I. Capacity Selection: Basic Knowledge
Newton's three laws of motion:
1. Any object remains at rest or in uniform rectilinear motion until it is compelled to change that state by forces exerted on it by other objects.
2. When an object is acted upon by a net external force, it will accelerate. The direction of the acceleration is the same as the direction of the net external force, and the magnitude of the acceleration is directly proportional to the magnitude of the net external force and inversely proportional to the inertial mass of the object.
3. The action and reaction forces between two objects lie on the same straight line, are equal in magnitude, and are opposite in direction.
Methods for determining torque from external forces
Torque = Force × Radius = Force × [Amount moved in 1 revolution / (2 × π)] = Force × [Circumference / (2 × π)]
Accelerating torque = radius × mass × acceleration
Acceleration = Velocity V / Time; Accelerating Torque = Radius × Mass × Velocity V / Time
Speed V = Distance / Time
= radius × angle / time = radius × angular velocity
Accelerating torque = radius × mass × radius × angular velocity / time
= radius 2 × mass × angular acceleration
Its inertia is radius^2 × mass.
The moment of inertia is defined as: J = ∑ mi * ri^2 (1) where mi represents the mass of a point mass of the rigid body, and ri represents the perpendicular distance of the point mass to the axis of rotation. The moment of inertia is a physical quantity that characterizes the magnitude of the rotational inertia of a rigid body. It is related to the mass of the rigid body and the distribution of the mass relative to the axis of rotation. The moment of inertia of a rigid body is determined by three factors: mass, mass distribution, and the position of the axis of rotation. (2) The rotation of the same rigid body is different about different axes of rotation. Whenever the moment of inertia is mentioned, it is necessary to specify which axis it is about in order to make sense.
Inertia conversion
Basic factors for servo motor selection: torque, speed, moment of inertia, power, and the relationship between torque and speed.
P = N*T ÷ 9549.3
Below the rated speed, constant torque output; above the rated speed, constant power output (where P: power, unit is kW; N: rated motor speed, unit is RPM; T: rated torque, unit is Nm).
For example: A motor has a power of 200W and a rated speed of 3000RPM. What is its rated torque? From the above formula:
T=(9549.3 * P) ÷N=((9549.3 *0.2) ÷3000=0.64 Nm
For example:
1. This device has a vertical axis and a total mass of 20 kg.
2. The lead of the ball screw is 40mm.
3. The moving distance is 300mm.
4. The speed is 500 mm/s
II. Selecting Case Studies
Later, during the customer's design phase, the mechanical weight was increased by 20kg to 30kg.
What should we do? Should we choose a motor with a larger capacity?
No, because the motor's rated speed is 3000 rpm and the lead of the ball screw is 40 mm, so the linear speed can reach 2000 mm/s.
However, the actual customer only needs a speed of 500mm/s, so the lead can be changed to 10mm.
III. Case Summary:
1. The lead of the ball screw should be as small as possible while still meeting the required moving speed.
2. The motor speed should not be much lower than the rated speed, preferably around 90% of the rated speed.
3. After a design change, the capacity calculation must be redone.
