Losses in Spring Stacks

As a disc spring in a column slides along the guide surface, it creates friction, which results in a loss of force within the stack. Since each disc spring in the stack contributes to this reduction in force transfer, the remaining spring force will progressively decrease from the moving to the fixed end while the stack is compressed, and could finally reduce to zero. For this reason, the individual discs will be loaded differently. The differing stresses generated can also lead to a variation in life of the individual discs within the spring stack. It is therefore recommended to use a compensating safety factor when designing longer spring stacks.
This non-uniformity of load distribution increases with greater stack length, and may lead to sudden undampened release of the full force of the spring. This is particularly true with springs having a large h0/t ratio. For this reason the stack should be made as short as possible. Where the design will not allow this, good lubrication and a smooth guide surface will reduce friction. In many cases, the use of suitable stabilizing rings will contribute to stack stability. Contact surfaces can also be ground or fine tuned on the discs. It should be noted that disc springs machined in such a manner always have a somewhat steeper character line because the effective lever forces are reduced. This increase is about 10-15%.
stack of belleville washers

Friction and Damping

Since Belleville disc springs also known as Belleville Washers are disc springs they are utilized in stacks, friction levels are higher than equivalent coil springs. It is important to incorporate this into the design to keep friction losses minimized. The spring cross section revolves around the virtual center S which lines on the radius Y0. To prevent the individual discs from moving laterally during deflection it is important that the loading cross section is rectangular. All four corners should be slightly radiused with a recommended radius of 12.5 percent of the material thickness. This is the case if the point of contact between the guide and the spring bore is below the horizontal line through the virtual center S in the unloaded condition of the spring bore during deflection. The same rule applies with respect to the external diameter of stacks with external guides. In the case of very high coned springs with a ratio of h0/t>1, this condition is not fulfilled. With these springs a reduction of the internal diameter during the stroke must be allowed. This can lead to radial displacement of the individual disc springs during the stroke.
  • Friction on the Guides: resulting from the sliding movement of the individual disc springs during the working stroke.
  • Internal Friction: due to elastic deformation which occurs in all elastically deformed steel parts.
  • Friction on the End Abutments: the end disc springs of a stack have a small radial movement on the abutment faces which causes friction.This friction also occurs when only one disc spring is used.
  • Friction through Parallel Stacking: this is as described in detail below.
When springs are used in parallel friction is generated in proportion to the number of discs in parallel. Stacks with parallel sets should be fitted where damping is required. Since friction is transferred to heat, the heat generated by springs in parallel sets can be considerable depending on the frequency. Good lubrication is essential to prevent fretting corrosion.
Many tests with various spring sizes confirmed these values. The deviations in practice from the theoretical character lines are as follows, depending on the number of springs in parallel (+ means increase in load, – means decrease in load): disc springs with contact surfaces create slightly less friction, particularly on larger stacks. Well radiused disc spring edges and careful manufacture of the guide components greatly help to reduce friction. A considerable reduction in friction is also achieved by use of a high pressure grease with a molybdenum base.