A stepping motor with 200 steps angles ( = 200) is coupled to a leadscrew through a gear reduction of 5:1 (five rotations of the motor for each rotation of the leadscrew). The leadscrew has 2.4 threads/cm (which means the distance between two adjacent threads is 1 / 2.4 cm). The worktable driven by the leadscrew must move for 25 cm at a feed rate of 75 cm/min. Determine:

*The number of pulses required to move the table

*Required motor speed (rev/min).

*Pulse rate(pulses/sec) to achieve the desired table speed.

To determine the number of pulses required to move the table, we need to calculate the distance traveled by the leadscrew.

Distance traveled by the leadscrew = 25 cm

As mentioned, the leadscrew has 2.4 threads/cm. Therefore, the total number of threads on the leadscrew is:

Total number of threads on leadscrew = 25 cm * 2.4 threads/cm = 60 threads

Since the gear reduction ratio is 5:1, it means that for each rotation of the leadscrew, the motor will rotate 5 times. Therefore, the number of rotations required for the motor to move the table is:

Number of rotations of the motor = Total number of threads / Gear reduction ratio = 60 threads / 5 = 12 rotations

As given, the stepping motor has 200 steps per rotation, so the number of pulses required to move the table is:

Number of pulses = Number of rotations of the motor * Steps per rotation = 12 rotations * 200 steps/rotation = 2400 pulses

To calculate the required motor speed (rev/min), we need to determine the time taken by the motor to complete one rotation.

Time taken by the motor to complete one rotation = 1 / Feed rate = 1 / 75 cm/min

Since the motor needs to rotate 5 times for each rotation of the leadscrew (due to the gear reduction), the required motor speed is:

Required motor speed = 5 / (1 / Feed rate) = 5 * Feed rate = 5 * 75 cm/min = 375 cm/min

To convert the motor speed from cm/min to rev/min, we need to divide by the circumference of the leadscrew.

Circumference of the leadscrew = 2 * π * Radius = 2 * π * (1 / (2 * 2.4)) cm

Required motor speed (rev/min) = Required motor speed (cm/min) / Circumference of the leadscrew

To calculate the pulse rate (pulses/sec) to achieve the desired table speed, we need to divide the required motor speed (rev/min) by 60 (to convert to rev/sec) and multiply it by the number of pulses per revolution:

Pulse rate (pulses/sec) = (Required motor speed (rev/min) / 60) * Steps per rotation

Let's plug in the values to calculate the required motor speed and pulse rate:

Circumference of the leadscrew = 2 * π * (1 / (2 * 2.4)) = 2 * π * (1 / 4.8) ≈ 1.309 cm

Required motor speed (rev/min) = 375 cm/min / 1.309 cm ≈ 286.19 rev/min

Pulse rate (pulses/sec) = (286.19 rev/min / 60) * 200 pulses/rotation ≈ 954.63 pulses/sec

Therefore, the number of pulses required to move the table is 2400 pulses, the required motor speed is approximately 286.19 rev/min, and the pulse rate to achieve the desired table speed is approximately 954.63 pulses/sec.

To determine the number of pulses required to move the table, we need to first calculate the total distance the leadscrew needs to travel.

Distance = 25 cm

Since there are 2.4 threads/cm, the total number of threads on the leadscrew is:

Total threads = Distance x Threads/cm
Total threads = 25 cm x 2.4 threads/cm = 60 threads

Since the motor is coupled through a gear reduction of 5:1, the number of rotations the motor needs to make will be 5 times the number of rotations of the leadscrew.

Number of rotations of the leadscrew = Total threads / Threads per rotation
Number of rotations of the leadscrew = 60 threads / (1 rotation / 2.4 threads) = 144 rotations

Number of rotations of the motor = Number of rotations of the leadscrew x Gear reduction ratio
Number of rotations of the motor = 144 rotations x 5 = 720 rotations

Since the stepping motor has 200 steps/rotation, the total number of steps required to move the table is:

Number of steps = Number of rotations of the motor x Steps per rotation
Number of steps = 720 rotations x 200 steps/rotation = 144,000 steps

Therefore, the number of pulses required to move the table is 144,000 pulses.

To determine the required motor speed in rev/min, we can use the formula:

Motor speed (rev/min) = Feed rate (cm/min) / Threads per rotation
Motor speed = 75 cm/min / 2.4 threads/rotation = 31.25 rev/min

Therefore, the required motor speed is 31.25 rev/min.

To calculate the pulse rate (pulses/sec) to achieve the desired table speed, we know that 1 rev/min is equal to x pulses/sec (where x is the pulse rate). We can calculate the pulse rate using the following formula:

Pulse rate (pulses/sec) = Motor speed (rev/min) * Steps per rotation / 60 sec/min
Pulse rate = 31.25 rev/min * 200 steps/rotation / 60 sec/min = 104.17 pulses/sec

Therefore, the pulse rate required to achieve the desired table speed is approximately 104.17 pulses/sec.