The Aspects Of Servo Motor Sizing

By Wilfred Voss,
Copperhill Technologies Corporation

1.    Overview

The vast majority of automated manufacturing systems involve the use of sophisticated motion control systems that, besides mechanical components, incorporate electrical components such as servo motors, amplifiers and controllers.

The straightforward task for the motion system design engineer is to specify the smallest motor and drive  combination that can provide the torque, speed and acceleration as required by the mechanical set up. However, all too often engineers are familiar with the electrical details, but do lack the knowledge how to calculate the torque requirements of the driven mechanical components. This will lead in many cases to improperly sized motion control applications. The impact, economically as well as technically, will be one of the topics in the following chapters.

Modern motor sizing software packages, such as VisualSizer-Professional, provide the convenience of computing all necessary equations and selecting the optimum motor/drive combination within minutes; they are, however, mainly used to circumvent the timely process of selecting a motor manually. While motor sizing programs can have an educational value to some degree, most of them do not provide any reference on how the equations were derived.

Some basic knowledge of inertia and torque calculations can have a profound impact on the motion system performance. Simple details, like when to use a gearbox in a motion system, may not only help to reduce costs, but will most certainly improve the system performance.

2.    The Importance of Servo Motor Sizing

The importance of servo motor sizing should not be underestimated. Proper motor sizing will not only result in significant cost savings by saving energy, reducing purchasing and operating costs, reducing downtime, etc.; it also helps the engineer to design better motion control systems.

 2.1    Why Motor Sizing?

The servo motor represents the most influential cost factor in the motion control system design, not only during the purchasing process, but especially during operation. A high-torque motor will require a stronger and thus more expensive amplifier than smaller motors. The combination of higher torque motor plus amplifier results not only in higher initial expenses, but will also lead to higher operational costs, in particular increased energy consumption. It is estimated, that the purchase price represents only about 2% of the total life cycle cost; about 96% is electricity.

Proper servo motor sizing will not only assure best system performance; it also provides considerable cost savings.

The conventional method of servo motor sizing is based on calculations of the system load, which determines the required size of a motor. Standard praxis demands to add a safety factor to the torque requirements in order to cover for additional friction forces that might occur due to the aging of mechanical components. However, the determination of the system load and the selection of the right servo motor can be extremely time consuming. Each motor has its individual rotor inertia, which contributes to the system load torque, since Torque equals Inertia times Acceleration. The calculation of the system torque must be repeated for each motor that is being considered for the application.

As a result, it is not an easy task to select the optimum motor for the application considering the vast amount of available servo motors in the marketplace. Many motors, that are currently in action, have been chosen mostly due to the fact that they are larger than required and were available short-term (e.g. from inventory). The U.S. Department of Energy estimates that about 80% of all motors in the United States are oversized.

The main reasons to oversize a motor are:

• Uncertain load requirements

• Allowance for load increase (e.g. due to aging mechanical components)

• Availability (e.g. inventory)

Not only is the power consumption higher than it should be; there are also some serious technical considerations.

2.2    Technical Aspects

Oversizing a motor is naturally more common than undersizing. An undersized motor will consequently not be able to move the load adequately (or not at all) and, in extreme cases, may overheat and burn out, especially when it cant dissipate waste heat fast enough. Larger motors will stay cool, but if they are too large they will waste energy during inefficient operation. After all, the motor sizing process can also be seen as an energy balancing act.

AC motors tend to run hot when they are loaded too heavily or too lightly. Servo motors, either undersized or oversized, will inevitably start to vibrate or encounter stalling problems.

One of the major misconceptions during the motion design process is that selecting a larger motor than required is only a small price to pay for the capability to handle the required load, especially since the load may increase during the lifetime of the application due to increased mechanical wear. However, as demonstrated in the picture below, the motor efficiency deteriorates quickly when the motor operates below the designed load.

Picture 2.2.1: Example Efficiency vs. Load

Picture 2.2.1 shows an example of two motors, 10 HP and 100 HP. In both cases there is a sharp decline of the motors efficiency at around 30% of the rated load.

However, the curves as shown in the picture, will vary substantially from motor to motor and it is difficult to say when exactly a motor is oversized. As a general rule of thumb, when a motor operates at 40% or less of its rated load, it is a good candidate for downsizing, especially in cases where the load does not vary very much. Servo motor applications usually require short-term operation at higher loads, especially during acceleration and deceleration, which makes it necessary to look at the average (RMS) torque and the peak torque of an application.

There are, however, advantages to oversizing:

• Mechanical components (e.g. couplings, ball bearings, etc.) may, depending on the environment and quality of service, encounter wear and as a result may produce higher friction forces. Friction forces contribute to the constant torque of a mechanical set up.

• Oversizing may provide additional capacity for future expansions and may eliminate the need to replace the motor.

• Oversized motors can accommodate unanticipated high loads.

• Oversized motors are more likely to start and operate in undervoltage conditions.

In general, a modest oversizing of up to 20% is absolutely acceptable.

High efficiency motors, compared to standard motors, will maintain their efficiency level over a broader range of loads (see picture 2.2.2) and are more suitable for oversizing.

Picture 2.2.2: Example High/Low Efficiency Motors

2.3    The Objective of Motor Sizing

The main objective of motor sizing is based on the good old American sense for business: Get the best performance for the lowest price. As we have learned from a previous chapter the price contains the following components:

• Purchasing Costs 2%

• Repair, Service, Maintenance, etc. 2%

• Operating Costs (Electricity) 96%

In order to get the best performance for the best price it is mandatory to find the smallest motor that fulfills the requirements, i.e. the motor that matches the required torque as close as possible. The basic assumption (which is true for the majority of cases) is that small torque is in direct proportion to smaller size, lower costs and lower power consumption. Smaller power consumptions also result in smaller drive/amplifier size and price.

From a technical standpoint it is also desirable to find a motor whose rotor inertia matches the inertia of the mechanical setup as close as possible, i.e. the optimum ratio between load to rotor inertia of 1 : 1. The inertia match will provide the best performance. However, for servo motors a ratio of up to 6 : 1 still provides a reasonable performance. Any higher ratios will result in instabilities of the system and will eventually lead to total malfunction.

In many cases it makes sense to add a gear between motor and the actual load. A gear lowers the inertia that is reflected to the motor in direct proportion of the transmission ratio. This scenario allows to run smaller motors, however, with the price of the gear added to the system. On the other hand the price reduction by using a smaller motor/drive combination may more than just compensate for the gears price.

In review the objective of motor sizing is to:

• Get the best performance for the best price

• Match the motors torque with the load torque as close as possible

• Match the motors inertia with the load inertia as close as possible

• Find a motor that matches or exceeds the required speed

3.    The Motor Sizing and Selection Process

The motor sizing and selection process is based on the calculation of torque and inertia imposed by the mechanical set up plus the speed and acceleration required by the application. The selected motor must be able to safely drive the mechanical set up by providing sufficient torque and velocity.

Once the requirements have been established, it is easy to look either at the torque vs. speed curves or motor specs and choose the right motor.

The sizing process involves the following steps:

1. Establishment of motion objectives

A written outlining of the motion control application will help to establish the necessary parameters needed for the next steps.

• Required positioning accuracy ?

• Required position repeatability ?

• Required velocity accuracy ?

• Linear or rotary application ?

• If linear application: Horizontal or vertical application?

• Thermal considerations Ambient temperature ?

• What motor technologies are best suited for the application ?

2. Selection of mechanical components

The engineer must decide which mechanical components are required for the application. For instance, a linear application may require a leadscrew or a conveyor. For speed transmission a gear or a belt drive may be used.

• Direct Drive ?

• Special application or standard mechanical devices ?

• If linear application: Use of linear motor or leadscrew, conveyor, etc. ?

• Reducer required Gearbox, belt drive, etc. ?

• Check shaft dimensions select couplings

• Check mechanical components for speed and acceleration limitations

3. Definition of a load (duty) cycle

The engineer must define the maximum velocity, maximum acceleration, duty cycle time, acceleration and deceleration ramps, dwell time, etc., specific to the application.

• Define critical move parameters such as velocity, acceleration rate

• Triangular, trapezoidal or other motion profile ?

• If linear application: Make sure the duty cycle does not exceed the travel range of linear motion device.

• Jerk Limitation required ?

• Consideration of thrust load ?

• Does the load change during the duty cycle ?

• Holding brake applied during zero velocity ?

4. Load calculation

The load is defined by the torque that is required to drive the mechanical set up. The amount of torque is determined by the inertia reflected from the mechanical set up to the motor and the acceleration at the motor shaft.

• Calculate inertia of all moving components

• Determine inertia reflected to motor

• Determine velocity, acceleration at motor shaft

• Calculate acceleration torque at motor shaft

• Determine non-inertial forces such as gravity, friction, pre-load forces, etc.

• Calculate constant torque at motor shaft

• Calculate total acceleration and RMS (continuous over duty cycle) torque at motor shaft

5. Motor Selection

The motor must be able to provide the torque required by the mechanical set up plus the torque inflicted by its own rotor. Each motor has its specific rotor inertia, which contributes to the torque of the entire motion system. When selecting a motor the engineer needs to recalculate the load torque for each individual motor.

• Decide the motor technology to use (DC brush, DC brushless, stepper, etc.)

• Select a motor/drive combination

• Does motor support the required maximum velocity ? If no, select next motor/drive.

• Use rotor inertia to calculate system (motor plus mechanical components) acceleration (peak) and RMS torque

• Does motors rated torque support the systems RMS torque? If no, select next motor/drive.

• Does motors intermittent torque support the systems peak torque? If no, select next motor/drive.

• Does the motors performance curve (torque over speed) support the torque and speed requirements? If no, select next motor/drive.

• If the ratio of load over rotor inertia exceeds a certain range (for servo motors 6:1) consider the use of a gearbox or increase the transmission ratio of the existing gearbox. Servo motors should not be operated over a ratio of 10:1.

The following flow chart demonstrates the motor sizing and selection process: