The importance of servo motor sizing should never be underestimated. Properly sizing a motor not only leads to substantial cost savings—reducing energy consumption, purchasing and operating expenses, and downtime—but also enables engineers to design more efficient and reliable motion control systems. However, in an era where modern technology emphasizes tuning and programming, fundamental knowledge of mechanical systems and their impact on motor speed, inertia, and torque requirements appears to be diminishing.
Servo motor sizing involves a series of mathematical equations, which, although well-documented, are often presented without direct relevance to the sizing process. This book focuses specifically on servo motor sizing, providing a detailed exploration of inertia and torque calculations for standard mechanical components, as well as a comprehensive guide to the motor selection process.
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Table of Content
1. Overview
2. The Importance of Servo Motor Sizing
2.1 Why Motor Sizing?
2.2 Technical Aspects
2.3 The Objective of Motor Sizing
3. The Motor Sizing and Selection Process
3.1 Selection of mechanical components
3.2 Definition of a load cycle
3.2.1 Triangular motion profile
3.2.2 Trapezoidal motion profile
3.2.3 Motion profile processing
3.2.4 Motion profile calculation
3.2.5 Motion profile equations
3.2.6 Jerk Limitation
3.2.6.1 S-Curve Calculation
3.3 Load calculation
3.3.1 Load maximum speed
3.3.2 Load inertia and maximum torque
3.3.3 Load RMS torque
3.4 Motor Selection
3.4.1 Matching Motor Technologies to Applications
3.4.1.1 Stepper Motors
3.4.1.2 DC Brush Motors
3.4.1.3 DC Brushless Motors
3.4.1.4 AC Induction Motors
3.4.2 Selection Criteria
3.4.2.1 Inertia Matching
3.4.2.2 Interpretation of Torque/Speed Curves
3.4.2.3 Servo Motor Performance Curves
3.4.2.4 Stepper Motor Performance Curves
3.4.2.5 Servos vs. Steppers
3.5 Special Design Considerations
3.5.1 Gearing
3.5.2 Holding Brake and Motor Torque Requirements
3.5.3 Vertical Applications
3.5.4 Thrust Forces
3.5.5 Load Variations
3.5.6 Multi-Dimensional (X-Y-Z) Applications
3.5.7 Thermal Considerations
3.6 Sample application – comprised
4. Load Inertia and Torque Calculation
4.1 Basic Calculations
4.1.1 Fundamental Equations
4.1.2 Solid Cylinder
4.1.3 Hollow Cylinder
4.1.4 Rectangular Block
4.2 Calculation of Mechanical Components
4.2.2 Chain Drive
4.2.3 Coupling
4.2.4 Gears
4.2.5 Gearbox / Servo Reducer
4.2.6 Belt-Pulley
4.2.7 Conveyor
4.2.8 Leadscrew
4.2.10 Nip Roll
4.2.11 Rack Pinion
4.2.13 Center Driven Winder
4.2.14 Surface Driven Winder
The Importance of Proper Servo Motor Sizing
Modern automated manufacturing systems rely heavily on sophisticated motion control systems that integrate both mechanical and electrical components, including servo motors, amplifiers, and controllers.
The first and most fundamental task of a motion system design engineer—before tuning and programming the electrical components—is to specify the smallest motor and drive combination that can reliably provide the necessary torque, speed, and acceleration for the mechanical setup.
However, many engineers are well-versed in electrical components but lack the expertise to accurately calculate the torque requirements of the driven mechanical elements. In some cases, they attempt to size the system around a preselected motor, investing valuable time in figuring out how to move the load under given constraints. This approach often leads to improperly sized motion control applications, resulting in both economic and technical inefficiencies—topics that will be explored in the following chapters.
The Role of Motor Sizing Software
Modern motor sizing software, such as VisualSizer, simplifies the process by computing all necessary equations and identifying the optimal motor/drive combination within the shortest time. While these tools offer convenience, they are often used as a shortcut to bypass the time-consuming manual selection process. Unfortunately, most of these programs do not provide insights into how the underlying equations are derived, limiting their educational value.
Having a fundamental understanding of inertia and torque calculations can significantly improve motion system performance. For example, knowing when to incorporate a gearbox into a system can lead to cost reductions and enhanced efficiency. The following chapters provide a comprehensive guide to the motor sizing process, including detailed inertia and torque calculations for standard mechanical components.
Why Motor Sizing?
Servo motors are among the most significant cost factors in motion control system design—not only in terms of initial purchase price but also throughout their operational lifespan. A high-torque motor requires a more powerful and expensive amplifier, increasing both upfront and long-term energy costs. Notably, the purchase price of a motor represents only about 2% of its total life cycle cost, while 96% is attributed to electricity consumption.
Proper servo motor sizing not only ensures optimal system performance but also results in substantial cost savings.
Traditionally, servo motor sizing involves calculating the system load to determine the appropriate motor size. Engineers typically add a safety margin to account for additional friction forces that may arise due to mechanical wear. However, this process can be time-consuming, as each motor’s individual rotor inertia contributes to the total system load torque. Since torque equals inertia times acceleration, the system torque calculation must be repeated for each motor under consideration.
Selecting the optimal motor from the vast number of available options is no easy task. Many motors currently in use were chosen primarily because they were oversized and readily available in inventory. In fact, the U.S. Department of Energy estimates that approximately 80% of all motors in the United States are oversized.
Common Reasons for Oversizing Motors
- Uncertainty about load requirements
- Allowance for increased friction due to mechanical aging
- Availability of oversized motors in inventory
While oversizing can sometimes be beneficial, it also results in higher-than-necessary power consumption and technical inefficiencies—issues that will be discussed in the next section.
Technical Aspects of Motor Sizing
Oversizing a motor is far more common than undersizing. While an undersized motor may fail to move the load effectively (or at all), an oversized motor wastes energy and operates inefficiently. AC motors, for instance, tend to run hot when loaded either too heavily or too lightly. Servo motors, when significantly undersized or oversized, can suffer from vibrations and stalling issues.
One of the most common misconceptions in motion system design is that selecting a larger motor than necessary is a small price to pay for reliability—especially since the load may increase over time due to mechanical wear. However, motor efficiency deteriorates rapidly when the motor operates below its designed load capacity.
For example, a 10 HP and a 100 HP motor both experience a steep decline in efficiency at around 30% of their rated load. Although efficiency curves vary between motors, a general rule of thumb is that if a motor operates at 40% or less of its rated load, it is a good candidate for downsizing—especially if the load remains relatively constant.
There are cases where modest oversizing (up to 20%) is acceptable or even beneficial:
- Compensating for increased friction due to mechanical wear (e.g., couplings, bearings)
- Allowing for potential future system expansions
- Accommodating unexpected load variations
- Ensuring functionality in undervoltage conditions
- Using high-efficiency motors, which maintain better performance across a range of loads
Motor selection is fundamentally a business decision aimed at achieving the best performance for the lowest cost. As previously mentioned, the lifecycle cost distribution of an electrical motor is approximately:
- 2% – Purchase cost
- 2% – Maintenance and repairs
- 96% – Operating cost (electricity consumption)
Thus, finding the smallest motor that meets torque and speed requirements is critical for cost efficiency. A smaller motor generally translates to lower power consumption, reduced amplifier size, and lower overall expenses.
The Key Principles of Motor Sizing
To optimize motor selection, engineers should aim to:
- Maximize performance while minimizing costs
- Match the motor’s torque as closely as possible to the required load torque
- Achieve an optimal load-to-rotor inertia ratio (ideally 1:1, though ratios up to 6:1 are acceptable for servo motors)
- Select a motor that meets or slightly exceeds the required speed
In many cases, incorporating a gear between the motor and the load can significantly improve system performance. Gears reduce the inertia reflected to the motor in direct proportion to the transmission ratio, enabling the use of smaller motors. While this adds the cost of the gearbox, the overall savings from using a smaller motor and drive system often outweigh the additional expense.
Conclusion
Proper servo motor sizing is a critical aspect of motion control system design, impacting both economic efficiency and technical performance. The following chapters will delve deeper into practical motor selection strategies, detailed inertia and torque calculations, and real-world applications of motor sizing techniques.
By applying the principles outlined in this book, engineers can optimize their designs for maximum efficiency, reliability, and cost-effectiveness.
