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LX Units - Calculating service life using preselection and calculation tool

ConstructionLinear Motion

Industrial reliability and longevity are key – especially for linear units that operate under high loads and in demanding production environments. But how can you accurately determine the service life of a linear unit? This blog post will show you how to precisely calculate the service life and what factors affect the durability of your systems. Avoid unplanned downtime, optimize your maintenance intervals, and rely on the precise design of your linear components.

Calculating service life

The service life of a linear unit is determined by the durability of its individual major components. This includes, among other things, the profile rail guide with guide carriage, the bearing unit of the ball screw drive, and the ball screw drive itself. The interaction between all these carefully matched components ensures precise movement and high stability of the system . The individual mechanical components of a linear unit are subject to different loads and wear mechanisms. The service life must therefore be calculated separately for each of the main components. The guide rail supports the load and provides precise movement, while the ball screw converts the rotary motion into linear motion, while also absorbing axial loads. The bearing unit in turn must be able to absorb the forces and moments that occur and to efficiently transfer them to the housing of the linear unit. Since the service life of the entire linear unit is limited by the component that fails first, the shortest calculated service life must be used as a reference value for the entire unit.

Prerequisites for calculating the service life of linear units

The service life calculation begins by selecting a temporary model number for the linear unit. This is usually based on the following underlying parameters:

  • Effective stroke ls (mm): The actual stroke of the linear unit to be traversed in one direction of travel during a duty cycle.
  • Load mass W (kg): Weight of the transported load acting on the linear unit.
  • Maximum speed v (mm/s): The highest speed achieved during operation.

This selection serves as an initial guideline for determining a suitable model with sufficient load capacity and dynamics. After an initial model selection is made, a speed diagram (v-t diagram) must be developed for the application.

What is a v-t diagram?

A v-t diagram or a speed diagram is used to represent the planned movement cycle of the linear unit over time. It thus visualizes the travel speed of the guide carriage over the distance traveled from the starting point to the end point (stroke).

The individual phases traversed by the guide carriage, such as acceleration, constant speed, and deceleration, can thus be more easily evaluated when visualized in this manner. The linear guide motion profile may differ between the forward and return paths. A v-t diagram is therefore created for both the forward and return paths.

The created v-t diagram helps to estimate the load on the mechanical components, in particular guide elements and drive. This information is essential for the service life calculation, as acceleration and braking phases, peak loads, and constant speeds affect the strain on the unit. The conditions set for the speed diagram will later serve as the basis for the selection and service life calculation.

Example illustration of a v-t diagram
Example illustration of a v-t diagram

The complete cycle of a linear unit consists of the path from the start-point to an end-point and back to the start-point. The v-t diagram only looks at one of the two paths and, in our example, assumes identical values for the return path.

What does a v-t diagram show?

The speed diagram of a linear unit shown here follows a trapezoidal graph: After an acceleration phase, the system reaches the maximum speed, moves at a constant speed over a certain distance, and then enters the braking phase until it stops. On the return path, this cycle repeats itself in our example. Depending on the application, the v-t diagram may on its path from the start-point to the end-point also feature multiple acceleration and deceleration phases or non-linear accelerations or decelerations. The same applies to the return path.

Example illustration of a v-t diagram with acceleration, constant, and braking phases
Example illustration of a v-t diagram with acceleration, constant, and braking phases

Maximum number of cycles per minute

A linear unit not only moves once from a defined starting point to a target point, but also repeats this movement continuously. A complete cycle always includes:

  • a forward movement
  • a return movement

The v-t diagram therefore describes part of this cycle (forward or reverse). The total time is therefore analyzed to determine the maximum cycles possible per minute, as indicated by the v-t diagrams for the forward and return paths.

Example calculation

The following determines the times and cycles that are relevant for the service life calculation using specified example parameters:

vmax = 250 mm/s (maximum speed)
a = 833 mm/s2 ( acceleration)
ls = 200 mm (effective stroke)

It is assumed that the acceleration phase (t1) and deceleration phase (t3) are linear and symmetric.

t1 = accelerate
t2 = constant speed
t3 = decelerate

t_{1} = t_{3} =\frac{V_{max}}{a} = \frac{250mm/s}{833mm/s^2} = 0,3s

Paths l1 for acceleration and l3 for deceleration

l_{1} =l_{3}= \frac{1}{2} \times a \times t_{1}^{2} = \frac{1}{2} \times 833mm/s^2 \times 0,3s^{2} = 37,5mm

Path l2 at constant speed

l_{2} = l_{s} - l_{1} - l_{3} = l_{2} = 200mm - 37,5mm - 37,5mm = 125mm

Time t2 at constant speed

t_{2} = \frac{l_{2}}{V_{max}} = \frac{125mm}{250mm/s} = 0,5s

Cycle time t (forward and return movement)

t_{Zyklus} = \left\{t_{1} + t_{2} + t_{3} \right\} \times 2 = \left\{0,3s + 0,5s + 0,3s\right\} \times 2 = 2,2s

Maximum number of cycles per minute

\frac{60s}{2,2s} = 27,27min^{-1}

Exerted load and moments

The exerted load W is one of the main factors influencing the service life of a linear unit, as it directly affects mechanical components such as the guide rail, ball screw, and bearings. Unfavorable load distribution or excessive loading can lead to premature wear and consequently to a shortened service life.

Example illustration of the position and effect of load W
Example illustration of the position and effect of load W

In principle, the following applies: The higher the load, the greater the stress on material and the shorter the service life. In particular, the guide rail and the rolling bearings are subject to higher fatigue, since they are subjected to greater stress due to the increasing weight.

Not only the absolute magnitude of the load is critical, but also the nature and distribution of the load. Eccentrically acting loads, for example, generate tilting moments that result in one-sided loading on the guide and in non-uniform wear. Dynamic loads resulting from high accelerations, shocks, or rapid changes in direction expose the mechanics to high alternating loads. These require robust construction with vibration damping properties and precise bearing selection.

Load moments on an LX unit with one guide carriage
Load moments on an LX unit with one guide carriage
Load moments on an LX unit with two guide carriages
Load moments on an LX unit with two guide carriages

The exertion of forces plays a crucial role for the design and service life calculation of a linear unit. This force represents the load to be moved or absorbed and can act in all three spatial directions (x, y, z). However, not only is the absolute magnitude of the force critical, but also where it is introduced and how it is distributed. If it is exerted eccentrically, i.e. not precisely at the center of gravity, additional moments are created, which are described as rotational loads.

These moments work together with the actual load force and often exert more stress on the linear unit, as they can create uneven forces within the guide carriages and bearing units, thus accelerating wear.

The reference metric for the exact specification and analysis of these loads is the zero point of the linear unit. All position data, force introductions and moments are clearly defined in relation to this zero point so that load conditions can be calculated consistently and reproducibly.

Preselection of an LX unit for calculating the service life

For LX linear units, we therefore consider the 3 fundamentally affected areas:

• Guide rail
• Ball screw drive
• Bearing unit

Some LX linear units can also be equipped with 2 guide carriages. Since an LX unit with one guide carriage is loaded differently than with 2 guide carriages, the load capacity for calculating the service life must be determined depending on the number of carriages. Similarly, due to gravity and the resulting moments, it makes a difference whether the LX unit is operated horizontally, vertically or horizontally on its side.

Step 1: Narrowing down based on the required effective stroke

Before the service life can be calculated, it is first necessary to check whether a specific length or type series even has the technical specs to cover the required travel distance (stroke). From an economic point of view, the smallest possible series that meets the required conditions is usually preferred.

Table: LX units - effective stroke by series and rail length
Type With MX lube unit Carriage Rail length (mm)
75 80 100 125 150 175 200 250 300 350 (340)* 400 (390)* 450 (440)* 500 (490)* 550 (540)* 600 (590)*
LX15 - Long, 1 pc 26.9 - 51.9 76.9 101.9 126.9 151.9 - - - - - - - -
MX Long, 1 pc - - 43.9 68.9 93.9 118.9 143.9 - - - - - - - -
LX20 - Long, 1 pc - 16.5 36.5 - 86.5 - 136.5 186.5 236.5 - - - - - -
MX Long, 1 pc - - - - 76.5 - 126.5 176.5 226.5 - - - - - -
- Long, 2 pcs - - - - - - 79.5 129.5 179.5 - - - - - -
LX26 - Long, 1 pc - - 17 - 67 - 117 167 217 267 317 - - - -
MX Long, 1 pc - - - - - - 105 155 205 255 305 - - - -
- Long, 2 pcs - - - - - - - 91 141 191 241 - - - -
LX30 - Long, 1 pc - - - 29 54 - 104 154 204 254 304 354 404 454 504
- Short, 1 pc - - - 54.5 79.5 - 129.5 179.5 229.5 279.5 329.5 379.5 429.5 479.5 529.5
MX Long, 1 pc - - - - - - 90 140 190 240 290 340 390 440 490
MX Short, 1 pc - - - - 65.5 - 115.5 165.5 215.5 265.5 315.5 365.5 415.5 465.5 515.5
- Long, 2 pcs - - - - - - - - 116 166 216 266 316 366 416
- Short, 2 pcs - - - - 17 - 67 117 167 217 267 317 367 417 467
LX45 - Long, 1 pc - - - - - - - - - 210.4 260.4 310.4 360.4 410.4 460.4
- Short, 1 pc - - - - - - - - - 24.97 297.9 347.9 397.9 447.9 497.9
MX Long, 1 pc - - - - - - - - - 194.4 244.4 294.4 344.4 394.4 444.4
MX Short, 1 pc - - - - - - - - - 231.9 281.9 331.9 381.9 431.9 481.9
- Long, 2 pcs - - - - - - - - - 88.8 138.8 188.8 238.8 288.8 338.8
- Short, 2 pcs - - - - - - - - - 163.8 213.8 263.8 313.8 363.8 413.8
Effective stroke dimensions include 2.5 mm margin at each end
* ( ) Rail length for LX45

This example table shows that several types of linear units are suited for the required travel distance (stroke), starting at a construction length of 300 mm. The smallest suited size is used as the basis for further preselection and service life calculation. This procedure permits a design optimized for cost-efficiency. A switch to larger variants may gradually be required only when it is shown in a later step that the smallest selected size does not withstand the loads.

In the given example, with a frame size of 300 mm, the linear units LX20, LX26 and LX30 are suited for the effective stroke of 200 mm required in our example calculation.

Step 2: Narrowing down based on the permissible load

After selecting all linear units in the first step that can at least cover the required effective stroke, the second preselection step is the verification of the required load capacity. The user must therefore check whether the previously filtered linear units can accommodate and move the specified load mass W. For this purpose, the load ratings from the manufacturer data sheets are used.

Approximate preliminary determination of the expected force exertion

F_{e.max} = m * g = 10kg *9,81m/s^2 =98,1N
Table: LX units rated load
  Type LX1502 LX2001 LX2005 LX2602 LX2605 LX2610 LX3005_B LX3010_B LX3005_S LX3010_S LX4510_B LX4520_B LX4510_S LX4520_S
Carriage Long Long Long Long Short Long Short
Guide rail Dyn. basic load C0 (N) 2072 3277 6522 9732 6305 18450 11826
Static load rating C0a (N) 3701 6199 11871 17218 9271 32441 17175
Radial play (mm) -3…0 -3…0 -4…0 -4…0 -4…0 -6…0 -6…0
Ball screw drive Dyn. load rating C0 (N), high 208 482 822 1712 1600 782 1831 1129 1831 1129 4167 2499 4167 2499
Static load rating C0a (N), high 265 642 1026 2251 2097 961 2389 1386 2389 1386 5945 3381 5945 3381
Screw shaft dia. (mm) 5 6 6 8 8 8 10 10 10 10 15 15 15 15
Lead (mm) 2 1 5 2 5 10 5 10 5 10 10 20 10 20
Core dia. 4.534 5.3 4.918 6.4 6.46 6.46 8.2 8.2 8.2 8.2 11.7 11.7 11.7 11.7
Ball center dia. 5.15 6.15 6.3 8.3 8.3 8.3 10.3 10.3 10.3 10.3 15.5 15.75 15.5 15.75
Bearing (axial) Dyn. load rating Ca (N) 678 730 1637 2702 2702 4355 4355
Perm. static load C0a (N) 415 461 1205 2197 2197 4106 4106
Rail load ratings apply per carriage. Use our technical calc software to calculate actual service life

The comparison of the dynamic load ratings C0 with Fe.max shows that the linear units LX20, LX26 and LX30 are suited.

Step 3: Narrowing down based on maximum speed

After preselection based on the effective stroke and the load capacity, the third step is to check whether the remaining linear units can reliably reach the required maximum speed.

Table: LX units - max. travel speed (mm/s)
Type Lead
(mm)		 Rail length (mm) Rail length (mm)
75 80 100 125 150 175 200 250 300 350 400 450 500 550 600 340 390 440 490 540 590
LX15 2 330 - 330 330 330 330 330 - - - - - - - - - - - - - -
LX20 1 - 190 190 - 190 - 190 - - - - - - - - - - - - - -
5 - - 694 - 694 - 694 694 633 - - - - - - - - - - - -
LX26 2 - - 290 - 290 - 290 290 290 - - - - - - - - - - - -
5 - - - - 521 - 521 521 521 521 446 - - - - - - - - - -
10 - - - - 1040 - 1040 1040 1040 1040 890 - - - - - - - - - -
LX30 5 - - - 410 410 - 410 410 410 410 410 410 370 300 250 - - - - - -
10 - - - - 830 - 830 830 830 830 830 830 740 600 500 - - - - - -
LX45 10 - - - - - - - - - - - - - - - 550 550 550 550 550 550
20 - - - - - - - - - - - - - - - 1110 1110 1110 1110 1110 1110
The values listed in the table are reference values calculated from the critical speed of the ball screw and the ball screw diameter.
Please note these are not guaranteed values based on motor speed and operating conditions.

The table shows that all three series can reach the specified maximum speed of 250 mm/s with a length of 300 mm.

However, the analysis cannot be strictly limited to travel speed and loading of the components, but must also take into account the mechanical design, in particular the pitch of the ball screw drive. The pitch of a ball screw determines how much linear travel the guide carriage covers per revolution of the lead screw. As a rule, the positioning accuracy and the repeatability of the ball screw drive become more precise with a smaller thread pitch; therefore, the search is made for the smallest pitch at which the maximum planned travel speed can be achieved. In this case, this would be the linear unit LX2602 with a pitch of 2 mm per revolution.

As the cycle is executed, speeds vary during the acceleration, constant speed, and deceleration phases. In addition, these phases are usually also of different lengths. An average speed must therefore be used when considering the service life.

Calculating the average speed nm with the unit LX2602

n_{2} = {\frac{(\frac{l_2}{p})}{t_{2}} \times 60} = n_{2} = {\frac{(\frac{125mm}{2mm})}{0,5s} \times 60s/min} = 7500 (min^{-1})
n_{1} = n_{3} = \frac{7500(min^{-1})}{2} = 3750(min^{-1})
n_m = \frac{n_1 \times t_1 + n_2 \times t_2 + n_3 \times t_3}{(t_1 + t_2 + t_3)}
n_m = \frac{ 3750(min^{-1}) \times 0,3s + 7500(min^{-1}) \times 0,5s + 3750(min^{-1}) \times 0,3s}{(0,3s + 0,5s + 0,3s)} = 5454,55 (min^{-1})

Example calculation for comparison with p = 5 mm pitch (LX2605)

n_{2} = {\frac{(\frac{l_2}{p})}{t_{2}} \times 60} = n_{2} = {\frac{(\frac{125mm}{5mm})}{0,5s} \times 60s/min} = 3000 (min^{-1})
n_{1} = n_{3} = \frac{3000(min^{-1})}{2} = 1500 (min^{-1})
n_m = \frac{1500(min^{-1}) \times 0,3s + 3000(min^{-1}) \times 0,5s + 1500(min^{-1}) \times 0,3s}{(0,3s + 0,5s + 0,3s)} = 2181,82 (min^{-1})

The pitch should always be selected in connection with the requirements of the application. Different applications place different priorities on force, speed, accuracy, or dynamics. The user must therefore select the combination suited for the respective application, taking into account all of these aspects.

Summary of all predefined, derived, and determined parameters

Linear unit preselection: LX2602

• Load mass W: 10 kg
• Maximum allowed revolutions: 6000 RPM • Maximum speed vmax: 250 mm/s
• Acceleration a: 833 mm/s2
• Alignment: horizontal
• Effective stroke (Travel Distance) Ls: 200 mm

calculated values:

t1 = 0.3s (time of acceleration)
t2 = 0.5s (time at constant speed)
t3 = 0.3s (time to decelerate)
l1 = 37.5mm (path for acceleration)
l2 = 125mm (path at constant speed)
l3 = 37.5mm (path for deceleration)
nm= 27.27 (maximum number of cycles per minute)

Based on the determined values, the linear unit LX2602 with a length of 300 mm can be selected as a preliminary choice. This pre-selection is temporary and needs to be reviewed. The MISUMI calculation tool can be used for this check.

Calculate service life using MISUMI’s calculation tool

The calculation tool enables fast and accurate calculation of linear unit service life. Automated input and processing of relevant parameters such as load, speed, and mounting direction can reduce sources of error and accurately simulate realistic load scenarios. The tool also provides descriptive graphics such as v-t diagrams, which visualize the motion profile and show optimization opportunities. By adjusting the input values, different configurations can be directly compared, which in turn allows a more efficient selection of the appropriate linear unit. The calculation process is divided into four steps. Note that the calculation tool requires numerical values to be entered in English format, i.e. the decimal separator is shown as a point.

Selecting the Linear Unit

In a first step, the specific model of the LX series is selected in the calculation tool. Enter the total length of the linear unit here and determine how the unit will be installed and what forces will act on it.

The following values can be entered using the calculation example above:


• Part Number: 2602
• Version: high quality, without cover
• Number of carriages: 1
• Length: 300 (mm)
• Alignment: Horizontal

Operating conditions

The operating conditions that are important for the service calculation are defined in a second step. This includes, among other things, the distance between two carriages (lb), if two carriages are used. The maximum possible travel distance (lmax) depends on the base length entered in the previous data entry screen. The safety factor or load coefficient (fW) takes into account various external influences, such as vibrations, shocks, or uneven load distribution. These vary depending on the selected operating conditions.

• Travel Distance ls: 200 mm
• Speed v: 250 mm/s
• Accelerating/braking t1: 0.3 s
• Cycles per minute n1: 27.27
• Load coefficient fw: 1.2 (results from the operating condition selected below)

Operating conditions: no external influences due to vibration and low speed, calculated from the maximum travel speed:

\frac{250 mm/s \times 60 s}{1000 mm/m} = 15 m/s

Assembly conditions

The assembly conditions are taken into account in the third step of the calculation. This step defines how the load affects the linear unit. The weight and center of gravity location values are important because they determine the forces and moments acting on the linear unit. Eccentric loads with high X or Y values create additional tilting moments that can place more stress on the unit and shorten its service life. Uneven load distribution affects stability, causes uneven wear, and may increase friction. If large moments occur, it makes sense to choose a second guide or a more stable design to better absorb the load and optimize the service life. Entering the values permits calculating the load and possible tilting moments correctly.

Our application example assumes a mass W of 10 kg with the following center of mass in the coordinate system:

• X = 0 mm
• Y = 17mm
• Z = 26mm

Coordinate system with one guide carriage
Coordinate system with one guide carriage
Coordinate system with two guide carriages
Coordinate system with two guide carriages

Calculation and results

In the final step, the results are determined and displayed based on the entries. The calculation is performed for all three areas: the guide rail, the ball screw, and the bearing unit. The service life is specified by the calculation tool in kilometers, hours, and years, making it easier to compare with other applications and service life values. The determined values can be saved as an HTML report. This has the advantage that different constellations can be calculated and easily compared with each other.

Finally, the service life values of the three main components are clearly compared in table form. Because the shortest service life is critical to the overall life of the LX linear unit, this value is used as the basis for evaluating the entire unit. If the service life of only one of the three components falls short of the application requirements, the calculation must be performed again with a larger-sized unit.

Only when all individual components meet the specifications and their service life is sufficiently dimensioned can the considered LX linear unit be classified as suited and approved for use.

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