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Chapter 6
Stiffness and Damping of Power Transmission Systems and Drives

## Excerpt

Power transmission systems and drives are extremely important units for many machines and other mechanical devices. Stiffness of these systems might be a critical parameter due to several factors depending on specifics of the device. Some of these factors are as follows:

1. Natural frequencies of power transmission systems and drives may play a significant role in vibratory behavior of the system, especially if some of them are close to other structural natural frequencies and/or to excitation frequencies from input (driving) devices such as internal combustion engines or from output (driven) devices, such as reciprocal compressions and pumps or milling cutters. Correct calculations of torsional natural frequencies depend on accurate information on inertia and stiffness of the components. While calculation of inertias is usually a straightforward procedure, calculation of stiffness values is more involved.

2. In precision devices, correct angular positioning between the driving and driven elements is necessary even under loaded condition. Inadequate stiffness of the drive mechanism connecting the driving and driven elements may disrupt proper functioning of the device.

3. Self-excited vibrations in positioning and production systems frequently develop due to inadequate stiffness of the drive mechanisms. Some examples include stick-slip vibrations of carriages and tables supported by guideways, chatter in metal-cutting machine tools, intense torsional vibrations in drives of mining machines, etc.

4. Low torsional stiffness and, especially, torsional backlash disrupt performance of widely used servo-controlled power transmission systems and require more advanced/expensive control systems.

• 6.1 Basic Notions
• 6.2 Compliance of Mechanical Power Transmission and Drive Components
• 6.2.1 Basic Power Transmission Components
• 6.2.1a Stiffness of Ball Screws
• 6.2.2 Compliance of Pneumatic System Components
• 6.2.3 Compliance of Hydraulic System Components
• 6.2.4 Dynamic Parameters of Electric Motors (Actuators)
• 6.3 Parameter Reduction in Mathematical Models
• 6.4 Practical Examples of Structural Compliance Breakdown
• 6.4.1 A Hydraulically Driven Robot
• 6.4.2 Electromechanically Driven Robot of Jointed Structure
• 6.4.3 Electromechanically Driven Parallelogram Robot with Harmonic Drive
• 6.4.4 Electromechanically Driven Spherical Frame Robot
• 6.4.5 Summary
• 6.5 More on Stiffness and Damping of Antifriction Bearings and Spindles
• 6.5.1 Stiffness of Spindles
• 6.5.2 Stiffness and Damping of Antifriction Bearings
• 6.6 Damping in Power Transmission Systems
• References
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