## Digital Loading Gauge – precise measurement and adjustment of pressure load on top arm

###### Author: András Novák (R&D Engineer)

**Description of the system**

Swinsol’s Digital Lauding Gauge precisely measures the toparm pressure load and perfectly adjusts pressure settings – equally balanced between both side rollers.

A controlled pressure load reduces the one- sided friction on the cots, while guaranteeing constant production performance and yarn quality.

The top roller holder in a compact ring spinning machine presses the delivery roller to the bottom cylinder forced by a sheet metal spring. Due to the geometric conditions, the pressing force of the delivery roller impacts the pressing force of the top roller. In order to compensate this impact correctly, the exact amount of the change in force must be determined.

**Basic Calculations**

The top roller holder (pink) is connected to a spring-pushed arm (purple) through the top roller’s shaft (yellow) in point “A”. The top roller holder can rotate around this point. The spring-pushed arm is connected to the top arm with a pin in point “E”. The top roller holder is pushed to the bottom cylinder (green) by the sheet metal spring (white) in point “B”. The delivery roller (cyan) pushes the bottom cylinder in contact point “C”. And at least the top roller pushes the bottom cylinder in contact point “D”.

The force in point “C” – which is generated by the top roller holder – affects the contact force of the top roller in point “D”. The purpose of the following calculation is to show how much the magnitude of the force affected in the radial direction at point “D” has changed.

##### Part 1

We start by calculating the reaction force in the top roller holder at point “A”. The top roller holder has three specific points where the forces act. The reaction force is applied at point “A”. The sum of the moments of the forces acting on this point must be zero. Since the connection of the component here allows rotation. In point “B” the force of the sheet metal spring is applied. We can assume the direction of the force to be perpendicular to the contact surface (because of the low friction between the spring and the end of the top arm). In point “C” the pushing force of the delivery roller is applied. Since two rollers are in contact here, the force must be radial and there is no torque. As the line of action of this force passes through the connecting axis of the top roller holder and the delivery roller, point “C” can be considered as part of the top roller holder (due to the offset of the forces in the direction of their line of action).

The basis of the calculation is that the sum of the torques of the forces acting on point “A” is zero.

The *F _{A }*reaction force cannot exert a torque on point “A”. Therefore, the moment which can be calculated at point “A” will be the sum of the moments exerted by the forces acting at points “B” and “C”.

The pushing force of the delivery roller on the bottom cylinder is:

Due to the contact point of the rollers, the direction of this force is:

Take point “A” as the origin. The position of point “C” is as follows:

We can calculate the moment of the *F*_{c }force at point “A” as follows:

The distance between the two points:

The distance between point “A” and the line of action of the force:

The torque of the F_{c }force on point “A”:

The moment of the F_{B }force at point “A” as follows:

The position of point “B” from the origin:

The direction of the force generated by the spring:

The distance between the two points:.

The distance between point “A” and the line of action of the force:

This negative value means that the force will generate a torque to the opposite direction on point “A”.

The torque of the* F _{B} *force on point “A”:

Which means:

Substituting this into the torque equation:

In a closed system, the vectorial sum of the forces is zero.

The reaction force *F _{A}* can be decomposed into its components according to the two coordinate axes.

The x-axis component:

The y-axis component:

The reaction force *F _{A}*:

Because *F _{Ax}* < 0 , the direction of the reaction force:

##### Part 2

We continue by calculating the forces on the spring-pushed arm (purple). The spring-pushed arm has three specific points where the forces act. At point “E” the reaction force is applied. The sum of the moments of the forces acting on this point must be zero. Since the connection of the component here allows rotation. At point “A” the reaction force of the top roller holder acts.

The arm of the bottom cylinder pushes through the top roller at point “D”. There is a fourth point, where the main spring pushes the arm, but since we are calculating the force difference caused by the top roller holder, it is not necessary to calculate with this.

The method is the same as in the first part. The sum of the torques of the forces acting on point “E” is zero.

The moment that can be calculated at point “E” will be the sum of the moments exerted by the forces acting at points “A” and “D”.

The force at point “A” is equal with the reaction force of the top roller holder:

However, the direction of this force is opposite:

Take point “E” as the origin. The position of point “A” is as follows:

We can calculate the moment of the *F _{A}’* force at point “A” as follows:

The distance between the two points:

The distance between point “E” and the line of action of the force:

The torque of the *F _{A}’* force on point “E”:

The top roller can freely rotate around point “A”, therefore the force at point “D” must be radial to the top roller. Since the force passes through points “A” and “D”, it makes no difference which of the two points we calculate on.

According to the geometry, the direction of this force is:

The position of point “D” from the origin:

The distance between the two points:

The distance between point “E” and the line of action of the force:

The torque of the *F _{D}* force on point “E”:

Substituting this into the torque equation:

The force which the top roller holder takes from the spring-pushed arm:

This means that as a result of the 39.19 N force exerted on the delivery roller, this design takes 33 N force off from the top roller.

##### Measurements

In the following we prove the correctness of the calculations. The best way for checking the load on the rollers is to use Swinsol’s Digital Loading Gauge. This tool precisely measures the pressing force of the shaft – individually on both sides.

We measure the load of the delivery roller. When using Swinsol’s Digital Loading Gauge it is very important to set the gauge in the parallel direction of the acting force between the roller and the bottom cylinder. This direction will always be radial to the contact point.

The measured load of the delivery roller is 2.01 kg on the left side and 1.985 kg on the right side.

The sum of the forces are:

Now we measure the load on the top roller. Since we would like to know the impact of the delivery roller, we measure with and without it. Then we subtract the two results from each other. The measured load of the top roller without the top roller holder is 9.345 kg on the left side and 9.325 kg on the right side.

The sum of the forces are:

Now we reassemble the top roller holder, the spring and the delivery roller, and measure the load of the top roller. The measured load of the top roller with the top roller holder is 7.665 kg on the left side and 7.65 kg on the right side.

The sum of the forces are:

The measured loading force difference of the top roller is:

##### Summary

In our recent analysis, we evaluated the impact of a delivery roller on the load distribution between rollers in a spinning setup. The delivery roller is applied to the bottom cylinder using a sheet metal spring, which in turn influences the load on the top roller.

To quantify this effect, Swinsol’s Digital Loading Gauge was used to measure the exact pushing force exerted by the delivery roller. From these measurements and the known geometric conditions, we calculated the corresponding reduction in the load on the top roller.

Our findings showed that when the delivery roller applies a force of 39.19 N, the top roller’s load is reduced by 33 N. Experimental validation further confirmed this, with the measured force adjustment being 32.91 N—closely aligning with the calculated value. This consistency underscores the accuracy of our method.

In practical terms, this means that when installing the delivery roller, the load on the top roller must be increased by approximately 3.4 kg to maintain optimal spinning performance. This adjustment ensures that the same spinning effect is achieved, allowing for precise control and improved efficiency in the spinning process.