Sears 536 292522 Brass Worm Gear for 2hp Cultivator UPDATED

Sears 536 292522 Brass Worm Gear for 2hp Cultivator

Worm Gear Mesh Geometry, Elements of Metric Gear Engineering (Cont.)

Effigy 9-two

9.1 Worm Mesh Geometry

Although the worm tooth form can be of a diverseness, the well-nigh popular is equivalent to a V-type screw thread, as in Effigy ix-1. The mating worm gear teeth have a helical lead. (Note: The proper noun "worm wheel" is often used interchangeably with "worm gear".) A central department of the mesh, taken through the worm'southward axis and perpendicular to the worm gear'due south axis, as shown in Figure ix-two , reveals a rack-type tooth of the worm, and a curved anfractuous tooth class for the worm gear. Still, the involute features are only truthful for the central section. Sections on either side of the worm axis reveal nonsymmetric and noninvolute molar profiles. Thus, a worm gear mesh is not a true involute mesh. Also, for conjugate action, the center distance of the mesh must be an exact indistinguishable of that used in generating the worm gear.

To increment the length-of-action, the worm gear is made of a throated shape to wrap effectually the worm.

Figure 9-iii

nine.1.1 Worm Tooth Proportions
Worm tooth dimensions, such as addendum, dedendum, force per unit area angle, etc., follow the aforementioned standards equally those for spur and helical gears. The standard values use to the central section of the mesh. Come across Figure 9-3a . A loftier pressure level angle is favored and in some applications values as high as 25° and xxx° are used.

ix.1.2 Number Of Threads
The worm tin be considered resembling a helical gear with a loftier helix angle.

For extremely high helix angles, at that place is one continuous molar or thread. For slightly smaller angles, there can be 2, three or even more than threads. Thus, a worm is characterized by the number of threads, z_westward .

9.1.3 Pitch Diameters, Pb and Atomic number 82 Bending
Referring to Figure 9-3 :

where:

9.1.4 Center Altitude

9.2 Cylindrical Worm Gear Calculations
Cylindrical worms may be considered cylindrical type gears with spiral threads. Generally, the mesh has a xc° shaft angle. The number of threads in the worm is equivalent to the number of teeth in a gear of a screw type gear mesh.

Figure 9-4

Thus, a 1-thread worm is equivalent to a one-tooth gear; and ii-threads equivalent to two-teeth, etc. Referring to Figure ix-4 , for a atomic number 82 angle ɣ, measured on the pitch cylinder, each rotation of the worm makes the thread accelerate one lead.

In that location are four worm tooth profiles in JIS B 1723, as defined below.

Type I Worm: This worm tooth contour is trapezoid in the radial or axial plane.
Type II Worm: This tooth profile is trapezoid viewed in the normal surface.
Type 3 Worm: This worm is formed by a cutter in which the tooth profile is trapezoid form viewed from the radial surface or axial plane set at the lead angle. Examples are milling and grinding profile cutters.

Type IV Worm: This tooth contour is involute equally viewed from the radial surface or at the lead angle. It is an involute helicoid, and is known past that name.

Type III worm is the most pop. In this blazon, the normal pressure bending α _n has the trend to become smaller than that of the cutter, α _c .

Per JIS, Blazon Three worm uses a radial module m_t and cutter force per unit area bending α _c = 20° as the module and pressure angle. A special worm hob is required to cutting a Blazon III worm gear. Standard values of radial module, yard_t , are presented in Table 9-ane .

Table nine-1

Table 9-2

Because the worm mesh couples nonparallel and nonintersecting axes, the radial surface of the worm, or radial cross section, is the same as the normal surface of the worm gear.

Similarly, the normal surface of the worm is the radial surface of the worm gear. The common surface of the worm and worm gear is the normal surface. Using the normal module, m_n , is virtually popular. Then, an ordinary hob can be used to cutting the worm gear.

Table nine-ii presents the relationships among worm and worm gear radial surfaces, normal surfaces, axial surfaces, module, pressure angle, pitch and lead.

Figure 9-4

Reference to Figure 9-4 can assist the understanding of the relationships in Table 9-two . They are like to the relations in Formulas (6-eleven) and (vi-12) that the helix angle β exist substituted past (xc° – ɣ). We tin can consider that a worm with pb angle ɣ is almost the same equally a screw gear with helix angle (xc° – ɣ).

Table nine-3

Figure nine-5

9.two.1 Axial Module Worm Gears
Table 9-3 presents the equations, for dimensions shown in Figure nine-v , for worm gears with axial module, 1000_ten, and normal pressure angle α _northward = xx°.

Table 9-4

ix.2.2 Normal Module System Worm Gears
The equations for normal module system worm gears are based on a normal module, thou_n , and normal pressure angle, α_northward = 20°. Encounter Tabular array 9-iv .

Effigy 9-6

9.3 Crowning Of The Worm Gear Tooth
Crowning is critically important to worm gears (worm wheels). Not merely can it eliminate abnormal molar contact due to incorrect assembly, but it also provides for the forming of an oil film, which enhances the lubrication consequence of the mesh. This tin favorably affect endurance and transmission efficiency of the worm mesh. At that place are four methods of crowning worm gears:

1. Cutting Worm Gear With A Hob Cutter Of Greater Pitch Diameter Than The Worm.

A crownless worm gear results when it is made past using a hob that has an identical pitch diameter as that of the worm. This crownless worm gear is very difficult to assemble correctly. Proper molar contact and a consummate oil film are usually not possible.

However, it is relatively like shooting fish in a barrel to obtain a crowned worm gear by cutting information technology with a hob whose pitch diameter is slightly larger than that of the worm. This is shown in Effigy ix-half dozen . This creates teeth contact in the eye region with space for oil film formation.

2. Recut With Hob Eye Distance Adjustment.

The starting time stride is to cut the worm gear at standard eye altitude. This results in no crowning. Then the worm gear is finished with the same hob by recutting with the hob axis shifted parallel to the worm gear axis by ±Δ h. This results in a crowning issue, shown in Effigy nine-7 .

Figure 9-7

3. Hob Axis Inclining Δθ From Standard Position.

Figure 9-viii

Figure 9-9

In standard cutting, the hob axis is oriented at the proper bending to the worm gear axis. After that, the hob axis is shifted slightly left and then right, Δθ, in a plane parallel to the worm gear axis, to cut a crown effect on the worm gear tooth. This is shown in Figure 9-viii . Only method 1 is popular. Methods 2 and 3 are seldom used.

4. Utilize A Worm With A Larger Pressure Angle Than The Worm Gear.

This is a very complex method, both theoretically and practically. Usually, the crowning is done to the worm gear, but in this method the modification is on the worm. That is, to modify the pressure angle and pitch of the worm without changing the pitch line parallel to the axis, in accordance with the relationships shown in Equations 9-four:

In order to raise the pressure angle from before change, α _x ', to later on change, α _x , it is necessary to increase the axial pitch, p_x ', to a new value, p_x , per Equation (9-iv). The amount of crowning is represented as the space between the worm and worm gear at the meshing point A in Figure nine-nine .

This amount may be approximated by the following equation:

Figure nine-x

where:
d_i = Pitch diameter of worm
m = Factor from Table 9-5 and Figure 9-x
p_x = Axial pitch afterward alter
p_x ' = Axial pitch earlier change

Table 9-6

An example of calculating worm crowning is shown in Table 9-6 .

Because the theory and equations of these methods are so complicated, they are beyond the scope of this handling. Usually, all stock worm gears are produced with crowning.

9.4 Self-Locking Of Worm Mesh
Self-locking is a unique characteristic of worm meshes that can be put to reward. It is the characteristic that a worm cannot be driven by the worm gear. It is very useful in the pattern of some equipment, such every bit lifting, in that the drive can end at any position without concern that information technology can slip in reverse. However, in some situations it can exist detrimental if the system requires contrary sensitivity, such as a servomechanism.

Self-locking does not occur in all worm meshes, since it requires special weather condition equally outlined hither. In this analysis, only the driving forcefulness interim upon the tooth surfaces is considered without whatsoever regard to losses due to bearing friction, lubricant agitation, etc. The governing conditions are as follows:

Let F_u1 = tangential driving strength of worm

where:
α _n = normal pressure angle
ɣ = pb angle of worm
µ = coefficient of friction
F_n = normal driving force of worm

If F_u1 > 0 and so in that location is no self-locking effect at all. Therefore, F_u1 ≤ 0 is the critical limit of self-locking.

Let α _n in Equation (9-6) be xx°, and then the condition:

F_u1 ≤ 0 will become:
(cos 20° sin ɣ – µ cos ɣ) ≤ 0

Figure 9-eleven

Effigy 9-11 shows the critical limit of cocky-locking for lead angle ɣ and coefficient of friction µ. Practically, it is very hard to assess the exact value of coefficient of friction µ. Further, the bearing loss, lubricant agitation loss, etc. can add together many side furnishings. Therefore, information technology is not easy to constitute precise self-locking conditions. Still, it is true that the smaller the atomic number 82 angle ɣ, the more likely the self-locking status will occur.

Section x: TOOTH THICKNESS

In that location are direct and indirect methods for measuring molar thickness. In full general, there are three methods:

• Chordal Thickness Measurement
• Span Measurement
• Over Pin or Ball Measurement

Effigy 10-ane

ten.1 Chordal Thickness Measurement
This method employs a molar caliper that is referenced from the gear's outside bore. Thickness is measured at the pitch circle. See Figure 10-i .

Table 10-one

x.1.1 Spur Gears
Table 10-1 presents equations for each chordal thickness measurement.

Table 10-2

ten.1.2 Spur Racks And Helical Racks
The governing equations become unproblematic since the rack molar profile is trapezoid, as shown in Table ten-2 .

Table 10-3

Table 10-4

Table x-v

Figure 10-2

x.1.3 Helical Gears
The chordal thickness of helical gears should be measured on the normal surface ground as shown in Table 10-iii . Table 10-four presents the equations for chordal thickness of helical gears in the radial arrangement. Come across Effigy ten-two and Table 10-5 for Gleason direct bevel gears.

Table 10-6

Table x-half dozen presents equations for chordal thickness of a standard straight bevel gear.

If a standard straight bevel gear is cut by a Gleason straight bevel cutter, the tooth angle should be adapted according to:

Table x-7

This angle is used equally a reference in determining the circular tooth thickness, s, in setting upwards the gear cut auto.

Table x-7 presents equations for chordal thickness of a Gleason screw bevel gear.

Figure x-3

Effigy x-3 shows how to determine the round tooth thickness factor K for Gleason spiral bevel gears.

The calculations of circular thickness of a Gleason spiral bevel gear are and so complicated that we do not intend to go further in this presentation.

Table 10-eight

ten.1.five Worms And Worm Gears
Table 10-8 presents equations for chordal thickness of axial module worms and worm gears.

Table 10-ix

Tabular array ten-9 contains the equations for chordal thickness of normal module worms and worm gears.

10.ii Span Measurement Of Teeth
Span measurement of teeth, s_thousand , is a measure over a number of teeth, z_m , made by means of a special molar thickness micrometer. The value measured is the sum of normal circular tooth thickness on the base circle, s_bn , and normal pitch, p_en (z_m – one).

10.two.1 Spur And Internal Gears

Tabular array ten-10

The applicable equations are presented in Table 10-10 .

Figure 10-4

Figure ten-iv shows the span measurement of a spur gear. This measurement is on the outside of the teeth. For internal gears the molar contour is opposite to that of the external spur gear. Therefore, the measurement is betwixt the inside of the tooth profiles.

Table 10-11

Table 10-12

10.2.2 Helical Gears
Tables x-11 and 10-12 present equations for bridge measurement of the normal and the radial systems, respectively, of helical gears.

There is a requirement of a minimum bare width to brand a helical gear span measurement. Let b_min be the minimum value for blank width. Then

where β _b is the helix angle at the base cylinder,

From the above, nosotros can determine that at least 3mm of Δb is required to make a stable measurement of s_thousand .

Figure 10-6

Effigy x-7

10.3 Over Pivot (Ball) Measurement
As shown in Figures 10-6 and 10-7 , measurement is made over the exterior of two pins that are inserted in diametrically reverse tooth spaces, for even tooth number gears; and as shut as possible for odd tooth number gears.

Figure 10-8

Figure 10-9

Effigy 10-10

Figure 10-11

The procedure for measuring a rack with a pin or a ball is as shown in Figure ten-9 by putting pivot or ball in the tooth space and using a micrometer betwixt it and a reference surface. Internal gears are similarly measured, except that the measurement is between the pins. Encounter Figure 10-10 . Helical gears tin but be measured with assurance. In the case of a worm, three pins are used, as shown in Figure x-11 . This is similar to the process of measuring a screw thread. All these cases are discussed in detail in the following sections.

Notation that gear literature uses "over pins" and "over wires" terminology interchangeably. The "over wires" term is often associated with very fine pitch gears because the diameters are appropriately small.

ten.3.1 Spur Gears

In measuring a gear, the size of the pin must be such that the over pins measurement is larger than the gear's outside diameter. An platonic value is one that would place the indicate of contact (tangent point) of pin and tooth profile at the pitch radius. All the same, this is non a necessary requirement. Referring to Figure 10-8 , following are the equations for calculating the over pins measurement for a specific tooth thickness, s, regardless of where the pin contacts the tooth profile:

For fifty-fifty number of teeth:

For odd number of teeth:

where the value of φ _ane is obtained from:

When tooth thickness, s, is to exist calculated from a known over pins measurement, d_grand , the above equations can be manipulated to yield:

where

In measuring a standard gear, the size of the pin must meet the condition that its surface should have the tangent bespeak at the standard pitch circle. While, in measuring a shifted gear, the surface of the pin should have the tangent point at the d + 2xk circumvolve.

Table 10-13

Table 10-xiv

Table x-15

The ideal diameters of pins when calculated from the equations of Table 10-13 may not be practical. So, in practice, nosotros select a standard pin bore close to the platonic value. After the actual diameter of pin d_p is determined, the over pin measurement d_g can be calculated from Tabular array 10-14 .

Table 10-fifteen is a dimensional tabular array under the condition of module k = 1 and pressure angle α = 20° with which the pin has the tangent point at d + 2xm circumvolve.

Table ten-16

Table 10-16A

x.three.2 Spur Racks And Helical Racks
In measuring a rack, the pin is ideally tangent with the tooth flank at the pitch line. The equations in Table 10-sixteen can, thus, be derived. In the instance of a helical rack, module thou, and force per unit area bending α, in Tabular array 10-16 , can exist substituted by normal module, yard_{due north} , and normal pressure angle, α _northward , resulting in Table 10-16A .

» Internal Gears - Connected on page 6

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Sears 536 292522 Brass Worm Gear for 2hp Cultivator UPDATED

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