Torque capacities

To simplify the complex procedure of determining total torques, one technique is to use a dynamic torque analysis table. See page 25; charting torque values in tabular form allows easy summation of forces to see what maximum values must be met. But how is such a chart filled out?

First, all cycled components should be listed. It's easiest if the system pieces are listed starting from the load, and working to the clutch/brake. Then, enter the reflected inertia for each componen; these are the values we calculated using their weights and K values. Next, enter the drive efficiency associated with each component. (Many of these values can be obtained from vendors; otherwise, good engineering judgement returns acceptable estimates.)

These efficiency values are then used to determine efficiency factors — numbers expressing the relative effect each component has on the system. They're determined by multiplying all the efficiency values at or below the component considered on the table. For the boxes in our example, the value is 1 × 0.8 × 1 × 0.9 × 0.8 × 1 × 1 = 0.58. For our reducer, it's 0.8 × 1 × 1 =0.8.

The first torque to calculate is load torque T_L. For our conveyor example, this is force seen at the drive pulley — required to move the system at constant velocity. It can be found by solving for static equilibrium, made easier with free-body diagrams for key points of force interaction: At the box, slider and belt, and head pulley. (Loads in our example are due to weight of the boxes and frictional forces.) After determining the load requirement, we apply the associated efficiency factor and reflect it back to the clutch/brake. So load torque at the clutch/brake equals:

The next step is to calculate the inertial clutch torque for each component:

Once entered into the table, the T_ic values are added together to determine the total inertial clutch torque required.

The sum of the inertial clutch and load torque is the dynamic clutch torque required: T_dc = T_ic + T_L. In our case, this is 552 + 584 = 1,136 in.-lb. This is the value that should be used in selecting a clutch.

A similar process is used to determine braking requirements. The first step: Find dynamic braking requirements by calculating the actual inertial torque of each component using:

Speed change is actually negative here. Once again, enter data into the table and sum T_ib values for total inertial brake torque required. The sum of the inertial brake torque and the load torque is the dynamic brake torque required T_db =T_ib + T_L — in our case, -1032 + 584 = -448 in.-lb. This is one of the values that should be used in selecting a brake.

Note that inertial brake torque is that required to deceleration the system — not necessarily equal to holding torque. In fact, the former is often much larger. Also, load torque is the same for acceleration as it is for deceleration. Why? Once the boxes are stopped, friction F₂ acts in the other direction — because friction always opposes motion. If this total dynamic brake requirement is the same sign as the clutch/torque it indicates that the system will decelerate in less time than required, and no brake is required to stop the system — though one may still need a holding brake.

The final step is calculating holding brake torque requirements. This is torque required to keep the system stopped; all the inertial torques disappear here. It's similar to load torque, but different because frictional forces act in the opposite direction when the system is stopped.

Sign convention

During dynamic torque analysis, it's important to adhere to one sign convention. Each (inertial and load) torque is considered separately. Load torque is found by solving for static equilibrium. To prevent the sign for load torque from changing during the analysis:

1. The direction of torque required to accelerate the mass of the system is always considered positive.

2. If load torque acts in the direction of the acceleration or inertial torque, then it is considered to be positive. Static free-body diagrams make this orientation easier to identify.

3. The sign of the deceleration inertial torque is opposite the sign for the acceleration torque.

Load torque is generally considered to be positive, especially if the load is predominately a friction or inertia load. It is possible, however, for the load torque to be negative. This could happen if the weight of the load, or some other kind of stored energy like a compressed spring, helps the system accelerate.

For more information, call (513) 868-0900 or e-mail info@forcecontrol.com.