1 new design method 1.1Gleason wheel blank design midpoint normal modulus is mn=2r2cos2z2(1)
Where z2 is the number of large gear teeth; 2 is the large wheel helix angle; r2 is the big wheel pitch circle radius.
The mid-point working tooth height of the large wheel is h=fh2r2cos2z2 (2), where fh is the midpoint tooth height coefficient.
The gear head clearance is c=0.15h 0.05(3) The full tooth height at the midpoint is hmt=h c=1.15h 0.05(4) The height of the tooth at the midpoint of the big wheel is ha2=fah(5)
Where fa is the large gear tooth height factor.
The formula for calculating the root height at the midpoint of the big wheel is hf2=hmt-ha2=(1.15-fa)h 0.05(6)
1.2 Displacement gear wheel blank design The displacement gear design discussed in this paper, the full tooth height at the midpoint of the big wheel, the root cone angle of the big wheel, the cone angle and the outer diameter of the large wheel are unchanged, and the teeth at the midpoint of the large wheel are corrected. The top height is h
A2=f
In ah(7), fa is the correction of the large gear tooth height coefficient, and the data designed by Gleason wheel blank calculation is not taken.
The formula for calculating the root height hf2=hmt-ha2=(1.15-f
a) h 0.05 (8) At this time, the pitch angle, the pitch of the pitch, the apex angle, the root angle, and the modulus of the large wheel of the large wheel have changed. When the wheel blank parameters of the big wheel are calculated, the wheel blank parameters of the small wheel can be calculated.
1.3 Correction method of hypoid gear pressure angle In the Gleason wheel blank design, in order to have the same strength on both sides of the tooth, it is generally desirable to have the same induced curvature at the joints on both sides of the gear tooth, thereby extracting two teeth The calculation formula of the lateral pressure angle is the average pressure angle of the hypoid gear pair; the ultimate pressure angle of the hypoid gear.
In practical applications, the time and load of most rotating devices such as cars and tractors are much higher than the time and load of reverse rotation. That is to say, the usage rate of the tooth surface on one side of the gear is much higher than the other side. Tooth surface, therefore, in the design, we increase the strength during forward rotation by correcting the pressure angle of the forward rotation tooth surface. The pressure angle correction amount in the pressure angle type on both sides of the corrected tooth surface.
2 Examples The basic parameters of the wheel blank of the hypoid gear pair studied in this paper can be found in the geometric model of the new scheme discussed and the variation of the pitch circle of the large wheel midpoint.
Basic parameters of wheel blanks for hypoid gear pairs Small wheel large gear teeth 940 tooth width (mm) 77 small wheel offset distance (mm) 38 big wheel big end pitch diameter (mm) 508 average pressure angle () 22.5 axis Intersection angle () 90 small round midpoint nominal helix angle () 49 rotation to left-handed right-handed geometric model 1. Gleason scheme large wheel midpoint equivalent gear 2. New design scheme big wheel midpoint equivalent gear big wheel midpoint equivalent gear pitch circle In the change, H1K1 and H2K2 are the axes of the small wheel and the big wheel before the displacement, respectively.
1K1 is the axis of the small wheel after the displacement. K1 and K2 are the intersections of hypoid gears before displacement, K
1. K2 is the intersection of the hypoid gear after displacement; H1 and H2 are the front wheel of the displacement, the apex of the large wheel cone, H
1 is the apex of the small wheel cone after displacement; P, P
They are the nodes of the small wheel and the big wheel before and after the displacement; the axis angle and offset of the gear pair before and after the displacement are unchanged, ie K
1K2=K1K2=e; r2, r
2 is the radius of the big wheel pitch circle before and after the displacement.
In the middle, rf2 and rd2 are the root circle radius and the tip circle radius of the large wheel midpoint equivalent gear, respectively, rv2, r
V2 makes the pitch circle radius of the equivalent gear of the large wheel before and after the displacement.
In the actual working condition, an aligned hypoid gear pair is generally engaged by a plurality of tooth pairs. In order to better explain the influence of the tooth shape change on the root stress, this paper considers the same load and acts in the same role. The change in root stress is analyzed in the case of points. The gears use the same tool under the same single load (10kN, acting in the middle of the tooth length and at the same distance from the root). The tool tip distance is 5.588mm, and the tool tooth angle for small wheel cutting is 10 31), using the new wheel blank design scheme (fa=0, pressure angle correction amount=3) and Gleason wheel blank design scheme, the calculated comparison between the root stress and outer diameter is shown in Table 2. See the comparison of the normal chord tooth thickness.
2 New wheel blank design and Gleason wheel blank design plan tooth root stress, outer diameter comparison Gleason wheel blank design scheme new design scheme stress change small wheel root maximum tensile stress (MPa) 21.21480016.618750 new scheme reduced 21.66 small Gear root maximum compressive stress (MPa) 36.13125029.575710 new scheme to reduce the maximum tensile stress of 18.14 large tooth roots 3 new wheel blank design scheme and Gleason wheel blank design scheme normal chord tooth thickness comparison Gleason wheel blank design scheme new design The outer diameter of the outer wheel of the large wheel of the scheme is thick (the actual root height when machining the large wheel before the root of the large wheel is displaced) (mm) 7.53277.3161 small round midpoint normal chord Thick (from the small tooth root is the height of the midpoint of the large wheel before the displacement) (mm) 18.559718.8138 In order to balance the maximum tensile stress of the tooth root of the large and small teeth, the corrected blade top distance is 4.826mm, which is respectively adopted A comparison of the root stress calculated by the wheel blank design and the Gleason wheel blank design.
Under the same large wheel load torque (5000Nm), the maximum contact stress of the hypoid gear tooth surface obtained by the new design is 1216MPa; for the Gleason wheel blank design, the maximum contact stress of the tooth surface is 1011MPa. But under normal circumstances, The gear is damaged due to the tensile stress of the root. Since the maximum contact stress of the tooth surface of this example is relatively small, the new design proposed in this paper is feasible.
4Revised the new design of the blade top and the tooth root stress of the Gleason wheel blank design. Gleason wheel blank design scheme New design scheme Stress change Small tooth root maximum tensile stress (MPa) 21.21480017.245990 New scheme reduction 18.71 small wheel Root maximum compressive stress (MPa) 36.13125030.739270 new scheme to reduce the maximum tensile stress (MPa) of 14.92 large tooth roots 33.07421028.948060 new scheme to reduce the maximum compressive stress (MPa) of 12.48 large tooth roots 51.97531049.878530 new scheme Increase 4.05
3 Conclusions (1) In the design of the hypoid gear, the maximum height coefficient of the tooth surface can be flexibly selected, and the pressure angle of the tooth surface for forward rotation can be corrected to reduce the maximum tensile stress of the root.
(2) In the design of the hypoid gear, reduce the height coefficient of the large gear teeth, the outer diameter of the large wheel does not change, and the outer diameter of the small wheel increases; for correcting the pressure angle of the tooth surface for forward rotation, the original The tool for cutting the small wheel is used for cutting the tooth, and it is not necessary to use a new tool.

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