Stepping Motor Physics

Introduction

In any quantitative analysis of electromechanical systems, strict adherence to consistent units of measurement is essential. Inconsistent or ambiguous units can introduce significant calculation errors, misapplication of physical formulas, and ultimately lead to system performance failures or design flaws. This guide on stepping motor physics follows internationally accepted standard unit systems—ensuring clarity, reproducibility, and accuracy in both theoretical analysis and practical design.

We will operate within coherent unit systems, primarily the International System of Units (SI) and the British Gravitational System (BGS). For example, in the BGS system, a force of one pound-force (lbf) accelerates a mass of one slug at one foot per second squared (ft/s²). This consistent force-mass-acceleration relationship lies at the core of Newtonian mechanics and must be rigorously maintained in all motion-related calculations.

A frequent—yet often problematic—engineering convention is the use of non-coherent units such as pounds-mass (lbm) for mass or kilograms-force (kgf) for force. These do not align directly with the Newtonian frameworks employed here and require careful conversion before being applied in dynamical equations.

Therefore, it is critical to convert all given parameters into consistent SI or BGS units before performing calculations. Neglecting this step will inevitably distort results for torque, inertia, angular acceleration, resonant frequency, and other key motor characteristics—undermining performance predictions and potentially compromising system reliability.

By maintaining disciplined unit management throughout the design and analysis process, engineers can ensure accurate modeling, valid performance comparisons, and successful implementation of stepper motor systems in precision motion applications.

Additionally, while angles are often intuitively expressed in degrees, all angular calculations in rotational dynamics (such as step angle, angular velocity, and acceleration) should be performed in radians to maintain consistency with the underlying physical laws. The following diagram illustrates the core physical relationship between force, mass, and acceleration that underpins all subsequent discussions on motor motion and control:

Figure 1: Fundamental relationship between force, mass, and acceleration in a stepper motor system.

By establishing a disciplined approach to units and measurement from the outset, we create a reliable foundation for exploring the static and dynamic behavior of stepper motors—from basic torque production and half-stepping techniques to complex resonance effects and high-speed performance limits.