Energy optimization by Robust Design - enabling CO2 emission reductions - RD8

Energy optimization by Robust Design – enabling CO2 emission reductions

GHG Scope 3

CO2 emissions reduction by energy optimization

50% – 100% reduction of energy loss in dynamic interfaces in product population outliers

Higher performance of all products in a production series (population). Elimination of energy loss in a population of products by eliminating friction in dynamic interfaces.


19% energy savings by robust design

A simple example for illustrating the effect of over constraints in designs with moving mechanics: a rotation shaft supported by 3 bearings in a frame. The result of a kinematic review of this design is that it is over-constrained in the y-direction by the middle bearing and over-constrained in Rz by all 3 bearings.

For this example – the only impact of the “y” over constraint is considered.

Illustration of over constraints in the design.

The effect of the over constraint in the y-direction is illustrated to the right. 

A deflation of δ is simulated.

For this example, a δ variation of 0.2 mm is assumed (due to tolerance variation).

Illustration of a deflection of center bearing.

Simulation of the shaft in FEM (Finite Element Method)

results in stiffness of the shaft of:

The resulting force, F_R, from the assumed deflection, is given by:

The friction force F_μ can be calculated by multiplying the friction coefficient by the radial force F_R. The friction in the bearing is assumed to be 0.1 – resulting in a friction force F_μ:

The friction force can be used to calculate a torque loss due to the over constraint. This is given by the friction force multiplied by the radius. The radius, in this case, is r = 5mm.

The conclusion is that the over constraint will add an additional 335Nmm in resistance for the shaft to rotate. This torque the user or motor will have to overcome. It will need to be evaluated if it can be accepted.

Assuming a fictive case where a 2.0 Nm output is needed from a motor driving the shaft.

Due to the noise from the over constraint in the worst case tolerance scenario, it was calculated that an additional torque of 0.335 Nm is needed.

This is equivalent to 0.04 kW. 

In the ideal case where there is no variation – 0.21 kW is needed to provide a 2.0 Nm output (1000 RPM assumed).

In the worst case, the motor will need to provide 2.3 Nm output as 0.3 Nm will be consumed for friction in the system. 

When comparing the ideal and worst-case scenario, it is seen that a 19% additional energy consumption is present.

By robust design the noise can be eliminated and thus the additional 19% energy consumption can be saved. 

By robust design, the goal is to eliminate all energy loss from samples that are off target. 

By eliminating over constraints in the design this can be achieved.

An average mechanical product have app. 10 – 20 over constraints per interface – thus if involved in dynamic relations this leads to a energy loss. By systematically eliminating these it is anticipated that 50%-100% of the energy loss due to over constraints can be eliminated by robust design. 


The example is illustrated in the figure to the right:

  • In the target case where shaft and bearings are perfectly aligned there is no energy loss
  • The more the tolerances drift – the more the effect of the bearing arrangement over constraints come into play (visualized by orange / red colors)
  • By Robust Design alternative designs (represented by a green cloud) the energy loss can be eliminated thus moving the distribution towards target center with 0% energy loss.

Energy loss can be converted into CO2 emissions equivalents.

Histogram: distribution of products and energy loss due to misaligned bearing arrangement.


35% reduction of over-engineering

Another effect of the over-constraint design and the need for a larger motor is over-engineering.

To ensure that the product will work during worst case situations (where additional torque is needed – as illustrated above) the designers need to accommodate this situation by dimensioning the product to this worst case. In this example a motor with a sufficient torque output is needed. In nominal condition a motor of 2.0 Nm is needed – for worst case a 2.3 Nm motor is needed. In many cases a safety factor is needed, hence an even bigger motor is needed. For this example a 2.5 Nm motor is chosen as this is a standard component.

One of the effects of this is added weight. In this case for a stepper motor the weight difference is 0.35 kg  – hence more material consumption in both motor and the rest of the product-construction. This is referred to as over-engineering. Furthermore cost is often also effected by over-engineering.

Illustration: 35% added weight due to over engineering

Illustration of over-engineering

Reach out at for a perspective on how Robust Design can add energy savings to your products.

Robustness Philosophy

Axiomatic design & classic robust design on top of a foundation of kinematic design.

Design for sensitivity, complexity reduction and decoupling – based on a kinematic design foundation.

RD8 Robust Design Philosophy