Reliability Analysis of the Electric Robot

An electric robot considered here is the one that conducts a “normal” industrial task, while its maintenance and programming are conducted by humans. The robot is subject to the following seven assumptions/factors [8,9]:

i Supervising controller/computer directs all joints.

ii Transducer sends all appropriate signals to the joint controller.

iii Microprocessor control card controls each and every joint.

iv Interface bus permits interaction between the supervisory controller and the joint control processors.

v Motor shaft rotation is transmitted to the appropriate limb of the robot through a transmission unit.

vi Each and every joint is coupled with a feedback encoder (transducer).

vii Direct current (DC) motor actuates each joint.

In regard to reliability, the block diagram shown in Figure 5.3 represents the electric robot under consideration.

Figure 5.3 shows that the electric robot under consideration is made up of two hypothetical subsystems 1 and 2 in series. Subsystem 1 represents no movement due

Block diagram for estimating the non-occurrence probability (reliability) of the undesirable movement of the electric robot

FIGURE 5.3 Block diagram for estimating the non-occurrence probability (reliability) of the undesirable movement of the electric robot.

Block diagram representing two subsystems shown in Figure 5.3

FIGURE 5.4 Block diagram representing two subsystems shown in Figure 5.3: (a) subsystem 1, (b) subsystem 2.

to external factors, and subsystem 2 represents no failure within the robot causing its movement.

In turn, as shown in Figure 5.4(a), Figure 5.3 subsystem 1 is composed of two hypothetical elements A and В in series and subsystem 2 is made of five parts (i.e., interface, end effector, supervisory controller/computer, joint control, and transmission) (Figure 5.4(b)) in series.

Furthermore, the Figure 5.4(a) element A is composed of two hypothetical subelements X and Y in series as shown in Figure 5.5.

With the aid of Figure 5.3, we obtain the following equation for the probability of non-occurrence of the undesirable electric robot movement (i.e., reliability):

Block diagram representing Figure 5.4 (a) element A. where

FIGURE 5.5 Block diagram representing Figure 5.4 (a) element A. where

Rem is the probability of non-occurrence (reliability) of the undesirable electric robot movement.

Rsl is the independent subsystem l’s reliability.

/?s2 is the independent subsystem 2’s reliability.

For independent elements A and B, the reliability of subsystem 1 in Figure 5.4(a) is given by

where

Ra is the element A’s reliability.

RB is the element B’s reliability.

For hypothetical and independent subelements, the element A’s reliability in Figure 5.5 is

where

Rx is the reliability of subelement X (i.e., the maintenance person’s reliability in regard to causing the robot’s movement).

Ry is the reliability of subelement Y (i.e., the operator’s reliability in regard to causing the robot’s movement).

Similarly, the reliability of subsystem 2 in Figure 5.4(b), for independent parts, is given by

where

Rjc is the reliability of the joint control.

Re/ is the reliability of the end-effector.

RJ: is the reliability of the drive transmission.

Rsc is the reliability of the supervisory controller/computer. Ri is the reliability of the interface.

Example 5.7

Assume that the following reliability data values are specified for the above type of electric robot:

RB = 0.95 Ry = 0.93 Rx = 0.90 Rjc = 0.94 Ref = 0.92 ^,=0.96 **=0.91 Rj = 0.97

Calculate the probability of non-occurrence (reliability) of the undesirable electric robot movement.

By inserting the given data values into Equation (5.16) and (5.17), we obtain and

By substituting the above-calculated value for RA and the specified value for RB into Equation (5.15), we obtain

By inserting the above-calculated values into Equation (5.14), we get

Thus, the probability of non-occurrence (reliability) of the undesirable electric robot movement is 0.5826.

Reliability Analysis of the Hydraulic Robot

A hydraulic robot considered here is composed of five joints and, in turn, each joint is controlled and driven by a hydraulic servomechanism. The robot is subject to the following seven assumptions/factors [7,9]:

i Hydraulic fluid is pumped from the reservoir.

ii Under high flow demand, an accumulator assists the pump for supplying additional hydraulic fluid.

iii Unloading valve is employed for keeping pressure under the maximum limit.

iv Position transducer provides the joint angle codes and, in turn, the scanning of each code is conducted by a multiplexer.

v Servo valve controls the motion of each hydraulic actuator. This motion is transmitted directly or indirectly (i.e., through gears, chains, rods, etc.) to the robot’s specific limb and, in turn, each limb is coupled to a position transducer.

vi Operator makes use of a teach pendant for controlling the arm-motion in teach mode.

vii Conventional motor and pump assembly generates pressure.

The hydraulic robot under consideration with respect to reliability is represented by the block diagram shown in Figure 5.6. This figure shows that the hydraulic robot is composed of four subsystems: subsystem 1 (electronic and control subsystem), subsystem 2 (hydraulic pressure supply subsystem), subsystem 3 (gripper subsystem), and subsystem 4 (drive subsystem), in series. In turn, as shown in Figure 5.7 hydraulic pressure supply subsystem (i.e., block diagram (a)) is composed of two parts (i.e., piping and hydraulic equipment/component) in series and gripper subsystem (i.e., block diagram (b)) is also composed of two parts (i.e., control signal and pneumatic system) in series.

Block diagram of the hydraulic robot under consideration

FIGURE 5.6 Block diagram of the hydraulic robot under consideration.

Block diagram representing two subsystems shown in Figure 5.6

FIGURE 5.7 Block diagram representing two subsystems shown in Figure 5.6: (a) hydraulic pressure supply subsystem and (b) gripper subsystem.

Block diagram representing subsystem 4 (i.e., drive subsystem) shown in Figure 5.6

FIGURE 5.8 Block diagram representing subsystem 4 (i.e., drive subsystem) shown in Figure 5.6.

Furthermore, as shown in the Figure 5.8, the drive subsystem (shown in Figure 5.6) is composed of five parts (i.e., joints 1, 2, 3, 4, and 5) in series.

With the aid of Figure 5.6, we get the following expression for the probability of the non-occurrence of the hydraulic robot event (i.e., undesirable hydraulic robot movement causing damage to the robot other equipment as well as possible harm to humans):

where

Re is the reliability of the independent electronic and control subsystem.

Rh is the reliability of the independent hydraulic pressure supply subsystem. Rg is the reliability of the independent gripper subsystem.

R(, is the reliability of the independent drive subsystem.

Rhr is the hydraulic robot reliability or the probability of the non-occurrence of the hydraulic robot event (i.e., undesirable robotic arm movement causing damage to the robot/other equipment as well as possible harm to humans).

For independent parts, the reliabilities Rh,Rg,andRd of hydraulic pressure supply subsystem, gripper subsystem, and drive subsystem, using Figures 5.7(a), 5.7(b), and 5.8, respectively, are

and

where

Rp is the reliability of the piping.

Rhc is the reliability of the hydraulic component.

Rcs is the reliability of the control signal.

Rps is the reliability of the pneumatic system.

Rj is the reliability of joint j; for j = 1, 2, 3,4, 5.

For constant failure rates of independent subsystems shown in Figure 5.6, in turn, of their independent parts shown in Figure 5.7 and Figure 5.8; from Equations (5.18) through (5.21), we get

where

ke is the constant failure rate of the electronic and control subsystem.

А/, is the constant failure rate of the hydraulic pressure supply subsystem, is the constant failure rate of the gripper subsystem.

Arf is the constant failure rate of the drive subsystem.

Xp is the constant failure rate of the piping.

V is the constant failure rate of the hydraulic component.

Xcs is the constant failure rate of the control signal.

Xps is the constant failure rate of the pneumatic system.

A, is the constant failure rate of the joint /, for i = 1, 2, 3, 4, 5.

By integrating Equation (5.22) over the time interval [0,oo], we obtain where

MTTOHRUE is the mean time to the occurrence of the hydraulic robot undesirable event (i.e., undesirable arm movement causing damage to the robot/other equipment and possible harm to humans).

Example 5.8

Assume that the constant failure rates of the above type of hydraulic robot are Ae = 0.0008 failures/hour, Xp = 0.0007 failures/hour, khc = 0.0006 failures/hour, A0. = 0.0005 failures/hour, Xps = 0.0004failures/hour, and А,=А2=Аз=А45 = 0.0003 failures/hour. Calculate the mean time to the occurrence of the hydraulic robot undesirable event (i.e., undesirable arm movement causing damage to the robot/other equipment and possible harm to humans).

By inserting the given data values into Equation (5.23), we obtain

Thus, the mean time to the occurrence of the hydraulic robot undesirable event (i.e., undesirable arm movement causing damage to the robot/other equipment and possible harm to humans) is 222.2 hours.

 
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