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Stepper vs Servo Motor: Torque, Lost Steps & Control Explained

In automation design, the choice between a Stepper Motor and a Servo Motor is often decided by budget. But looking at the price tag alone is a mistake that leads to machine failure. Steppers are excellent for holding loads stationary (high holding torque). Servos are kings of high-speed motion. If you choose a stepper for a high-speed application, it will lose torque and "miss steps." If you choose a servo for a simple low-speed application, you have wasted $500. This guide explains the physics behind the choice. Table of Contents 1. Open Loop vs. Closed Loop (The Risk) 2. The Torque Curve: Speed Kills Steppers 3. Inertia Mismatch 4. Selection Summary Advertisement 1. Open Loop vs. Closed Loop (The Risk) The biggest difference is not the motor itself, but how it is controlled. Figure 1: Steppers run "blind" (Open Loop). Servos use an encoder to verify position (Closed Loop). ...
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Column Design Guide: Euler's Formula for Buckling (Part 4)

Engineering visualization of a long slender column buckling under compressive load.

Figure 1: Elastic buckling is a geometric instability. Long columns fail by sudden bowing, not by material yielding.

Entering the Euler Domain

In Column Design (Part 3), we established the "Decision Rule." If your actual Slenderness Ratio (KL/r) is greater than the Column Constant (Cc), your column is classified as Long.

For these slender members, failure occurs via Elastic Instability. We calculate the Critical Load (Pcr) using the famous formula derived by Swiss mathematician Leonhard Euler in the 18th century.

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The Euler Formula

The critical buckling load is defined as:

Pcr =
Ï€2 E A
(KL / r)2

We can also express this in terms of the Moment of Inertia (I) by substituting r2 = I/A. This is often the more convenient form for design:

Pcr =
Ï€2 E I
(KL)2
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Engineering Insight: Stiffness vs. Strength

Look closely at the variables in the formula above. The buckling load depends on:

  • Length (L): Longer columns buckle easier.
  • Cross-section (I or A): Thicker columns resist buckling.
  • Material Stiffness (E): The Modulus of Elasticity.

Notice what is missing? The Yield Strength (Sy) is not in the equation.

Critical Design Note

For long columns, there is no benefit to using a high-strength alloy steel over a standard low-carbon steel. Both have roughly the same Modulus of Elasticity (E ≈ 207 GPa).

If you need to increase the buckling load of a long column, you must increase the Moment of Inertia (I) or change the End Fixity (K), not the material grade.

What about Short Columns?

If your column was classified as "Short" (where KL/r < Cc), the Euler formula is invalid because the material will yield before it buckles. For this, we need a different equation.

Continue to Part 5:
Column Design (Part 5): The J.B. Johnson Formula

References

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