The data on the following pages is designed to assist you in selecting the proper screw size for your application. However, we don’t expect you to be experts in this process. We are ready to assist you in your selection right from the beginning, or simply to help double check your work. Contact our Sales Engineering department for assistance (sales@creativemotioncontrol.com):
Dynamic Load Rating (C):
Dynamic load is used to calculate the life of planetary roller screws. The dynamic load rating is defined as the load (constant in magnitude and direction) under which 90% of a statistically-significant number of apparently-identical planetary roller screws reach an operating life of \(10^6\) revolutions (\(L_{10}\)) at which time pitting begins occur in the rolling contact surfaces. In order to prevent deformations that could impair the proper function and operation of the planetary roller screw, a safety factor (\(S_0\)) should be used when selecting a roller screw on the basis of its dynamic and static load ratings. Roller screws should not regularly be operated above 90% of the dynamic load rating.
Static Load Rating (Co):
Static Load rating (\(C_0\)) is a load that, if exceeded, could cause permanent deformation at the most heavily-loaded contact surfaces equal to .0001 times the curvature diameter of the rolling element.
Special Load/Stroke Considerations:
For operations with short-loaded-stroke applications, the life of the roller screw is significantly compromised. This is generally defined as any loaded stroke less than 1.5 times the length of the roller screw nut assembly, where the loads occur primarily on the same portion of the shaft on each stroke (such as with presses, cutters, crimpers, etc.). A special calculation must be used to estimate life in these cases. Fortunately, CMC has developed special processes and materials that can be used to dramatically extend life in these circumstances. Contact CMC for assistance.
Applications that have limited space but aggressive performance requirements may suggest operating the roller screw at or above the dynamic load capacity. This is sometimes possible, but only under specific circumstances. Contact CMC for assistance.
Theoretical Life:
Theoretical life (\(L_{10}\) or \(L_h\)) is the operating time reached by 90% of a group of apparently identical planetary roller screws operating under the same conditions prior to the initial appearance of pitting of the rolling contact surfaces.
Theoretical life is calculated as:
\(L_{10} = \left( \frac{C} {F_m} \right)^3\) or \(C_{req}= F_m \cdot \left( L_{10} \right)^\frac{1}{3}\)
Where:
\(L_{10}\)= Life (millions of shaft revolutions)
\(C\) = Dynamic load capacity (kN)
\(F_m\) = Cubic mean load (kN)
\(C_{req}\)= Required dynamic load capcity (kN)
Theoretical life, normally expressed in multiples of \(10^6\) revolutions, can be expressed in different operating units (e.g. hours):
\(L_h = \frac{10^6 \cdot (\frac{C}{F_m})} {60 \cdot n_{eq}}\)where:
\(L_h\) = Life (hours)
\(n_{eq}\)= Screw equivalent rotational speed (rpm)
Equivalent Load:
Operating loads can be quantified by the incremental load and stroke characteristics that the system is subject to — masses, inertia, etc. For systems with varying conditions (changes of load magnitude, duration, and/or speed), a more complex calculation is required. Please contact CMC sales engineering for more information on these types of applications.
The equivalent load used for determining screw life is calculated as the cubic mean operating load. This is dependent on the load-stroke profile and can be calculated as:
\(F_m=\frac{ \left( F_1^3 L_1 + F_2^3 L_2 + F_3^3 L_3 + \ldots + F_n^3 L_n\right)^\frac{1}{3} }{ \left( L_1 + L_2 + L_3 + \ldots L_n +\right)^\frac{1}{3}}\)where:
\(F_1, F_2, F_3 \ldots F_n\)= Incremental force components of stroke (kN)
\(L_1, L_2, L_3 \ldots L_n\)= Incremental stroke components associated with each load (mm)
Rigidity of Roller Screw:
The rigidity of a roller screw assembly is a function of many parameters, including nut rigidity, bearing support rigidity, screw shaft rigidity, mounting housing rigidity, and mounting arrangement. If known, all these parameters can be assembled in the following formula:
\(C_s = \left( \frac{1 }{C_n} + \frac{1 }{C_b} + \frac{1 }{C_h} \right)^{-1}\)where:
\(C_s\) = Total system rigidity
\(C_n\)= Screw shaft rigidity
\(C_b\)= Nut rigidity
\(C_h\)= Housing rigidity
The screw rigidity can be calculated as:
\(C_s = 165 \cdot d_0 \cdot f_e\)\(C_s\) = Rigidity of the screw
\(d_0\) = Screw pitch diameter (mm)
\(f_e\)= Shaft stiffness factor
The nut rigidity can be calculated as follows:
\(C_n = f_n \cdot \left( F_{ax} \right)^\frac{1}{3}\)\(F_{ax}\) = Applied load (N)
\(f_n\) = Nut stiffness factor (provided upon request)
Column Strength:
If the screw is subject to compressive loads, its ability to resist bucking under the specific loading conditions must be evaluated. The buckling capacity of the screw can be evaluated as follows:
\(F_c= \frac{34 \cdot f_3 \cdot d_2^4 \cdot 10^3}{L^2}\)where:
\(F_c\) = Buckling strength (N)
\(f_3\) = Shaft stiffness factor dependent on end condition (see table)
\(d_2\)= Screw shaft root diameter (mm)
\(L\) = Free length (distance between support bearings)
Critical Speed:
The maximum achievable rotational velocity of a CMC roller screw is affected by these parameters:
- Diameter and free length of the screw
- End support configuration
- Rotational speed capability
- Rotating component (nut or screw)
The critical speed of the screw shaft is calculated as follows:
\(n_{cr} = \frac{f_1 \cdot d_1 \cdot 10^7 }{L^2}\)where:
\(n_{cr}\) = Critical speed of screw shaft (no safety factor) (rpm)
\(f_1\) = End support stiffness factor
\(d_1\) = Screw outside diameter (mm)
Efficiency and Driving Torque:
The efficiency of a planetary roller screw and friction in the system varies based on its operating parameters. This calculation is a simplification of the screw selection process that can change based on the following variables:
\(\mathrm{eta} = \frac{1}{1 + \frac{\pi \cdot d_0}{P_h}\mu}\) \(\mathrm{eta_1} = 2 – \frac{1}{\mathrm{eta}}\) \(\mathrm{eta_p} = 0.9 \cdot \mathrm{eta}\)where:
\(\mathrm{eta}\) = Theoretical direct efficiency (converting shaft rotation into axial motion)
\(\mathrm{eta_1}\)= Theoretical indirect efficiency (backdriving)
\(\mathrm{eta_p}\)= Practical efficiency. The value of 0.9 should be used as an average value between the practical efficiency of a new screw and that of a normally-run screw for all industry applications in all normal working conditions.
\(P_h\)= Lead of screw (mm)
\(d_0\)= Pitch diameter of screw (mm)
\(\mu\)= Coefficient of friction
Torque Required:
To move some axial load at constant speed, the screw requires the following input torque:
\(T= \frac{F \cdot P_h }{2 \cdot \pi \cdot \mathrm{eta}_P \cdot 10^3}\)where:
\(T\) = Required input torque (Nm)
\(P\) = Axial load developed by screw(N)
To restrain some axial load, the screw must be equipped with a brake. The required restraining torque is calculated as:
\(T_B = \frac{F \cdot P_h \cdot \mathrm{eta}_1}{2 \cdot \pi \cdot 10^3}\)where:
\(T_B\) = Required braking torque (Nm)
NOTE: Start-up torque will be greater than the value \(T_B\).
LUBRICATION:
As a general rule, the same lubricants are used for planetary roller screws as for rolling-element bearings (either oil or grease). The type of lubricant used depends mostly on the operating and maintenance conditions.
Grease Lubrication:
Grease is the most common form of lubrication for CMC roller screws and provides an effective solution for most applications. The viscosity of grease is rated with ISO VG levels just as with oils, and this information is typically provided by grease manufacturers. Re-greasing intervals depend on the screw arrangement, size and operating conditions.
Oil Lubrication:
A centralized recirculating oil system is ideal due to its ability to continually supply filtered, temperature-controlled oil at prescribed flow rates. While such systems are optimal, they are often impractical from a cost and/or complexity perspective, and alternate solutions can achieve effective results if properly configured.