How to determine the rotation speed of an electric motor formula?
Based on the formula n = (1 - S)60f/p where n is the rotor rotation speed, S is slip, f is the frequency of the supply network, p is the number of pole pairs. There are three ways to regulate the rotation speed of an asynchronous motor: - changing the slip. This method is used in wound rotor motors.
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DC motors
Resonance frequency: formula
In addition to AC machines, there are electric motors connected to a DC network. The speed of such devices is calculated using completely different formulas.
Rated rotation speed
The speed of a DC machine is calculated using the formula in the figure below, where:
- n – number of revolutions per minute,
- U – network voltage,
- Rya and Iya – armature resistance and current,
- Ce – motor constant (depending on the type of electric machine),
- Ф – stator magnetic field.
These data correspond to the nominal values of the parameters of the electric machine, the voltage on the field winding and the armature or the torque on the motor shaft. Changing them allows you to adjust the rotation speed. It is very difficult to determine the magnetic flux in a real motor, so calculations are made using the current flowing through the field winding or armature voltage.
Formula for calculating the speed of a DC motor
The speed of commutator AC motors can be found using the same formula.
Speed adjustment
Adjustment of the speed of an electric motor operating from a DC network is possible within a wide range. It is possible in two ranges:
- Up from nominal. To do this, the magnetic flux is reduced using additional resistances or a voltage regulator;
- Down from par. To do this, it is necessary to reduce the voltage on the armature of the electric motor or connect a resistance in series with it. In addition to reducing the speed, this is done when starting the electric motor.
Knowing what formulas are used to calculate the rotation speed of an electric motor is necessary when designing and setting up equipment.
Angular velocity
When a body moves in a circle, not all its points move at the same speed relative to the axis of rotation. If we take the blades of an ordinary household fan that rotate around a shaft, then the point located closer to the shaft has a rotation speed greater than the marked point on the edge of the blade. This means they have different linear rotation speeds. At the same time, the angular velocity of all points is the same.
Angular velocity is the change in angle per unit time, not distance. It is denoted by the letter of the Greek alphabet – ω and has a unit of measure: radians per second (rad/s). In other words, angular velocity is a vector tied to the axis of rotation of the object.
The formula for calculating the relationship between rotation angle and time interval is:
ω = ∆ϕ/∆t,
Where:
- ω – angular velocity (rad/s);
- ∆ϕ – change in the angle of deflection when turning (rad.);
- ∆t – time spent on deviation (s).
The designation of angular velocity is used when studying the laws of rotation. It is used to describe the motion of all rotating bodies.
Angular velocity formula
Angular velocity in specific cases
In practice, they rarely work with angular velocity values. It is needed in the design development of rotating mechanisms: gearboxes, gearboxes, etc.
You can calculate it using the formula. To do this, use the connection between angular velocity and rotational speed.
ω = 2*π / Т = 2*π*ν,
Where:
- π – number equal to 3.14;
- ν – rotation speed, (rpm).
As an example, the angular velocity and rotational speed of the wheel disk when moving a walk-behind tractor can be considered. It is often necessary to reduce or increase the speed of the mechanism. To do this, a device in the form of a gearbox is used, with the help of which the speed of rotation of the wheels is reduced. At a maximum speed of 10 km/h, the wheel makes about 60 rpm. After converting minutes to seconds, this value is 1 rpm. After substituting the data into the formula, the result will be:
ω = 2*π*ν = 2*3.14*1 = 6.28 rad/s.
For your information. A reduction in angular velocity is often required in order to increase the torque or tractive effort of mechanisms.
Gear speed reducer for motor cultivator
How to determine angular velocity
The principle of determining angular velocity depends on how the circular motion occurs. If uniform, then the formula is used:
ω = 2*π*ν.
If not, then you will have to calculate the values of the instantaneous or average angular velocity.
The quantity we are talking about is a vector quantity, and Maxwell’s rule is used to determine its direction. In common parlance - the gimlet rule. The velocity vector has the same direction as the translational movement of a screw with a right-hand thread.
Maxwell's rule for angular velocity
Let's look at an example of how to determine the angular velocity, knowing that the angle of rotation of a disk with a radius of 0.5 m varies according to the law ϕ = 6*t:
ω = ϕ / t = 6 * t / t = 6 s-1
The vector ω changes due to rotation in space of the rotation axis and when the value of the angular velocity modulus changes.
Speed concept
When we compare the movement of any bodies, we say that some bodies move faster, while others move slower. We use such simple terminology in everyday life, talking, for example, about traffic. In physics, the speed of movement of bodies is characterized by a certain value. This quantity is called speed. General definition of speed (if the body is moving uniformly):
Velocity during uniform motion of a body is a physical quantity that shows how far the body has traveled per unit time.
By uniform motion of a body it is meant that the speed of the body is constant. The formula for finding speed: $v=frac$, $s$ is the path traveled by the body (that is, the length of the line), $t$ is the time (that is, the period of time during which the path was traveled).
According to the international SI system, the unit of linear speed is derived from two basic units - the meter and the second, that is, it is measured in meters per second (m/s). This means that the unit of speed is the speed of such uniform motion that a body travels a distance of one meter in one second.
Try asking your teachers for help
Speed is also often measured in km/h, km/s, cm/s.
Let's look at a simple example of a speed calculation problem.
Task. Moving uniformly, the train covers 219 km in 4 hours. Find its speed of movement.
Solution. $v=frac<219 km><4 h>=54.75frac<km><h>$. Let's convert kilometers into meters and hours into seconds: $54.75frac<km><h>=frac<54750 m><3600c>approx 15.2frac<m>$.
From the example we see that the numerical value of the speed differs depending on the selected unit of measurement.
In addition to the numerical value, speed has a direction. The numerical value of a quantity in physics is called the modulus. When a physical quantity also has a direction, then this quantity is called a vector quantity. That is, speed is a vector physical quantity.
In writing, the velocity module is denoted by $v$, and the velocity vector by $vec v$.
In turn, such quantities as path, time, length and others are characterized only by a numerical value. Then they say that these are scalar physical quantities.
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In the case when the movement is uneven, the concept of average speed is used. Average speed formula: $v_<aver>=frac$, where $s$ is the entire path traveled by the body, $t$ is the entire time of movement. Let's look at an example of a medium speed problem to understand the difference.
Task. Some vehicles cover a distance of 213 km in 2.5 hours. Find it $v_<av>$.
Answer. $85.2 frac<km><h>$ or $23.7frac<m> <s>$.
Examples
- On gramophone records, the speed is indicated in revolutions per minute (rpm). Standard speed values are 16+2⁄3, 33+1⁄3, 45 or 78 rpm (5⁄18, 5⁄9, 3⁄4, or 1.3 rpm, respectively).
- Modern dental drills have rotation speeds of up to 800,000 rpm (13,300 rpm).
- The second hand of a watch rotates at a frequency of 1 rpm.
- CD players read at 150 kB/s and therefore rotate at approximately 500 rpm (8 rps) at the inner edge and 200 rpm (3.5 rps) at the outer edge . CD drives operate at speeds that are multiples of these numbers, even when using variable read speed.
- DVD players usually also read discs at a constant linear speed. The rotation speed varies from 1,530 rpm (25.5 rps) when reading at the inner edge to 630 rpm (10.5 rps) at the outer edge of the disk. DVD drives also operate at speeds that are multiples of the above numbers.
- The rotation speed of the washing machine drum can range from 500 to 2000 rpm (8–33 rps) during spinning.
- The TPP generator turbine rotates at 3000 rpm (50 rpm) or 3600 rpm (60 rpm), depending on the country (see Alternating Current#Frequency Standards). The generator shaft of a hydroelectric power station can rotate slower: up to 2 rps (in this case, the network frequency of 50 Hz is obtained due to the presence of a larger number of poles of the stator coils).
- A passenger car engine usually operates at a rotation speed of 2500 rpm (41 rpm), at idle speed - about 1000 rpm (16 rpm), and maximum speed 6000-10,000 rpm (100 -166 r/s).
- An airplane propeller typically rotates at speeds between 2000 and 3000 rpm (30-50 rps).
- A computer hard drive with ATA or SATA interfaces rotates at a speed of 5400 or 7200 rpm (90 or 120 rpm), as a rare exception - 10,000 rpm, and server hard drives with SCSI and SAS interfaces use a speed of 10,000 or 15,000 rpm (160 or 250 rpm).
- The engine of a Formula 1 car can develop 18,000 rpm (300 rps) (according to the regulations for the 2009 season).
- A uranium enrichment centrifuge rotates at 90,000 rpm (1500 rps) or faster.
- A gas turbine engine rotates at tens of thousands of revolutions per minute. Model airplane turbines can reach speeds of up to 100,000 rpm (1,700 rps), and the fastest ones can reach 165,000 rpm (2,750 rps).
- A typical 80mm computer fan spins at 800-3000 RPM and is powered by 12V DC.
- The turbocharger can reach a speed of 290,000 rpm (4800 rpm), while 80,000–200,000 rpm (1000–3000 rpm) are used for quiet driving.
- The rotation speed of a space station, such as the Stanford torus, to achieve 1 g of gravity that is comfortable for humans, must be 2 rpm or less to minimize the effect of motion sickness (see Coriolis force).
How to determine angular velocity: what is this quantity?
From a physical and mathematical point of view, this value can be defined as follows: these are data that show how quickly a certain point rotates around the center of the circle along which it moves.
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This seemingly purely theoretical value has considerable practical significance when operating a car. Here are just a few examples:
- It is necessary to correctly correlate the movements with which the wheels rotate when turning. The angular speed of a car wheel moving along the inner part of the trajectory must be less than that of the outer one.
- You need to calculate how fast the crankshaft rotates in the car.
- Finally, the car itself, when going through a turn, also has a certain value of motion parameters - and in practice, the stability of the car on the highway and the likelihood of capsizing depend on them.
