Select figure to enlarge.

Aspecialty manufacturer recently completed construction of a 16- station printer. Each station, dedicated to a different ink color, uses a brushless dc servo motor to drive an ink squeegee across the silk screen, Figure 1.

Each of the 16 squeegees attaches to its station carriage and disburses ink across the silk screen onto the printing surface. Linear bearings on the machine frame support each carriage, which is fastened between the pulleys. Two timing belts wrap around the pulleys. When the pulleys rotate, the timing belt pulls the carriage across the silk screen, Figure 2.

Pneumatic cylinders raise and lower the squeegee to the screen. The motor experiences the greatest load when the squeegee presses against the screen.

Determining criteria

The first steps are to determine required motor speed and the torque required by the application. Engineers placed a limit on the maximum carriage speed at 40 in./sec because if it travels too fast, the ink can’t penetrate the screen and adhere to the print surface. The radius of the pulleys is 0.8 in.

Because this application uses a belt drive system, the motor speed was determined using the following equation:

Which resulted in:

N_m = 477.5 rpm      (1B)

To determine the torque, six loading conditions must be defined:
• Acceleration torque.
• Deceleration torque.
• Friction torque with the squeegee up.
• Friction torque with the squeegee down.
• Breakaway torque with the squeegee up.
• Breakaway torque with the squeegee down.

Engineers measured the breakaway torque by attaching a torque wrench to one pulley on a prototype machine. The breakaway torque is 46 oz-in. with the squeegee up and 137 oz-in. with the squeegee down.

Friction torque was measured by connecting a dc motor with a known torque constant to one of the prototype’s pulleys. They measured the motor’s current while driving the load at a constant speed. The current measurement was then multiplied by the motor’s torque constant. The friction torque was 35 oz-in. with the squeegee up and 116 oz-in. with the squeegee down.

The design engineers set the acceleration and deceleration times at 0.1 second. The carriage on their prototype weighs 640 oz, the four pulleys each weigh 3 oz, and the two belts together weigh 16 oz. The radius of the pulleys was 0.8 in. The acceleration torque, T_a, was then calculated:

Solving, with:
W_c = 640 oz
r= 0.8 in.
n = 4 pulleys
W_p = 3 oz/pulley
W_b = 16 oz
J_m = 0 (because a motor hasn’t been selected yet)
V_l = 40 in./sec
t_a = 0.1 sec

Then:
T_a = 549 oz-in.

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