Moment load: a breakdown torque is converted into a force
If a load is off-center or cantilevered on a single carriage, a pitching or rolling moment is generated that subjects the carriage to a local load far exceeding the pure radial force. For design purposes, this moment is converted into an equivalent point load:
P₀ = P_R + (C₀ / M₀) · M_c
P₀ = statically equivalent load · P_R = applied radial force · C₀ = static load rating · M₀ = permissible static rated torque of the carriage · M_c = applied torque
From P₀, the static load-bearing capacity is calculated as usual as S₀ = C₀ / P₀. A second carriage on the same rail absorbs the moment as a pair of forces instead: The greater the distance between the carriages, the smaller the additional force per carriage—often a more cost-effective solution than the next larger size.
Preload and Parallelism
Insufficient preload leads to backlash and positional drift when the load direction changes; excessive preload increases friction and heat generation and disproportionately shortens service life because the internal load increases. Rule of thumb: Use high preload only when stiffness is required and under oscillating loads; otherwise, select the medium standard class.
Two parallel rails fastened together must be mounted within the permissible parallelism tolerance—otherwise, the carriages will become distorted, the preload will increase uncontrollably, and service life will be significantly reduced. To ensure this, the “master rail” is aligned at its contact edge, and the second rail is then calibrated.
Accuracy classes
Ball guides are available in the accuracy classes Normal (C), High (H), and Precision (P); precision classes are used for positioning accuracies in the micrometer range. High-quality profiled rail and crossed-roller guides in classes P or SP often incorporate a cage positive guidance system to prevent cage drift under dynamic loads or vibration.
Stiffness and Machining Accuracy
Stiffness describes the ratio of load to elastic deformation (N/µm). Low stiffness leads to position-dependent displacements under shear force and compromises the dimensional accuracy of the workpiece. In addition to the rolling element geometry (rollers are stiffer than balls), preload, the number of carriages, rail spacing, and assembly forces influence the system stiffness.
Mnemonic
Worked example
Given
Size 25 carriage with C₀ = 38 kN and a permissible rated torque of M₀ = 350 Nm. Applied loads: radial force P_R = 8 kN, plus a bending moment M_c = 70 Nm from a cantilevered mass.
Calculation (one carriage)
- Moment component as force: (C₀/M₀) · M_c = (38,000/350) · 70 ≈ 7,600 N
- Equivalent load: P₀ = 8,000 + 7,600 = 15,600 N
- Static safety: S₀ = 38,000 / 15,600 ≈ 2.4 – too close for the standard design range (5–8)
Solution using a second carriage spaced 200 mm apart (load centered): The pitching moment acts as a force pair: 70 Nm / 0.2 m = 350 N. Carrying the maximum load: P₀ = 8,000/2 + 350 = 4,350 N → S₀ = 38,000/4,350 ≈ 8.7 – this also meets the standard design requirements.
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