BEVEL GEARS
STRAIGHT BEVEL GEARS
• Bevel gears are used to transfer motion between non-parallel shafts, usually at
90° to one another.
• The teeth of a straight bevel gear are straight and lie along an element of the
conical surface.
STRAIGHT BEVEL GEARS
• Lines along the face of the
teeth through the pitch
circle meet at the apex of
the pitch cone.
• The centerlines of both the
pinion and the gear also
meet at this apex.
• In the standard
configuration, the teeth are
tapered toward the center
of the cone.
GEOMETRICAL FEATURES OF STRAIGHT BEVEL GEARS
STRAIGHT BEVEL GEARS
• The pitch cone angles for the pinion and the gear are determined by the ratio of
the number of teeth. Note that their sum is 90°.
• For a pair of bevel gears having
a ratio of unity, each has a pitch
cone angle of 45°.
• Such gears, called miter gears,
are used simply to change the
direction of the shafts in a
machine drive without affecting
the speed of rotation.
STRAIGHT BEVEL GEARS
• The pressure angle ∅, is
typically 20°, but 22.5° and
25° are often used to avoid
interference.
• The minimum number of
teeth for straight bevel gears
is typically 12.
FORCES ON STRAIGHT BEVEL GEARS
• Because of the conical shape of bevel gears and because of the involute-tooth
form, a three-component set of forces acts on bevel gear teeth.
• It is assumed that the three forces act concurrently at the midface of the teeth
and on the pitch cone
• The radial load acts toward the center of the pinion, perpendicular to its axis,
causing bending of the pinion shaft.
• The axial load acts parallel to the axis of the pinion, tending to push it away from
the mating gear. It causes a thrust load on the shaft bearings. It also produces a
bending moment on the shaft because it acts at the distance from the axis equal
to the mean radius of the gear.
• The values for the forces on the gear can be calculated by the same equations for
the pinion, if the geometry for the gear is substituted for that of the pinion.
𝑷𝒊𝒏𝒊𝒐𝒏 𝑷𝒊𝒕𝒄𝒉 𝒄𝒐𝒏𝒆 𝒂𝒏𝒈𝒍𝒆:
𝑭𝒕𝑷
𝜸 = 𝒕𝒂 𝒏−𝟏 𝑵𝑷 /𝑵𝑮 𝑭𝒙𝑷
𝑭𝒓𝑷 𝑭𝒓𝑷
𝑷𝒊𝒏𝒊𝒐𝒏 𝑴𝒆𝒂𝒏 𝒓𝒂𝒅𝒊𝒖𝒔:
𝒅 𝑭
𝒓𝒎 = − 𝒔𝒊𝒏γ
𝟐 𝟐 𝑭𝒙𝑮 𝑷𝒊𝒏𝒊𝒐𝒏 𝑹𝒂𝒅𝒊𝒂𝒍 𝑭𝒐𝒓𝒄𝒆:
𝑭𝒓𝑷 = 𝑭𝒕 𝒕𝒂𝒏𝝓𝒄𝒐𝒔𝜸
𝑻𝒐𝒓𝒒𝒖𝒆 𝑻𝒓𝒂𝒏𝒔𝒎𝒊𝒕𝒕𝒆𝒅: 𝑭𝒓𝑮
𝑻 = 𝑷/𝟐𝝅𝒏 𝑷𝒊𝒏𝒊𝒐𝒏 𝑻𝒂𝒏𝒈𝒆𝒏𝒕𝒊𝒂𝒍 𝒇𝒐𝒓𝒄𝒆:
𝑻
𝑭𝒕𝑷 =
𝑭𝒕𝑮 𝒓𝒎
𝑭𝒕𝑷 = 𝑭𝒕𝑮
𝑭𝒙𝑷 = 𝑭𝒓𝑮 𝑷𝒊𝒏𝒊𝒐𝒏 𝑨𝒙𝒊𝒂𝒍 𝑭𝒐𝒓𝒄𝒆:
𝑭𝒓𝑮
𝑭𝒙𝑷 = 𝑭𝒕 𝒕𝒂𝒏𝝓𝒔𝒊𝒏𝜸
𝑭𝒓𝑷 = 𝑭𝒙𝑮
Compute the values for the geometrical features listed
in Table for a pair of straight bevel gears having a
diametral pitch of 8, a 20° pressure angle, 16 teeth in
the pinion, and 48 teeth in the gear. Specify a suitable
face width. The shafts are at 90°.
Calculate the forces on the pinion and
the gear if they are transmitting 2.50 hp
with a pinion speed of 600 rpm. The
geometry factors computed The data
are summarized here.
