Operating principle and scope. Worm gear (Figure 11.19) refers to gear transmissions with intersecting shaft axes. The crossing angle is usually 90°. The movement in worm gears is converted according to the principle of a screw pair or according to the principle of an inclined plane. A worm gear consists of a screw called a worm (Figure 11.20) and gear wheel, called a worm wheel (Figure 11.22). When the worm rotates around its axis, its turns move along the generatrix of its cylindrical surface and sets the worm wheel into rotation. The worm and worm wheel are produced by cutting teeth using special tool from whole blanks. In a worm gear, just like in a gear, there are diameters of dividing cylinders (Figure 11.19): d 1 – dividing diameter of the worm, d 2 – pitch diameter of the worm wheel. Touch point pitch diameters called the pole of engagement.
Figure 11.19 – Worm gear diagram.
Advantages of worm gears:
1. Possibility of obtaining a large gear ratio in one stage (i= 8 – 200).
2. Smooth and silent operation.
3. Compactness (small dimensions).
4. Self-braking (impossibility of transmitting torque from the worm wheel to the worm).
5. Damping properties reduce machine vibration levels.
Disadvantages of worm gears:
1. Significant friction in the engagement zone.
2. Heating of the transmission.
3. Low efficiency.
Worm gears used in devices with limited power (usually up to 50 kW).
Figure 11.20 – Worms.
Worm gears are used in the dividing and feeding mechanisms of gear cutting machines, longitudinal milling machines, deep boring machines, lifting and traction winches, hoists, mechanisms for lifting loads, booms and turning of automobile and railway cranes, excavators, elevators, trolleybuses and other machines.
Worms. Based on the shape of the surface on which the thread is cut, they are distinguished into cylindrical (Figure 11.20, a) and globoid (Figure 11.20, b) worms. According to the shape of the thread profile - with a rectilinear (Figure 11.21, a) and curved (Figure 11.21, b) profile in the axial section. Cylindrical worms are most often used. In worms with a rectilinear profile in the axial section, in the end section the turns are outlined by an Archimedean spiral, therefore they are called an Archimedean worm, which is similar to a lead screw with a trapezoidal thread.
Involute worms have an involute profile in the end section and therefore are similar to helical involute wheels, in which the number of teeth is equal to the number of worm runs. Basic geometric parameters worm: = 20° -profile angle(in an axial section for Archimedean worms and in a normal section of a tooth with a cutting involute worm); R - pitch of the worm and wheel teeth, corresponding to the pitch circles of the worm and wheel; t= axial module; z 1. – number of worm passes; – worm diameter coefficient; – helix angle 
; d 1 =qm – diameter of the pitch circle (hereinafter, see Figure 11.21); d a 1 = d 1 + 2m– diameter of the protrusion circle; d fl = d 1 – 2,4m– diameter of the circle of the depressions; b 1 – the length of the cut part of the worm, it is determined by the condition of using the simultaneous engagement of the largest number of wheel teeth [with z 1= 1...2 b 1 >(11 + 0.06z 2) m at z 1 = 4 b 1 ≥(12.5 + 0.09z 2) m].
Figure 11.21 – Shape of the worm thread profile and basic geometric parameters
Values m And q standardized.
Worm wheels. When cutting without offset (Figure 11.22):
d 2= z 2 m– diameter of the pitch circle in the main section;
d a 2 = d 2 + 2m – diameter of the protrusion circle in the main section;
d f 2 = d 2 – 2,4m– diameter of the circle of the depressions in the main section;
a w= 0.5(q + z 2)m – center distance.
Table 11.3 dimensions b 2 -- worm wheel width and d aM 2 – largest diameter wheels corresponding to the angle of encirclement of the worm by the wheel 2δ = 100° for power transmissions:
Table 11.3
Note. The number of wheel teeth from the non-cutting condition is taken as follows:
Precision manufacturing. For worm gears, the standard provides twelve degrees of accuracy. For gears that require high kinematic accuracy, III, IV, V and VI degrees of accuracy are recommended; for power transmissions, V, VI, VII, VIII and IX degrees of accuracy are recommended.
Figure 11.22 – Basic geometric parameters of the worm wheel
Gear ratio. In a worm gear, as opposed to a gear gear, the peripheral speed v 1 And v 2 do not match (see Fig. 11.23). They are directed at an angle of 90° and are different in size; the relative movement of the dividing cylinders does not roll in like those of gear cylindrical and bevel gears, but they slide. With one revolution of the worm, the wheel will rotate through an angle covering the number of wheel teeth equal to the number of runs of the worm. The wheel will make a full revolution at worm revolutions, that is
Because z 1 can be equal to 1, 2 or 4 (which a gear cannot have), then a large gear ratio can be obtained in one worm pair.
Sliding in engagement. When moving, the turns of the worm slide along the teeth of the wheel, as in a screw pair. Sliding speed v s directed tangentially to the helix of the worm. As a relative speed, it is equal to the geometric difference between the absolute speeds of the worm and the wheel, which are the peripheral speeds v l And v 2(see Fig. 11.19 and Fig. 11.23); or, at the same time
Rice. 11.23. Sliding speed determination scheme
where is the angle of elevation of the helix of the worm. Because< 30°, то в червячной передаче v 2 less v 1 a v s more High slippage in worm gears causes reduced efficiency, increased wear and a tendency to seize.
Worm gear efficiency determined by formula (11.48). The only difference is in the definition of gearing losses. By analogy with screw pair Efficiency engagement with the leading worm is determined by the formula:
Efficiency increases with increasing number of worm passes (increases) and with decreasing friction coefficient or friction angle f. If the leading wheel is the wheel, then the direction of the forces changes and then we get
When ≤, 3 = 0, transmission of motion in the opposite direction (from the wheel to the worm) is impossible. We get a self-braking worm pair.
It has been experimentally established that the friction coefficient depends on the sliding speed. With increase v s decreases This is explained by the fact that the increase v s leads to a transition from semi-fluid friction modes to liquid friction. The friction coefficient values also depend on the roughness of the friction surfaces and the quality of the lubrication.
For preliminary calculations, when and v s are not known, the efficiency can be selected using the average values from Table 11.4.
Table 11.4
After determining the transmission dimensions, the efficiency is clarified by calculation.
Meshing forces. In the worm gear (see Fig. 11.24) there are: circumferential force of the worm F t 1, equal to the axial force of the worm F a 2,
wheel circumferential force F t 2, equal to the axial force of the worm F a 1
radial force
(11.71)
Normal strength
(11.72)
In the axial plane of force Ftz And Fr are components F n = F n cos(projection of normal force onto the axial plane). T 1 -- moment on the worm, T 2- torque on the wheel:
T 2 =T(11.73)
Basic performance and calculation criteria. Worm gears are calculated using bending stresses and contact stresses. This is where wear and seizing occurs more frequently. This is due to high sliding speeds and unfavorable sliding direction relative to the contact line. To prevent jamming, special antifriction pairs of materials are used: worm - steel, wheel - bronze or cast iron.
Rice. 11.24. Forces in the worm gear
The intensity of wear depends on contact stresses. The main calculation is carried out using contact stresses. The bending stress calculation is performed as a test calculation.
Calculation based on contact stresses. The equation
(11.74)
They are also used to calculate worm gears. For Archimedean worms, the radius of curvature of the worm turns in the axial section is ρ 1 = . Then, using formula (11.8) taking into account equation (11.20), we obtain
By analogy with helical gear, specific load of worm gears
where is the total length contact line(see Fig. 11.22); α = 1.8...2.2 – end overlap coefficient in the middle plane of the worm wheel; ≈ 0.75 – coefficient that takes into account the reduction in the length of the contact line due to the fact that contact is not provided along the full arc of girth 2δ. After substitution into formula (11.74) we get
DISADVANTAGES, CLASSIFICATION, WHEEL MATERIALS
WORM GEARS: DESIGN FEATURES, ADVANTAGES AND
A worm gear consists of a screw, called a worm, and a worm wheel, which is a type of helical gear. The axes of the transmission shafts intersect, the angle of intersection is usually 90 0.
Picture 1
Unlike a helical gear, the rim of a worm wheel has a concave shape, which helps to somewhat fit the worm and, accordingly, increase the length of the contact line. The worm thread can be single-start or multi-start (2, 4).
Advantages:
Possibility of getting big gear ratio;
Smooth and quiet operation;
Possibility of obtaining self-braking (when changing the input).
Flaws:
Relatively low efficiency (with a single-start worm - 0.72; with a two-start worm - 0.8; with a four-start worm - 0.9);
The need to use expensive anti-friction materials for the wheel;
Increased wear and heat.
Worm gears are classified according to various criteria:
1) in the shape of a worm:
With a cylindrical worm (Figure 2a);
With a globoid worm (Figure 2b);
B) with a globoid worm
Figure 2
2) according to the shape of the worm coil profile:
With an Archimedean worm (according to GOST 19036-81 designated -ZA). In the axial section, the tooth profile has the shape of a trapezoid, in the end section - the shape of an Archimedean spiral (Figure 3a);
With a convolute worm having a rectilinear outline of a coil in a normal section (Figure 3b);
An involute worm (ZJ), which is a helical gear with a small number of teeth and a large angle of inclination (in the end section the tooth has an involute profile (Figure 3c).
Figure 3
Due to high sliding speeds, the materials of the worm pair must have anti-friction properties, wear resistance and a reduced tendency to jam.
Worms are made from carbon or alloy steels. The greatest load capacity is possessed by pairs in which the worm turns are heat-treated to high hardness, followed by grinding.
Worm wheels are made mainly of bronze, less often of cast iron.
Tin bronzes of type OF10-1, ONF are considered the best material, however, they are expensive and in short supply. They are used at high speeds V s =5...25 m/s. Tin-free bronzes, for example aluminum-iron bronzes of the Br.AZh9-4 type, have increased mechanical characteristics, but have reduced extreme pressure properties. They are used at V s<5m/c. Чугун применяют при V s <2м/с, преимущественно в ручных приводах.
In worm gears, the standard profile angle is taken to be 20°: for Archimedean worms in the axial section, for convolute worms - in the normal section, for involute worms - in the normal section of the helical rack that engages the worm. The distance between the same points of the corresponding lateral sides of two adjacent turns of the worm, measured parallel to the axis, is called the design pitch and is designated P. The ratio P/π is called the modulus. Module (m) is a standard parameter: for a worm it is axial, for a worm wheel it is end-face.
Consisting of two moving links - a worm and a gear and designed to transmit and transform rotational motion between orthogonal intersecting axes. A worm is a link whose outer surface is shaped like a screw. A worm wheel is a gear with helical teeth that meshes with a worm.
Types of worm gears and worms (according to GOST 18498-73):
1.according to the type of dividing surface of the worm
Cylindrical worm gears - the worm and wheel in the gear have cylindrical pitch and initial surfaces;
Globoid worm gears - the dividing and initial surfaces of the worm are formed by rotating a segment of the arc of the dividing or initial surface of the paired worm wheel around the axis of the worm;
2. by the type of theoretical end profile of the worm coil
Archimedean worm (ZA) - the profile is made along an Archimedean spiral;
Involute worm (ZI) - the profile is made along the involute of the circle;
Convoluted worm (ZN) - the profile is made along an elongated involute.
(Fig. 14.4)
Geometry of gearing of a cylindrical worm gear:
Calculation of the gearing geometry of a cylindrical worm gear is regulated by GOST 19650 - 74. The relationship between the main parameters of the worm - the diameter of the initial cylinder d w1, the stroke of the helix pz1 and its angle of inclination bw - is established by the following relation
(Fig. 14.5)
Relationship between the stroke of the helix pz1 and pitch of a multi-start screw p1
Calculation of gear geometry:
Initial data
m— axial module;
q— worm diameter coefficient;
z1— number of worm turns;
aw— center distance;
x— worm displacement coefficient;
u- gear ratio.
Tool Options
h* = (h*w + c*1) is the coil height coefficient;
h*a— head height coefficient;
s*— coefficient of design thickness;
r*f— coefficient of radius of curvature of the transition curve;
c*1.2 = 0.25 … 0.5 ; s* = 0.75 H p ; r*f = 0.3 … 0.45
(Fig. 14.6)
Calculation of geometric parameters:
1.Number of wheel teeth
2. Offset factor (if the center distance is specified)
*Center distance (if offset coefficient is specified)
3. Pitch diameters
4. Initial diameters
5. Pitch angle turn of the worm
6. Initial elevation angle turn of the worm
7. Main elevation angle worm turns (only for ZI worms)
and main diameter of the worm
8.Height turn of the worm
9.Head height turn of the worm
10. Vertex diameters
worm turns
worm wheel teeth in the middle end plane
11.Dimensions of depressions
worm wheel
12. Largest diameter worm wheel
13. Crown width worm wheel
14. Cut length worm (at x=0)
Geometric indicators of the quality of engagement:
1. There is no cutting of the worm wheel teeth if
(at small helix angles, the transmission of motion from the worm wheel shaft to the worm becomes impossible)
Flaws :
high sliding speed along the tooth line, leading to an increased tendency to seize (special lubricants and materials are required for the worm wheel ring gear),lower efficiency and higher heat dissipation.
Worm gears are a kinetic pair designed to transmit torque. Consists of a worm and a wheel.
A prerequisite is that the shafts form a right angle with each other. Features the following advantages:
- increased gear ratios (up to 300 and above);
- smooth contact and noiselessness;
- transmitted power reaches 60 kW.
The disadvantage of the kinetic couple is that the part has a rather low efficiency (0.7-0.92), and with strong heating and prolonged operation it can quickly fail. At the same time, the cost of bronze from which the wheel is made is quite high.
Our company makes transfers according to drawings and finished samples in small and large batches.