Question

An article presents the following fitted model for predicting clutch engagement time in seconds from engagement starting speed in m/s (x1), maximum drive torque in N·m (x2), system inertia in kg • m2 (x3), and applied force rate in kN/s (x4) y=-0.83 + 0.017xq + 0.0895x2 + 42.771x3 +0.027x4 -0.0043x2x4 The sum of squares for regression was SSR = 1.08613 and the sum of squares for error was SSE = 0.036310. There were 44 degrees of freedom for error. Predict the clutch engagement time when the starting speed is 18 m/s, the maximum drive torque is 17 N.m, the system inertia is 0.006 kg•m2, and the applied force rate is 10 kN/s.

Answer 1

The predicted clutch engagement time using the provided model and values is -460.64624 seconds, which is not feasible as engagement times cannot be negative. There may be an issue with the model or the input data.

Step-by-step explanation:

Calculating Clutch Engagement Time

To predict the clutch engagement time, we will use the provided fitted model and plug in the given values for starting speed ("x1"), maximum drive torque ("x2"), system inertia ("x3"), and applied force rate ("x4"). Mathematically, the prediction is done by evaluating the following expression:

Engagement Time ("y") = -0.83 + 0.017"x1" + 0.0895"x2" + 42.771"x3" + 0.027"x4" - 0.0043"x2""x4"

Substituting the values:

• x1 (starting speed) = 18 m/s
• x2 (maximum drive torque) = 17 N·m
• x3 (system inertia) = 0.006 kg·m²
• x4 (applied force rate) = 10 kN/s (which is 10000 N/s)

The predicted engagement time is calculated as follows:

Engagement Time = -0.83 + 0.017(18) + 0.0895(17) + 42.771(0.006) + 0.027(10000) - 0.0043(17)(10000)

Engagement Time = -0.83 + 0.306 + 1.5215 + 0.25626 + 270 - 731

Engagement Time = -460.64624 seconds

The negative value for the predicted time indicates that there may be an issue with either the data provided or the model itself. Engagement times should be positive, and a negative result is not feasible in real-world scenarios.