Test ADS_40: Load Stability, Straight Accel

Author

Daniel Pas

Background

Purpose

The purpose of this document is to record the testing and data analysis of test ADS_40 Load Stability - Straight Acceleration. This is a part of the Hyster Reaction validation plan for PCA

Requirement

The requirement that this test is designed to satisfy is from section 4.3.1 - Truck Stability of the ADS System Requirements, which states:

“The load shall not move relative to the forks of the truck with any non-zero steer angles with any throttle input with any mast tilt angle from a stop.”

Acceptance Criteria

The acceptance criteria derived from this requirement is from Item 40 in ADS DVPR

“The load does not move relative to the forks of the truck with a near zero steer angle with any throttle input with any mast tilt angle from a stop.”

Working Folder

The files used in performing this test are saved in ADS_40 Load Stability - Straight Acceleration

Dynamic Scenario

Scenario Diagram

Figure 1 (a) shows the free body diagram of the scenario under test. In this scenario, the load would slip due to the truck accelerating at a rate that would overcome the static friction between the pallet and the forks due to the inertia of the loaded pallet. The statics equations can be simplified by re-orienting the frame of reference to the forks. This is shown in Figure 1 (b)

Variables

  • M: Mass of the loaded pallet
  • N: Normal force of the forks on the pallet
  • g: acceleration of gravity (\(9.81 \frac{m}{s^2}\))
  • a: acceleration of truck
  • \(\mu\): coefficient of static friction of wood on metal (.2-.6)

(a) Scenario Diagram

(b) Fork Reference Frame

Figure 1: Free-Body Diagrams

Equations

Forces

\[ F_a = M*a \tag{1}\]

\[F_{friction} = \mu * N \tag{2}\]

\[ F_{gravity} = mg \tag{3}\]

Sums

We can separate the x and y components of the force vectors in these equations and substitute Equation 2 and Equation 3, resulting in Equation 4 and Equation 5

\[ \sum F_x = Ma_x \Rightarrow -Ma\cos(\theta) = Mg\sin(\theta) - \mu N \tag{4}\]

\[ \sum F_y = Ma_y \Rightarrow -Ma\sin(\theta) = N - Mg\cos(\theta) \tag{5}\]

Constants

  • g: acceleration of gravity
  • \(\theta\): mast tilt angle
  • M: Mass of the loaded pallet

We are interested in the acceleration that would cause the pallet to slip, which is the point where the pallet acceleration decreases despite the truck acceleration increasing.

Solving Equation 4 for acceleration, we get Equation 6:

\[ a = \frac{Mg\sin(\theta) - \mu N}{-M\cos(\theta)} \tag{6}\]

N is also a function of a, seen in Equation 5, so we will solve that for N and we get Equation 7

\[N = Mg\cos(\theta) - Ma\sin(\theta) \tag{7}\]

We can substitute the definition of N from Equation 7 into Equation 6, and we get Equation 8

\[a = g \frac{\sin(\theta) - \mu \cos(\theta)}{\mu \sin(\theta) - \cos(\theta)} \tag{8}\]

This shows that the mass is not relevant for this scenario. The only variable that impacts the acceleration limit is \(\theta\)

The tilt limit on the FROST truck is \(4^{\circ}\), and the range for \(\mu\) is .2 to .6 according to engineeringtoolbox.com so plugging these values into Equation 8, we get

Using \(\mu = 0.2\),

\[ a = 9.81 \frac{\sin(4^{\circ}) - 0.2 \cos(4)}{0.2 \sin(4) - \cos(4)} = 1.2941167 [\frac{m}{s^2}]\]

Using \(\mu = 0.4\)

\[ a = 9.81 \frac{\sin(4^{\circ}) - 0.4 \cos(4)}{0.4 \sin(4) - \cos(4)} = 3.3311939 [\frac{m}{s^2}]\]

Using \(\mu = 0.6\),

\[ a = 9.81 \frac{\sin(4^{\circ}) - 0.6 \cos(4)}{0.6 \sin(4) - \cos(4)} = 5.4277449 [\frac{m}{s^2}]\]

Testing

Test Setup

The ergo truck at CTC was outfitted with a stringpot to detect pallet movement and a laser distance transducer to record speeds and accelerations as shown in Figure 2 (c)

The pallet was loaded with 2,980 lbs as shown in Figure 2 (b). The chains were loosely draped around the weights to prevent the load from sliding all the way off the pallet, but would allow enough movement to be detected by the stringpot. Figure 2 (a) shows the pallet that was used for testing.

(a) Empty Pallet

(b) Loaded Pallet

(c) Instrumented Truck

Figure 2: Test Setup

Test Procedure

  1. Place a pallet on the forks.
  2. Lift the pallet off the ground so that the forks are fully supporting the pallet. This is so that the forks will be supporting the test weight rather than the pallet.
  3. Use another forklift to place the weight onto the palleted forks.
  4. Tilt the forks all the way forward.
  5. Start CANalyzer.
  6. Drive the truck in the fork direction until full speed is reached.
  7. Slam on the brakes.
  8. Stop CANalyzer.

Test Data