Considerations in the Application of Flexural Pivots
The seminal 1962 paper on flexural pivot engineering — Henry Troeger, Bendix Corp.
Henry Troeger, Chief Engineer, Advanced Design — The Bendix Corp., Utica Division, Utica, New York
Overview
This seminal 1962 paper introduced the standardized, mass-produced cylindrical flexural pivot. It details the advantages (no friction or backlash, no lubrication, insensitivity to contamination, wide environmental range) and limitations (limited angular travel, torsional spring rate, center shift, load capacity) of flexural pivots, along with the ten engineering characteristics a designer must consider when applying them.
Key Highlights
11 Standard Diameters
0.125" through 1.000" in eleven sizes
Three Angular Stops
±7.5°, ±15°, and ±30° — thinner springs allow more travel
AISI 420 Steel
Corrosion-resistant steel flexures as the standard material
Brazed Construction
High-temperature alloy brazing eliminates joint slippage hysteresis
10 Design Characteristics
A complete checklist for pivot application engineering
Cantilever & Double-End
Two configurations for different load and constraint needs
The Cylindrical Flexural Pivot
The standardized cylindrical flexural pivot has two adjacent sleeves, each with an annular sector projecting into the other but not touching. The two sectors are joined by flat crossed flexures. The sleeves, sectors, and flexures are secured by high-temperature alloy brazing and heat-treated to spring temper. The cantilever type has two adjacent concentric sleeves of the same diameter; either may be mounted in the support. The double-end type has three adjacent sleeves — the outer two secured together and rotatable with respect to the center sleeve — permitting a bridge-type support with higher radial loads and more rigid constraint.
Advantages & Limitations
Advantages: absence of rolling or coulomb friction and backlash, no lubrication required, insensitivity to contamination, and the ability to operate over a wide range of environmental conditions including vacuum, pressure, low and high temperature, and radiation. Limitations: limited angular travel, torsional spring rate (often an advantage), the centrode and center shift, and — depending on angular travel and available space — load capacity.
Ten Characteristics to Consider
- Center shift and centrode (kinematics of the moving member)
- Torsional spring rate
- Angular travel
- Linearity
- Hysteresis
- Radial and axial load capacity
- Radial spring rate
- Fatigue life
- Environmental adaptability
- Alignment (avoid spurious stresses with flexible self-aligning supports)
Mounting Methods
- Free fit in hole with set screw
- Press fit in hole using tools that avoid stressing the flexures
- Cement or solder in place
Application Example
An air data sensor transducer illustrates the benefit: substituting a cylindrical flexural pivot for previously used ball bearings eliminated eight parts, removed test rejections due to dirt or improper bearing adjustment, saved assembly time, permitted larger and fewer tolerances, and improved performance — achieving a sensitivity of three feet at 10,000 feet altitude.
Considerations in the Application of Flexural Pivots — PDF
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