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How does one go about testing the robot once it is built? How does one predict the number of hours it can operate? I see most of the industrial robots for instance robotic arms have warranty of 12-18 months, how did they arrive at such an estimate, clearly testing for 12-18 months is not on option, so what is the procedure for determining the lifespan?

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Testing of each individual robot produced (or any other product) is manufacturer and product specific. The tests will be small and quick, looking for unexpected problems in the manufacturing process.

Manufactures will test a few robots (that they don't sell) extensively so that they can make predictions about how the robot will perform over time, find unanticipated problems, learn how to improve future models, and how to manage customer expectations. Designs can be, and are, tested for years. The manufacturer will rely on good manufacturing practices and random sampling to insure that the actual device you receive has a performance similar to the tested devices.

Design engineers use lifespan calculations when designing. For many of the components like bearings, transmissions, and flexible wiring, the manufacturers provide data and calculations to estimate life based on the operating conditions. This data and calculations are derived from testing the manufacturer does on their own products.

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    $\begingroup$ Good answer. There is also an entire field of Reliability Engineering that is able to predict lifespans of devices by analyzing the test results from multiple units under test, for a shorter time period than the actual lifespan of the devices. There is also Highly Accelerated Life Testing, which stresses the devices in predictable ways to determine expected lifespans. It is an interesting field of engineering, based primarily on statistical measures of the performance of a small population of units. $\endgroup$
    – SteveO
    May 2, 2017 at 6:01
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In general, robotic arm is more mechanical than electrical. Manufacturers would use power law to increase vibration stress to accelerate life of their products. They will pick several product, estimate mean life and predict reliability and life of the model. It is called accelerated life test and can be used for failure analysis and life predict. Highly accelerated life testing (HALT) also accelerates life of product, but it cannot predict life range of tested unit. It is widely used to cause failures and thus improve design by exposing weakness of product.

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In order to analyze and predict the lifespan of an industrial robot arm correctly, two things need to be done:

  1. Calculate the lifespans of the individual components that can fail.

  2. Calculate the lifespan of the composite system of the robot arm.


The 2nd step is more straightforward.

If the mean time to failure (MTTF) of the $i$th component is $t_i$, the probability that the component will not fail before time $t$ is usually modeled with the exponential distribution:

$$R_i(t) = e^{-{t/t_i}}$$

The probability that a system with $n$ such components with MTTF $t_1$, $t_2$, ... $t_n$ will not fail is:

$$R(t) = e^{-\lambda t} = R_1(t)\cdot R_2(t) \cdots R_n(t) = e^{-t\left[ (1/t_1)+(1/t_2)+\cdots (1/t_n) \right]} $$ so that the MTTF of the overall system is given by: $$\frac{1}{\lambda} = \frac{1}{\frac{1}{t_1}+\frac{1}{t_2}+...\frac{1}{t_n}}$$


The first step is more difficult.

The essential components of the robot arm are the different revolute joints. In general, each joint includes an actuator with a motor and a gearbox, so the set of failure times that must be considered are: $$\left\{ t_{m1},t_{g1},t_{m2},t_{g2},...,t_{mD},t_{gD} \right\}$$ where $t_{mk}$ is the motor MTTF of the $k$th actuator, $t_{gk}$ is the gearbox MTTF of the $k$th actuator, and $D$ is the number of degrees of freedom in the arm.

But each of these will depend on the load - i.e. torque - that the motor or gearbox must sustain over time, and this can be difficult to calculate because it varies over time.

For example, a gearbox may be specified in terms of the number of cycles for which less than 10% of gearboxes tested under the same conditions might fail ($L_{10}$) under the application of some torque (e.g. rated torque). If one operates the gearbox at less than this particular torque, then $L_{10}$ will be longer, empirically according to some power law that depends on the gearbox design. For harmonic drives, for example, $L_{10}$ is roughly proportional to the cube of the torque:

$$L_{10}(T) \approx L_{10}(T_r)\left( \frac{T_r}{T} \right)^3 $$

Assuming failure times are exponentially distributed, $L_{10}$ and MTTF $1/\lambda$ are related: $$ L_{10} = -\frac{\ln{0.9}}{\lambda} $$

So to be rigorous, one needs to take into consideration the robot arms trajectory over time in order to understand the output torque at each joint over time and somehow compute how the lifetime is impacted. It is very complex. There is a paper here that discusses some simulations in this context.

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