Shaper Power Consumption Analysis

Understanding the power consumption in a shaper machine during a laboratory test is crucial for optimizing machining operations. This calculation involves determining the volume of material removed per unit of time and then applying the specific power consumption rate. Let's break down the given parameters and calculate the total power consumption.

Shaper Machine Parameters

We are provided with the following data from the laboratory test on the shaper machine:

• Feed (\(f\)): This is the distance the tool advances into the workpiece for each stroke. It is given as \(2 \, \text{mm/stroke}\).
• Depth of Cut (\(d\)): This is the thickness of the material removed by the cutting tool in one pass. It is given as \(4 \, \text{mm}\).
• Length of Stroke (\(L\)): This is the total distance the cutting tool travels during one cutting cycle. It is given as \(300 \, \text{mm}\).
• Specific Power Consumption (\(P_s\)): This is the power required to remove a unit volume of material. It is given as \(0.05 \, \text{kW/cm}^3 \text{ per minute}\).
• Number of Working Strokes per Minute (\(N\)): This indicates how many times the cutting action occurs in one minute. It is given as \(20\).

Material Removal Rate Calculation

To find the total power consumption, we first need to determine the volume of material removed per minute. This is done in two steps: calculating the volume removed per stroke and then multiplying it by the number of working strokes per minute.

1. Volume of material removed per stroke (\(V_{\text{stroke}}\)):

   The volume of material removed in one stroke is the product of the feed, depth of cut, and length of stroke.

   $$V_{\text{stroke}} = f \times d \times L$$

   Substituting the given values:

   $$V_{\text{stroke}} = 2 \, \text{mm} \times 4 \, \text{mm} \times 300 \, \text{mm}$$

   $$V_{\text{stroke}} = 2400 \, \text{mm}^3$$

   Since the specific power consumption is given in \(\text{kW/cm}^3\), we need to convert the volume from \(\text{mm}^3\) to \(\text{cm}^3\). We know that \(1 \, \text{cm} = 10 \, \text{mm}\), so \(1 \, \text{cm}^3 = (10 \, \text{mm})^3 = 1000 \, \text{mm}^3\).

   $$V_{\text{stroke}} = \frac{2400 \, \text{mm}^3}{1000 \, \text{mm}^3/\text{cm}^3} = 2.4 \, \text{cm}^3$$

2. Total volume of material removed per minute (\(V_m\)):

   This is calculated by multiplying the volume removed per stroke by the number of working strokes per minute.

   $$V_m = V_{\text{stroke}} \times N$$

   Substituting the values:

   $$V_m = 2.4 \, \text{cm}^3/\text{stroke} \times 20 \, \text{strokes/minute}$$

   $$V_m = 48 \, \text{cm}^3/\text{minute}$$

   This \(V_m\) represents the material removal rate (MRR) of the shaper.

Power Consumption Calculation

Finally, we can calculate the total power consumption by multiplying the total volume of material removed per minute by the specific power consumption.

$$P = V_m \times P_s$$

Substituting the calculated material removal rate and the given specific power consumption:

$$P = 48 \, \text{cm}^3/\text{minute} \times 0.05 \, \text{kW/cm}^3 \text{ per minute}$$

$$P = 2.4 \, \text{kW}$$

Thus, the power consumption of the shaper under the given laboratory test conditions is \(2.4 \, \text{kW}\).

Here is a summary of the calculation:

This detailed step-by-step approach ensures an accurate calculation of the power consumed by the shaper machine based on its operational parameters and specific power consumption.