The effect of carrier locking position on the dynamic characteristics of gapless miniature linear guideway

The analysis of the load position of the miniature linear guideway is very important for the dynamic friction characteristics of the linear motion equipment. In this paper, a miniature guideway dynamic friction coefficient tester will be designed. And the effect of load position, movement speed, and load on the friction force of linear guideway will be investigated according to the gapless. The experimental results show that the friction force will be dependent on the load position, load, and movement speed. Among them, the lowest frictional load position can be obtained at any speed of movement and load condition, which occurs at the central load position. The main reason for this is that the effect of the moment is minimum. On the same load position and movement speed, then load is proportional to friction. In the case of fixed load and load position, the effect of velocity on friction is positively correlated in the longitudinal offset position. The frictional force is aggravated by the unevenly distributed pressure on the inner ball due to the moment generated by the slider. At the same time, by observing the loading and the inclination angle of the carrier in the experiment with the laser displacement meter, it can be found that the inclination angle also tends to increase when the load increases.


Introduction
Linear guideway is mainly composed of guide rails, sliders, and balls.They are widely used in the fields of tooling machines, semiconductor equipment, intelligent automation machines, medical equipment, and robots.For more efficient, accurate, and smooth motion, the friction force should be as low as possible.To study the frictional characteristics, this paper will be observed the load position, load weight, and movement rate.These three factors are the most directly related to the friction force based on the actual assembly conditions.The present study on the dynamic characteristics of the linear guideway is mainly focused on the contact stiffness, vibration, and friction characteristics of linear guideways during operation.Miura [1] and et al. investigated the frictional fluctuations generated in the motion of linear guideways.Wang et al [2] proposed a new dynamic reliability analysis method for linear guideways with random parameters of response error.Sakai and Tanaka [3] investigated the natural friction of linear guideways.Ling et al [4] proposed a numerical method for calculating the longitudinal stress distribution of linear guideways during straightening and for calculating the straightening stroke taking into account the stress inheritance behaviour.Zhang et al [5] developed an equivalent kinetic model of a ball screw feeding system using the aggregate parameter method taking into account the effect of acceleration and conducted a study on a ball screw feeding system driven by different accelerations. 2 Chlebus and Dybala [6] introduced a method to calculate the static properties of linear guideway contact using finite element analysis.In general, the study of the dynamic characteristics and service life of the linear guide is mainly focused on the roller ball linear guide and does not involve the significant effect of the load position on the dynamic friction characteristics.Therefore, this study takes a linear guideway as the research object and observes its friction change process under various conditions.Most of the previous studies on the detection of the dynamic friction coefficient of linear guideways are conducted manually.There is poor detection accuracy, the experimental method consumes time and labor costs, and there is a potential concern of insufficient reproducibility.Hence, the subsequent industry is developing automatic measurement equipment to solve the concerns of time consuming manual measurement and lack of reproducibility.So, this study is intended to focus on the frictional force generated by the linear guideway during the execution of motion.Based on the experimental design, it is expected that this study can improve the accuracy of the measurement of the coefficient of dynamic friction of the linear guideway, effectively detect its friction characteristics and calculate the product life of the linear guideway.

Pure rolling friction
When the rolling element is stationary and the contact point is subjected to a positive force N and a frictional force F (Figure 1).When both are rigid, the rolling moment M r is generated at the contact point against the horizontal force, and the horizontal force increases with F and M r under the influence of the positive force N. Rolling occurs when M r reaches M rmax , and sliding occurs when F reaches the maximum static friction force F s .The contact will generate a sufficient friction coefficient.In other words, when M r reaches M rmax , F is not at the maximum static friction force F s and pure rolling occurs.The condition is Where V cm is the center of mass velocity (m/s), ω is the angular velocity (rad/s), and r is the rolling body radius (mm).
To simulate the contact and friction of the rolling element in contact, the calculation of the rolling friction according to Hibbeler [7] can be derived from the following equation The moment can be expressed by the following equation In the formula (2) and, (3), and (4), M r is the rolling moment (N-m), N is the forward force (N), μ r is the rolling friction coefficient, F is the friction force (N), and r is the rolling body radius (mm)

Pure sliding friction
The direction of sliding friction is tangential to the contact surface, and the opposite of the relative motion of the object (Figure 2).Sliding friction is proportional to the positive force.The formula can be derived from the following equation where μ s is the sliding friction coefficient, F is the sliding friction force (N), N is a positive force (N).

Rolling friction with sliding friction
When the friction force is less than the rolling friction force and greater than the sliding friction force.
In this case, this friction is called rolling plus sliding friction.

Bending stress
The load at different load positions will have a great influence on the load-carrying capacity and friction during the operation of the slider.Therefore, by calculating the moment and bending stress, the variation of bending stress of the slider at each load position can be known.
where σ i is the bending stress (i.e.i=A, B, C, D) caused by different load positions: 1, 2, 3, 4 for the four corners of the slider in Figure 3, P is the force, A is the force area (i.e.slider area), M X is the Xaxis moment, M Y is the Y-axis moment, I X is the X-axis moment of inertia, I Y is the Y-axis moment of inertia, h' is the slider width, and b' is the slider length.
In equation ( 6), the X-axis moment and Y-axis moment based on Figure 3 are where h is the carrier width, b is the carrier length, and P is the force.The bending stresses caused by different load positions are calculated by taking the moments obtained in (6).The moment of inertia of the rectangle can be affected by the load position on the X-axis or by the moment on the Y-axis (Figure 3), therefore (9) where I X is the X-axis moment of inertia, I Y is the Y-axis moment of inertia, a is the width of the minislider, and b is the height of the mini-slider.

Tester system testing and design analysis
The friction coefficient test machine design is mainly divided into the test machine structure design module, as well as the test experiment flow design module, and the structure design module.It is mainly divided into the following two parts.

Power drive
First of all, in the power drive part, this study uses a servo motor with a ball guide screw to be the power transmission of the linear guideway dynamic friction coefficient test machine in this study.In the testing process of horizontal movement, this study uses a linear guideway with a slider and screw support to do the mutual matching.The technical efficacy and purpose of the design of the tester can be stabilized in the horizontal movement during the experiment.
The second part of the structural design module is the test sample installation.This study designs a test specimen testing mechanism, which mainly uses a linear guideway mounting mechanism.With the slider combination, this research's power drive is used to drive the test structure to pull the linear guideway.To achieve the purpose of reciprocal movement, the linear guideway slider is connected to the fixed point configuration sensor.

Experimental process
In the design and experimental stage of the tester system of this study, to make this study meet the actual needs of the industry, this study was installed according to the assembly method required by the current leading manufacturers in the industry.In this study, the dynamic friction characteristics of the miniature guideway were tested in the parameters of each speed and preload level under central load, longitudinal offset load, transverse offset load, and oblique offset load shown in Figure 4.

Experimental equipment
This study is on the structure of the dynamic friction coefficient measurement of linear guideways.
Mainly by the said machine base, the object to be tested mount, the slider limiting member, the track pulling mechanism, the fixed point configuration type sensor, and the sensing linkage member, etc.The miniature linear guideway dynamic friction coefficient tester is shown in Figure 5.

Miniature linear guideway dynamic friction coefficient tester
The test system of linear guideway is shown in Figure 5.In this study, there is a linear guideway mount to be used as the connection power transmission of the test system and the test mechanism of the linear guideway.A linear guideway loading carrier and test specimen holder will be used as the test specimen mount for test specimens.In the design of the lubrication part, this study will use the oil cup filling mechanism as the circulating oil lubrication system.In this study, the system is designed as a ball screw transmission system.The ball screw is used as the power source of the testing mechanism to drive the reciprocal motion of the testing mechanism and its loading carrier.

Test
The miniature linear guideway tested by this tester is small in size, light in weight, high in rigidity, and high in precision.Suitable for use in small machines and miniaturized equipment, so it can be applied to semiconductor manufacturing equipment, IC assembly, precision measuring instruments, and other precision and high-priced equipment.In this research, the material of the experimental sample is mostly made of stainless steel and alloy steel for testing.The sliders and the steel balls between the guideway are used for rolling guidance.The Gödel-type four-point contact design can withstand the load from all directions.The test machine can be highly rigid and have high-precision characteristics.

Linear guideway
In this study, the linear guideway module is used as the experimental sample for this study.In the part of the linear guideway module and slider, the content includes rail, slider, end cover, steel ball, etc.

Laser displacement sensor
The monitoring equipment used for the load carrier is the CD5-30A laser displacement sensor produced by OPTEX.The wavelength of the laser displacement meter is 650 nm/658 nm, the measurement range is 30±5 mm, the output power is 390 μm/1 mW/5 mW, the highest accuracy of measurement is 0.2 μm, and the vibration resistance is from 10 to 55 Hz in double amplitude.

Load cell
The load cell used in this study is the FUTEK model LSB200 tensile load cell for the micro load.The specifications are ±0.1% of RO for non-linearity, ±0.5% of RO for the hysteresis range, and 0.05% of RO for repetition accuracy.

Experimental design
In the power transmission part of the study, the test sample part is designed with a structural carrier.And the oil circulation device is designed to give the sample effective lubrication.The two are connected most effectively.
The granite carrier was used as a support at the bottom of the tester carrier (Figure 5).This study requires the overall granite carrier and the tester to be installed flat and parallel to give the most stable test table.In the test sample assembly, for the different accuracy levels of the miniature linear guideway, the running parallelism accuracy of the sliding seat relative to the base of the linear guideway is by the running parallelism accuracy with the change of the length of the guideway.Put the miniature linear guideway flat on the bed, and the base surface of the side of the guideway is aligned with the assembly surface of the bed, and try to lock the screw to confirm whether the bolt hole conforms.And fix the base surface of the miniature linear guideway roughly on the assembly surface of the machine table.Use the side fixing screws to lock the miniature linear guideway side datum surface to the bedside assembly surface to confirm the miniature linear guideway position.Use the torque wrench to tighten the bottom base surface of the miniature guideway to the bottom assembly surface of the bed table in order.

Results and discussions
Finally, measured the frictional forces of the linear guideway on the going and return movements when subjected to different carrier positions and different loads via the load cell are shown in Figures 6~13 and Tables 1~4.

Validation experiment
By collecting the experimental data and simulating the friction surface with the software, the results are shown in Figure 14.The prediction of the friction force is derived as follows.The predicted coefficient of determination (R 2 ) is 0.99938, which confirms the accuracy of the fitted surface.In addition, the results were verified by the experiment as shown in Figure 15.The experimental parameters were selected as follows: a load of 200 N and a speed of 800 mm/s.The software with the following equation estimated the experimental friction force to be 6.888N, and the experimental result was 6.654 N. The percentage error was 3.520%.Table 5 is the estimated experimental friction and percentage error using the prediction formula, and Table 6 is predictive estimation of friction for the central load forward strokes and error percentage.

Slider offset experiment
To understand the relationship between the results under the experimental parameters and the offset between the miniature linear guideway, a laser displacement sensor was set up and zeroed before the experiment by applying a load to each position on the carrier.The variation of the displacement captured by the laser displacement meter is used as the experimental deviation for investigation.
Figures 17 to 28 show the deviations of linear guideways subjected to different positions and different loads.Table 7 is the tilt angle for the different condition load experiment deviation.

Conclusion
In this paper, the dynamic frictional characteristics of the gapless miniature linear guideway are studied.The relationship between the friction force and the design parameters is discussed and the conclusion is as follows.
(1) In the load position and load are the same but different movement rates, the positive load position shows the friction change by the speed of the smallest trend.In the longitudinal offset position, there is a significant effect of speed on the friction force.This is because when the load is in the longitudinal position, the moment generated by the slider causes unevenly distributed pressure on the internal balls.This phenomenon tends to be aggravated by the speed effect.In the transverse offset load position, the friction force is not related to the movement rate.The reason is that when subjected to transverse load, the force in the single row steel ball is distributed evenly.In the oblique offset load positions, the miniature linear guideway is subjected to moments in both directions during motion.So the stability is low in this load condition.Therefore, there is no significant trend in the effect of rate on friction when it is already unstable.(2) It is observed that the frictional force increases with increasing load at any load position.It is obvious to observe that the frictional force tends to increase with the increase of load at any load position.Because of the influence of the moment, the positive load position can be subjected to a higher load than the other load positions.11 by taking the common load of the three respectively.As it is mentioned in point 1 of the above conclusion.The oblique offset load positions are subjected to the moment of torque in both directions when the miniature linear guideway is moving.Therefore, the stability is low under this load condition.So in the comparison of the longitudinal offset load position and transverse offset load position, it shows that the friction force in the transverse offset load position is higher than that in the longitudinal offset load position.This is because the moment applied at the transverse offset load position can be higher than that at the longitudinal offset load position.(4) The comparison results of the slider deflection characteristics are examined by laser displacement sensor.The results show that the maximum amplitude will not be changed by the level of experimental load, but the inclination angle will have a positive trend with the level of load.

Figure 3
Figure 3 is a schematic diagram of loading carrier, where point 1 is the position of central load, point 2 is the position of longitudinal offset load, point 3 is the position of transverse offset load, and point 4 is the position of oblique offset load.

Figure 11 .
Figure 10.Friction force for forward strokes.Figure 11.Friction force for back strokes.

( a )
Laser displacement meter measurement position.(b) When there is no load on the carrier.When the carrier has a load.(d) The difference between unloaded and loaded applied tilt angle and deflection are shown.Figure 16.Tilt angle and offset difference illustration.The tilt angle θ can be obtained by using the offset difference A and offset difference B and the measurement interval 220 mm is shows in Figures 16.The calculation method is θ = sin −1 ( |Offset differenceA|+|Offset differenceB| 220 )

( 3 )
When the load and velocity are the same, but the load positions are different.It is observed in the longitudinal offset load position, transverse offset load position, and oblique offset load position ICPMMT-2023 Journal of Physics: Conference Series 2631 (2023) 012015 IOP Publishing doi:10.1088/1742-6596/2631/1/012015

Table 1 .
.1.Experimental friction for the central load forward and back strokes Maximum friction range for positive load experiment.

Table 2 .
Maximum friction range for longitudinal offset load experiment.

Table 3 .
Maximum friction range for transverse offset load experiment.

Table 4 .
Maximum friction range for oblique offset load experiment.

Table 6 .
Predictive estimation of friction for the central load forward strokes and error percentage.

Table 7 .
The tilt angle for the different condition load experiment deviation.