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Profile Rail Guides - Allowable Loads of Linear Guides
In industrial applications, precision and reliability are important – especially for profile rail guides used in demanding conditions. But how can permissible loads be calculated correctly to minimize the risk of failure while maximizing efficiency? In our blog, we explain the key calculation variables, such as dynamic and static load capacity, and provide insights into the distribution of forces and moments. Benefit from in-depth expertise that helps you design your applications.
Correctly Calculate Allowable Loads
From dynamic and static load capacity to the effect of load moments to varying load scenarios, the correct calculation of the permissible load determines the suitability, efficiency, service life and reliability of profile rail guides or Linear guides. In this blog, we explore the various influencing variables, show how load moments are analyzed and calculated, and explain the influence of load changes on the design of linear guides.
When designing and calculating a linear guide, it may be useful to take a closer look at the different types of profile rail guides, their basic properties and permissible loads. In addition to precision, torsional stiffness and load capacity, each system has different characteristics and properties in terms of space requirements, ease of maintenance, travel speed and so on. The process in which the linear guide is integrated should also be carefully analyzed. What forces, moments, and travel speeds are expected? It must also be considered here whether the main load occurs primarily when the guide carriage is stationary (static) or when the guide carriage is moving (dynamic).
In order to determine the basic suitability of a profile rail guide for a specific load scenario, basic parameters for the different versions and sizes are provided by the manufacturer. These parameters include, among others, the dynamic load rating C, the static load rating C0, as well as the permissible static moments in the pitch direction, yaw direction, and roll direction.
As a Japanese manufacturer, MISUMI specifies the dynamic load ratings and load moments for its linear guides and profile rail guides with ball rolling elements, deviating from DIN ISO 14728-1, based on a travel distance of 50 km.
Dynamic load rating for profile rail guides
The dynamic load rating C is the maximum load a profile rail guide can support during operation under motion without affecting the expected service life. Exceeding the dynamic load rating will result in bearing overload, causing premature failure or reduced precision and significantly shortening the expected service life. In practice, a system is never operated at the limit of the actual load capacity, but always taking into account a safety reserve. The values C and C0 are then used to determine the remaining safety factor. The dynamic load rating depends on the design of the guide, the materials used, and the number of contact points. Systems with higher dynamic load ratings can handle heavier loads.
Static load rating for profile rail guides
The static load rating C0 is the load at which a permanent deformation of 0.01% of the diameter of the rolling element is created at the contact points between the tracks and the rolling elements. It is an important measure for applications where the system is exposed to static loads for extended periods of time, such as positioning tasks. Exceeding the static load rating can cause permanent damage and loss of precision. Just like with the dynamic load rating, a safety reserve is always taken into account for the actual design of the profile rail guide in practice.
The static safety factor
The static safety factor fs is another characteristic when designing profile rail guides.
It describes the relationship between the manufacturer’s rated static load capacity C0 and the actual static load P acting on the guide.
Similar to the load capacity C0, the static safety factor is also used for the static moment loads of the profile rail guide and here describes the ratio between the static moments specified by the manufacturer (MA , MB , MC) and the static moments actually acting on the guide in the spatial coordinate system (Mr , Mp , My). The static safety factor thus indicates how far the actual maximum expected load of the profile rail guide is below its load limit.
A valid calculation of the actual load of a profile rail guide is very extensive and requires precise knowledge of all loads and stresses that may occur. Therefore, empirically determined values are used to simplify the calculation. The static safety factor f s is such an empirical value. It allows a simplified adaptation of the values calculated for the static state to the actual expected operating conditions. A higher selected f s value increases the safety margin in the design of the profile rail guide and makes failure due to overloading less likely. At the same time, choosing a factor that is too large can lead to oversizing. In practice, the empirically determined safety factors must be taken into account as a common simplification to ensure that the loads are always below the limits.
The recommended values for the static safety factor vary depending on the application area and the operating conditions.
| Operating conditions | Lower limit of fS |
|---|---|
| Under normal operating conditions | 1 to 2x safety |
| If smooth running is required | 2 to 4x safety |
| If vibrations and shocks are present | 3 to 5x safety |
Load torques on the guide trolley of the profile rail guide
The function of the guide carriages in profile rail guides is to absorb loads and precisely guide movements. However, if the force is applied outside the center of gravity of the guide carriage, additional rolling, tilting, or yaw stress is created by leverage. A load torque resulting from this force, also called torque load, acts on the guide unit.
The manufacturer specifies the permissible static moments of the three possible axes of rotation for each profile rail guide. These may be named differently depending on the manufacturer. Misumi uses the designations MA, MB and MC to indicate these moments.
If one considers the load of the profile rail guide due to possible moments in a spatial coordinate system, a moment load acts in three possible axes of rotation. These are named MA, MB and MC by the manufacturer for MISUMI profile rail guides. The following maximum permissible static moments are shown:
The moment occurs when a load is applied outside the rolling element contact surface.
- MA pitch moment: Force-induced rotary motion about the Y-axis (transverse to the rail)
- MB yaw moment: Force-induced rotation about the Z-axis (vertical to the rail)
- MC roll moment: Force-induced rotary motion about the X-axis (along the rail)
Calculating the Static Moment
The static moment is the load torque that occurs while the load is acting on the system. It must be determined for all three possible axes of rotation of the profile rail guide and, like the static load rating C0, is determined based on the permanent deformation of the rolling elements installed in the guide carriage.
M_p = F \times L_p
M_y = F \times L_y
M_r = F \times L_r
Static Moments:
- M p in pitch direction (M A / f s)
- M y in yaw direction (M B / f s)
- M r in roll direction (M C / f s)
Effective distance of force F:
- L p in pitch direction
- L y in yaw direction
- L r in roll direction
The static moments Mp , My and Mr calculated in this way must now be compared with the permissible static moments specified by the manufacturer, taking into account the expected operating conditions. For this purpose, the manufacturer-specified moments M A , M B and M C are divided by the corresponding calculated static moments M p , M y and M r. Each of the quotients calculated for the 3 axes of rotation is then compared with the safety factor f s.
The static safety factor fs assigns a value range for the lowest limit value to each defined operating condition. The ratios of all three rotary axes must be within or above the value range applicable to the operating condition. The comparison with the static safety factor fs determined on the basis of empirical experience allows an estimation of the planned safety.
Based on the values of the above table for operating conditions with expected vibrations and shocks, all 3 ratios would have to be within the safety factor f s of 3 to 5 or higher. If the quotient of one of the calculated moments falls below the value range of the static safety defined for this operating condition, it must be weighed whether a lower safety may be sufficient and can be accepted or whether another size or series must be used.
f_s \ge \frac{M_A}{M_p}
f_s \ge \frac{M_B}{M_y}
f_s\ge \frac{M_C}{M_r}
Calculation of applied static load
After all static moments have been checked for compliance with the static safety factor, the load Pc, also called the payload, actually applied to the profile rail guide can be determined.
Calculation for horizontal mounting
P_c = F + \frac{C_0}{M_C} \times M_r + \frac{C_0}{M_A} \times M_p
- P c = Force applied (N)
- F = downward force (N)
- C0 = Static load rating (N)
- M C = permissible stat. Moment - rolling direction
- M A = permissible stat. Moment - pitch direction
- M r = moment in rolling direction
- M p = moment in pitch direction
Calculation for side mounting
P_c = F + \frac{C_0}{M_C} \times M_r + \frac{C_0}{M_B} \times M_y
- P c = Force applied (N)
- F = downward force (N)
- C0 = Static load rating (N)
- M C = permissible stat. Moment - rolling direction
- M B = permissible stat. Moment - yaw direction
- M r = moment in rolling direction
- M y = Moment in yaw direction
Load impact on multiple guide carriages
The consideration and calculation of load impact differ significantly depending on whether the load is applied to a single guide carriage or distributed over multiple guide carriages. In the case of a single guide carriage, it must absorb all forces by itself. In contrast, with multiple guide carriages, the load is split and thus the load on each individual carriage is reduced. The distribution of the load and moments depends on the symmetric or asymmetric arrangement of the carriages as well as the position of the applied load.
The dimensioning of a single guide carriage is entirely based on the maximum load it must bear. This ensures that the permissible load ratings are not exceeded, as this directly affects the service life of the profile rail guide. In the case of several guide carriages, however, the dimensioning only takes into account the respective proportion of the total load that a carriage bears. Overall, the load distribution of several guide carriages allows for more efficient use of the load capacity and often allows for smaller dimensions of the individual carriages.
The load acting on the profile rail guides at constant speed can be calculated using the following formulas.
Horizontal axes
P_1 = \frac{1}{4} W+ \frac {X_0}{2X} W + \frac {Y_0}{2Y} W
P_2 = \frac{1}{4} W- \frac {X_0}{2X} W + \frac {Y_0}{2Y} W
P_3 = \frac{1}{4} W+ \frac {X_0}{2X} W - \frac {Y_0}{2Y} W
P_4 = \frac{1}{4} W+ \frac {X_0}{2X} W - \frac {Y_0}{2Y} W
(W = acting load in Newtons)
Lateral horizontal axes (wall mounting)
P_1 = P_2 = P_3 = P_4 = \frac{ℓ_1}{2Y} W
P_{1S} = P_{3S} = \frac{1}{4} W+ \frac {X_0}{2X} W
P_{2S} = P_{4S} = \frac{1}{4} W- \frac {X_0}{2X} W
(W = acting load in Newtons)
Vertical axes (wall mounting)
P_1 = P_2 = P_3 = P_4 = \frac{ℓ_1}{2X} W
P_{1S} = P_{2S} = P_{3S} = P_{4S} = \frac{Y_0}{2X} W
(W = acting load in Newtons)
(A = thrust force)
Accelerating and decelerating of horizontal axes
The formulas shown so far always assume a constant-speed motion. However, linear guides perform a reciprocating motion. When considering a motion cycle, it can be simplified into an acceleration phase (t1), a constant velocity phase (t2), and a deceleration phase (t3). Acceleration and deceleration result in a change in load conditions on the guide carriage.
The following formulas are used for the calculation of the load acting on the profile rail guides during acceleration and deceleration. For simplicity, the example shown here assumes a horizontal application and a centrally positioned point of application of the force W.
When accelerating from standstill
P_1 = P_3 = \frac{1}{4}W ( 1+\frac{2V_1\times ℓ_1}{g\times t_1 \times X})
P_2 = P_4 = \frac{1}{4}W ( 1-\frac{2V_1\times ℓ_1}{g\times t_1 \times X})
W = acting load in Newtons
V1 = travel speed in mm/s
t1 = time in seconds
DV = direction of travel
ℓ1 = effective distance
X = linear guide length in mm
(A in sketch) = thrust force
g = 9.8 x 10-3 mm/s²
At constant speed
P_1 = P_2 = P_3 = P_4= \frac{1}{4}W
W = acting load in Newtons
(A in sketch) = thrust force
g = 9.8 x 10-3 mm/s²
When decelerating to a standstill
P_1 = P_3 = \frac{1}{4}W ( 1-\frac{2V_1\times ℓ_1}{g\times t_3 \times X})
P_2 = P_4 = \frac{1}{4}W ( 1+\frac{2V_1\times ℓ_1}{g\times t_3 \times X})
W = acting load in Newtons
V1 = travel speed in mm/s
t3 = time in seconds
DV = direction of travel
ℓ1 = effective distance
X = linear guide length in mm
(A in sketch) = thrust force
g = 9.8 x 10-3 mm/s²
Average load under load change conditions
While the above formulas allow the load acting on the profile rail guide to be determined for the conditions of acceleration, constant speed, and deceleration, the guide carriages of the linear guide support the object load while simultaneously performing reciprocating motions. Repeated acceleration, deceleration, starting, and stopping change the speed of the guide carriages and thus also that of the supported object. Due to its inertia, the supported object opposes this change in velocity. The load actually acting on the guide carriages and the resulting moments are thus constantly changing.
In order to reflect the respective operating conditions as comprehensively as possible, 4 load change cases are considered and an average load (PM) is determined depending on the load change case.
Load change variants for profile rail guides
The individual load changes for profile rail guides describe the repeated change of the loads acting on the guide during operation. These changes may differ in both the magnitude of the load and its direction. The travel distance ℓ, which describes the reciprocating movement of the guide, is decisive. Any change in speed or direction of the guide carriages corresponds to a fluctuating load Regular fluctuating loads can lead to material fatigue and bearing damage – how to avoid the latter is described in our blog article on the causes and prevention of bearing damage. For the service life calculation, the number of fluctuating loads is determined based on the travel distance and the operating cycles in order to correctly evaluate the mechanical stress.
The analysis and consideration of load changes are important criteria that not only influence the sizing and design of the linear guide, but also the selection of suitable lubricants to evenly distribute the load and minimize wear. An incorrect estimation of the load changes can lead to premature failure of the linear guide and thus to machine downtime.
Load changes on profile rail guides can be divided into different forms. They differ in the way the load varies over time and have different effects on the stresses on the guide. The type of load change has a direct impact on the service life of the guide and must be carefully considered in the design and service life calculation. For this purpose, a mean load Pm, which depends on the respective load case, is determined in different ways.
Stepwise fluctuating load
A step-like fluctuating load (see 1 in the example figure above) occurs when the load changes between different values in clearly defined steps. This is the case, for example, when a machine regularly switches between two or more load levels, such as during tool changes or the machining of different workpieces. Each stage represents a specific load that remains constant over a period of time before abruptly moving to the next stage. The calculation of the mean load for stepwise fluctuating loads is typically carried out via a weighted average of the different load levels, taking into account their respective duration.
Example of a fluctuating load as a function of distance in steps over the total working distance (m):
P_m = \sqrt[3]{\frac{1}{l} \times (P_1^3 \times l_1 + P_2^3 \times l_2 +... + P_n^3 \times l_n)}
Calculation basis:
working distance l1 under load P1 / working distance l2 under load P2 / working distance ln under load Pn
Constant fluctuating load
A constant fluctuating load, on the other hand, describes a periodic change in the load that occurs in a uniform rhythm. This is characteristic of applications where there is continuous vibration or rotation, such as in linear slides with sinusoidal motion. Here, the load oscillates symmetrically around an average value, and the amplitude and frequency of the load changes remain constant throughout the cycle. The equivalent load at constant fluctuating loads is derived from the peak values of vibration and load change frequency.
P_m = \frac{1}{3} \times (P_{min}+ 2 \times P_{max})
Pmin = minimum fluctuating load / Pmax = maximum fluctuating load
Sinusoidal fluctuating load
Sinusoidal fluctuating loads represent a special form of constant load change in which the load varies continuously and evenly in a sinusoidal curve. Such fluctuating loads are common in applications involving oscillating motions, such as vibration systems, machine tools with oscillating components, or repetitive harmonic motion robot systems. The fluctuating loads periodically between a minimum and a maximum, with transitions that are smooth and without sudden jumps. An approximate calculation is possible over the total working distance (m):
Load\:Change\:Variant\: 3a\enspace\enspace\enspace P_m = 0.65 \times P_{max}
Load\:Change\:Variant\: 3b\enspace\enspace\enspace P_m = 0.75 \times P_{max}
