Cylindrical gears are gears in which the tooth profile is formed on a circular cylindrical face, including the following types:

Straight spur gear: Teeth form along the birth line of the cylinder face Beveled cylindrical gear: Teeth form in a cylindrical spiral V-shaped cylindrical gear: Teeth tilt in opposite directions to form a V shape.

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### 1.1/ Basic parameters of cylindrical gears

Tooth pitch: The distance between two profiles on the same side of two adjacent teeth measured on the gear circle. (symbol p1)Module: Is the ratio between tooth pitch and number ð (symbol m: in mm) The number of modulus of gears is standardized and specified according to TCVN 2257-77 as follows: :Sequence 1: 1.0; 1.25; 1.5; 2.0; 2.5; 3; 4; 5; 6; 8; ten; twelfth; 16; 20.Sequence 2: 1.125; 1.375; 1.75; 2.25; 2.75; 3.5; 4.5; 5.5; 7; 9; 11; 14; 18; 22. for each modulus m and number of teeth Z we have one standard gear.Division ring: is the circle of the gear with a diameter equal to the standard modulus m multiplied by the number of teeth Z of the gear.When two gears the teeth are properly matched, the two dividing rings of the two gears are in contact (the dividing ring coincides with the rolling ring of the gear) The tooth pitch calculated on the dividing circle is called the split tooth pitch. Peak ring: The circle passing through the top of the tooth, the diameter of the apical ring is denoted as da Baseline: is the circle passing through the bottom of the tooth, denoted by df.Teeth height: is the distance between the top ring and the bottom ring. The tooth height is denoted by h. divided into two parts: Tooth tip height: (ha) is the radial space between the top ring and the split ring. Tooth root height: (hf) is the radial distance between the divider ring and the bottom ring. Tooth thickness: Is the length of the arc over the dividing ring of a tooth, denoted St. Tooth width: Is the length of the arc over the division ring of the tooth groove, denoted et.Basic circle: Is the circle forming the profile declaration body, symbol db.Minging angle: An angle formed by the common tangent of the two base circles and the two dividing circles at the contact of the pair of standard matching gears. The symbol is .

Note: the modulus is the main parameter of the gear, the other parameters of the gear are calculated according to the modulus.

Tooth apex height: ha = m Root height: hf = 1.25.m Tooth height: h = ha + hf = 2.25 m Divider ring diameter: d = m.Z Peak ring diameter: da = d + 2. ha = m(Z+2) Bottom ring diameter: df = d – 2df = m(Z-2,5)Teeth: pt = ð.mGrad angle: anneaf = 0.25.m

### 1.1/ Drawing convention of cylindrical gears

TCVN 13-78 specifies the drawing of cylindrical gears as follows:

The vertex ring and the generating line of the vertex cylinder are drawn with solid solid lines. The dividing circle and the generating line of the dividing cylinder are drawn with dashed lines, not showing the bottom ring and the generating line of the bottom cylinder. In the longitudinal section of the gear wheel. , the part of the tooth is cut, but no dashed lines are specified, then the bottom student is drawn with a solid solid line. To represent slanted teeth or V-shaped teeth, specify a few thin strokes representing the inclined direction of the teeth. and clearly show the angle of inclination. When necessary, the profile of the tooth can be drawn. It is allowed to approximate the profile of the crown teeth with a circular arc as shown in the following figure. The center of the arc is on the base circle, the radius R = d/5 ( d: is the diameter of the ring).

How to draw cylindrical gears

When drawing helical gears, the structures of helical gears are calculated according to the modulus m and shaft diameter dB as follows: Tooth length: b = (8..10).m Ring thickness: s = (2. .4)mHole diameter: dm = ( 1.5 .. 1.7)bB Disc thickness: K = (0,35..0,5)b Diameter of circle of center of holes on disc: D’ = 0.5 (Do + dm)Disk hole diameter: do = 0.25(Do – dm)Hole length: lm = (1.0 .. 1.5)db. Disc rim inner diameter: Do = da – (6..10)m.In the above formulas, when the gears are made of steel, the coefficient is small, and the coefficient of cast iron is large.

## 2/ Draw the bevel gear convention

### 2.1/ Concepts

The bevel gear transmission is used to transmit rotation between two intersecting shafts, the angle between the two shafts is usually 90 degrees.

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Bevel gears include: straight teeth, bevel teeth and curved teeth … The teeth of bevel gears are formed on the conical face, so the size, the modulus change with the tooth length, the more towards the top of the bevel, the size of the bevel gear. the smaller the tooth.

### 2.1/ Gear parameters

Divider ring diameter: de = meZTeeth height: he = 2.2.me Height of tooth tip: ha = me Tooth root height: hf = 1.2 me.Angular apex of taper face: ọApex ring diameter: dae = de + 2.haecocranial = me(Z + 2.cocranial) Diameter of basal ring: dfe = de – 2.hfe.cocranial = me(Z – 2.4.cocranial)Teeth length b: usually equal to ( 1/3)Re (The length of the birth path of the divided bevel) When drawing a bevel gear, we only need to know the modulus, number of teeth, and the angle of the tip of the divided bevel.

### 2.1/ How to draw bevel gear

The drawing convention for bevel gears is similar to the convention for drawing cylindrical gears. On the projection plane perpendicular to the axis of the bevel gear, draw the top ring of the big bottom and the small bottom, the dividing ring of the big bottom.

Pair of mesh bevel gears whose shafts intersect to form an angle other than 900, then the split ring projection of the bevel gear in the projection plane is drawn as a line round.

A pair of engaged spur gears with shafts perpendicular to each other are drawn as in the case of a mated spur gear, and a pair of engaged bevel gears are drawn as shown in Figures 8.21 and 8.22:

3/ Gears, Screws

### 3.1/ Concepts

Screw transmission – worm gear is used to transmit motion between two diagonal axes, the angle between the two diagonal axes is usually 90 degrees, usually the motion is transmitted from the worm to the worm gear with a very large gear ratio.

This transmission has very good self-braking ability. The screw shaft has a common structure like a threaded shaft.

Depending on the face forming the lace, people are divided:

Cylindrical screw: thread formed on a circular cylindrical face. Concave screw: thread formed on a rotating circular concave face.

### 3.2/ Parameters of screw and worm gear

a/ Screw shaft

The modulus of the screw and the worm gear is equal, how the dimensions are calculated according to that modulus. The threaded section length b1 of the screw is taken according to the engagement condition. When drawing, b1 can be obtained by the following formula:

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Z2: is the number of teeth of the worm gear.

b/ Worm gear

The teeth of the worm gear are formed on the torus face. The pitch diameter and modulus of the worm gear are determined on the cross-section. The modulus of the worm gear is equal to the modulus of the worm. Other parameters of the worm gear are calculated according to the modulus and number of teeth.

Diameter of dividing ring: d2 = m.Z2 Diameter of top ring: da2 = d2 + 2.ha = m(Z+2) Diameter of bottom ring: df2 = d2 + 2.hf = m(Z-2,4)Dimension the width of the worm gear b2 is taken according to the diameter of the top face of the screw. The angle of the wormhole 2. is usually taken as the limiting angle of the two ends of the worm gear according to the following formula: Sin ọ = b2/(da1 – 0, 5m); normally 2.ọ = 90 .. 100 Max. diameter of gear ring: daM2 Axial distance between screw shaft and worm gear. aw = 0.5.m(q + Z2)

### 3.3/ How to draw gears and screws

The worm gear and the worm are drawn according to TCVN 13-76. For a screw, on a projection plane parallel to the axis of the screw, draw the base plane generation with a thin line, and on a projection plane perpendicular to the plane of the axis draw the base circle.

When it is necessary to show the profile of the tooth, a partial or extracted image is used.

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For a screw on a projection plane perpendicular to the axis of the worm gear, draw the circle of the largest vertex of the ring with a solid solid line and a divided circle by the dashed line; Do not draw the top circle and the bottom circle.

For worm gear and worm gear, in the engagement area, the tooth apex of the worm and the worm gear are drawn with a bold crescent. On the cross section the screw is not drawn in front of the worm gear. See figure 8.23 ​​: