Question

A CNC machine has one of its linear positioning axes as shown in the figure, consisting of a motor rotating a lead screw, which in turn moves a nut horizontally on which a table is mounted. The motor moves in discrete rotational steps of 50 steps per revolution. The pitch of the screw is 5 mm and the total horizontal traverse length of the table is 100 mm. What is the total number of controllable locations at which the table can be positioned on this axis? 

 

• A. 5000
• B. 2
• C. 1000
• D. 200

Hint:

In CNC and control systems, the fundamental unit of movement is often called the Basic Length Unit (BLU) or resolution. It's the smallest increment of motion the system can produce. Total controllable positions = Total Travel / BLU.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
The problem asks for the total number of distinct positions the CNC table can take. This depends on the smallest possible movement the table can make (the resolution or Basic Length Unit, BLU) and the total travel length.
Step 2: Key Formula or Approach:
1. Calculate the linear distance the table moves for one revolution of the screw. This is equal to the pitch.
2. Calculate the linear distance the table moves for one step of the motor. This is the resolution or BLU. \[ \text{BLU} = \frac{\text{Pitch}}{\text{Steps per revolution}} \] 3. Calculate the total number of controllable locations by dividing the total travel length by the BLU. \[ \text{Total Locations} = \frac{\text{Total Traverse Length}}{\text{BLU}} \] Note that this calculation gives the number of steps. The number of locations is typically one more than the number of steps (including the start position). However, in CNC terminology, it usually refers to the number of addressable points, which is equivalent to the number of steps. Let's assume the latter.
Step 3: Detailed Calculation:
Given:
- Steps per revolution = 50
- Pitch = 5 mm
- Total Traverse Length = 100 mm
1. Calculate the Basic Length Unit (BLU):
This is the linear movement per motor step. \[ \text{BLU} = \frac{\text{Pitch}}{\text{Steps per revolution}} = \frac{5 \text{ mm}}{50 \text{ steps}} = 0.1 \text{ mm/step} \] 2. Calculate the Total Number of Steps (and Locations):
The total number of steps required to cover the entire traverse length is: \[ \text{Total Steps} = \frac{\text{Total Traverse Length}}{\text{BLU}} = \frac{100 \text{ mm}}{0.1 \text{ mm/step}} = 1000 \text{ steps} \] Since each step corresponds to a unique controllable location, the total number of controllable locations is 1000. (If we were to count the start point at 0 and the 1000th step, it would be 1001 locations, but 1000 is the standard interpretation and matches the options).
Step 4: Final Answer:
The total number of controllable locations is 1000.
Step 5: Why This is Correct:
The resolution of the system is correctly calculated as the pitch divided by the number of steps per revolution. The total number of addressable points is then this resolution divided into the total travel distance. The calculation is straightforward.