Cushion Capacity and Sizing

High rotational velocity and/or large mass in rotary motion can cause damaging impact at the end of stroke. Deceleration and absorption of rotating system energy can be achieve with cushions, external shock absorbers or fluid circuit devices which reduce speed as the actuator approaches the end of travel.

Cushions are the simplest design alternative, but consideration must be given to the cushion energy absorption capacity. Exceeding rated cushion capacity can reduce actuator life or result in severe actuator damage. To determine if a cushion is suitable for the application, calculate the total energy that must be absorbed and compare with the cushion capacity rating.

Energy of Application

E_k = Energy of mass in motion (kinetic energy)

E_k = 1/2 J w²

E_p = Propelling energy of actuator

E_p = P_pC_tq_d

E_g = Gravitational energy of lifting or lowering weight

E_g = W r_aq_dsinf_bar

Total Energy, where: E_t = E_k + E_p +/- E_g

E_g is added if weight is falling or subtracted if weight is rising

Note: If weight is rotating in horizontal plane, the gravitational energy is zero.

Horizontal Rotational Deceleration

Two 50 lb parts are positioned diameterically opposed on a 150 lb rotary transfer table which swings through 180° in a horizontal plane. The table radius is 50 in and the radius to the parts is 40 in. Rotational velocity of the table as it enters the cushion deceleration is 80°/sec or (80+57.3) 1.40 rad/sec. A model 3,700 actuator operating at 1,500 psi has been selected to propel the load.

Kinetic Energy

E_k = 1/2 J w²

Moment of Inertia: J = J_table + J_load

Propelling Energy

E_p = P_pC_tq_d

Torque Factor (C_t) for Model 3,700 (1.23 lb-in/psi)

Deceleration Arc (q_d) for Model 3,700 (0.33 radians)

E_p = P_pC_tq_d = (1500 psi) (1.23 lb-in/psi) (0.33 rad) = 609 lb-in

Gravitational Energy

E_g = 0 for horizontal rotation

Total Energy

E_t = E_k + E_p +/- E_g

E_t = 883 + 609 + 0 lb-in = 1,492 lb-in

Total energy to be absorbed in the example is 1,492 lb-in. the cushion capacity of Model 3,700 when properly adjuste, is 1,670 lb-in. this is adequate to absorb the deceleration requirement.

Caution: See caution note on Rotary Formulas

Vertical Rotational Deceleration

A material handling rollover mechanism transfers a 100 lb machine part through 180° in a vertical plane from a 9 o'clock to a 3 o'clock position. The radius arm to the part grippers is 40 in and the effective weight and radius of the arms and grippers can be approximated by two 40 in long rods weighing 70 lb a piece. Rotational velocity of the mechanism as it enters the cushion deceleration arc is 40°/sec or (40/57.3) 0.70 rad/sec. A Model 15,000 actuator operating at 2,000 psi has been sellected to propel the load.

Kinetic Energy

E_k = 1/2 J w²

Moment of Inertia J = J_arm + J_load

Propelling Energy

E_p = P_pC_tq_d

Torque Factor (C_t) for Model 15,000 (5.0 lb-in/psi)

Deceleration Arc (q_t) for Model 15,000 (0.34 rad)

E_p = P_p C_t q_d = (2,000 psi) (5.0 lb-in/psi) (0.34 rad) = 3,400 lb-in

Gravitational Energy

E_g = W r_aq_dsinf_bar

W r_a = (100 lb) (40 in) + 2(70 lb) 1/2(40 in) = 6,800 lb-in.

Deceleration Arc (q_d) for model 15,000 (0.34 rad or 19.6°

Total Energy

E_t = E_k + E_p +/- E_g

E_t = 212 + 3,400 + 2,289 lb-in = 5,901 lb-in

Total energy to be absorbed in the example is 5,901 lb-in. The cushion capacity of Model 15,000 is 6,290 lb-in. this is adequate to absorb the deceleration requirement.

when the energy developed exceeds the capacity of the cushion, consider the following:

• Reduce weight of object in motion
• Reduce rotational velocity
• Employ external shock absorbers
• Add proportional hydraulics to the circuit to reduce propelling energy during deceleration.

CAUTION: Cushion needle adjustment is a crucial factor in achieving optimum cushion performance. If the needle valve setting is too far open, cushion capacity will be reduced or rendered ineffective; if set too tight, cushion action will generate shock and pressure spikes in excess of actuator rating.