Page 266 - Analysis and Design of Machine Elements

Analysis and Design of Machine Elements
244
where
d 4
I – moment of inertia,I = f 1 ;
64
l – span between two bearings, usually l = 0.9d ,where d = mz ;
2 2 2
[y] – allowable deflection, usually select [y] = (0.001–0.0025) d ,where d is reference
1
1
diameter of the worm.
9.3.4 Efficiency and Thermal Capacity
9.3.4.1 Efficiency of Wormgear Drives
Efficiency is defined as the ratio of output power to input power. Compared with other
gearing systems, wormgear drive has a much lower mechanical efficiency, mainly due
to friction loss.
The efficiency of enclosed wormgear drive is determined by meshing efficiency ,
1
bearing efficiency and efficiency due to churning of lubricating oil, which gives
2 3
= (9.21)
1 2 3
The meshing efficiency is calculated by [11]
1
tan
= (9.22)
1
tan( + )
v
where
v – equivalent friction angle, which can be obtained from
= arctan f v (9.23)
v
where equivalent coefficient of friction f can be estimated by sliding velocity from
v
Figure 9.5. When the lead angle is equal to or less than the equivalent friction angle,
that is, ≤ , self-locking will occur [1]. Self-locking can be utilized when it is desired
v
to hold a mechanism at a preset position.
The product of bearing efficiency and efficiency is usually within the range of
3
2
0.95–0.96. Thus, the total efficiency of an enclosed wormgear drive is
tan
=(0.95 ∼ 0.96) (9.24)
tan( + )
v
Both lead angles and equivalent friction angles, or equivalent coefficients of friction,
affect meshing efficiency . Figure 9.6 illustrates the relationship graphically. Obviously,
1
the larger the lead angle, the higher the efficiency. From the definition of lead angle in
Eq. (9.5), it is clear that the number of threads has major effect on lead angle. To obtain
a high efficiency, a multiple-threaded worm should be used. However, the efficiency
∘
increases with lead angle only until approximately 45 , beyond that, the increase of lead
angle will have negative effect on efficiency and may also cause difficulties in worm
fabrication. Therefore, commonly used numbers of thread are limited to 1, 2, 4 and 6
only, and the efficiency for the initial design can be correspondingly selected as 0.7, 0.8,
0.9 and 0.95.

9.3.4.2 Thermal Analysis
In a worm gearing, heat is generated by teeth meshing, bearings rolling and oil churning.
The heat must be dissipated to the ambient atmosphere at such a rate that oil operating
∘
temperature is kept below 80 C. Otherwise, viscosity decreases severely and lubricant
deteriorates rapidly, which will greatly reduce the lubricity of oil.