Proper sizing is a crucial aspect of motor selection. If a motor is undersized, it will not be able to control the load, leading to overshoot and ringing.
Over-sizing a system is as bad as under-sizing – it may control the load but it will also be larger and heavier, as well as more expensive in terms of price and cost of operations. It may not physically fit and it certainly will cost more. It will use up more valuable space in a control cabinet or on the shop floor.
All too frequently, vendors simply get a call asking for a motor of a certain horsepower. The engineer may be buying a motor the same size as that of a previous platform. They may have added a hefty safety margin to compensate for changes. They may have used a 10:1 or 5:1 ratio of load and inertia to motor inertia – or some mixture of the above.
The goal should be to specify a motor that provides the speed, acceleration, and torque required to position the load at the designated location and the desired time. It may include a safety margin designed to compensate for motor-two-motor variation or expected changes in the running condition of the machine. The safety margin should be added on top of an informed calculation, however.
A common mistake is to choose a motor with a continuous-duty torque equal to the maximum torque requirement of the application (typically seen during extreme accelerations/decelerations). Motion control applications frequently consist of brief, rapid moves. To choose a motor rated to generate this torque continuously means essentially paying for more motor than necessary.
To effectively size the motor, it is necessary to calculate the load inertia (JL). The ratio of load inertia to motor inertia (essentially, rotor inertia) gives a measure of how effectively the motor can control the load. A high inertia ratio indicates the system that will have difficulty controlling the load. A low inertia ratio (e.g. 4:1 or 1:1) indicates that the motor will do a very effective job of controlling the load, but it also reveals that the motor may be oversized for the system
Often, designers include the actual load, the gearbox, and the motor, but leave belts, pulleys, and other mechanical things out of the equation. They just move to the next major size or use the same frame size but one that produces more torque. This is where the whole 10% oversize approach comes from.
The selection process involves the collection of data followed by detailed analysis. It requires knowledge of the mechanical system, the operating parameters, and the circumstances under which the equipment will be used. It must also include details of the operating environment, for if these are not considered at an early stage, the selected system may not be suitable.
Inertia – the tendency of an object to resist changes in acceleration – is one of the primary challenges in motion control. The motor needs to be able to apply sufficient force (in a linear system) or torque (in a rotational system) to change the acceleration of the load and do so in a controlled fashion.
The main constraints that have to be considered during the sizing procedure can be summarised as follows:
In addition, two application regimes need to be considered:
The difference between these two application regimes can be illustrated by a lathe. The spindle drive of a lathe is a continuous duty application, as it runs at a constant speed under constant load; the axis drives are an intermittent duty application, due to the acceleration and deceleration required to follow the required tool path.
The drives of robots and machine tools continually change speed to generate the required motion profile. The selection of the gear ratio and its relationship to the generated torque of the motor needs to be fully considered. If the load is required to operate at a constant speed, or torque, the optimum gear ratio can be determined. In practice, cases to be considered include acceleration with and without an externally applied load torque and the effects of variable load inertias.
A knowledge of the required speed range of the load and an initial estimation of the gear ratios required will permit the peak motor speed to be estimated. To prevent the motor not reaching its required speed, due to fluctuations in the supply voltage, the maximum speed required should be increased by a factor of 1.2. This factor is satisfactory for most industrial applications, but may be refined for a special application, for example when the system has to operate from a restricted supply as found in applications as diverse as aircraft and offshore oil platforms.
As the peak speed of a motor is dependent on the supply voltage, periods of low voltage need to be considered. As a guideline, a drive is normally sized so that it can run at peak speed at 80% of the nominal supply voltage. If a system is fed from a supply vulnerable to brownouts or blackouts, considerable care will have to be taken to ensure that the drive, its controller and the load are protected from damage; this is particularly acute with microprocessor systems, which, if not properly configured, may lock-up or reset without warning, leading to a possible catastrophic situation.
Where acceleration performance is all important, the motor inertia must be added to the reflected load inertia, and the torque required to accelerate this total inertia at the required rate must be determined. A motor-drive combination will be needed with a peak torque capability of at least 1.5 to 2 times this value to ensure sufficient torque capability.
The peak torque of the motor-drive combination must exceed, by a safe margin of at least 15%, the sum of the estimated friction torque plus acceleration torque plus any continuous torque loading present during acceleration. If this is not achievable, a different motor or the gear ratio will be required.
On very high-performance machines, the latest crop of auto-tuning drives can very effectively compensate for machine resonances and vibration, supporting accurate performance even at very high speeds. Electromagnetic compatibility has a considerable influence on the design and application of a system.
The mechanical requirements of the motor must be identified at an early stage in the sizing and selection procedure. Frequently overlooked items include any dimensional and orientation restrictions resulting from the mechanical design.
If these can be identified at an early stage it may prevent unsatisfactory performance once the equipment is installed. In particular, if the motor is mounted in the vertical position, special shimming or bearing preloads may be required.
In the determination of the drive requirements, friction torques are perhaps the most difficult aspect of the motor sizing procedure.
In the case of a rotating shaft, a bearing is the most widely used method of support. Many different types are available, of which the most common is the roller and ball bearing.
A conventional gear train is made up of two or more gears to change the angular velocity and torque between an input and output shaft. Gearboxes provide an important tool for managing inertia. A gearbox reduces inertia by the square of the gear ratio. The trade-off is that gearboxes also cut motor speed. Most servo motors operate at speeds between 2000 and 6000rpm, which enables them to operate at a useful speed even when used with a high-reduction-ratio gearbox.
Spur or helical gearwheels are normally employed within conventional gear trains. The spur gear has the advantage of producing minimal axial force, which reduces the problem of any motion of the gear bearings.
Helical gears are widely used in robotic systems as they give a higher contact ratio compared with spur gears for the same speed change ratio, the penalty being axial gear load.
The limiting factors in gear transmission are the stiffness of the gear teeth, which can be maximised by selecting the largest diameter gear wheel practical for the application, together with minimising the backlash or lost motion between individual gears.
In a lead screw, there is direct contact between the screw and the nut, which leads to a relatively high friction and hence an inefficient drive. For precision applications, ball screws are used due to their low friction and hence good dynamic response.
A ball screw is identical in principle to a lead screw, but power is transmitted to the nut via linear ball bearings, in the thread of the nut.
The use of a toothed belt or chain drive is an effective method of power transmission between motor and load, while still retaining synchronism
In the linear drive application, the same procedures which have been applied to lead and ball screw can be applied to a belt drive.
A very good reference on motor sizing can be found on the web at: