Usually, when we are machining a worm gear, the basic worm of the standard worm gear hob (hereinafter referred to as the hob) conforms to the working worm that the worm wheel is meshed with. The main parameters are modulus, pressure angle, index circle diameter, number of heads, and spiral. The direction and the spiral angle are the same as those of the worm, and when machining the worm wheel, the machining center distance of the hob is the same as the working center distance, so that the worm wheel can theoretically ensure proper meshing with the worm. This paper introduces a new method of machining a worm gear using a non-standard large-diameter worm gear hob (ie, a hob with a larger diameter than the conventional worm wheel hob, hereinafter referred to as a large-diameter hob).
1. Design of large diameter hob
(1) Determining the modulus and pressure angle of the large-diameter hob The condition that the worm wheel and the worm can be properly meshed is that the end face modulus of the worm wheel is equal to the axial modulus of the worm, and the end face pressure angle of the worm wheel is equal to the axial pressure angle of the worm. Can be expressed by the following formula
Where m t2 is the worm wheel end modulus; m x1 is the axial modulus of the worm; αt2 is the end face pressure angle of the worm wheel; αx1 is the axial pressure angle of the worm.
and
Where mn2 is the worm wheel normal modulus; mn1 is the worm normal modulus; αn2 is the worm wheel normal pressure angle; αn1 is the worm normal pressure angle; β is the worm wheel helix angle; λ is the worm helix angle.
It can be concluded from equations (3) to (7)
Mn2= mn1 (8)
Nn2 = αn1 (9)
Therefore, the condition that the worm wheel and the worm can be correctly meshed can also be described as: the worm wheel normal modulus is equal to the worm normal modulus, and the worm wheel normal pressure angle is equal to the worm normal pressure angle.
When the hob is machining the worm wheel, its normal modulus and normal pressure angle are equal to the worm wheel normal modulus and normal pressure angle. Therefore, in order to ensure that the worm wheel of the large-diameter hob can be properly meshed with the worm, it is necessary to ensure that the normal modulus and the normal pressure angle of the large-diameter hob are equal to the normal modulus and the normal pressure angle of the worm wheel.
(2) Determining the outer diameter of the large-diameter hob Figure 1 is a comparative diagram of the machining of the worm gear by the large-diameter hob and the ordinary hob. It can be clearly seen from the figure that the worm wheel processed by the large-diameter hob has cut more materials. In the case of contact spot detection (detection under no-load conditions), it was found that the worm wheel contact processed by the large-diameter hob was very small (see Fig. 2), which was due to the worm wheel machined by the large-diameter hob, which was drummed in the tooth direction. Shaped by the shape. However, as the load increases, the contact spots will become larger and larger. The worm wheel is drum-shaped in the tooth direction, just like the modification of the gear, which is beneficial to improve the bearing capacity of the worm wheel and reduce the transmission noise of the rod pair. However, if the drum shape is too large, it will seriously affect the design bearing capacity of the worm gear. When the machining worm wheel increases with the outer diameter of the worm wheel hob, the drum shape will also increase. Therefore, when selecting a large diameter hob, the outer diameter of the hob should not be too large. Under normal circumstances, the outer diameter of the hob should not be exceeded. The sum of 5 times modulus (large diameter hob outer diameter ≤ hob outer diameter + 5 times worm gear modulus).
(3) Determining the pitch circle normal tooth thickness of the large-diameter hob The indexing scallop thickness of the hob determines the groove width of the machined worm wheel. In order to ensure that the mesh gap between the worm wheel and the worm that is machined by the large diameter hob does not change, the diameter of the large diameter hob index must be equal to the tooth thickness of the indexing circle of the hob.
(4) It is determined that the normal modulus of the helical angle hob of the large diameter hob is the same as the normal modulus of the worm wheel. The number of heads of the hob is the same as the number of matching worm heads, and the hob indexing circle can be determined by the cutter designer. Given, then calculate the helix angle of the large diameter hob according to the formula below
λ knife = arctan (nmx knife / d knife) (10)
Mx knife = mn knife / cos λ knife (11)
In the formula, the λ knife is the hob spiral angle; n is the number of the hob head; the d knife is the hob index circle diameter; the mx knife is the hob axial modulus; the mn knife is the hob normal modulus.
(5) Determination of other parameters of large-diameter hob In order to ensure that the worm gear of large-diameter hob can be properly meshed with the worm, the large-diameter hob must also meet the following conditions: 1 The large-diameter hob has the same spiral direction as the hob. 2 large diameter hobs and hobs have the same number of heads.
The 3 large diameter hob is the same type as the basic worm of the hob.
2. Processing of worm gear
It can be known from formulas (10) and (11) that the helix angle of the large-diameter hob is smaller than that of the hob, and as the diameter of the hob increases, the helix angle gradually decreases, so before installing the large-diameter hob, The helix angle of the hob must be determined according to the outer diameter of the hob for the tool to be installed. In order to ensure that the worm wheel helix angle of the large diameter hob is the same as the helix angle of the hob machining, the hob tool holder must be turned by an angle θ when installing the hob.
θ=β-λ knife (12)
In the formula, the λ knife is a large diameter hob spiral angle.
Due to the influence of the accuracy of the machine tool holder, when using a large-diameter hob to machine the worm wheel, the contact worm wheel must be tested for contact spots. According to the contact spot condition, the hob installation angle is fine-tuned to ensure that the worm gear contact spot is in the worm gear. In the middle, the formal machining of the worm gear can begin.
3. Illustration
Let's take a worm wheel processed by our factory in large quantities as an example to illustrate the design principle of large diameter hob and hob machining worm gear. The basic parameters are as follows:
(1) worm gear parameter end face modulus m t2=2.5; number of teeth z2=30; normal pressure angle αn2=20°; helix angle β=5° 6′ 8′′; center distance a=51.5mm; helix direction is right-handed .
(2) Worm vice drive type Normal straight profile.
(3) worm parameter axial modulus mx1=2. 5; number of heads z1 = 1; normal pressure angle αn1 = 2 0°; helix angle λ = 5°6′8′′; spiral direction is right-handed; The tooth thickness s n1 = 3.91 (-0.02/-0.07) mm; the index circle diameter d 1 = 28 mm; the tip circle diameter da1 = 33 mm.
According to the worm and worm gear parameters, the design parameters of the hob are as follows:
Mx knife = 2.5, αn knife = 20 °. The diameter of the hob index circle is 28mm; the diameter of the hob tip circle is 34.25mm; the helix angle λ=5°5′8′′; the hob spiral direction is right-handed; the number of heads is k=1; the basic worm type is Straight profile. The normal tooth profile is shown in Figure 3.
According to the worm and worm gear parameters, the parameters of the large diameter hob are designed as follows: mx knife '= 2.495 5, αn knife' = 20°. The diameter of the hob index circle is 38mm; the diameter of the hob tip circle is 44.25mm; the helix angle λ=3° 45′ 26′′; the hob spiral direction is right-handed; the number of heads is k=1; the basic worm type is Straight to the side.
Since the diameter of the large-diameter hob is 44.25 mm, the hob can be designed as an inner hole structure during structural design, which not only reduces the manufacturing cost of the tool, but also shortens the manufacturing cycle of the tool.
When the length of the hob is the same, the worm gears processed by the two types of hobs are statistically found to have substantially the same efficiency of the two hobs, but the durability of the large-diameter hobs is higher.
In addition, it has been found through experiments that the worm gears processed by the above two types of hobs can meet the product design requirements, but the worm gears processed by the large diameter worm gear hobs are better than the standard worm gear hobs in the transmission noise and load carrying capacity. .
4. Conclusion
The worm gear processed by the large-diameter hob can fully meet the requirements of use, and can improve the load capacity of the worm wheel, reduce the transmission noise of the worm gear pair, and reduce the processing cost in mass production.
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