A CNC worktable is driven in a linear direction by a lead screw connected directly to a stepper motor. The pitch of the lead screw is 5 mm. The stepper motor completes one full revolution upon receiving 600 pulses. If the work table speed is 5 m/minute and there is no missed pulse, then the pulse rate being received by the stepper motor is

The correct option is 10 kHz.

To understand why this is the correct answer, we can break down the relationship between the physical motion of the CNC worktable and the pulse rate received by the stepper motor step-by-step.

Step 1: Understand the Given Parameters
We are given the following values:
- Lead screw pitch ($p$) = 5 mm per revolution. This means one full 360-degree rotation of the lead screw moves the table linearly by 5 mm.
- Motor steps/pulses per revolution ($N$) = 600 pulses. This means the motor requires 600 pulses to complete one full revolution.
- Worktable speed ($v$) = 5 m/minute.

Step 2: Convert Units
To perform consistent calculations, let's first convert the worktable speed from meters per minute to millimeters per second.
Since 1 meter = 1000 millimeters and 1 minute = 60 seconds:

$$v=\frac{5\text{ m}}{1\text{ minute}}=\frac{5\times 1000\text{ mm}}{60\text{ seconds}}=\frac{5000}{60}\text{ mm/s}=\frac{250}{3}\text{ mm/s}$$

Step 3: Calculate the Rotational Speed of the Screw (Revolutions per Second)
Now we calculate how many revolutions the lead screw (and thus the motor, since it is directly connected) must make per second to achieve this linear speed:

$$\text{Rotational speed }\left(n\right)=\frac{\text{Linear speed }}{\text{Pitch}}=\frac{v}{p}$$
Substituting our values:

$$n=\frac{(250/3)\text{ mm/s}}{5\text{ mm/rev}}=\frac{50}{3}\text{ revolutions per second (rps)}$$

Step 4: Determine the Pulse Rate
The pulse rate represents the number of pulses sent to the stepper motor per second. Since the motor requires 600 pulses for each revolution, we can find the frequency of pulses as follows:

$$\text{Pulse Rate }\left(f\right)=\text{Rotational speed }\left(n\right)\times \text{Pulses per revolution }\left(N\right)$$
Substituting the calculated values:

$$f=\frac{50}{3}\times 600\text{ pulses/second}$$
Simplifying the expression:

$$f=50\times 200=10,000\text{ Hz}$$
Converting Hz to kilohertz (1 kHz = 1000 Hz):

$$f=10\text{ kHz}$$
Thus, the pulse rate being received by the stepper motor to drive the worktable at the specified speed is exactly 10 kHz.