Bevel, Helical and Worm Gears(2)

Spiral and Hypoid gears

1) Spiral gear

These gears are also known as crossed helical gears. These gears are mounted on shafts that which do not intersect and which are at an angle to each other. The angle is usually 90 degree. We have already know that spiral gears are also known as skew gears or screw gears which are used to connect and transmit motion between two non-parallel and non-intersecting shafts. The pitch surfaces of the spiral gears are cylindrical and the teeth have the point contact. These gears are only most suitable for the transmitting small power. We have seen that helical gears connected on parallel shafts that are of opposite hand. But the spiral gears may be of the same hand or on opposite hand.

2) Hypoid Gears

A hypoid is name given to a type of helical spiral gear. The main application of this is in the final drive of an automobile where the direction of drive carried by it has to be turned through 90 degrees in order to power-driven wheels. Conventional type straight-cut or spur-cut gears with perpendicular teeth which are considered to be too noisy in use and that of normal spiral bevel does not always give sufficient contact area. The hypoid gear places the pinion off-axis to the crown wheel that allows pinion to be larger in diameter. In a normal passenger car the pinion is always offset to a bottom of crown wheel. This provides for longer tooth contact and serendipitously allows propeller shaft which drives the pinion to be lowered and reducing the "hump" intrusion in the passenger compartment floor.

The hypoid gear incorporates some sliding and it can be considered halfway between a straight-cut gear and a worm gear. Some special gear oils are needs for hypoid gears because the sliding action creates extreme pressure between teeth.

These gears are similar to spiral bevel gears with the difference that the axes of shafts do not intersect. The distance between hypoid pinion axis and the axis of hypoid gear is called the offset. If offset is zero then the hypoid gears become spiral bevel gears. Shaft angle is usually 90 degrees but other angles are also possible. Because shafts do not intersect so bearings can be provided on both sides of the gear which will result in extra of rigidity. High reduction of hypoid gears permit ratios between 10:1 and 20:1 and even high as 360:1, in fine pitches.

Theory of helical gears & tooth geometry

Fig: Helical gear

A helical gear has teeth in form of helix around the gear. Gear path angular edge is helix and after unwind generates involute helicoid curve. Teeth inclined to the axis of rotation. It has application as other gears but no noise and more gradual engagement during teeth meshing. Inclined tooth develop both thrust load and bending couples which are not in the spur gear. It also transmit motion from non-parallel shaft also. Gear must have same helix angle and same right/left helix. Line of contact (with parallel axis) is diagonal across the face of tooth. Also for heavy and smooth load transfer and high speed. Gear contact ratio is minor importance than contact area.

Terms used in Helical Gears

The following terms in connection with helical gears as shown in

1. Helix angle: It is a constant angle made by helices with that axis of rotation.
2. Axial pitch: It is distance of parallel to axis between similar faces of that adjacent teeth. It is the same as the circular pitch and therefore denoted by p_c. The axial pitch can also be defined as circular pitch in plane of rotation or diametral plane.
3. Normal pitch: It is distance between similar faces of the adjacent teeth along a helix on pitch cylinders normal to the teeth. It is denoted by p_N. The normal pitch may be defined as circular pitch in normal plane which is a plane perpendicular to teeth. Mathematically,

Normal pitch(p_N) = p_c cos α

Proportions for Helical Gears

Though the proportions for helical gears are not standardized so the following are recommended by American Gear Manufacturer's Association (AGMA),

Pressure angle which is in the plane of rotation, φ = 15° to 25°

Helix angle, α = 20° to 45°

Addendum = 0.8 m (Maximum)

Dedendum = 1 m (Minimum)

Minimum total depth = 1.8 m

Minimum clearance = 0.2 m

Thickness of tooth = 1.5708 m

Parallel and crossed shafts for helical gears

1) Helical Gears Connecting Parallel Shafts

Helical gears connecting parallel shafts will run more and more smoothly and quietly than spur gears. Particularly when the helix angle is great enough to ensure that there is continuous contact from the one tooth to next tooth. The pair of helical gears used to connect parallel shafts must have same pitch, pressure angle and helix angle but they will be opposite hand gears that is one will be a left-hand gear and the other a right-hand gear.

2) Helical Gears that connecting Non-Parallel Shafts

Helical gears used to connect non-parallel shafts are commonly called the spiral gears or crossed axis helical gears. If the shaft angle is 90 degrees, the gears will be of same hand and sum of helix angles will be equal to the shaft angle (90 degrees). Helical gears used on non-parallel shafts which must have same normal pitch and normal pressure angles. They may, however, be of the same or opposite hand depending on the shaft angle.

References:
1. H.H. Mabie and C. F. Reinholtz, “Mechanism and Dynamics of Machinery”, Wiley.
2. J.S. Rao & R.V. Dukkipati Mechanisms and Machine Theory, New Age International (P) Limited..
3. J.E. Shigley and J.J. Uicker, Jr., “ Theory of Machines and Mechanisms”, McGraw Hill.
4. B. Paul, “Kinematics and Dynamics of Planar Machinery”, Prentice Hall.
5. C. E. Wilson, J.P. Sadler and W.J. Michels, “Kinematics and Dynamics of Machinery”, Harper Row.