Overview for servo motor sizing
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 first straightforward task for the motion system design engineer, before tuning and programming the electrical components, is to specify – preferably 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 of how to calculate the torque requirements of the driven mechanical components. In other cases they try to size their application around the motor and spend valuable time to figure out how to move the load under the given circumstances. Such an approach will lead 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-ProfessionalTM, 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.
The following chapters will provide a comprehensive insight into the motor sizing process including detailed descriptions of inertia and torque calculations of standard mechanical components.
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.
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 costs; about 96% is electricity.
Proper servo motor sizing will not only assure best system performance; it also provides considerable cost savings.
Picture 1.1: Lifecycle costs of an Electrical Motor
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. 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 can’t 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 2.1: Example Efficiency vs. Load
Picture 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 oversizedRMS) 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: Example High/Low Efficiency Motors
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 lifecycle costs of an
electrical motor are:
- 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 gear’s price.
In review the objective of motor sizing is to:
- Get the best performance for the best price
- Match the motor’s torque with the load torque as close as possible
- Match the motor’s inertia with the load inertia as close as possible
- Find a motor that matches or exceeds the required speed
