Drive motors for metal cutting machine tools include two types: feed servo motors and spindle servo motors. When selecting motors, machine manufacturers often worry about insufficient cutting force and tend to choose larger motors. This not only increases the manufacturing cost of the machine tool but also makes it larger and less compact. This article uses examples to illustrate how to select the optimal motor size to control manufacturing costs.
Machine tool drive motors include two categories: feed servo motors and spindle servo motors. When selecting motors, machine manufacturers often worry about insufficient cutting force and tend to choose larger motors. This not only increases the manufacturing cost of the machine tool but also makes it larger and less compact. Therefore, it is essential to select the optimal motor size through specific analysis and calculations.
I. Selection of Feed Drive Servo Motor
1. In principle, the servo motor should be selected based on the load conditions. There are two types of loads on the motor shaft: damping torque and inertia load. Both types of loads must be calculated correctly, and their values should meet the following conditions:
1) When the machine tool is running under no-load, the load torque applied to the servo motor shaft should be within the continuous rated torque range of the motor throughout the entire speed range, that is, within the continuous working area of the torque-speed characteristic curve.
2) The maximum load torque, loading cycle, and overload time are all within the allowable range of the provided characteristic curves.
3) The torque of the motor during acceleration/deceleration should be within the acceleration/deceleration zone (or intermittent working zone).
4) For loads requiring frequent starting, braking, and periodic changes, the root mean square value of the torque in one cycle must be checked. It should be less than the continuous rated torque of the motor.
5) The magnitude of the load inertia applied to the motor shaft will affect the motor's sensitivity and the accuracy of the entire servo system. Generally, when the load is less than the motor rotor inertia, the above effect is minimal. However, when the load inertia reaches or exceeds five times the rotor inertia, it will significantly impact sensitivity and response time. It may even prevent the servo amplifier from operating within its normal adjustment range. Therefore, this type of inertia should be avoided. The recommended relationship between the servo motor inertia Jm and the load inertia Jl is as follows:
1=Jl/Jm5
2. Calculation Method of Load Torque: The formula for calculating the load torque applied to the servo motor shaft varies depending on the machine. However, regardless of the type of machine, the load torque referred to the motor shaft should be calculated. Generally, the load torque referred to the servo motor shaft can be calculated using the following formula:
Tl = (F * L / 2πμ) + T0
Where: Tl is the load torque (Nm) referred to the motor shaft.
The force required to move the worktable along axis F
Mechanical displacement per revolution of motor shaft (m)
For the ball screw nut, the frictional torque of the bearing portion is converted to the value on the servo motor shaft (NM).
efficiency of μ-drive system
Table feed diagram
F depends on the weight of the worktable, the coefficient of friction, the cutting force in the horizontal or vertical direction, and whether a counterweight is used (for the vertical axis). If it is in the horizontal direction, the value of F-axis is given in the example above.
When there is no cutting: F = μ * (W + fg)
During cutting: F = Fc + μ * (W + fg + Fcf)
W: Weight of the slider (worktable and workpiece) in kg
μ: coefficient of friction
Fc: Reaction force of cutting force
fg: Secure with a strip
Fcf: The force (kg) exerted on the worktable by the cutting force acting on the surface of the slider, i.e., the positive pressure of the worktable pressing against the guide rail.
The following points should be paid special attention to when calculating torque.
(a) The frictional torque generated by the inserts must be fully considered. Typically, the torque calculated solely from the weight of the slider and the coefficient of friction is very small. Special attention should be paid to the torque generated by the insert clamping and the precision errors of the slider surface.
(b) The torque generated by the preload of the bearings and nuts, as well as the friction of the ball contact surfaces due to the preload of the leadscrew, cannot be ignored, especially in small, lightweight equipment. This torque response affects the overall torque, so special attention must be paid to it.
(c) The reaction force of the cutting force increases the friction of the worktable, thus the point bearing the cutting reaction force is usually separate from the point bearing the driving force. As shown in the figure, at the instant of bearing a large cutting reaction force, the load on the slider surface also increases. When calculating the torque during cutting, the increase in frictional torque caused by this load should be taken into account.
(d) Frictional torque is greatly affected by the feed rate. It is necessary to study and measure the changes in friction caused by changes in the speed table support (slider, balls, pressure), the slider surface material, and lubrication conditions. Correct values have been obtained.
(e) Typically, even on the same machine, torque varies depending on factors such as adjustment conditions, ambient temperature, or lubrication conditions. When calculating load torque, try to obtain accurate data by utilizing parameters accumulated from measurements on similar machines.
3. Calculation of Load Inertia. All moving parts driven by the motor, whether rotary or linear, contribute to the motor's load inertia. The total load inertia on the motor shaft can be obtained by calculating the inertia of each driven component and adding them together according to a certain rule.
1) The moment of inertia of a cylinder, such as a ball screw or gear, when rotating around its central axis can be calculated using the following formula:
J=（πγ/32）＊D4L（kgcm2）
If the structure is made of steel, it can be calculated using the following formula:
J=（0.78＊10-6）＊D4L（kgcm2）
Where: γ is the density of the material (kg/cm2)
D is the diameter of the cylinder (cm).
The length of cylinder L (cm)
2) The inertia of an axially moving object, such as a workpiece or worktable, can be calculated using the following formula:
J = W * (L/2π)² (kg/cm²)
In the formula: W represents the weight (kg) of the object moving linearly.
The distance (cm) that the L motor travels per revolution in the straight line.
3) The moment of inertia of the cylinder moving around its center is shown in the figure:
Moment of inertia of a cylinder moving around its center
Examples of this type of situation include gears with large diameters. To reduce inertia, evenly distributed holes are often drilled into the disk. In this case, the inertia can be calculated as follows:
J = Jo + W * R² (kg/cm²)
In the formula: Jo is the moment of inertia (kgcm2) of the cylinder rotating about its center line.
The weight of the cylinder (W) in kg
R is the radius of rotation (cm).
4) Calculation of inertia relative to the motor shaft mechanical speed change: The calculation method for converting the load inertia Jo shown in the above figure to the motor shaft is as follows:
J = (N1/N2)2Jo
In the formula: N1 and N2 are the number of teeth of the gear.
4. Torque during motor acceleration or deceleration
Torque during motor acceleration or deceleration
1) The acceleration torque is calculated based on linear acceleration and deceleration as follows:
Ta=（2πVm/60＊104）＊1/ta（Jm+JL）（1-e-ks.ta）
Vr=Vm{1-1/ta.ks（1-e-ksta）
Ta (acceleration torque in Nm)
Motor speed (r/min) during rapid movement of Vm
Ta accelerates time (sec)
Jm motor inertia (Nms2)
JL load inertia (Nms2)
The point at which Vr acceleration torque begins to decrease
Ks servo system position loop gain (sec-1)
The acceleration torque curve of the motor when accelerating according to an exponential curve is shown in the figure below:
Acceleration torque curve of the motor when accelerating according to an exponential curve
At this point, the torque To, where the velocity is zero, can be given by the following formula:
To==（2πVm/60＊104）＊1/te（Jm+JL）
Te exponential curve acceleration/deceleration time constant
2) When a phased speed command is input, its speed curve and torque curve are shown in Figure 4.
At this point, the accelerating torque Ta is equivalent to To, which can be obtained by the following formula (ts=ks).
Ta==（2πVm/60＊104）＊1/ts（Jm+JL）.
5. The required torque during frequent starting and braking of machinery necessitates checking for motor overheating. This requires calculating the root mean square (RMS) value of the motor torque over one cycle, ensuring this RMS value is less than the continuous torque of the motor. Motor RMS value:
Trms=√[（Ta+Tf）2t1+Tf2t2+（Ta-Tf）2t1+To2t3]/T weeks
Where: Ta is the accelerating torque (NM)
Tf frictional torque (NM)
Torque (N·M) during the stopping period.
The known time for t1t2t3t weeks can be seen in Figure 5.
t1t2t3t time diagram known by Zhou
6. Torque calculation for periodically changing loads (as shown in Figure 6) also requires calculating the root mean square (RMS) torque value Trms over one cycle. This value must be less than the rated torque. This ensures the motor does not overheat and operates normally.
Torque calculation diagram for periodically changing load
II. Limitations on Load Inertia
Load inertia is closely related to the motor's response and rapid traverse ACC/DEC time. When carrying a load with high inertia, the motor needs a longer time to reach the speed command when it changes. When performing high-speed circular cutting with dual-axis synchronous interpolation, the error generated by a load with high inertia will be larger than that of a load with low inertia.
Generally, the aforementioned problems do not occur when the load inertia is less than the motor inertia. If it exceeds five times the motor rotor inertia, servo motors typically exhibit adverse reactions. For example, in high-speed laser cutting machine tools, the load inertia must be designed to be lower than the motor rotor inertia. Delta servo motors have a unique advantage in this regard, with a high load inertia ratio, making their advantages even more pronounced in this industry.
