincidence degree of the spiral bevel gear is 71% larger than that of the straight bevel gear, the contact stress of the former only accounts for 54.6% of the latter, and the equivalent strain of the one-time only funds for 54.6% of the latter. 46.3%, the equivalent bending stress of the former only accounts for 61.9% of the latter, and the equivalent bending strain of the tooth heel of the one-time only accounts for 54.5% of the latter. The generated noise is also smaller than the last. Spiral bevel gears have higher comprehensive mechanical properties than straight bevel gears.
| Node number | 1 | 2 | 3 | 4 | 5 |
| Equivalent stress/Mpa | 24.677 | 16.021 | 22.781 | 21.075 | 17.595 |
| Node number | 6 | 7 | 8 | 9 | 10 |
| Equivalent stress/Mpa | 31.808 | 19.667 | 18.229 | 32.324 | 15.532 |
| Node number | 1 | 2 | 3 | 4 | 5 |
| Equivalent stress/Mpa | 10.16 | 9.2802 | 18.383 | 11.846 | 12.444 |
| Node number | 6 | 7 | 8 | 9 | 10 |
| Equivalent stress/Mpa | 8.105 | 8.0783 | 1.8952 | 2.458 | 1.1662 |
Finally, the deformation of the spiral bevel gear teeth is smaller than that of the straight bevel gear. Therefore, it can be concluded that the vibration and impact generated by the spiral bevel gear pair during the transmission process will be reduced, and the noise will also be reduced. Based on the above conclusions, the rotatable horizontal spindle head of the CNC gantry machining centre should be driven by a spiral bevel gear pair, which will reduce the noise from 70 decibels before replacement to 60 decibels, and the noise has been reduced.
