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Flexible couplings and universal joints explained for mechanical power transmission, covering misalignment types, angular velocity variation, and practical engineering limits.
Figure 1: Flexible couplings transmit torque while accommodating axial, radial, and angular misalignment.
1. Flexible Couplings
Shafts that are out of alignment (misalignment) either laterally or angularly can be connected using various designs of flexible couplings. These couplings also allow a limited amount of axial movement (end float) in one or both shafts, protecting bearings from excessive loads.
There are several common design methodologies:
- Disk & Diaphragm: Transmit torque through metallic disks or flexible diaphragms. Excellent for high speed and zero backlash.
- Elastomeric: Flanges contain projections that engage molded rubber, urethane, or spiders. These dampen vibration and accommodate uneven motion.
- Link & Belt: A simpler design consisting of flanges connected by links or leather belts.
- Gear Couplings: Use toothed flanges that mesh with a sleeve. They allow relative movement but generally require lubrication.
- Bellows: Use metallic bellows that flex elastically. These handle angular, axial, and parallel misalignment with high torsional stiffness and zero lubrication.
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2. The Universal Joint (Cardan Joint)
Figure 2: The Universal Joint connects intersecting shafts but introduces velocity fluctuation.
Originally known as the Cardan or Hooke’s joint, this coupling connects two shafts whose axes intersect at an angle. While ubiquitous, they have specific engineering limitations.
Design Rule: A universal joint does not perform satisfactorily if the shaft angle α exceeds 45°.
In most power transmission applications, limit the angle to 20°–25°. Angles larger than this result in excessive vibration and wear, unless the application involves very low speed and low power.
In most power transmission applications, limit the angle to 20°–25°. Angles larger than this result in excessive vibration and wear, unless the application involves very low speed and low power.
The Velocity Problem
The angular velocity of the driven shaft is not constant. Even if the driving shaft rotates at a perfectly uniform speed, the driven shaft undergoes periodic acceleration and deceleration twice per revolution.
Therefore, single universal joints should not be used in applications where uniform motion precision is essential. To cancel this effect, engineers often use two U-joints in series (a Double Cardan shaft) or a Constant Velocity (CV) joint.
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3. Calculating Velocity Fluctuation
If shaft A rotates at a constant speed:
- Maximum Speed: Occurs when the drive shaft yoke is perpendicular to the plane of the shaft angle.
- Minimum Speed: Occurs when the drive shaft yoke lies in the plane of the shaft angle (90° later).
Engineering Calculation Example
Formulas:
- ωmax = ωin × sec(α)
- ωmin = ωin × cos(α)
Scenario: Drive shaft rotates at 100 RPM with a shaft angle of 25°.
- Max Speed: 100 × sec(25°) ≈ 110.34 RPM
- Min Speed: 100 × cos(25°) ≈ 90.63 RPM
- Total Fluctuation: 19.71 RPM
Figure 3: Angular velocity fluctuation of the driven shaft over one revolution.
Some technical content adapted from Wikipedia.org
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