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General Engineering Reviews | Engineering Applications and Design
When designing or modifying a automotive, truck or other vehicle drive line
(drive shaft) it is very important to understand the application and philosophy
behind calculating drive line angles. There are a number of highly technical
mathematical equations that are required to determine the precise angles of the
drive line.
When determining the optimum drive line angles for a vehicle, a good rule of
thumb to follow is the six to one-and-a-half rule. The drive line working angle
should not exceed six degrees, and the adjoining u-joints at either end of a
shaft should be different by no more than one-and-a-half degrees. When u-joints
are arranged this way, the angles are said to be "canceled."
Designers should remember that if the six to one-and-a-half degree angle
boundaries are exceeded, the u-joint is working in unfamiliar, undesirable
territory, resulting in drive line, and potentially, drive train problems.
Generally speaking, if a drive line is used in low speed applications, the
angles can be higher. On the other hand, great care must be exercised with
higher speed applications to keep the angles below the recommended residual
angles.
To calculate the residual angles of the drive line, operators can refer to
Society of Automotive Engineers (SAE) publication AE-7 (Section 3.1.1, Cardan or
Hooke Universal Joint).
For vehicles equipped with a two-joint drive line system, the following chart
can be a helpful aid in determining the optimum operating angles.
Calculation of Allowable Difference
Between Joint Angles For Two-Joint System
Drive line
RPM |
Angle
of joint #1 |
| 0 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
| Allowable
Angles of joint #2 |
| 1500 |
7.3 |
7.4 |
7.6 |
7.9 |
8.3 |
8.9 |
9.5 |
10.1 |
10.8 |
11.6 |
| 1600 |
6.9 |
6.9 |
7.1 |
7.5 |
7.9 |
8.5 |
9.1 |
9.8 |
10.5 |
| 1700 |
6.5 |
6.5 |
6.8 |
7.1 |
7.6 |
8.2 |
8.8 |
9.5 |
| 1800 |
6.1 |
6.2 |
6.4 |
6.8 |
7.3 |
7.9 |
8.5 |
9.3 |
| 1900 |
5.8 |
5.9 |
6.1 |
6.5 |
7.0 |
7.6 |
8.3 |
9.1 |
| 2000 |
5.5 |
5.6 |
5.8 |
6.2 |
6.8 |
7.4 |
8.1 |
| 2100 |
5.2 |
5.3 |
5.6 |
6.0 |
6.6 |
7.2 |
8.0 |
| 2200 |
5.0 |
5.1 |
5.4 |
5.8 |
6.4 |
7.1 |
7.8 |
| 2300 |
4.8 |
4.9 |
5.2 |
5.6 |
6.2 |
6.9 |
| 2400 |
4.6 |
4.7 |
5.0 |
5.5 |
6.1 |
6.8 |
| 2500 |
4.4 |
4.5 |
4.8 |
5.3 |
5.9 |
6.6 |
| 2600 |
4.2 |
4.3 |
4.7 |
5.2 |
5.8 |
6.5 |
| 2700 |
4.1 |
4.2 |
4.5 |
5.0 |
5.7 |
| 2800 |
3.9 |
4.0 |
4.4 |
4.9 |
5.6 |
| 2900 |
3.8 |
3.9 |
4.3 |
4.8 |
5.5 |
| 3000 |
3.7 |
3.8 |
4.2 |
4.7 |
5.4 |
| 3100 |
3.5 |
3.7 |
4.1 |
4.6 |
5.3 |
| 3200 |
3.4 |
3.6 |
4.0 |
4.6 |
5.3 |
| 3300 |
3.3 |
3.5 |
3.9 |
4.5 |
5.2 |
| 3400 |
3.2 |
3.4 |
3.8 |
4.4 |
To use the above chart:
- Find the RPM speed of the drive line.
- Next find the lower joint angle which is along the top of the chart from
left to right.
- Then, look up the maximum allowable second joint angle next to the speed.
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